Risk Analysis for Dam Safety A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Version: Delta July 2008
Reclamation Document: Risk Analysis Methodology – Appendix E Corps of Engineers Document: UFC URS Document: 22238839 UNSW Document: UNICIV R 446
THE UNIVERSITY OF NEW SOUTH WALES
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
-Disclaimer-
Reference: “A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping” Draft Guidance Document dated July 31, 2008.
The following report represents a draft working document for internal use by the Bureau of Reclamation and the Corps of Engineers. If a copy of this document has been received, it should be used as information only. Methodologies described in the document are under evaluation. The Bureau of Reclamation and the Corps of Engineers have not endorsed it for estimating the probability of failure of embankment dams by internal erosion and piping. No effort will be made by either agency to provide anyone holding a copy with updates or corrections.
Authors:
Robin Fell, School of Civil and Environmental Engineering, University of New South Wales, Sydney
Mark Foster, URS Australia.
John Cyganiewicz, Bureau of Reclamation
George Sills, ERDC, US Army Corps of Engineers.
Noah Vroman, ERDC US Army Corps of Engineers.
Richard Davidson, URS Corporation.
Date: Status:
31 July 2008 Delta Version
Contents
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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1 Introduction------------------------------------------------------------------------------------------------- 1-1
1.1 General 1-1 1.2 Training 1-1 1.3 Terminology to Describe Embankment Types 1-1 1.4 Terminology 1-3
2 Methodology------------------------------------------------------------------------------------------------ 2-1
2.1 Introduction 2-1 2.2 General Process 2-1 2.3 Information Review 2-2
3 Failure Modes and Load Partitioning -------------------------------------------------------------- 3-1
3.1 Event Tree 3-1 3.2 General Failure Modes 3-3
3.2.1 Internal Erosion Through the Embankment 3-3 3.2.2 Internal Erosion Through the Foundation 3-5 3.2.3 Internal Erosion of the Embankment into or at the Foundation 3-5
3.3 Identification of Failure Paths 3-9 3.3.1 Overview 3-9 3.3.2 Examples 3-10
3.4 Failure Path Screening 3-13 3.4.1 Overview 3-13 3.4.2 Internal Erosion Through the Embankment 3-14 3.4.3 Internal Erosion Through the Foundation 3-21 3.4.4 Internal Erosion of the Embankment into or at the Foundation 3-22
3.5 Partitioning of the Reservoir Levels 3-23 3.5.1 “Normal” and “flood” loading levels 3-23 3.5.2 Pool of record level 3-23 3.5.3 Partitioning of reservoir levels 3-23 3.5.4 Assessing Frequencies of Reservoir Loading 3-25
3.6 Earthquake Load Partitioning 3-25
4 Application of Tables for Estimating Conditional Probabilities--------------------------- 4-1
4.1 General Approach 4-1 4.2 Historical Frequencies of Cracks and Poorly Compacted or High Permeability
Zones in Embankments 4-1 4.3 Historical Frequencies for Internal Erosion in and into the Foundation 4-4 4.4 Estimating Conditional Probabilities 4-4
4.4.1 Estimating Conditional Probabilities Using Relative Importance Factors and Likelihood Factors 4-4
4.4.2 Estimating Conditional Probabilities Using Scenario Tables 4-5 4.4.3 Estimating Conditional Probabilities Using Probability Estimate Tables 4-5
4.5 Length Effects 4-5
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4.6 Nature of the estimates of probabilities given by the Toolbox 4-13 4.6.1 The Toolbox gives “Best Estimate” Probabilities 4-13 4.6.2 Adjusting the Toolbox Best Estimates 4-13 4.6.3 Limitations of the methods used in the Toolbox 4-14 4.6.4 Assessment of probabilities of failure for failure modes which are not
covered by the Toolbox 4-15 4.7 Modelling uncertainty in the estimates of conditional probabilities 4-16
4.7.1 Purpose of this section 4-16 4.7.2 Sensitivity analysis 4-16 4.7.3 Uncertainty analysis 4-17
4.8 Summarizing (Making the case) 4-21 4.9 Combining Probabilities 4-22
4.9.1 Adding Probabilities for Static, Hydrological and Seismic Loads 4-22 4.9.2 Development of Fragility Curves 4-23
5 Probability of Initiation of Erosion in Transverse Cracks in the Embankment ------ 5-1
5.1 Overall Approach 5-1 5.2 Estimating the Probability of Transverse Cracking (P C ) in the Upper Part of the
Dam 5-2 5.2.1 Likelihood of a Transverse Crack Due to Cross Valley Differential
Settlement (IM1) 5-2 5.2.2 Likelihood of Transverse Cracking Resultant on Cross Section Settlement
due to Poorly Compacted Shoulders (IM4) 5-8 5.2.3 Likelihood Of Transverse Cracking Due To Differential Settlements In
Soil In The Foundation Beneath The Core (IM5) 5-11 5.2.4 Likelihood Of Transverse Cracking Due To Differential Settlements Due
To Embankment Staging (IM6) 5-13 5.2.5 Likelihood of Transverse Cracking due to Desiccation (IM7, IM8) 5-13
5.3 Estimating The Probability Of Transverse Cracking Or Hydraulic Fracture (P C ) In The Middle And Lower Parts Of The Dam 5-18 5.3.1 Likelihood of Transverse Cracking or Hydraulic Fracture Due To Cross
Valley Differential Settlement (IM9) 5-18 5.3.2 Likelihood Of Transverse Cracking Or Hydraulic Fracture Due To
Differential Settlement Causing Arching Of The Core Onto The Shoulders Of The Embankment (IM10) 5-19
5.3.3 Likelihood Of Transverse Cracking or Hydraulic Fracture Due To Differential Settlement In The Foundation Under The Core (IM11) 5-20
5.3.4 Likelihood of Transverse Cracking Or Hydraulic Fracture At The Foundation Contact Due To Small Scale Irregularities In The Foundation Profile Under The Core (IM12) 5-20
5.3.5 Probability Of Transverse Cracking or Hydraulic Fracture - Factors To Account For Observations And Measured Settlements 5-22
5.4 Estimation Of The Probability Erosion Will Initiate In A Crack Or Hydraulic Fracture In An Embankment (P IC ). 5-25 5.4.1 Overall Approach 5-25 5.4.2 Details Of The Method 5-27
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5.5 Estimation Of The Probability Of Transverse Cracks In The Embankment Caused By Earthquake (IM13) 5-37
6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment ---------------------------------------------------------- 6-1
6.1 Overall Approach 6-1 6.2 Estimation Of The Probability Of A Continuous Poorly Compacted or High
Permeability Zone In The Embankment Or On The Core-Foundation Contact 6-2 6.2.1 Poorly Compacted or High Permeability zone within the core (IM14) 6-2 6.2.2 Poorly Compacted or High permeability layer on the core-foundation
contact (IM15) 6-7 6.2.3 Poorly Compacted or High Permeability Layer in the Embankment due to
Freezing (IM16, IM17) 6-9 6.3 Probability Of A Poorly Compacted or High Permeability Zone Around A Conduit
or Features Allowing Erosion Into the Conduit 6-14 6.3.1 Poorly Compacted or High Permeability Zone Around A Conduit
Through The Embankment (IM18) 6-14 6.3.2 Features Allowing Erosion into a Conduit (IM19) 6-16
6.4 Poorly Compacted or High Permeability Zone or Gap Associated With A Spillway Or Abutment Wall 6-19 6.4.1 Approach 6-19 6.4.2 Poorly Compacted or High Permeability Zone Associated with a Spillway
Or Abutment Wall (IM20) 6-20 6.4.3 Crack/Gap Adjacent to a Spillway or Abutment Wall (IM21) 6-21 6.4.4 Differential Settlement Adjacent to a Spillway or Abutment Wall (IM22) 6-23 6.4.5 Wrap around details for connection of embankment dam to concrete
gravity dam (IM23) 6-24 6.5 Probability Of Poorly Compacted or High Permeability Zone - Factors To Account
For Observations 6-26 6.6 Estimation Of The Probability Of Initiation Of Erosion In A Poorly Compacted or
High Permeability Layer In The Embankment, Adjacent A Wall Or Around A Conduit 6-28 6.6.1 Screening Check On Soil Classification 6-28 6.6.2 Assessment Of The Probability Of Initiation Of Backward Erosion In A
Layer Of Cohesionless Soil or Soil with Plasticity Index ≤ 7 6-28 6.6.3 Probability Of Initiation Of Erosion By Suffusion In A Layer Of
Cohesionless Soil or Soil with Plasticity Index ≤ 7 (PI ≤ 12 for seepage gradients >4) 6-32
6.6.4 Probability Of Initiation Of Erosion In A Poorly Compacted or High Permeability Cohesive Soil Layer and in silt-sand-gravel soils in which collapse settlement may form a crack or flaw 6-35
6.6.5 Probability Of Initiation Of Erosion In A Poorly Compacted or High Permeability Cohesive Soil Layer Around A Conduit 6-37
6.6.6 Probability Of Initiation Of Erosion In A High Permeability Soil Due to Frost Action 6-37
6.7 Allowance for the Presence of Unknown and Unpredictable Flaws in the Core of the Embankment 6-38
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6.7.1 Background 6-38 6.7.2 Recommended Procedure 6-39 6.7.3 Suggested size and location of the flaw and the probability of occurrence 6-39 6.7.4 Assessing the Probability of Failure if the Flaw Were to Exist and
Reporting the Outcome of the Analysis 6-40
7 Probability of Initiation of Erosion in a Soil Foundation------------------------------------- 7-1
7.1 Screening Check on Soil Classification 7-1 7.2 Assessment Of The Probability Of Initiation Of Backward Erosion In A Layer Of
Cohesionless Soil or Soil with Plasticity Index ≤ 7 In The Foundation (IM24) 7-1 7.2.1 Description of Method 7-1 7.2.2 Estimation of the probability of heave or reaching the critical gradient
(P H ) from piezometer data and/or seepage flow net models. 7-3 7.2.3 An approximate method for assessing the probability of heave 7-5
7.3 Estimating the probability of backward erosion given heave has occurred 7-7 7.3.1 Probability of initiation and progression of backward erosion if sand boils
have been observed. 7-7 7.3.2 Estimating the probability of initiation and progression of backward
erosion where heave or reaching the critical gradient is predicted or sand boils have been observed at higher reservoir levels (P IH ) 7-7
7.3.3 Estimation of the probability of initiation and progression of backward erosion (P INH ) for cases where heave is not predicted. 7-9
7.3.4 Estimation of the total probability of initiation and progression for this reservoir stage 7-11
7.4 Estimation Of The Probability Of Initiation Of Suffusion In A Cohesionless Layer In The Foundation (IM25) 7-12
7.5 Estimation Of The Probability Of Initiation Of Erosion In A Crack In Cohesive Soil In The Foundation (IM26) 7-12 7.5.1 Overall Approach 7-12 7.5.2 Some Factors To Consider In This Assessment And Suggested Method
For Estimating The Probability Of A Continuous Crack 7-12
8 Probability of the Presence of Open or In Filled Defects in Rock Foundations ------------------------------------------------------------------------------------------------ 8-1
8.1 Overall Approach 8-1 8.2 Probability of one or more continuous in filled or open defects in the rock in the
foundation beneath the embankment (IM27) 8-4 8.2.1 Overview of method 8-4 8.2.2 Estimation of the probability of one or more continuous in filled or open
defects in the rock foundation beneath the embankment based on geologic and topographic data 8-5
8.2.3 Estimation of the probability of one or more continuous in filled or open defects in the rock foundation beneath the embankment based on site investigations and construction data 8-8
8.2.4 Effects Of Blasting On The Foundation 8-8
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8.3 Probability of one or more continuous open or in filled valley bulge or rebound features in the rock in the foundation beneath the embankment 8-10 8.3.1 Overview of method 8-10 8.3.2 Estimation of the probability of one or more continuous in filled or open
valley bulge or rebound features in the rock foundation beneath the embankment based on geologic and topographic data 8-11
8.3.3 Estimation of the probability of one or more continuous in filled valley bulge or rebound feature in the rock foundation beneath the embankment based on site investigations and construction data 8-13
8.4 Probability of one or more continuous open or in filled solution features in the rock in the foundation beneath the embankment 8-15 8.4.1 Overview of method 8-15 8.4.2 Estimation of the probability of one or more continuous in filled or
solution features in the rock foundation beneath the embankment based on geologic and topographic data 8-16
8.4.3 Estimation of the probability of one or more continuous in filled or open solution features in the rock foundation beneath the embankment based on site investigations, construction and monitoring data 8-18
8.5 Probability of one or more continuous open or in filled features associated with other geological features such as landslides, faults and shears 8-20 8.5.1 Overview of method 8-20 8.5.2 Estimation of the probability of one or more continuous in filled or open
other geological features in the rock foundation beneath the embankment based on site investigations and construction data 8-21
8.6 Width and extent of open or in filled defects or solution features in the embankment foundation 8-22 8.6.1 Extent of occurrence and width of defects associated with stress relief
defects in the valley sides 8-22 8.6.2 Width and extent of features associated with stress relief effects in the
valley floor – valley bulge or rebound 8-25 8.6.3 Width and extent of solution features 8-25
8.7 Likelihood of Defects or Solution Features being in filled 8-26 8.8 Likelihood of Grouting Not Being Effective in cutting off open or in filled defects
or solution or other features 8-26 8.9 Likelihood of Cut-off Walls Not Being Effective in cutting off open or in filled
defects or solution or other features 8-28 8.10 Probability that erosion of infill in the defects or solution feature initiates 8-30
8.10.1 Overview of Method 8-30 8.10.2 Estimation of the probability of erosion of in fill initiating based on
performance data 8-31 8.10.3 Estimation of the probability of erosion of infill initiating using first
principles 8-32 8.11 Probability that erosion of infill continues 8-32
8.11.1 Approach 8-32 8.11.2 Probability of Filtered or Unfiltered Exit 8-33
8.12 Combining probabilities for a continuous open defect in rock and describing the defects and solution features 8-33 8.12.1 Calculating weighted averages of estimates 8-33
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8.12.2 Summing probabilities 8-34 8.13 Describing the defects and solution features and failure modes 8-35
8.13.1 Describing the defects and solution features in relation to the embankment details 8-35
8.13.2 Describing the failure paths 8-36
9 Probability of Initiation of Erosion from Embankment into Foundation --------------- 9-1
9.1 General Principles 9-1 9.2 Overall Approach 9-1 9.3 Probability of a continuous pathway for erosion of the core of the embankment into
a rock foundation (Ppath) IM28 9-2 9.3.1 Probability of a continuous pathway of open defects and solution features
in the rock foundation (PCR) 9-2 9.3.2 Likelihood treatment of the embankment cut-off foundation does not
prevent contact of the core with open defects or solution or other features (PTI) 9-2
9.3.3 Probability of a continuous pathway for erosion of the core into a rock foundation (Ppath) 9-3
9.4 Probability of a continuous pathway of coarse grained layers in soil foundations (IM29) 9-4
9.5 Probability of the initiation of internal erosion by backward erosion or suffusion starting at the core-foundation contact. 9-5
9.6 Probability of initiation of scour at the core-foundation contact 9-6 9.6.1 The Steps to be followed 9-6 9.6.2 How to model scour into defects of varying width and persistence 9-6
9.7 Probability of erosion of the core following hydraulic fracture due to arching in a narrow cut-off trench 9-10
10 Probability of Continuation---------------------------------------------------------------------------10-1
10.1 Probability of Continuation for Internal Erosion in the Embankment 10-1 10.1.1 Internal Erosion Through the Embankment – Overall Approach 10-1 10.1.2 Probability for Continuation – Scenario 1 (Homogeneous zoning) 10-2 10.1.3 Probability for Continuation – Scenario 2 (Downstream shoulder can hold
a crack or pipe) 10-2 10.1.4 Probability for Continuation – Scenario 3 (Filter/transition zone is present
downstream of the core or a downstream shoulder zone which is not capable of holding a crack/pipe) 10-4
10.1.5 Probability for Continuation – Scenario 4 (Internal erosion into an open defect, joint or crack in the foundation, in a wall or conduit) 10-15
10.1.6 Probability for Continuation – Scenario 5 (Erosion into a toe drain) 10-16 10.2 Probability for Continuation for Internal Erosion Through the Foundation 10-17
10.2.1 Approach 10-17 10.2.2 Probability of Filtered or Unfiltered Exit 10-17
10.3 Probability of Continuation for Internal erosion of the embankment at or into the foundation 10-22 10.3.1 Erosion into open joints in rock foundation 10-22
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10.3.2 Erosion into coarse grained soil foundation 10-22
11 Probability of Progression----------------------------------------------------------------------------11-1
11.1 Overall Approach 11-1 11.2 Probability of Forming a Roof 11-1
11.2.1 Internal Erosion Through the Embankment 11-1 11.2.2 Internal Erosion through a Soil Foundation 11-1
11.3 Probability of Crack Filling Action Not Being Effective 11-4 11.3.1 Internal Erosion the Embankment 11-4 11.3.2 Internal Erosion Through the Foundation 11-4 11.3.3 Internal Erosion of the Embankment into or at the Foundation 11-4
11.4 Probability for Limitation of Flows 11-6 11.4.1 Flow limitation by upstream zone 11-6 11.4.2 Flow into/out of open joint in conduits 11-6 11.4.3 Flow into jointed bedrock 11-6
12 Probability of Detection, Intervention and Repair --------------------------------------------12-1
12.1 General Principles 12-1 12.2 Some Information on the Rate of Internal Erosion and Piping 12-2 12.3 Detection 12-5
12.3.1 Some General Principles 12-5 12.3.2 Assessing the Probability of Not Detecting Internal Erosion 12-6
12.4 Assessing the likelihood of Intervention and Repair 12-10 12.5 Calculation of Probability of Not Detecting and Not Intervening 12-12
13 Probability of Breach -----------------------------------------------------------------------------------13-1
13.1 Overall Approach and Screening 13-1 13.1.1 Screening of Breach Mechanisms 13-1
13.2 Estimation of the Probability of Breach by Gross Enlargement 13-3 13.2.1 Screening for internal erosion in the embankment, soil foundation, and
embankment into foundation; 13-3 13.2.2 Screening for internal erosion in a rock foundation; 13-4 13.2.3 Assessment for internal erosion in the embankment, soil foundation and
from embankment into foundation 13-4 13.2.4 Assessment for internal erosion in a rock foundation 13-5
13.3 Estimation Of The Probability Of Breach By Slope Instability 13-6 13.3.1 Approach 13-6 13.3.2 Estimation of the probability of slope instability initiates for internal
erosion in the embankment, soil foundation, and from embankment into foundation 13-6
13.3.3 Estimation of the probability of Slope Instability of the embankment initiates for internal erosion in a rock foundation 13-8
13.3.4 Loss of Freeboard due to Slope Instability 13-12 13.4 Estimation of the Probability of Breach by Sloughing or Unravelling 13-13
13.4.1 Approach 13-13
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13.5 Estimation of the Probability of Breach by Sinkhole Development 13-17 13.5.1 Approach 13-17 13.5.2 Probability of Sinkhole Formation 13-17 13.5.3 Probability of Loss of Freeboard due to Sinkhole Formation 13-17
14 References -------------------------------------------------------------------------------------------------14-1
15 List of Acronyms & Symbols ------------------------------------------------------------------------15-1
Appendices
Appendix A Navigation Table for Internal Erosion Through the Embankment Appendix B Navigation Table for Internal Erosion Through a Soil Foundation Appendix C Navigation Table for Internal Erosion Through a Rock Foundation Appendix D Navigation Table for Internal Erosion of the Embankment into or at the Foundation Appendix E Guidance for Failure Paths Not Covered by the Unified Method
List of Tables & Figures
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Tables
Table 3.1 - Screening of initiating mechanisms – Internal erosion due to concentrated leaks in transverse cracks in the upper part of embankment dams ............................................. 3-14
Table 3.2 - Screening of failure paths – Internal erosion due to concentrated leaks in transverse cracks in the middle and lower parts of embankment dams ..................................................... 3-17
Table 3.3 - Screening of failure paths – Internal erosion due to concentrated leaks in poorly compacted or high permeability zones in the embankment ............................................................. 3-18
Table 3.4 - Screening of failure paths – Internal erosion through the foundation................................... 3-21 Table 3.5 - Screening of failure paths – Internal erosion in the embankment into or at the foundation . 3-22 Table 3.6 - Example of reservoir level partitions .................................................................................... 3-24 Table 3.7 - Example of earthquake load partitions.................................................................................. 3-25 Table 4.1 - Estimated historical frequencies of cracking, hydraulic fracture or poorly compacted or
high permeability zones in embankment dams................................................................ 4-2 Table 4.2 - Historical frequencies for cracking or poorly compacted zone in the embankment dam
body. ................................................................................................................................ 4-3 Table 4.3 – Length Effects – Transverse cracking in the upper part of the embankment ......................... 4-7 Table 4.4 – Length Effects – Transverse cracking in the middle and lower parts of the embankment..... 4-9 Table 4.5 – Length Effects – Poorly compacted or high permeability zones in the embankment .......... 4-10 Table 4.6 – Length Effects – Internal erosion in the foundation and into the foundation....................... 4-11 Table 4.7 – Best estimate, likely high and likely low equivalence table................................................. 4-19 Table 5.1 - Factors influencing the likelihood of cracking or hydraulic fracturing in the upper part of
embankment dams - Cross Valley Differential Settlement (IM1) ................................... 5-2 Table 5.2 - Probability of a cracking or hydraulic fracture in the upper part of embankment dams-Cross
Valley Differential Settlement versus ∑ (Relative importance factor (RF) x (Likelihood factor(LF)) ................................................................................................... 5-3
Table 5.3 - Factors influencing the likelihood of cracking or hydraulic fracturing in the upper part of embankment dams-Differential settlement adjacent a cliff at the top of the embankment (IM2)................................................................................................................................ 5-4
Table 5.4 - Probability of a cracking or hydraulic fracture in the upper part of embankment-Differential settlement adjacent a cliff at the top of the embankment versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) ......................................................... 5-4
Table 5.5 - Factors influencing the likelihood of cracking or hydraulic fracturing in embankment due to cross valley arching (IM3)............................................................................................... 5-6
Table 5.6 - Probability of cracking or hydraulic fracturing in embankment due to cross valley arching versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) ...................... 5-6
Table 5.7 – Factors influencing the likelihood of cracking or hydraulic fracturing in the upper part of embankment - cross section settlement resulting from poorly compacted shoulders (IM4)................................................................................................................................ 5-8
Table 5.8 - Probability of a transverse crack or hydraulic fracture resultant on cross section settlement resulting from poorly compacted shoulders versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF))...................................................................................... 5-9
List of Tables & Figures
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Table 5.9 – Factors influencing the likelihood of cracking or hydraulic fracturing in the upper part of embankment dams- settlement resulting from differential settlements in soil in the foundation (IM5) ........................................................................................................... 5-11
Table 5.10 - Probability of a crack or hydraulic fracture due to differential settlement in the foundation versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) ................... 5-12
Table 5.11 – Factors influencing the likelihood of cracking in the upper part of embankment dams- cracking in the crest due to desiccation by drying (IM7) .............................................. 5-14
Table 5.12 - Probability of a transverse crack, cracking in the crest due to desiccation by drying versus
∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) ............................... 5-14 Table 5.13 – Screening Tool. Maximum likely depth of desiccation cracking for a gravel surface layer
with no road pavement cover based on climate............................................................. 5-15 Table 5.14 - Factors influencing the likelihood of cracking on seasonal shutdown layers during
construction and staged construction surfaces due to desiccation by drying (IM8) ...... 5-16 Table 5.15 - Probability of a transverse crack on seasonal shutdown layers during construction and
staged construction surfaces due to desiccation by drying versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) ....................................................... 5-17
Table 5.16 - Factors influencing the likelihood of cracking or hydraulic fracture in the middle and lower parts of embankment dams-cross valley differential settlements (IM9).............. 5-18
Table 5.17 - Probability of a transverse crack or hydraulic fracture in the middle and lower parts of embankment dams due to cross valley differential settlements versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) ...................................................... 5-18
Table 5.18 – Factors influencing the likelihood of cracking or hydraulic fracturing in the middle and lower parts of embankments - settlement resulting from arching of the core onto the shoulders (IM10) ........................................................................................................... 5-19
Table 5.19 - Probability of a transverse crack or hydraulic fracture in the middle and lower parts of embankment dams- settlement resulting from arching of the core onto the shoulders of the embankment versus∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) .............................................................................................................................. 5-20
Table 5.20 – Factors influencing the likelihood of cracking or hydraulic fracturing in the middle and lower parts of embankment dams due to small scale irregularities in the foundation profile under the core (IM12) ........................................................................................ 5-21
Table 5.21 - Probability of a transverse crack or hydraulic fracture in the middle and lower parts of embankment dams due to small scale irregularities in the foundation profile under the core versus∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) ............ 5-21
Table 5.22 - Settlement multiplication factors versus observed settlements........................................... 5-23 Table 5.23 - Cracking observation factors (applies to upper embankment only).................................... 5-24
Table 5.24 - Maximum likely width of cracking at the dam crest versus ∑ (Relative importance factor) x (Likelihood factor) for cracking in the upper part of the dam ........................ 5-27
Table 5.25 - Likely crack width at the depth shown versus maximum crack width at the dam crest determined from Table 5.24 for cracking in the upper part of the dam.( Depths in feet and meters) .................................................................................................................... 5-28
Table 5.26 – Examples of estimated maximum depths below the dam crest and widths of cracks formed by potential hydraulic fracture for cracking in the upper part of the dam ..................... 5-28
List of Tables & Figures
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Table 5.27 Representative erosion rate index (IHET) versus soil classification for non dispersive soils based on Wan and Fell (2002, 2004) ............................................................................. 5-30
Table 5.28 - Maximum likely width of cracking in the dam versus ∑ (Relative importance factor) x (Likelihood factor) for cracking in the middle and lower parts of the dam................... 5-31
Table 5.29 - Estimation of probability of initiation in a crack for ML or SM with <30% fines soil types5-33 Table 5.30 - Estimation of probability of initiation in a crack for SC with <40% fines, or SM with
>30% fines soil types..................................................................................................... 5-33 Table 5.31 - Estimation of probability of initiation in a crack for SC with >40% fines, or CL-ML soil
types............................................................................................................................... 5-34 Table 5.32 - Estimation of probability of initiation in a crack for CL or MH soil types......................... 5-34 Table 5.33 - Estimation of probability of initiation in a crack for CL-CH or CH with LL<65% soil
types............................................................................................................................... 5-35 Table 5.34 - Estimation of probability of initiation in a crack for CH with LL>65% soil types ............ 5-35 Table 5.35 - Estimation of probability of initiation in a crack for dispersive soils (CL, CH, CL-CH)... 5-36 Table 5.36 – Estimated hydraulic shear stress (N/m2) from water flowing in an open crack, versus
crack width and flow gradient ....................................................................................... 5-36 Table 5.37 – Initial Shear Stress assumed for Tables 5.29 to 5.35.......................................................... 5-37 Table 5.38 – Damage classification system (Pells and Fell, 2002, 2003) ............................................... 5-38 Table 5.39 – Estimation of the probability of transverse cracking from the damage class ..................... 5-39 Table 6.1 – Factors influencing the likelihood of poorly compacted or high permeability zones in the
embankment-cohesive soils (IM14) ................................................................................ 6-3 Table 6.2 – Factors influencing the likelihood of poorly compacted or high permeability zones in the
embankment-non cohesive soils (IM14) ......................................................................... 6-5 Table 6.3 - Probability of a poorly compacted or high permeability layer in the embankment
versus∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) (applies to upper, middle and lower parts of the embankment) ........................................................ 6-6
Table 6.4 – Factors influencing the likelihood of poorly compacted or high permeability zones on the core-foundation/abutment contact (IM15)....................................................................... 6-7
Table 6.5 - Probability of a poorly compacted or high permeability layer on the core foundation contact versus∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) ...................... 6-8
Table 6.6 – Factors influencing the likelihood of cracking and poorly compacted zones in the upper part of embankment dams due to freezing (IM16) ........................................................ 6-10
Table 6.7 - Probability of cracking or poorly compacted zones in the crest due to freezing versus
∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) .............................. 6-11 Table 6.8– Maximum likely depth of freezing induced flaws based on climate..................................... 6-11 Table 6.9 - Factors influencing the likelihood of high permeability layer on seasonal shutdown layers
during construction and staged construction surfaces due to freezing (IM17) .............. 6-12 Table 6.10 - Probability of a high permeability layer on seasonal shutdown layers during construction
and staged construction surfaces due to freezing versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) .......................................................................... 6-13
Table 6.11 – Factors influencing the likelihood of poorly compacted or high permeability zones along outside of a conduit. (IM18) .......................................................................................... 6-14
Table 6.12 - Probability of a poorly compacted or high permeability zone associated with a conduit versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) .................... 6-15
List of Tables & Figures
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Table 6.13 – Factors influencing the likelihood of initiation of erosion into a non-pressurized conduit when internal condition is known.................................................................................. 6-16
Table 6.14 – Factors influencing the likelihood of initiation of erosion into a non-pressurized conduit when the internal condition is not known (IM19) ......................................................... 6-17
Table 6.15 - Probability of initiation of erosion into a conduit versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF))........................................................................ 6-18
Table 6.16 - Probability of the development of piping along the conduit given erosion initiates into the conduit versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) from Table 6.11 ...................................................................................................................... 6-18
Table 6.17 – Factors influencing the likelihood of a poorly compacted or high permeability zone associated with a spillway or abutment wall (IM20)..................................................... 6-20
Table 6.18 - Probability of a high permeability zone associated with a spillway or abutment wall versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) ..................... 6-20
Table 6.19 – Factors influencing the likelihood of a crack or gap adjacent to a spillway or abutment wall (IM21).................................................................................................................... 6-21
Table 6.20 - Probability of a gap or crack associated with a spillway or abutment wall versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) ..................... 6-21
Table 6.21 - Factors influencing the likelihood of cracking or hydraulic fracturing due to differential settlement adjacent a spillway or abutment wall (IM22)............................................... 6-23
Table 6.22 - Probability of cracking or hydraulic fracture due to differential settlement adjacent a spillway or abutment wall versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) ..................................................................................................................... 6-23
Table 6.23 - Factors to be considered in assessing seepage gradients on wrap-around .......................... 6-24 Table 6.24 - Seepage observation factors................................................................................................ 6-27 Table 6.25 - Time to develop seepage gradient in cohesionless soils ..................................................... 6-30 Table 6.26 - Estimation of the probability of initiation and progression of backward erosion P IP in
cohesionless soils and soils with PI ≤ 7 for well compacted layers ............................. 6-32 Table 6.27 - Estimation of the probability of initiation and progression of backward erosion P IP in
cohesionless soils and soils with PI ≤ 7 for uncompacted layers ................................. 6-32 Table 6.28 - Seepage gradients at which suffusion may occur ............................................................... 6-34 Table 6.29 - Amount of collapse settlement which may occur on saturation versus compaction
properties ....................................................................................................................... 6-36 Table 6.30 - Width of frost induced flaw versus (RFxLF)...................................................................... 6-38 Table 7.1 – Estimation of the probability of heave or reaching the critical gradient (P H ) from the
calculated factor of safety against heave. ........................................................................ 7-4 Table 7.2 – Estimation of the probability of heave from embankment geometry and the foundation
permeability ratio kh/ kv for situations where there is no confining layer in the foundation........................................................................................................................ 7-5
Table 7.3 – Estimation of the probability of heave from embankment geometry and the foundation permeability ratio kh/ kv for situations where there is a confining layer in the foundation7-5
Table 7.4 – Estimation of the probability of initiation and progression of backward erosion in the foundation given heave is predicted (P IH ) ..................................................................... 7-9
List of Tables & Figures
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Table 7.5 – Estimation of the probability of initiation of backward erosion for cases where heave is not predicted (P INH ) ............................................................................................................ 7-11
Table 8.1 - Factors influencing the likelihood of a continuous in filled or open defect in the rock in the foundation beneath the embankment ............................................................................... 8-6
Table 8.2 - Factors influencing likelihood for topography........................................................................ 8-7 Table 8.3 - Probability of a continuous in filled or open feature in the rock foundation beneath the
embankment versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF)) . 8-7 Table 8.4 - Factors influencing the likelihood of a continuous in filled or open defects in the rock in the
foundation beneath the embankment ............................................................................... 8-9 Table 8.5 - Probability of a continuous in filled or open features in rock in the foundation beneath the
embankment versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF))8-10 Table 8.6 - Factors influencing the likelihood of a continuous in filled or open valley bulge or rebound
feature in the rock in the foundation beneath the embankment ..................................... 8-12 Table 8.7 - Probability of a continuous in filled or open valley bulge or rebound feature in rock in the
foundation beneath the embankment versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF)) ................................................................................................ 8-12
Table 8.8 - Factors influencing the likelihood of a continuous in filled or open valley bulge or rebound feature in the rock in the foundation beneath the embankment ..................................... 8-14
Table 8.9 - Probability of a continuous in filled or open valley bulge feature in rock in the foundation beneath the embankment versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF)) .................................................................................................................... 8-15
Table 8.10 - Factors influencing the likelihood of a continuous in filled or open solution feature in the rock in the foundation beneath the embankment ........................................................... 8-17
Table 8.11 - Probability of a continuous in filled or open solution features in rock in the foundation beneath the embankment versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF)) .................................................................................................................... 8-18
Table 8.12 - Factors influencing the likelihood of a continuous in filled or open solution feature in the rock in the foundation beneath the embankment ........................................................... 8-19
Table 8.13 - Probability of a continuous in filled or open solution features in rock in the foundation beneath the embankment versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF)) .................................................................................................................... 8-20
Table 8.14 - Factors influencing the likelihood of a continuous in filled or open geological feature in the rock in the foundation beneath the embankment ..................................................... 8-21
Table 8.15 - Probability of a continuous open or in filled features in the rock foundation beneath the embankment versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF))8-22
Table 8.16 – Probability of Defects or Solution Features being open or in filled................................... 8-26 Table 8.17 - Factors influencing the likelihood of grouting not being effective for continuous open
defects and solution features.......................................................................................... 8-27 Table 8.18 - Probability of grouting not being effective for continuous open defects or solution features
versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF))..................... 8-28 Table 8.19 - Factors influencing the likelihood of a cut-off in the foundation not being effective for
continuous open defects and solution features .............................................................. 8-29
List of Tables & Figures
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Table 8.20 - Probability of a cut-off not being effective for continuous open defects or solution features versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF))..................... 8-30
Table 8.21 Probability of erosion initiating based on performance data................................................. 8-31 Table 8.22 - Weighting factors for assessing probabilities of open or in filled defects and solution
features........................................................................................................................... 8-34 Table 9.1 - Probability of treatment of the cutoff foundation not preventing contact of the core with
open defects or solution features ..................................................................................... 9-3 Table 9.2 – Probability of a continuous pathway for erosion into soil foundation (IM29)....................... 9-4 Table 9.3 - Factors influencing the likelihood of hydraulic fracturing within the cutoff trench due to
arching ........................................................................................................................... 9-11 Table 9.4 - Probability of hydraulic fracturing in cut off trench due to arching versus ∑ (Relative
importance factor (RF)) x (Likelihood factor(LF)) ....................................................... 9-11 Table 10.1 Conditional Probability Ranges for Continuation (Scenario 2) ............................................ 10-3 Table 10.2 - Likelihood for Filters with Excessive Fines Holding a Crack ............................................ 10-8 Table 10.3 - Potential for Segregation of Filtering Materials.................................................................. 10-9 Table 10.4 – Gradation Limits to Prevent Segregation (USDA SCS 1994, USBR 1987, US Corps of
Engineers 1994)........................................................................................................... 10-10 Table 10.5 – Susceptibility of filter/transition zones to segregation versus weighted score (Relative
importance factor (RF)) x (Likelihood factor(LF)) ..................................................... 10-10 Table 10.6 – No erosion boundary for the assessment of filters of existing dams (after Foster and Fell
2001)............................................................................................................................ 10-11 Table 10.7 – Excessive and Continuing erosion criteria (Foster 1999; Foster and Fell 1999, 2001).... 10-11 Table 10.8 – Aid to judgement for estimation of probability for Continuing Erosion (PCE) when the
actual filter grading is finer than the Continuing Erosion Boundary........................... 10-12 Table 10.9 Example of Estimating Probabilities for No, Some, Excessive and Continuing Erosion for
the example shown in Figure 10.4............................................................................... 10-14 Table 10.10 - Continuing Erosion criteria for erosion into an open defect, .......................................... 10-15 Table 10.11 – Aid to judgement for estimation of probability for continuation for open
defects/joints/cracks..................................................................................................... 10-15 Table 10.12 – Probability of continuation for erosion into toe drains................................................... 10-16 Table 10.13 – Probability of by-passing the foundation filter for piping through the foundation or
piping from the embankment into the foundation ....................................................... 10-18 Table 11.1 – Probability of a soil being able to support a roof to an erosion pipe.................................. 11-3 Table 11.2 – Probability for crack filling action not stopping pipe enlargement – internal erosion
through the embankment ............................................................................................... 11-5 Table 11.3 – Probability that flow in the developing pipe will not be restricted by an upstream zone,
cut-off wall or a concrete element in the erosion path................................................... 11-7 Table 12.1 – A method for the approximation estimation of the time for progression of piping and
development of a breach, for breach by gross enlargement, and slope instability linked to development of a pipe (Fell et al 2001, 2003). .......................................................... 12-3
Table 12.2 - Rate of Erosion of the core or soil in the foundation .......................................................... 12-4 Table 12.3 – Influence of the material in the downstream zone of the embankment on the likely time
for development of a breach. ......................................................................................... 12-4 Table 12.4 – Qualitative terms for times of development of internal erosion, piping and breach (Fell et
al 2001, 2003). ............................................................................................................... 12-4 Table 12.5 – Factors influencing the likelihood of not observing a concentrated leak (Pnol) .................. 12-8
List of Tables & Figures
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Table 12.6 - Probability of not observing a concentrated leak (P nol ) versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) for internal erosion in an embankment ............ 12-8
Table 12.7 – Probability that given the leak is observable it is not detected given the time between the first appearance of the concentrated leak, and the frequency of inspections and/or reading of monitoring instruments................................................................................. 12-9
Table 12.8 – Assessment of the probability that given the concentrated leak is detected, intervention and repair is not successful (P ui ) ................................................................................ 12-11
Table 13.1 – Screening of breach mechanisms for internal erosion through the embankment, internal erosion in soil foundations, and from embankment into foundation ............................. 13-2
Table 13.2 – Probability of breach by gross enlargement of the pipe – Ability to support a pipe (Screening)..................................................................................................................... 13-3
Table 13.3 – Probability of breach by gross enlargement of the pipe ..................................................... 13-5 Table 13.4 – Factors which influence likelihood of breaching by instability of the downstream slope –
Slide Initiates for internal erosion in the embankment, in soil foundations, and from embankment into foundation. ........................................................................................ 13-7
Table 13.5 - Estimation of the probability of breach by slope instability – slide initiates for internal erosion in the embankment, in soil foundations, and from embankment into foundation versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) ..................... 13-8
Table 13.6 – Probability of seepage exits from defects or solution features in a rock foundation into the downstream shell (PS).................................................................................................... 13-9
Table 13.7 – Assessment of size of leak in defect or solution feature in a rock foundation relative to discharge capacity of foundation drains and downstream shell .................................. 13-10
Table 13.8 – Factors which influence likelihood of breaching by instability of the downstream slope –- Slide Initiates for internal erosion in rock foundation ................................................. 13-11
Table 13.9 - Estimation of the probability of breach by slope instability – slide initiates (Psi-i) for internal erosion in rock foundations versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) .............................................................................................. 13-11
Table 13.10 – Factors which influence likelihood of breaching by instability of the downstream slope – loss of freeboard .......................................................................................................... 13-12
Table 13.11 - Estimation of the probability of breach by loss of freeboard versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) ..................................................... 13-12
Table 13.12 – Factors which influence likelihood of breaching by unravelling – dams with an earthfill downstream zone ......................................................................................................... 13-14
Table 13.13 - Estimation of the probability of breach by sloughing (earthfill) versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) for internal erosion in the embankment, in soil foundations, and from embankment into foundation ................. 13-14
Table 13.14 - Estimation of the probability of breach by sloughing (earthfill) versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) for internal erosion in rock foundation.................................................................................................................... 13-15
Table 13.15 – Factors which influence likelihood of breaching by unravelling – dams with a rockfill downstream zone ......................................................................................................... 13-15
List of Tables & Figures
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Table 13.16 - Estimation of the probability of breach by unravelling (rockfill) versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) for internal erosion in the embankment, in soil foundations, and from embankment into foundation ................. 13-16
Table 13.17 - Estimation of the probability of breach by unravelling (rockfill) versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) for internal erosion in rock foundation.................................................................................................................... 13-16
Table 13.18 – Probability of a sinkhole or crest settlement developing (Ps-f) ....................................... 13-17 Table 13.19 – Factors which influence likelihood of breaching by sinkhole development – loss of
freeboard given sinkhole develops .............................................................................. 13-18 Table 13.20 - Estimation of the probability of breach by sinkhole development – loss of freeboard
given sinkhole develops versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) .................................................................................................................. 13-18
Figures
Figure 1.1 - Dam zoning categories .......................................................................................................... 1-2 Figure 1.2 - Soils types which are subject to internal instability and suffusion ....................................... 1-4 Figure 1.3 - Gradation of Broadly Graded Soils with Poor Self-Filtering Characteristics (Sherard 1979)1-4 Figure 3.1 - Flowchart for Internal Erosion in the Embankment .............................................................. 3-4 Figure 3.2 - Flowchart for Internal Erosion through a Soil Foundation.................................................... 3-6 Figure 3.3 - Flowchart for Internal Erosion through a Rock Foundation.................................................. 3-7 Figure 3.4 - Flowchart for Internal Erosion of the Embankment into or at the Foundation...................... 3-8 Figure 3.5 - Typical embankment dam showing some key features associated with potential internal
erosion failure paths....................................................................................................... 3-11 Figure 3.6 - Examples of embankment crest details which may result in relatively high likelihood of
internal erosion. ............................................................................................................. 3-12 Figure 3.7 - Example of an embankment with significantly different probabilities of internal erosion
above and below the top of the downstream berm ........................................................ 3-13 Figure 4.1 – Example fragility curve....................................................................................................... 4-24 Figure 5.1 - Definition of terms used to describe cross valley geometry .................................................. 5-3 Figure 5.2 - Cracking or hydraulic fracture adjacent cliffs due to differential settlement of the
embankment. Note that this mechanism only applies for Wb/Hw< 2.5............................ 5-5 Figure 5.3 – Longitudinal profiles of the dam showing the definition of terms for cross valley arching. 5-7 Figure 5.4 - Sloping core dam (a) Definitions of terms. (b) Limit of what constitutes a sloping core
dam. ............................................................................................................................... 5-10 Figure 5.5 – Typical scenarios which may lead to differential settlement in the foundation.................. 5-12 Figure 5.6 - Longitudinal section through staged embankment .............................................................. 5-13 Figure 5.7 Example of the estimation of crack width and flow gradient in the crack............................ 5-32 Figure 5.8 - Incidence of transverse cracking versus seismic intensity and damage class contours for
earthfill dams (Pells and Fell 2002, 2003)..................................................................... 5-38 Figure 5.9 - Incidence of transverse cracking versus seismic intensity and damage class contours for
earthfill and rockfill dams (Pells and Fell 2002, 2003) ................................................. 5-39 Figure 6.1 Example of poor detailing of seepage collars around a conduit (from FEMA 2005). ........... 6-15
List of Tables & Figures
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Figure 6.2 - Situations where a gap may form between the dam fill and spillway wall (a) Steep foundation adjacent spillway wall; (b) Change in slope of the retaining wall (Fell et al 2004).............................................................................................................................. 6-22
Figure 6.3 – Wrap around details for connection of embankment dam to concrete gravity dam............ 6-25 Figure 6.4 - Maximum point gradient, ipmt, needed for complete piping (initiation and progression for
an unfiltered exit) versus uniformity coefficient of soil (Schmertmann 2000). ............ 6-31 Figure 6.5 - Contours of the probability of internal instability for silt-sand-gravel soils and clay-silt-
sand-gravel soils of limited clay content and plasticity, Plasticity Index ≤ 12. (Wan and Fell 2004)................................................................................................................ 6-33
Figure 6.6 - Contours of the probability of internal instability for sand-gravel soils with less than 10% non-plastic fines passing 0.075 mm (Wan and Fell 2004). ........................................... 6-34
Figure 7.1 - An example of a situation where there is no continuous layer of cohesionless soil in the foundation and backward erosion cannot occur. ............................................................. 7-2
Figure 7.2 - Cross section of an embankment and dam foundation showing seepage flow net and definition of terms ........................................................................................................... 7-3
Figure 7.3 - Seepage model A of embankment dam and foundation (Maniam 2004). ............................. 7-6 Figure 7.4 - Seepage model B of embankment dam and foundation (Maniam 2004)............................... 7-6 Figure 7.5 - Seepage model C where foundation is overlain by low permeability clay (Maniam 2004).. 7-6 Figure 7.6 - Seepage model D used to represent the cracked downstream clay (Maniam 2004).............. 7-6 Figure 7.7 - Section through embankment and foundation showing definition of terms to estimate the
average gradient in the foundation sand. ......................................................................... 7-8 Figure 8.1 – Flow chart for estimating the probability, width, depth and spatial distribution of
continuous open defects and solution features in rock foundations. ............................... 8-2 Figure 8.2 – Assumed distribution of defect depths for defects related to stress relief effects in the
valley sides – (b) Jointed rocks such as thinly bedded sandstones, granite or basalt, and (c) for massive rocks (e.g. some granite). Figures from Fell et al 2004)....................... 8-24
Figure 8.3 – Definition of Δhp and hp. ..................................................................................................... 8-28 Figure 8.4 – Potential mechanisms for erosion of infill within a defect or solution feature. .................. 8-30 Figure 8.5 – Computation of probability of a continuous open defect or solution feature below the
embankment................................................................................................................... 8-35 Figure 9.1 – Examples of foundations with continuous open defects of varying width ........................... 9-7 Figure 9.2 - Definition of terms for arching across a cut-off trench. ...................................................... 9-10 Figure 10.1 – Example of the selection of representative grading curves (fine, average and coarse) for
the assessment of filter compatibility. ........................................................................... 10-7 Figure 10.2 – Approximate method for estimating DF15 after washout of the erodible fraction from a
suffusive soil or for soils susceptible to segregation. .................................................... 10-8 Figure 10.3 – Criteria for Excessive Erosion Boundary........................................................................ 10-12 Figure 10.4 - Example of plot showing filter/transition gradings compared to Filter Erosion
Boundaries. Evaluate the filter erosion boundaries for the representative fine, average and coarse gradings of the core material. .................................................................... 10-13
Figure 10.5 – Examples of scenarios of fully penetrating and partially penetrating foundation filter drains. .......................................................................................................................... 10-20
Figure 10.6 - Example of an embankment where much of the seepage flow will be to an unfiltered exit.10-21 Figure 10.7 - Example of an embankment where there is an unfiltered exit due to day lighting of the
foundation sand layer downstream of the dam. ........................................................... 10-21 Figure 12.1 – Sub-event tree for calculating the probability of not intervening. .................................. 12-12
SECTION 1 Introduction
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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1 Introduction
1.1 General
The United States Department of the Interior, Bureau of Reclamation (Reclamation) has developed a methodology for performing quantitative risk analysis for piping and internal erosion failure modes (i.e., Piping Toolbox) for embankment dams. Recently, under a cooperative agreement, the United States Army Corps of Engineers (USACE) has assisted in a revision of this toolbox. These methods are closely related to those developed at the University of New South Wales, Sydney, Australia and used in practice in Australia by URS and other consultants.
In discussions held in Denver in July 2005 between Reclamation, USACE, URS and Professor Fell it was recognised that some further development of the methods in the Toolbox was necessary to facilitate uniformity of application by risk analysis teams in Reclamation and USACE.
URS were commissioned by Reclamation and USACE to work with them to do this further development. This report presents the results of the study and the methods which were developed for estimating the probability of internal erosion and piping in embankment dams and their foundations.
1.2 Training
The Development Team strongly recommends that all risk analysts that will use this toolbox be trained in its use. The complexity of the issues and importance of the end product demands that all analysts fully understand the methodology.
The key goals of the training would be to provide an understanding of all features and components of the methodology; to outline for the analyst the supporting information and background that was used in the development of the methodology; and to guide the analyst through a detailed, real life example use of the methodology.
1.3 Terminology to Describe Embankment Types
In several of the tables provided to assist in assessing probabilities, the probability is linked to embankment type. The terms shown in Figure 1.1 have been adopted.
SECTION 1 Introduction
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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0. Homogeneous earthfill
Foundation filter
Embankment filter and/or
1. Earthfill with filter
Rock toe
Max 0.2H
2. Earthfill with rock toe
corecore downstream zoneof sand/gravel
3. Zoned earthfill
corecore downstream zoneof rockfill
4. Zoned earth and rockfill
core
rockfillrockfill
5. Central core earth and rockfill
concretefacing
earthfill
6. Concrete face earthfill
concretefacing
rockfill
7. Concrete face rockfill
Puddle core
8. Puddle core earthfill
concrete corewall
earthfill
9. Earthfill with corewall
concrete corewall
rockfill
10. Rockfill with corewall
hydraulic fill core
11. Hydraulic fill
Figure 1.1 - Dam zoning categories
SECTION 1 Introduction
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1.4 Terminology
The Unified Method uses the following terminology which should be adopted.
Internal erosion. Occurs when soil particles within an embankment dam or its foundation, are carried downstream by seepage flow. Internal erosion can initiate by concentrated leak erosion, backward erosion, suffusion and soil contact erosion.
Piping. Piping is the form of internal erosion which initiates by backward erosion, or erosion in a crack or high permeability zone, and results in the formation of a continuous tunnel called a ‘pipe’ between the upstream and the downstream side of the embankment or its foundation.
Backward erosion. Backward erosion involves the detachment of soils particles when the seepage exits to a free unfiltered surface, such as the ground surface downstream of a soil foundation or the downstream face of a homogeneous embankment or a coarse rockfill zone immediately downstream from the fine grained core. The detached particles are carried away by the seepage flow and the process gradually works its way towards the upstream side of the embankment or its foundation until a continuous pipe is formed.
Concentrated leak erosion. Erosion in a concentrated leak may occur in a crack in an embankment or its foundation, caused by differential settlement, desiccation, freezing and thawing, and by hydraulic fracture; or it may occur in a continuous permeable zone containing coarse and/or poorly compacted materials which form an interconnecting voids system. The concentration of flow causes erosion (sometimes called scour) of the walls of the crack or interconnected voids.
Flaw. A continuous crack, high permeability or poorly compacted layer in which a concentrated leak may form.
Suffusion and internal instability. Suffusion is a form of internal erosion which involves selective erosion of fine particles from the matrix of coarser particles (coarse particles are not floating in the fine particles). The fine particles are removed through the constrictions between the larger particles by seepage flow, leaving behind an intact soil skeleton formed by the coarser particles. Soils which are susceptible to suffusion are internally unstable. Coarse graded and gap graded soils, such as those shown schematically in Figure 1.2, are susceptible to suffusion. In these soils the volume of fines is less than the volume of voids between the coarse particles.
SECTION 1 Introduction
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0
1020
30
40
50
60
70
8090
100
0.001 0.01 0.1 1 10 100 1000
Particle size (mm)
% P
assi
ngCLAY TO SILT SAND GRAVEL
GAP GRADED SOIL
COARSELY GRADED SOIL WITH A FLAT TAIL OF FINES
Figure 1.2 - Soils types which are subject to internal instability and suffusion
Self-filtering. In soils which self-filter, the coarse particles prevent the internal erosion of the medium particles, which in turn prevent erosion of the fine particles. Soils which potentially will not self-filter include those which are susceptible to suffusion (internally unstable), and very broadly graded soils such as those which fall into the grading envelope shown in Figure 1.3 (Sherard 1979). The soils had particle size distributions which plotted nearly as a straight line, were typically of glacial origin, and the dams from which the soils were taken had all exhibited signs of internal erosion. The soils have a volume of fine particles greater than the volume of voids between the coarse sand and gravel fraction and the coarser particles are “floating” in the finer particles. The figure is not meant to define the boundary of such soils, only examples.
Figure 1.3 - Gradation of Broadly Graded Soils with Poor Self-Filtering Characteristics (Sherard 1979)
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Continuation. Continuation is the phase where the relationship of the particle size distribution between the base (core) material and the filter controls whether or not erosion will continue. Foster and Fell (1999, 2001) and Foster (1999) define four levels of severity of continuation from ‘no erosion’ to ‘continuing erosion.
No Erosion. The filtering material stops erosion with no or very little erosion of the material it is protecting. The increase in leakage flows is so small that it is unlikely to be detectable.
Some Erosion. The filtering material initially allows erosion from the soil it is protecting, but it eventually seals up and stops erosion.
Excessive Erosion. The filter material allows erosion from the material it is protecting, and in the process permits large increases in leakage flow, but the flows are self healing. The extent of erosion is sufficient to cause sinkholes on the crest and erosion tunnels through the core.
Continuing Erosion. The filtering material is too coarse to stop erosion of the material it is protecting and continuing erosion is permitted. Unlimited erosion and leakage flows are likely.
Progression. Progression is the third phase of internal erosion, where hydraulic shear stresses within the eroding soil may or may not lead to the enlargement of the pipe. Increases of pore pressure and seepage occur. The main issues are the likelihood of and rate of pipe enlargement and whether the pipe will collapse, whether upstream zones may control the erosion process by flow limitation and whether a pipe will extend through the low permeability zones of the embankment.
Breach. Breach is the final phase of internal erosion. It may occur by one of the following four phenomena (listed below in order of their observed frequency of occurrence).
• Gross enlargement of the pipe (which may include the development of a sinkhole from the pipe to the crest of the embankment).
• Slope instability of the downstream slope.
• Unravelling of the downstream face.
• Overtopping (e.g. due to settlement of the crest from suffusion and/or due to the formation of a sinkhole from a pipe in the embankment).
Annual Exceedance Probability (AEP): The estimated probability that an event of specified magnitude will be exceeded in any year.
Frequency: A measure of likelihood expressed as the number of occurrences of an event in a given time or in a given number of trials (see also likelihood and probability).
Likelihood: Conditional probability of an outcome given a set of data, assumptions and information. Also used as a qualitative description of probability and frequency.
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Probability: A measure of the degree of certainty. This measure has a value between zero (impossibility) and 1.0 (certainty). It is an estimate of the likelihood of the magnitude of the uncertain quantity, or the likelihood of the occurrence of the uncertain future event.
There are two main interpretations:
Statistical – frequency or fraction – The outcome of a repetitive experiment of some kind like flipping coins. It includes also the idea of population variability. Such a number is called an “objective” or relative frequentist probability because it exists in the real world and is in principle measurable by doing the experiment.
Subjective probability (degree of belief) – Quantified measure of belief, judgement, or confidence in the likelihood of an outcome, obtained by considering all available information honestly, fairly, and with a minimum of bias. Subjective probability is affected by the state of understanding of a process, judgement regarding an evaluation, or the quality and quantity of information. It may change over time as the state of knowledge changes.
Failure Path. A sequence of potential events starting from an initiating mechanism, such as a defect, flaw or seepage path in the dam or its foundation, and which may lead to an uncontrolled release of the reservoir.
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2 Methodology
2.1 Introduction
Risk is defined as the probability of a loss occurring in a given time period (annually) The equation for risk is;
Risk = [Probability of the loading] × [Probability of adverse response given the loading] × [Adverse consequence given the failure].
The first two components of this equation, when multiplied, produce the Annual Probability of Failure (APF) and are the main topic of this document.
2.2 General Process
The process for estimating the annual probability of failure by piping and internal erosion includes the following general steps:
Step 1: Review all information pertinent to piping and internal erosion (refer to Section 2.3 as an aid).
Step 2: Identify all potential failure paths associated with internal erosion and piping, considering each of the failure locations;
• Internal erosion through the embankment;
• Internal erosion through the foundation; and
• Internal erosion of the embankment into or at the foundation.
Screen those failure paths that are assessed to have negligible contribution to the annual probability of failure and document the reasons for their exclusion. Develop detailed descriptions and sketches of all realistic failure paths. Guidance is given in Sections 3.3 and 3.4.
Step 3: Decompose each of the potential failure paths into event trees. Generic event trees have been developed for each general failure mode the navigation tables in Appendices A to D. Select the event tree and associated navigation table that best fits the failure path being considered. If the failure path can not be matched with one of the generic event trees provided, then develop a different event tree using the guidance given in Appendix E.
Step 4: Select the loading partitions and estimate loading probabilities for each of the load conditions (static, seismic and hydrological) as described in Sections 3.5 and 3.6.
Step 5: Estimate the conditional probabilities for each node on the event tree, fully documenting the rationale. Specific guidance is given for estimating the conditional probabilities for various
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initiating mechanisms and failure locations in Sections 5 to 13. Navigation tables are provided in Appendices A to D to assist the user to find the location of the guidance tables for each node of the event tree. Guidance is also given in Appendix E for estimating probabilities for situations which are not covered by the method.
Step 6: Calculate the probability of failure by internal erosion and piping for each failure path and review for consistency between failure paths (Section 4.9).
Step 7: Use the annual probability of failure estimates in follow-on risk analysis and assessment.
2.3 Information Review
The quality and credibility of a risk estimate will suffer unless the analyst is fully aware of all pertinent information about piping and internal erosion. Typical information to review includes characteristics of the constructed project, such as embankment geometry, zoning, materials, construction methods, and seepage cut-off and control features; and characteristics of the setting, such as site geology and stratigraphy, and foundation material characteristics. Additional site information is provided by documented performance history.
To the maximum extent practicable, existing data from design and construction records, performance history, and post-construction investigations need to be reviewed. At preliminary stages of risk analysis, existing data supplemented by engineering judgment provide a sufficient basis for evaluation. If significant risk, including consideration of uncertainty, for the project is indicated, field investigations, laboratory testing, and additional analyses may be warranted. In some cases, however, it may be less expensive to simply fix the structure for the failure mode of concern.
A site visit to the dam has been found to provide valuable input into the risk analysis process. The site visit allows a better understanding of the layout of the dam and helps in the process of identifying potential failure paths.
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3 Failure Modes and Load Partitioning
3.1 Event Tree
The following generic sequence of events has been developed for internal erosion failure modes;
Reservoir Rises
Initiation – Flaw exists (1) (2)
Initiation – Erosion starts
Continuation – Unfiltered or inadequately filtered exit exists (consider: no erosion/some erosion/excessive erosion/continuing erosion)
Progression – Roof forms to support a pipe
Progression – Upstream zone fails to fill crack
Progression – Upstream zone fails to limit flows
Intervention fails
Dam breaches (consider all likely breach mechanisms)
Consequences occur
(1) A ‘flaw” is a continuous crack, high permeability or poorly compacted zone in which a concentrated leak may form.
(2) For Backward Erosion Piping (BEP) no flaw is required but a continuous zone of cohesionless soil in the embankment or foundation is required.
Generic event tree structures have been developed based on this sequence of events and these are presented in the Guidance Tables in Appendices A to D for each of the general failure modes.
Initiation is the first phase and considers the existence of a flaw such as a continuous crack or poorly compacted layer in which a concentrated leak may form. If a flaw exists, erosion must start to initiate for internal erosion to develop. There are several processes by which erosion can initiate in the embankment or foundation as follows;
• Concentrated leak erosion. Erosion can commence from the walls of a crack within the soil or within a poorly compacted layer.
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• Scour at the embankment –foundation contact. Erosion of the soil may occur where it is in contact with seepage passing through the foundation either through a coarse grained soil or open joints in rock.
• Backward erosion. Backward erosion involves the detachment of soils particles when the seepage exits to a free unfiltered surface. The detached particles are carried away by the seepage flow and the process gradually works its way towards the upstream side of the embankment or its foundation until a continuous pipe is formed.
• Suffusion. This is a form of internal erosion which involves selective erosion of fine particles from the matrix of coarser particles (coarse particles are not floating in the fine particles). The fine particles are removed through the constrictions between the larger particles by seepage flow, leaving behind an intact soil skeleton formed by the coarser particles.
Continuation is the phase where the relationship of the particle size distribution between the base (core) material and the filter controls whether or not erosion will continue. Foster and Fell (1999, 2001) and Foster (1999) define four levels of severity of continuation; No Erosion, Some Erosion, Excessive Erosion and Continuing Erosion.
Progression is the third phase of internal erosion, where hydraulic shear stresses within the eroding soil may or may not lead to the enlargement of the pipe. Increases of pore pressure and seepage occur. The main issues are whether the pipe will collapse and whether upstream zones may control the erosion process by flow limitation or crack filling.
Intervention fails is the fourth phase of the event tree, and this considers whether the internal erosion failure mechanism will be detected and whether intervention and repair will successfully stop the failure process.
Dam Breaches is the final phase of internal erosion. It may occur by one of the following four phenomena (listed below in order of their observed frequency of occurrence).
• Gross enlargement of the pipe (which may include the development of a sinkhole from the pipe to the crest of the embankment).
• Slope instability of the downstream slope.
• Unravelling of the downstream face.
• Overtopping (e.g. due to settlement of the crest from suffusion and/or due to the formation of a sinkhole from a pipe in the embankment).
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3.2 General Failure Modes
Failure by internal erosion of embankment dams is categorized into three general failure modes, which are;
• Internal erosion through the embankment,
• Internal erosion through the foundation, and
• Internal erosion of the embankment into or at the foundation.
3.2.1 Internal Erosion Through the Embankment
In this failure mode, internal erosion is occurs solely within the embankment. This includes internal erosion associated with through-penetrating structures, such as an outlet works, spillway or adjoining a concrete gravity structure.
The general process involved in assessing the probability of internal erosion through the embankment is summarized in the flowchart shown in Figure 3.1. A more detailed description of the process and a generic event tree is given in the navigation tables given in Appendix A.
Where applicable for a dam, separate event trees should be developed for the following cases;
• Internal erosion through cracks in the upper part of the embankment;
• Internal erosion through cracks in the middle/lower parts of the embankment;
• Internal erosion through a high permeability zone in the embankment;
• Internal erosion associated with a conduit/culvert penetrating through the embankment; and
• Internal erosion along the outside of a spillway wall or other concrete structure.
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CRACKING MECHANISMS: FAILURE PATHS:(a) WITHIN THE CORE
(a) CROSS VALLEY DIFFERENTIAL SETTLEMENT (BENCHES, CLIFF/WALL, CROSS VALLEY ARCHING)
(a) CROSS VALLEY DIFFERENTIAL SETTLEMENT
(b)
(b) CROSS SECTION SETTLEMENT DUE TO POORLY COMPACTED SHELLS
(b) DIFFERENTIAL SETTLEMENT LEADING TO ARCHING OF CORE
(c)
(c) DIFFERENTIAL SETTLEMENTS IN FOUNDATION
(c) DIFFERENTIAL SETTLEMENTS IN FOUNDATION
(d)
(d) DIFFERENTIAL SETTLEMENT DUE TO EMBANKMENT STAGING
(d) FOUNDATION CONTACT DUE TO SMALL SCALE IRREGULARITIES IN FOUNDATION PROFILE
(e)
(e) DESICCATION (AT CREST OR DURING CONSTRUCTION)
(e) DESICCATION DURING CONSTRUCTION
(a) ESTIMATE CRACK WIDTH - SUFFUSION(b) ESTIMATE INITIAL SHEAR STRESS TO INITIATE EROSION - BACKWARD EROSION(c) ESTIMATE CRACK WIDTH REQUIRED TO INITIATE EROSION - COHESIVE SOIL LAYER(d) COMPARE (a) AND (c)
SCENARIO 1: HOMOGENEOUS ZONING, NO FILTERSCENARIO 2: DOWNSTREAM SHOULDER OF COHESIVE MATERIALSCENARIO 3: FILTER/TRANSITION ZONE DOWNSTREAM OF CORESCENARIO 4: EROSION INTO OPEN CRACK/JOINTSCENARIO 5: EROSION INTO TOE DRAIN
WILL THE SOIL HOLD A ROOF?WILL CRACK FILLING ACTION STOP EROSION?WILL FLOW BE RESTRICTED BY AN UPSTREAM ZONE?
WILL IT BE DETECTED (IS IT VISIBLE/DETECTABLE, HOW OFTEN INSPECTED,)TIME TO FAILUREINTERVENTION ACTIONS (RELEASE, AVAILABILITY OF EQUIPMENT/MATERIALS)
GROSS ENLARGEMENT OF THE PIPESLOPE INSTABILITY OF THE DOWNSTREAM SLOPEUNRAVELLING OR SLOUGHING OF THE DOWNSTREAM SLOPESINKHOLE DEVELOPMENT OR CREST SETTLEMENT
PROBABILITY OF FAILURE
PROBABILITY OF INTERVENTION FAILS
ADJUSTMENT FACTORS TO ACCOUNT FOR OBSERVATIONS AND SETTLEMENT
WILL EROSION INITIATE WITHIN THE CRACK? WILL EROSION EROSION INITIATE IN THE HIGH PERMEABILITY ZONE?
ADJUSTMENT FACTORS TO ACCOUNT FOR OBSERVATIONS
LOADING CONDITION
MIDDLE/LOWER PART:
PROBABILITY OF INITIATION OF EROSION
UPPER PART:
IS A POORLY COMPACTED OR HIGH PERMEABILITY ZONE PRESENT IN DAM?WILL A TRANSVERSE CRACK OR HYDRAULIC FRACTURE DEVELOP IN THE DAM BODY?
WRAP AROUND DETAILS FOR CONNECTION TO CONCRETE GRAVITY DAM
PROBABILITY OF BREACH
PROBABILITY OF PROGRESSION
PROBABILITY OF CONTINUATION
ON CORE-FOUNDATION CONTACT
ASSOCIATED WITH A CONDUIT
ASSOCIATED WITH A SPILLWAY WALL
Figure 3.1 - Flowchart for Internal Erosion in the Embankment
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3.2.2 Internal Erosion Through the Foundation
This general failure mode involves internal erosion occurring solely within the foundation until the later stages of the breach process where the embankment starts to collapse. This is associated with internal erosion of an element within the dam foundation that is erodible.
The general process involved in assessing the probability of internal erosion through a soil foundation is summarized in the flowchart shown in Figure 3.2, and Figure 3.3 for a rock foundation. More detailed descriptions of the process are given in the navigation tables given in Appendix B for internal erosion in a soil foundation and Appendix C for internal erosion in a rock foundation.
3.2.3 Internal Erosion of the Embankment into or at the Foundation
Internal erosion initiates at the contact between the embankment and foundation owing to i) seepage through the embankment eroding material into the foundation, or ii) seepage in the foundation at the embankment contact, eroding the embankment material.
The general process involved in assessing the probability of internal erosion of the embankment into or at the foundation is summarized in the flowchart shown in Figure 3.4. A more detailed description of the process is given in the navigation tables given in Appendix D.
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PROBABILITY OF HEAVE PROBABILITY OF NO HEAVEPROBABILITY OF INITIATION AND
PROGRESSION OF BACKWARD EROSION
PIPING GIVEN HEAVE HAS OCCURRED
PROBABILITY OF INITIATION AND PROGRESSION OF
BACKWARD EROSION PIPING GIVEN HEAVE HAS NOT
OCCURRED
(a)(b)
(a) IS SOIL POTENTIALLY INTERNALLY UNSTABLE? (c) (b) PROBABILITY SOIL IS INTERNALLY UNSTABLE (d) (C) PROBABILITY SUFFUSION WILL BEGIN
IF UNFILTERED - PROBABILITY = 1.0
WILL THE SOIL HOLD A ROOF?WILL CRACK FILLING ACTION STOP EROSION?WILL FLOW BE RESTRICTED BY AN UPSTREAM ZONE?
WILL IT BE DETECTED (IS IT VISIBLE/DETECTABLE, HOW OFTEN INSPECTED,)TIME TO FAILUREINTERVENTION ACTIONS (RELEASE, AVAILABILITY OF EQUIPMENT/MATERIALS)
GROSS ENLARGEMENT OF THE PIPESLOPE INSTABILITY OF THE DOWNSTREAM SLOPEUNRAVELLING OR SLOUGHING OF THE DOWNSTREAM SLOPESINKHOLE DEVELOPMENT OR CREST SETTLEMENT
ESTIMATE CRACK WIDTH REQUIRED TO INITIATE EROSIONCOMPARE (a) AND (c)
IF FILTERED EXIT, ASSESS IN TERMS OF FILTER EROSION CRITERIA
PROBABILITY THAT THE EXIT WILL BE A FILTERED OR UNFILTERED EXIT
IS THERE A CONTINUOUS LAYER OF COHESIONLESS SOIL ?ESTIMATE THE PROBABILITY OF SUFFUSION
ESTIMATE CRACK WIDTHESTIMATE INITIAL SHEAR STRESS TO INITIATE
WILL EROSION INITIATE WITHIN THE CRACK?
IF SOIL IS COHESIONLESS,WILL BACKWARD EROSION INITIATE?
SCREENING CHECK ON SOIL CLASSIFICATION: IS THE FOUNDATION SOIL COHESIONLESS OR COHESIVE?
IS THERE A LAYER OF SOIL IN WHICH A CONTINUOUS CRACK OR INTERCONNECTED PATTERN OF CRACKS
MAY EXIST ?
PROBABILITY OF INITIATION AND PROGRESSION OF BACKWARD EROSION PIPING
LOADING CONDITION
PROBABILITY OF FAILURE
PROBABILITY OF INTERVENTION FAILS
IS THERE A CONTINUOUS LAYER OF COHESIONLESS SOIL ?
OR, WILL SUFFUSION INITIATE?
PROBABILITY OF BREACH
PROBABILITY OF PROGRESSION
PROBABILITY OF CONTINUATION
PROBABILITY OF INITIATION OF EROSION
IF SOIL IS COHESIVE, WILL EROSION INITIATE THROUGH A CRACK IN THE SOIL?
Figure 3.2 - Flowchart for Internal Erosion through a Soil Foundation
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IF UNFILTERED - PROBABILITY = 1.0
WILL THE SOIL HOLD A ROOF?WILL CRACK FILLING ACTION STOP EROSION?
WILL FLOW BE RESTRICTED BY AN UPSTREAM ZONE?
WILL IT BE DETECTED (IS IT VISIBLE/DETECTABLE, HOW OFTEN INSPECTED,)TIME TO FAILUREINTERVENTION ACTIONS (RELEASE, AVAILABILITY OF EQUIPMENT/MATERIALS)
GROSS ENLARGEMENT OF THE PIPESLOPE INSTABILITY OF THE DOWNSTREAM SLOPEUNRAVELLING OR SLOUGHING OF THE DOWNSTREAM SLOPESINKHOLE DEVELOPMENT OR CREST SETTLEMENT
LOADING CONDITION
PROBABILITY OF FAILURE
PROBABILITY OF INTERVENTION FAILS
PROBABILITY OF BREACH
PROBABILITY OF PROGRESSION
PROBABILITY OF CONTINUATION
PROBABILITY OF INITIATION OF EROSION
FOR IN FILLED DEFECTS, GROUTING IS ASSUMED TO BE INEFFECTIVE?FOR OPEN DEFECTS, IS GROUTING EFFECTIVE?
PROBABILITY OF ONE OR MORE CONTINUOUS OPEN OR IN FILLED DEFECTS (STRESS RELIEF VALLEY SIDES, VALLEY BULGE, SOLUTION FEATURES AND OTHER GEOLOGICAL FEATURES)
IS THE DEFECT OPEN OF INFILLED?
DOES EROSION OF THE IN FILL INITIATE?
DOES EROSION OF THE IN FILL CONTINUE?
COMBINE THE PROBABILITY ESTIMATES FOR OPEN DEFECTS AND IN FILLED DEFECTS THAT HAVE ERODED
IDENTIFY THE FAILURE MODES AND BREACH MECHANISMS WHICH MAY DEVELOP FROM THE PRESENCE OF THESE FEATURES
IF FILTERED EXIT, ASSESS IN TERMS OF FILTER EROSION CRITERIA
PROBABILITY THAT THE EXIT WILL BE A FILTERED OR UNFILTERED EXIT
Figure 3.3 - Flowchart for Internal Erosion through a Rock Foundation
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IF UNFILTERED - PROBABILITY = 1.0
WILL THE SOIL HOLD A ROOF?WILL CRACK FILLING ACTION STOP EROSION?WILL FLOW BE RESTRICTED BY AN UPSTREAM ZONE?
WILL IT BE DETECTED (IS IT VISIBLE/DETECTABLE, HOW OFTEN INSPECTED,)TIME TO FAILUREINTERVENTION ACTIONS (RELEASE, AVAILABILITY OF EQUIPMENT/MATERIALS)
GROSS ENLARGEMENT OF THE PIPESLOPE INSTABILITY OF THE DOWNSTREAM SLOPEUNRAVELLING OR SLOUGHING OF THE DOWNSTREAM SLOPESINKHOLE DEVELOPMENT OR CREST SETTLEMENT
LOADING CONDITION
PROBABILITY OF FAILURE
PROBABILITY OF INTERVENTION FAILS
IS THERE A CONTINUOUS PATHWAY OF OPEN JOINTS IN THE ROCK IN THE BASE OR SIDES OF THE CORE TRENCH OR AT
THE CORE-FOUNDATION CONTACT ?
WILL EROSION INITIATE IN A HYDRAULIC FRACTURE ACROSS THE CORE TRENCH ?
WILL SCOUR INITIATE AT THE CORE-FONDATION CONTACT ? OR
WILL BACKWARD EROSION PIPING INITIATE ? ORWILL SCOUR INITIATE AT THE CORE-FONDATION CONTACT ? ORWILL EROSION INITIATE IN A HYDRAULIC FRACTURE ACROSS THE CORE TRENCH ?
PROBABILITY OF BREACH
PROBABILITY OF PROGRESSION
PROBABILITY OF CONTINUATION
PROBABILITY OF INITIATION OF EROSION
IF FOUNDATION IS SOILWILL EROSION INTO COARSE GRAINED SOIL INITIATE?
IF FOUNDATION IS ROCK,WILL EROSION INTO OPEN ROCK JOINTS INITIATE?
SCREENING CHECK FAILURE PATH: SOIL OR ROCK FOUNDATION?
IS THERE A CONTINUOUS PATHWAY OF COARSE GRAINED SOILS IN THE SOILS IN THE BASE OR SIDES OF THE CORE TRENCH OR AT THE
CORE-FOUNDATION CONTACT ?
WILL BACKWARD EROSION PIPING INITIATE ? OR
IF FILTERED EXIT, ASSESS IN TERMS OF FILTER EROSION CRITERIA
PROBABILITY THAT THE EXIT WILL BE A FILTERED OR UNFILTERED EXIT
Figure 3.4 - Flowchart for Internal Erosion of the Embankment into or at the Foundation
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3.3 Identification of Failure Paths
3.3.1 Overview
A potential failure path is a sequence of events starting from an initiating mechanism, such as a defect, flaw or seepage path in the dam or its foundation, and which may lead to an uncontrolled release of the reservoir. The risk analysis team should go through a discussion of all potential failure paths and develop a thorough understanding of the sequence of events and the potential location of seepage and erosion paths through the embankment and foundation. The sequence of events and seepage pathways should be documented by annotating cross sections and longitudinal sections of the embankment and its foundation to help visualise the failure path. An example is given in Section 3.3.2. The development of the failure paths should consider the following;
• The general event tree structure as described in Section 3.1.
• Potential initiating mechanisms for each of the failure locations, as summarized in Figures 3.1 to 3.4;
• Zoning of the embankment, including the configuration of internal filter and drainage measures;
• Foundation geology and stratigraphy; and
• Filtered and unfiltered exit points of seepage.
The possibility of overlooking potentially important failure modes is reduced by considering the particular details if the dam and it’s appurtenant structures, such as details of walls retaining the embankment, conduits through the embankment, by assembling construction photographs and reports and inspecting the dam as part of the failure modes assessment. It is also reduced by having the failure modes assessment done by a team which includes the engineer and geologist most familiar with the dam, dam operating and surveillance staff, and facilitated by a person experienced in failure modes analysis.
The development team has strived to address all failure modes that, in their experience, occur in embankment dams. Procedures are also suggested to handle failure modes not well covered in this methodology. However, in the end, as pointed out by the late Ralph Peck in his paper “The Risk of the Oddball”, there remains the potential that even with the “… efforts of even the most experienced engineers the most significant potential failure mode may occasionally be overlooked.”
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3.3.2 Examples
The following sketch depicts an example of the description of a failure path for an initiating event involving seepage through a poorly compacted layer in the embankment. It is followed by a description of the failure mode for seepage path A.
A
B
CZone 1(SC)
Zone 2(SM)
Zone 2(SM)
Drainage Blanket
Riprap onGravel Bedding El. 500
El. 460Downstream Slope
Protection (Cobbles)
“Initiating event: Poorly compacted layer
Failure Path Description: The reservoir rises to elevation 466 feet, which is 1 foot above the historic high reservoir elevation. A low density zone exists in the Zone 2 at this elevation due to a thick lift being placed during original construction of the embankment that was not compacted well by the equipment being used. Upon saturation from the reservoir, the bottom of this layer settles and separates from the upper portion of the layer leaving a gap (i.e., as a result of collapse settlement of the poorly compacted layer). Seepage flows through this gap achieve sufficient velocity (i.e., sufficient gradient and gap width) to initiate erosion and begin a concentrated leak erosion process. The downstream cobble layer (slope protection) does not filter the Zone 2 material or the material does not have sufficient overburden and the slope protection layer blows off from reservoir pressure reaching the layer. A roof forms through the Zone 2 material. The riprap bedding layer does not function as a crack stopping material because it does not have sufficient volume due to its limited thickness or it is not of the proper gradation to be filtered by the downstream slope protection material. There is no upstream zone of material to limit flows. Wet spots and flowing water appear on the downstream face of the embankment, but these seepage expressions are not seen by either the public or project personnel. If the seepage expressions are seen and reported, intervention efforts are unsuccessful because the efforts simply do not stop the erosion process or the erosion progresses too rapidly allow meaningful intervention efforts to be implemented. The gap widens which leads to increased seepage velocities and more erosion of the Zone 2 material. Eventually this process of increasing seepage velocities and erosion progresses to full breach. The breach occurs by mechanisms typical for this type of embankment (i.e. gross enlargement of the developing pipe, slope instability, or sinkhole development).”
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Spillwaycrest CrestCrest
Spillwaywalls
Outletconduit
Intaketower
A B
C
D
E
FG
FSLNo filters above FSLFilters
Rockfill
Alluvium
Rock
Earthfill core
A, BCD,E
FG
Adjacent spillway walls.Adjacent outlet conduit.Related to irregularitiesin the foundation profile.In the foundation.From embankment tofoundation.
LEGEND
PLAN
ELEVATION
SECTION
Rockfill
Figure 3.5 - Typical embankment dam showing some key features associated with potential internal erosion failure paths.
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Figure 3.5 shows a fairly typical embankment dam, with a concrete spillway structure. Failure paths that could be considered for this dam include:
a) Internal erosion adjacent the spillway walls at A and B.
b) Internal erosion adjacent to and into the outlet conduit C.
c) Internal erosion over irregularities in the foundation e.g. at D for piping in the upper part of the embankment, and E for piping in the lower part, where there are likely to be low stresses and a potential for cracking and hydraulic fracture due to differential settlement.
d) Internal erosion for the remainder of the embankment, for example in high permeability layers.
e) Internal erosion in the alluvium foundation (F).
f) Internal erosion from the embankment to foundation at G.
For many dams, it is more likely that features likely to lead to initiation of internal erosion are in the upper part of the dam. This is because cracking due to differential settlement over large scale irregularities in the foundation profile is more likely to be present near the crest. Continuation is also more likely because often the detailing of the dam design, or as built, will give no or little filter protection. Figure 3.6 gives examples of this with increased likelihood of flood loading near the crest of the dam.
Figure 3.6 - Examples of embankment crest details which may result in relatively high likelihood of internal erosion.
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Figure 3.7 is an example where there is a significantly different probability of internal erosion above the berm than below because the upper part is essentially a homogeneous dam while the sandy gravel in zone 2 may act as a filter. This is best managed in the analysis by considering internal erosion above the berm (the upper part of the embankment) separately to below the berm (the middle and lower parts of the embankment).
Figure 3.7 - Example of an embankment with significantly different probabilities of internal erosion above and below the top of the downstream berm
While considering failure paths in this amount of detail may seem to be a lot of extra work, experience shows that it is necessary to do the analysis in this detail to allow proper consideration of the probability of failure, and in reality it makes assessment of conditional probabilities easier because factors are not being lumped together.
3.4 Failure Path Screening
3.4.1 Overview
The purpose of the failure path screening process is to systematically review the potential failure paths/modes that have been identified and eliminate those from further consideration that are assessed to have negligible contribution to risk.
The failure path is evaluated by listing the adverse factors that make the failure mode “more likely” and the favorable factors that make the failure mode “less likely”. These are based on the team’s understanding of the dam and background material.
Flow path B
Flow path A
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Screening of the failure paths is also evaluated using the screening criteria for the various initiating mechanisms which are summarized in Tables 3.1 to 3.5.
Each failure path is then screened by the analysis team based on the consideration of the list of the more likely and less likely factors, and using the initiating mechanism screening criteria. The primary intent is to identify those failure paths that are clearly so remote as to be negligible or non-credible. These screened failure paths are not carried forward into the risk analysis. The rationale for the inclusion or exclusion of each potential failure path should be fully documented.
3.4.2 Internal Erosion Through the Embankment
In Table 3.1, the “upper” part of the embankment is the upper 1/3rd measured at the maximum height section and continuing across the valley at this level. In Table 3.2 the “lower” part of the embankment is below the top 1/3rd.
Table 3.1 - Screening of initiating mechanisms – Internal erosion due to concentrated leaks in transverse cracks in the upper part of embankment dams
Initiating Mechanism Exclude the Failure Path if the Following Conditions are Satisfied
Reference Section and
Table
IM1 – Transverse cracking due to cross valley differential settlement
No exclusions apply – always include this failure path
Section 5.2.1, Table 5.1
IM2 – Transverse cracking due to differential settlement adjacent to a vertical cliff at the top of the embankment
Exclude if;
(1) There is no vertical cliff in contact with the embankment
OR
(2) A wide bench is present at the base of the cliff (Wb/Hw > 2.5, refer to Figure 5.2),
OR
(3) The abutment slope below the cliff is gentle (β1 < 25°, refer to Figure 5.2)
Section 5.2.1, Table 5.3
IM3 – Transverse cracking due to cross valley arching
Exclude if;
The width of valley to dam height ratio W v /H > 2, (refer to Figure 5.3).
Section 5.2.1, Table 5.5
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Initiating Mechanism Exclude the Failure Path if the Following Conditions are Satisfied
Reference Section and
Table
IM4 – Transverse cracking resultant on cross section settlement
Exclude if;
(1) The dam is zoning type homogeneous earthfill, earthfill with filter drains or zoned earthfill.
OR
(2) Evidence from relative settlements of core and shoulders that the materials have a similar modulus.
OR
(3) Finite Element Analyses have demonstrated that stresses are such that hydraulic fracture is very unlikely.
Section 5.2.2, Table 5.7
IM5 – Transverse cracking due to differential settlements in the foundation beneath the core
Exclude if;
There is no compressible soil in the foundation below the core
Section 5.2.3, Table 5.9
IM6 – Transverse cracking due to differential settlements due to embankment staging
Exclude if;
The embankment construction was not staged
Section 5.2.4
IM7 – Cracking in the crest due to desiccation by drying
Exclude if;
The reservoir stage being considered is below the likely depth of desiccation cracking.
Section 5.2.5, Table 5.11
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Initiating Mechanism Exclude the Failure Path if the Following Conditions are Satisfied
Reference Section and
Table
IM8 – Cracking on seasonal shutdown layers during construction and staged construction due to desiccation by drying
Exclude if;
The reservoir stage being considered is below the level of the seasonal shutdown surface.
OR
This mechanism only applies above the level of saturation of the core. Below that any desiccation cracks should have swelled and closed.
OR
This mechanism only applies where there has been a seasonal shutdown during construction, or the embankment has been staged.
OR
Very good control and clean up practices used – desiccated layers removed from the embankment and replaced with new soil or adequately reworked to specified moisture content.
Section 5.2.5, Table 5.14
IM13 – Cracking due to earthquake No exclusions apply – always include this failure path
Section 5.5
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Table 3.2 - Screening of failure paths – Internal erosion due to concentrated leaks in transverse cracks in the middle and lower parts of embankment dams
Failure Path/Location Exclude the Failure Path if the Following Conditions are Satisfied
Reference Section and
Table
IM9 – Transverse cracking due to cross valley differential settlement
Exclude if; Uniform abutment profile without benches
Section 5.3.1, Table 5.16
IM10 – Transverse cracking due to differential settlement causing arching of the core onto the shoulders of the embankment
Exclude; (1) For all dam zoning types other than central core earth and rockfill (or gravel shells), and puddle core earthfill dams.
OR (2) Dam has a wide core (W/H>1.0)
OR (3) Core has higher modulus than shells. Shoulders poorly compacted or dumped. Core compacted >98% SMDD.
Section 5.3.2, Table 5.18
IM11 – Transverse cracking or hydraulic fracture in the lower part of the embankment due to differential settlement in the foundation under the core
Already considered in upper part of dam, Sections 5.3.3 and 5.2.3, Table 5.9
IM12 – Transverse cracking at the foundation contact due to small scale irregularities in the foundation profile under the core
Exclude if; The persistence of the irregularity across the width of the core is less than 50% of the core base width
Section 5.3.4, Table 5.20
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Table 3.3 - Screening of failure paths – Internal erosion due to concentrated leaks in poorly compacted or high permeability zones in the embankment
Failure Path/Location Exclude the Failure Path if the Following Conditions are Satisfied
Reference Section and
Table
IM14 – Poorly compacted or high permeability layer in the embankment
Exclude if; All soils are very well compacted with lift thicknesses less than 8 inches, with good documentation and records; (1) For cohesive soils (Plasticity Index > 7), ≥98% standard dry density ratio, moisture content 2% dry to 1% wet of OWC; OR
(2) For cohesionless soils and soils with PI ≤ 7, >75% relative density.
Section 6.2.1, Table 6.1 for cohesive soils (PI>7)
Table 6.2 for cohesionless soils
IM15 – Poorly compacted or high permeability layer on the core-foundation contact
Exclude if; (1) Contact soils are well compacted on a regular foundation surface with good documentation and records OR
(2) Uniform or regular rock surface or surface treated with shotcrete or concrete to correct slope irregularities, and soils well compacted (contact soil compacted using special compaction methods (e.g. rubber tyres, use more plastic material, compaction wet of OWC).
OR (3) Uniform well compacted soil foundation, with good mixing, bonding and compaction of contact fill. OR
(4) Compacted soil foundation
Section 6.2.2, Table 6.4
IM16 – Poorly compacted or high permeability layers in the crest due to freezing
Exclude if; The climate is such that temperatures do not fall below freezing point except possibly overnight or for a day or two. OR
If the reservoir stage being considered is below the likely depth of freezing
Section 6.2.3.1, Table 6.6
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Failure Path/Location Exclude the Failure Path if the Following Conditions are Satisfied
Reference Section and
Table
IM17 – Seasonal shutdown layers during construction and staged construction surfaces due to freezing
Exclude if;
The climate is such that temperatures do not fall below freezing point except possibly overnight or for a day or two. OR Very good control and clean-up practices were used – Frozen layers removed from the embankment and replaced with new soil or adequately reworked to specified moisture content. OR
If the reservoir stage being considered is below the likely depth of desiccation cracking
Section 6.2.3.2, Table 6.9
IM18 – Poorly compacted or high permeability zone around a conduit through the embankment
Exclude if; (1) There is no conduit passing through the embankment, OR
(2) The conduit is totally embedded in a trench excavated in non-erodible rock, backfilled to the surface with concrete
Section 6.3.1, Table 6.11
IM19A, IM19B – Erosion into a (non-pressurized) conduit
Exclude if;
(1) There is no conduit passing through the embankment, OR
(2) Careful internal inspection of conduit showing no evidence of open joints or cracks.
Section 6.3.2, Table 6.13
IM20 – Poorly compacted zone associated with a spillway or abutment wall
Exclude if;
(1) There is no spillway or abutment wall in contact with the embankment
Section 6.4.2, Table 6.17
IM21 – Crack/gap adjacent to a spillway or abutment wall
Exclude if;
(1) There is no spillway or abutment wall in contact with the embankment
Section 6.4.3, Table 6.19
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Failure Path/Location Exclude the Failure Path if the Following Conditions are Satisfied
Reference Section and
Table
IM22 – Differential settlement adjacent to a spillway or abutment wall
Exclude if;
(1) There is no spillway or abutment wall in contact with the embankment OR
(2) A wide bench is present at the base of the wall (Wb/Hw > 2.5, refer to Figure 5.2), OR (3) The abutment slope below the wall is gentle (β1 < 25°, refer to Figure 5.2)
Section 6.4.4, Table 6.21
IM23 – Wrap around details for connection of embankment dam to concrete gravity dam
Exclude if;
(1) There is no wrap around connection of an embankment dam to a concrete gravity dam.
Section 6.4.5, Table 6.23
Note. Cohesionless soils are soils with zero Plasticity Index
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3.4.3 Internal Erosion Through the Foundation
Table 3.4 - Screening of failure paths – Internal erosion through the foundation
Initiating Mechanism Exclude the Failure Path if the Following Conditions are Satisfied
Reference Section and
Table
All modes of internal erosion of the foundation (backward erosion, suffusion, erosion in a crack)
Exclude if; (1) The soil layer beneath the dam is isolated by a cut-off trench founded in non-erodible rock. (Note that erosion across the cut-off trench is considered separately in internal erosion of the embankment into or at the foundation).
Section 7
IM24 – Backward erosion in a cohesionless soil foundation Suffusion in a cohesionless soil in the foundation
Exclude if,
(1) The foundation soil has a Plasticity Index ≥ 7. OR
(2) If the cohesionless soil or soil with PI ≤ 7 layer is not continuous below the embankment (i.e. it terminates beneath the dam, refer to Figure 7.1)
Section 7.2
IM25 – Suffusion in a cohesionless soil in the foundation
Exclude if,
(1) The foundation soil has a Plasticity Index ≥ 7. OR
(2) The proportion of the finer fraction is less than 40% of the total mass of the soil.
Section 7.4
IM26 – Erosion in a crack in cohesive soil in the foundation
Exclude if,
(1) The foundation soil is cohesionless.
Section 7.5
IM27 – Erosion in defects in a rock foundation
No exclusions apply Section 8
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3.4.4 Internal Erosion of the Embankment into or at the Foundation
Table 3.5 - Screening of failure paths – Internal erosion in the embankment into or at the foundation
Initiating Mechanism Exclude the Failure Path if the Following Conditions are Satisfied
Reference Section and
Table
IM28 – Internal erosion of the embankment into or at a rock foundation
Exclude if;
(1) Rock foundation below the core is comprised of rock containing closed rock defects (<1 mm wide) or defects open less than 3D 95 ,of the fine limit of the core OR
(2) Rock foundation below the core has been adequately treated (e.g. shotcrete, slush grouting mortar treatment)
Section 9.3
IM29 – Internal erosion of the embankment into or at a soil foundation
Exclude if;
(1) Soil foundation below the core is comprised of fine grained soils with greater than 12% fines (fraction finer than No 200 sieve (0.075mm)), and the soil does not contain macrostructure such as root holes, relic joints or solution features. OR
(2) Soil foundation below the core is comprised of sands (SP or SW) which are filter compatible with the embankment materials (i.e. satisfy the No Erosion criteria, refer to Section 10.1.4).
Section 9.4
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3.5 Partitioning of the Reservoir Levels
3.5.1 “Normal” and “flood” loading levels
It has been USACE and Reclamation practice to determine the risks for “normal” and “flood” loading separately.
For storages which are operated to store water for irrigation or hydropower, the top of “normal” loading is the top of active conservation level (“full supply level”) or for example the level of the crest in an un-gated spillway. For many dams this level is achieved in most years of operation and has an annual probability of being reached approaching 1.0.
For a flood control storage the normal loading is the reservoir level that is sustained year in and year out. For most of these dams there is usually a minimum pool level set.
For a ‘dry dam’, there is no normal water level and all water levels are associated with storing a flood and are regarded as flood loadings.
The probabilities of failure estimated for each of the flood loading partitions can be used as point estimates for developing fragility curves (refer to Section 4.9.2).
3.5.2 Pool of record level
The pool of record (POR) level is the maximum level the reservoir has reached during its operation. It is also known as “historic high reservoir level” and “water surface of record”. It is an important level because the embankment and its foundations have been tested up to this level.
3.5.3 Partitioning of reservoir levels
The reservoir levels should be partitioned to coincide with:
• The top of active conservation (full supply) level
• Flood pool of record level (also called historic high reservoir level).
• Changes in design. For example at 1 in 1000 Annual Exceedance Probability (AEP) flood in Figure 3.6(a); and at 1 in 50 AEP flood in Figure 3.6(b).
• Embankment crest level.
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• Geological features which occur above a particular level in the foundation (e.g. a highly permeable gravel layer).
• Topographic features such as major changes in foundation profile if these are above the pool of record.
For flood control storages it will probably be necessary to partition at for example 1 in 100 AEP and 1 in 1000 AEP flood levels even if these do not coincide with design features. For flood control dams which have not yet experienced a flood reaching the reservoir spillway crest level this may be used as a partition boundary.
If it is the policy of the agency to separate “normal” and “flood” risks then one reservoir partition level will need to coincide with the reservoir level at the boundary between these cases.
Table 3.6 shows an example of reservoir level partitioning.
Table 3.6 - Example of reservoir level partitions
Reservoir Level Significance
Annual Exceedance Probability of the
reservoir level
Reservoir Level Partition Range
Probability/annum the reservoir level
is in this range RL100 Minimum pool level
of record (or “Minimum pool of
record”)
1.0
RL100 – RL200 0.5
RL200 Top of active conservation level
(or “Full pool”)
0.5
RL200 – RL205 0.48
RL210 Pool of record level (or “Historic high reservoir level”)
0.02
RL205 – RL215 0.0199
RL215 Embankment crest level
(or “Dam crest flood”)
0.0001
>RL215 0.0001
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3.5.4 Assessing Frequencies of Reservoir Loading
For internal erosion and piping it is the annual probability that the level in the partition is exceeded regardless of how long for, not the proportion of time the reservoir is above the level. This is because internal erosion and piping often develops quite quickly and may go from initiation to breach in hours or days.
3.6 Earthquake Load Partitioning
Evaluate the peak ground bedrock acceleration and earthquake magnitude versus Annual Exceedance Probability (AEP) for the site. Partition the loads to form a table as shown in Table 3.7.
Table 3.7 - Example of earthquake load partitions
Earthquake peak ground acceleration
Representative earthquake magnitude
Annual exceedance Probability of the
earthquake loading
Probability/annum the loading is in this
stage 0.99
< 0.10g 6.0 0.01
0.009
0.20g 6.0 0.001
0.0009
0.30g 7.0 0.0001
0.0001
The earthquake peak ground acceleration values should be selected to coincide with the damage class contours given in Figure 5.8 for earth dams and Figure 5.9 for earthfill and rockfill dams. It is recommended that the minimum peak ground acceleration level be taken as 0.1g. If a particularly vulnerable element exists within the dam (e.g. transverse cracks are known to exist above a change in foundation slope), then the minimum PGA to be analysed could be reduced to 0.05g.
Probabilities of failure should be developed for each of the earthquake loading ranges.
It will also be necessary to consider the reservoir level at the time of the earthquake. This is done by developing the plot of reservoir level versus the proportion of time the reservoir level is exceeded. This is modelled as the first node in the event tree before the earthquake loading.
In some situations the reservoir may rise to higher levels before repairs to cracks caused by seismic loading can be affected, or cracking may be undetected. The possibility of these scenarios should be assessed.
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4 Application of Tables for Estimating Conditional Probabilities
4.1 General Approach
For each failure mode the conditional probabilities at each node in the event tree are estimated for each reservoir and earthquake load partition. They are used in the event trees to calculate probabilities of failure for each load partition. These probabilities are conditional on the reservoir or earthquake loading and are known as the “system response”.
The estimation of conditional probabilities is covered in Sections 5 to 13, with Sections 5 to 9 covering Initiation of Erosion, Section 10 Continuation, Section 11 Progression, Section 12 Detection, Intervention and Repair, and Section 13 Breach.
Tables are presented within the sections to give guidance on the estimation of conditional probabilities. These tables have been developed to model the physical processes so far as practical. The probabilities have been assessed using the expert judgement of the workshop attendees. Where practical these have been anchored to historic data. This has mainly been possible in the estimation of the probability of initiation of erosion in concentrated leaks and is discussed further in Section 4.2 and in the Supporting Document.
4.2 Historical Frequencies of Cracks and Poorly Compacted or High Permeability Zones in Embankments
Concentrated leak erosion may occur in cracks caused by differential settlement, desiccation, or in poorly compacted zones. In poorly compacted zones initiation of erosion may be a result of the voids between aggregated soil particles giving higher permeability and continuous open paths, or collapse settlement of the poorly compacted layer leading to a flaw or continuous open path in which water can flow and erode the sides of the flaw as happens in a crack.
Estimated frequencies of the occurrence of cracking, hydraulic fracture or poorly compacted or high permeability zones in embankments are presented in Table 4.1. They have been determined from analysis of historic dam accidents and failures, allowing for under reporting of the incidents in the database, cracking which may have been present in the dams in the database but were sufficiently resistant to erosion for erosion not to initiate, the cracks sealed by swelling, were above the Pool of Record (POR) of the dams, or erosion was stopped by filters. Details of the database and the analysis are given in the Supporting Document.
The frequencies in Table 4.1 are for a crack, hydraulic fracture or poorly compacted or high permeability zone being present, and do not include the assessment of whether erosion initiates in the crack, hydraulic fracture or poorly compacted or high permeability zone. These historic frequencies have been used as a basis for anchoring the estimated probabilities of a flaw being present in which erosion may initiate.
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When applying the historic frequencies to predict future behaviour it is assumed that the “Reservoir Level above Pool of Record” values apply when the reservoir level exceed the pool of record level by at least one foot (0.3 meters). This is so the above pool of record frequencies apply when the reservoir is testing significant new areas of the dam.
Table 4.1 - Estimated historical frequencies of cracking, hydraulic fracture or poorly compacted or high permeability zones in embankment dams.
Estimated historical frequencies of cracking, hydraulic fracture or poorly compacted or high permeability zones Location of
cracking/Poorly compacted or high permeability Zone First filling
Reservoir Level above Pool of
Record
Reservoir Level below Pool of
Record
In embankment (dam body) 0.014 0.014 0.001 per annum
Associated with conduit 0.01 0.01 0.0007 per annum
Associated with concrete wall or structure through embankment
0.004 0.004 0.0003 per annum
The historical frequencies for cracking or poorly compacted or high permeability zone in the dam body were further subdivided into the various mechanisms of crack formation. This was necessary so as to avoid the double counting of the historical frequencies when the probabilities for each initiating mechanism are added together. Table 4.2 presents the estimated historical frequencies for each of the mechanisms.
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Table 4.2 - Historical frequencies for cracking or poorly compacted zone in the embankment dam body.
Estimated historical frequencies of cracking, hydraulic fracture or poorly compacted or high permeability
zones
Mechanism for Cracking or Poorly Compacted or high permeability Zone
Proportion of Cases
Reservoir Level above Pool of
Record
Reservoir Level below Pool of Record (per
annum)
All incidents (cracking, hydraulic fracture and poorly compacted or high permeability zone)
100% 0.014 0.001
Cracking and hydraulic fracture 63%
In upper part (47%) 0.007 0.0005 In middle/lower part (16%) 0.002 0.0002
Poorly compacted or high permeability zone in upper and lower parts (total) 37% 0.005 0.0004
As described in the Supporting Document, the historical frequencies presented in Table 4.1 and Table 4.2 represent the average frequencies for cracks/ hydraulic fracture/poorly compacted or high permeability zones across the population of dams in the database. These represent a large number of dams of varying age and varying levels of engineering design and construction practice. They do not represent the historical frequencies for the “average dam” a term which has been applied previously (e.g. Fell et al 2003, 2004). It would be expected that the portfolio of well engineered Reclamation, USACE and Australian dams would have average probabilities estimated based on these historical data less than the average historical frequencies presented in the tables.
The historical frequencies for the “Below Pool of Record” case are quoted as annualized frequencies. For ease of application these are applied directly as conditional probabilities as the majority of dams have a seasonal cycle of reservoir fluctuation and reach a particular reservoir level each year.
The database of incidents is relatively small and because of this there should be no further subdivision of the failure and accident statistics.
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4.3 Historical Frequencies for Internal Erosion in and into the Foundation
The conditions in the foundations of dams are inherently more complex and varied than in the dam body, and hence historic frequencies for internal erosion in and into the foundation are more difficult to interpret and apply. One of the key issues for these modes of internal erosion is whether continuous seepage paths or open defects are present, and historic performance data provides very little information to aid in the assessment. For this reason, the use of historic performance data for anchoring the conditional probabilities for internal erosion through the foundation and internal erosion from the embankment into the foundation is not recommended.
4.4 Estimating Conditional Probabilities
4.4.1 Estimating Conditional Probabilities Using Relative Importance Factors and Likelihood Factors
Most of the Sections for estimation of conditional probabilities are structured so there is a Table of Factors affecting the likelihood. These tables are structured to show:
• The Factors
• The Relative Importance of this Factor (RF) with numeric weightings (usually three Factors with Relative Importance weightings of 3, 2 and 1).
• Likelihood Factors (LF) for which there are descriptions. Generally there are four for each Factor, with Likelihood weightings of 4, 3, 2 and 1.
There is then a second table which links ∑ (RF) x (LF) to the conditional probability. Where there is
historic data to “anchor” the probabilities these are shown; e.g. [0.0005] for Table 5.2, “Below POR”. The tables have two or more sets of probabilities. Where the “anchor” probabilities are estimated by expert judgement of the Toolbox development team they are shown with rounded brackets e.g. (0.003). The conditional probabilities on these tables are on a log scale, and interpolation between the bracketed probability values should be based on log interpolation.
The “Below POR” figures are for reservoir level stages with a representative level up to and 1 foot (0.3m) above the historic high reservoir pool level (POR). The “Above POR” figures are for representative reservoir level stages at least 1 foot (0.3m) above this historic high reservoir pool level.
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These anchor probabilities are a form of a “base rate frequency” and the approach used in the tables is a base rate frequency approach.
Those carrying out the risk analysis are required to choose which of the descriptors for each Factor best reflects conditions at the dam. Where there is little data this assessment should be made on the best available information and using judgement based on geological conditions and experience elsewhere on dams of similar age and design.
For some conditional probability estimates it has been necessary to modify the format of the table to better model Relative Importance or Likelihood distributions.
In the tables the term “negligible” means that the contribution to the probability of failure would be very small indeed, insufficient to affect the outcome.
4.4.2 Estimating Conditional Probabilities Using Scenario Tables
Where the number of factors affecting the estimation of conditional probabilities is few or to be based on limited data, “Scenario Tables” are used. These have been developed by the Toolbox development team based on published information, and the experience of the team members.
These tables present ranges of conditional probabilities within which the risk analysis team are to select their best estimate based on the details of the dam they are analyzing.
4.4.3 Estimating Conditional Probabilities Using Probability Estimate Tables
In some Sections, e.g. those describing the assessment of the probability of initiation of erosion in a crack, (Section 5.4.2) and initiation and progression of backward erosion in cohesionless soils (Section 6.6.2), the Toolbox development team have carried out analyses to simplify the estimation of conditional probabilities from input data which itself has significant uncertainty, and the analysis methods themselves have uncertain outputs.
The assumptions made to develop these tables are described in the Supporting Document.
4.5 Length Effects
The effect of the length of the embankment being considered may have an influence on the assessed probability of internal erosion and piping. The effect is dependent on the failure mode, how the embankment is partitioned for the analysis, and how the conditional probabilities are assessed.
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Many failure modes are independent of length because they are related to specific features in the embankment, such as a conduit, contact with a wall, and differential settlement of a major change in foundation profile. In many embankments, these failures modes contribute most to the likelihood of internal erosion and piping.
The failure modes which are potentially affected by length are cracking due to desiccation (either by drying and/or freezing), high permeability zones in the embankment (e.g. due to poorly compacted layers in the core), high permeability layer on the core-foundation contact, internal erosion of the embankment into or at a rock or soil foundation, and backward erosion in cohesionless soils in the foundations of dams. For these failure modes it is the likelihood of initiation of erosion for which length may be a factor. The length can be accounted for by considering it in determination of the probability; e.g. “what is the probability of a through going crack in the core due to desiccation in this 1000 feet length of embankment which so far as can be ascertained all has the same geometry, zoning and material properties?”
In statistical terms if all sections of the embankment are exactly the same, then they are perfectly correlated and the probability of at least one crack in the whole of the embankment is the same as for one section regardless of length. If each section is completely independent of the others, i.e. different construction materials, different specifications and construction methods, different cover (e.g. road pavement) over the core, then each section should be considered separately and the probabilities added using De Morgan’s rule;
P = 1 – (1-P1) x (1-P2) x (1-P3)…etc.
The following tables describe whether length effects are applicable to each of the internal erosion failure paths/location, and if so, the method of accounting for length effects. The notes for all of the tables are located after Table 4.6.
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Table 4.3 – Length Effects – Transverse cracking in the upper part of the embankment
Initiating Mechanism Sketch of Failure Mode Effect of length on
failure probability Comments
IM1 Transverse cracking due to cross valley differential settlement
Crack
Long Section
Crack
Long Section
No length effect but consider each abutment and add the calculated probabilities
In most cases one abutment or change in foundation profile will be much larger than the other, so it will be sufficient to calculate for this case only
IM2 Transverse cracking due to differential settlement adjacent a vertical cliff at the top of the embankment
Crack/Gap
Long Section
Crack/Gap
Long Section
No length effect but consider each abutment and add the calculated probabilities
In most cases one abutment cliff will be much larger than the other, so it will be sufficient to calculate for this case only
IM3 Transverse cracking due to cross valley arching
Crack
Long Section
Crack
Long Section
No length effect
IM4 Transverse cracking resultant on cross section settlement
Long Section
Long Section (a)
(b)Long Section
Long Section (a)
(b)
No length effect for case (a)
No length effect for case (b) but each part contributes and add the calculated probabilities
In most cases one part of the embankment will be larger than the other, so it will be sufficient to calculate for this part only
IM5 Transverse cracking due to differential settlements in the foundation beneath the core
Long Section
Compressible soil
Long Section
Long Section
(a)
(b)
(c)
Long Section
Compressible soil
Long Section
Compressible soil
Long Section
Long Section
(a)
(b)
(c)
No length effect for cases (a) and (b). No length effect for case (c) but each part contributes and add the calculated probabilities
IM6 Transverse cracking resulting from differential settlements due to embankment staging
Crack
Stage 2 Stage 1
Long Section
Crack
Stage 2 Stage 1
Long Section
No length effect. If more than one staging surface add the probabilities
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Initiating Mechanism Sketch of Failure Mode Effect of length on
failure probability Comments
IM7 Cracking in the core near the crest due to desiccation by drying
Long SectionLong Section
Length effects may apply. See Notes (1) and (2)
In many cases the nature of the embankment design and construction materials will be such that all sections are the same. Then the correlated condition exists, so length effects will be negligible.
IM8 Cracking on seasonal shutdown layers during construction and staged construction surfaces due to desiccation by drying
Crack
Stage 2 Stage 1
Long Section
Crack
Stage 2 Stage 1
Long Section
Same as IM6 Same as IM6
Notes. Refer to the end of Table 4.6 for notes.
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Table 4.4 – Length Effects – Transverse cracking in the middle and lower parts of the embankment
Initiating Mechanism Sketch of Failure Mode Effect of length
on failure probability
Comments
IM9 Transverse cracking due to cross valley differential settlement
Crack
Long Section
Crack
Long Section
No length effect but consider each abutment and add the calculated probabilities
In most cases one abutment or change in foundation profile will be much larger than the other, so it will be sufficient to calculate for this case only
IM10 Transverse cracking due to differential settlement causing arching of the core onto the shoulders of the embankment Long Section
Long Section (a)
(b)Long Section
Long Section (a)
(b)
No length effect for case (a)
No length effect for case (b) but each part contributes and add the calculated probabilities
In most cases one part of the embankment will be larger than the other, so it will be sufficient to calculate for this part only
IM11 Transverse cracking or hydraulic fracture in the lower part of the embankment due to differential settlement in the foundation under the core
Long Section
Compressible soil
Long Section
Long Section
(a)
(b)
(c)
Long Section
Compressible soil
Long Section
Compressible soil
Long Section
Long Section
(a)
(b)
(c)
No length effect for cases (a) and (b).No length effect for case (c) but each part contributes and add the calculated probabilities
IM12 Transverse cracking at the foundation contact due to small scale irregularities in the foundation profile under the core
Long SectionLong Section
No length effect, but allow for the number of irregularities and add the calculated probabilities.
See Note (3)
Notes. Refer to the end of Table 4.6 for notes.
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Table 4.5 – Length Effects – Poorly compacted or high permeability zones in the embankment
Initiating Mechanism Sketch of Failure Mode Effect of length on failure probability Comments
IM14 Poorly compacted or high permeability layer in the embankment
Long SectionPoorly compacted layers
Long SectionPoorly compacted layers
Length effects may apply. See Notes (1) and (4)
In many cases the nature of the embankment design and construction materials will be such that all sections are the same. Then the correlated condition exists, so length effects will be negligible
IM15 Poorly compacted or high permeability layer on the core-foundation contact
Long SectionPoorly compacted layer
Long SectionPoorly compacted layer
Length effects may apply. See Notes (1) and (5)
IM16, IM17 Cracking in the crest or seasonal shutdown layers during construction due to desiccation by freezing
Long SectionLong Section
Length effects may apply. See Notes (1) and (6)
In many cases the nature of the embankment design and construction materials will be such that all sections are the same. Then the correlated condition exists, so length effects will be negligible
IM18 High permeability zone around a conduit through the embankment
Long Section High Permeability Zone
Long Section High Permeability Zone
No length effect. If there is more than one conduit treat each separately and add the probabilities
IM19A Erosion into a (non-pressurized) conduit
IM19B Erosion into a (non-pressurized) conduit leading to erosion along the conduit
Long Section Erosion into Conduit
Long Section Erosion into Conduit
No length effect. If there is more than one conduit treat each separately and add the probabilities
IM20, IM21, IM22 Poorly compacted or high permeability zone, crack/gap associated with a spillway or abutment wall
Crack/Gap
Long Section
Crack/Gap
Long Section
No length effect. If there is more than one wall treat each separately and add the probabilities
Notes. Refer to the end of Table 4.6 for notes.
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Table 4.6 – Length Effects – Internal erosion in the foundation and into the foundation
Initiating Mechanism Sketch of Failure Mode Effect of length on failure probability Comments
IM24 Backward erosion in a cohesionless soil foundation
Suffusion in a cohesionless soil in the foundation
Long SectionLong Section
Length effects may apply. See Notes (1) and (7).
See Note 7
IM25 Erosion in a crack in cohesive soil in the foundation
Long SectionLong Section
Depends on the cause of the cracking. For desiccation induced cracking see IM6; for settlement induced cracking see IM9 or IM11
IM26 Erosion in open or in filled defects in a rock foundation
Long SectionLong Section
Length effects may apply. See Notes (1) and (7).
IM27 Internal erosion of the embankment into or at a rock foundation
Long SectionLong Section
Length effects may apply. See Notes (1) and (7).
See Note 7
IM28 Internal erosion of the embankment into or at a soil foundation
Long SectionLong Section
Length effects may apply. See Notes (1) and (7).
See Note 7
Notes for Tables 4.3 to 4.6; (1) If all sections of the embankment are exactly the same, then they are perfectly correlated and the probability of cracking in the whole of the embankment is the same as for one section regardless of length. If each section is completely independent of the others, i.e. different construction materials, different specifications and construction methods, different cover (e.g. road pavement) over the core, each section should be considered separately and the probabilities added using De Morgan’s rule. (2) The probabilities in Table 5.12 are determined by expert judgement and are for an embankment about 1600 feet (500 meters) long. The spacing of the cracks is likely to be about 5x crack depth, so there will be many cracks of maximum depth within the 500 meters. These probabilities will apply for embankments shorter than 1600 feet (500 meters) without adjustment for length.
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(3) The probabilities in Tables 5.20 and 5.21 are anchored against historic data, for which there were between 2 and 5 small scale irregularities. Use these figures unless there are greatly more than 5 small scale irregularities. (4) The probabilities in Tables 6.1, 6.2 and 6.3 are anchored on historic data and are for an embankment about 1600 feet (500 meters) long. There are likely to be a number of sections within 500 meters which have the conditions potentially leading to a flaw. These probabilities will apply for embankments shorter than 1600 feet (500 meters) without adjustment for length. (5) The probabilities in Tables 6.4 and 6.5 are anchored by relation to historic data and are for an embankment about 1600 feet (500 meters) long. There are likely to be a number of sections within 1600 feet (500 meters) which have the conditions potentially leading to a flaw. These probabilities will apply for embankments shorter than 1600 feet (500 meters) without adjustment for length. (6) The probabilities in Tables 6.6. 6.7, 6.9 and 6.10 are determined by expert judgement and are for an embankment about 1600 feet (500 meters) long. There are likely to be a number of sections within 1600 feet (500 meters) which have the conditions potentially leading to a flaw. These probabilities will apply for embankments shorter than 1600 feet (500 meters) without adjustment for length. (7) The foundation should be partitioned so that geotechnical conditions are essentially the same within a section. Within a section the correlated condition exists, regardless of its length. Estimate the probability of backward erosion or suffusion for each section and add the probabilities using De Morgan’s rule. Any section may have experience one or more sand boils. If these occurred at the same reservoir level for dams, the number of boils is not a factor in assessing the probability as one boil or many boils both mean initiation has occurred at that level. De Morgan’s rule is P = 1 – (1-P1) x (1-P2) x (1-P3)…etc.
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4.6 Nature of the estimates of probabilities given by the Toolbox
4.6.1 The Toolbox gives “Best Estimate” Probabilities
The methods in the Toolbox provide “best estimates” of the conditional probabilities and hence “best estimate” probabilities of failure.
The estimates are determined by expert judgement based on analyses and laboratory tests modelling the physical processes. They are designed to avoid systematic bias towards conservative or non-conservative probabilities.
Probabilities for some of the most important initiating modes within the embankment are calibrated against historic performance of dams from a large database of around 10,000 dams in the ICOLD (1986) survey of failures and accidents. This is discussed in detail in Section 4.2. Where this has not been possible expert judgement of the team developing the Toolbox based on extensive experience in dams and risk assessment has been used, taking into account the feedback from trials and reviews of the Toolbox in Reclamation and USACE.
The methods in the Toolbox are likely to be more reliable in assessing relative probabilities between failure modes and between dams than assessing absolute values.
4.6.2 Adjusting the Toolbox Best Estimates
4.6.2.1 Allowance for factors not included in the Toolbox methods
It is recommended that the Toolbox estimate be adopted except where there are factors not covered in the Toolbox tables which the risk analysis team believe affect the estimate of the conditional probability for the node in question. These factors may include observations or monitoring data, or physical factors not allowed for in the Toolbox. In these cases the best estimate should be determined by adjusting the toolbox estimate to allow for the additional factors. It would not be expected that this would generally result in conditional probabilities greatly different to those estimated by the Toolbox.
The additional factors should be described and the reasoning for the revised estimate provided in the risk analysis report.
4.6.2.2 What to do if the Toolbox estimates seem incorrect.
There may be cases where the toolbox estimates of failure probabilities are significantly different to what the risk analysis team would have expected. This may be due to 1) the logic (i.e. construction of the event tree)
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does not well match the perceived failure mode for the dam being analysed, 2) the RF and LF factors do not well represent what the team originally thinks are the key factors or actual observances, or 3) the probability value suggested in the toolbox does not well represent what the risk analyst thinks is appropriate. The suggested steps to follow for each of these situations are:
a) If the issue appears to be in the logic, look carefully at the failure mode being modelled to identify where the perceived difference has occurred. Experience has shown that the logic presented in the toolbox has stood the test of time and is normally considered appropriate. Issues with the logic are typically due to a less-than-full understanding of what is already presented in the toolbox. If there is still perceived to be an error in the toolbox logic, check with Agency personnel familiar with the toolbox to ascertain that a problem still exists. If in the end there still is an issue, then the failure mode could be developed into its own event tree or adjustments made to the portion of the toolbox event tree in question followed by assigning probabilities using one of the mapping schemes given in Appendix E or even use the original toolbox RF and LF factors if they are still appropriate. In this case the issue should also be referred to one of the current toolbox developers for consideration in future updates.
b) If there seems to be an issue in the RF and/or LF factors, fully discuss the factors presented to ascertain that the proposed new factors are indeed more important. Be sure that the failure mode is well understood and that the risk analyst has a good understanding of the available case histories upon which the toolbox has been built around. If in the end it appears that the factors should be adjusted or changed, make the changes/adjustments and document well what was done and why. The Agency Person who manages the Toolbox should oversee the corrections/adjustments.
c) If there seems to be an issue with the probabilities assigned, the risk analyst should be sure they are well aware of the database of historic precedent and experienced judgment that has been extensively used in the development of the method’s probabilities. Once the analyst is well armed with this information, the analyst is then equipped to assess the appropriateness of the prescribed probabilities and attempt an adjustment. The adjustment should be made, possibly assisted by one of the mapping schemes given in Appendix E, and then fully documented. In this case the issue should also be referred to one of the current toolbox developers for consideration in future updates.
4.6.3 Limitations of the methods used in the Toolbox
The Toolbox is based on the (2007) state of the art on modelling the mechanics of initiation of internal erosion in cracks and other flaws, by backward erosion and suffusion. The methods available are sufficient to form the basis of the Toolbox, and are to be preferred to methods based only on historic data, or expert judgement anchored on historic data such as those detailed in Fell et al (2003, 2004).
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The mechanics of continuation (filter action) are fundamentally simpler, more extensively researched and the methods are less subjective than for initiation, provided the data to do the analyses is available.
The modelling of progression, detection and intervention, and breach are more subjective and largely based on case studies and expert judgement.
The methods used here are a significant improvement on the methods described in Fell et al (2003, 2004) which have been used in Australia and as input to the Reclamation methods.
It is recommended that those using Fell et al (2003, 2004) now use the methods described in this Guidance Report.
Most of the logic, modelling, analysis, laboratory testing, expert elicitation techniques used in this document continues to be actively researched and/or studied. Case histories continue to occur that give more insight to the process involved. It is likely that these developments in understanding will result in improved methods for assessing probabilities of initiation, continuation, and progression of internal erosion, and breach mechanics. When this occurs it will be necessary to revise the Toolbox.
4.6.4 Assessment of probabilities of failure for failure modes which are not covered by the Toolbox
In some dams there may be failure modes which are not well modelled by the Toolbox. For these failure modes the risk analysis team should develop an event tree to model the failure mode. Conditional probabilities within the event tree should be estimated using the Toolbox where the nodes are common to the Toolbox event tree, and by expert judgement for the other nodes. Appendix E details how this should be done.
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4.7 Modelling uncertainty in the estimates of conditional probabilities
4.7.1 Purpose of this section
The Toolbox has been developed to provide “best estimate” values of conditional probabilities for the nodes in the event trees for all failure modes. Sometimes where there is considerable uncertainty or contradictory information in the data being used for the risk analysis a sensitivity analysis to gauge the effect of the likely range of estimates of conditional probability on one or two of the most critical nodes on the event tree may be modelled.
In some more detailed risk analysis it may be required that the uncertainty which is inherent in such estimates is modelled. This uncertainty may arise from limitations in the Toolbox methods used to estimate probabilities (a type of model uncertainty), the data available for the dam being analysed (epistemic uncertainty) and uncertainty associated with unpredictable variations of a random nature in data relied on for the risk analysis (aleatory uncertainty), uncertainty about the true accuracy and/or applicability of an analytical model used to assess the data, and measurement and parameter uncertainty of properties of materials in the dam and its foundation.
The effects of uncertainty in the estimates of conditional probability can be examined either with sensitivity analysis or modelling uncertainty in the event tree. Both approaches are described in this section. Reference should be made to Reclamation (2001b), Dam Safety Risk Analysis Methodology, Appendix T, Handling Uncertainty.
4.7.2 Sensitivity analysis
There will be some cases where the quality and quantity of data available to do the risk analysis is limited, and or is somewhat contradictory. For example data on filters or transition zones may be limited. In these cases it is recommended that the best estimate and the range of the best estimate for the node probability is calculated from this data and carried forward in the risk analysis as a sensitivity analysis. This means that there will be a best estimate and two other estimates representing the range of estimates of the frequency of failure to be reported for this failure mode. Alternatively only the upper and lower estimates are carried through so decision makers can gauge the importance of this data on the risk analysis.
This approach should be adopted when uncertainty is not being modelled as detailed in Section 4.7.3.
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4.7.3 Uncertainty analysis
In some situations the Agency for whom the risk analysis is being carried out may require that the uncertainty of the estimate of conditional probability in each node of the event tree be modelled. This uncertainty would then be used in Monte Carlo analyses to determine the distribution of estimates of the probability of failure.
The following sections provide some information on how uncertainty may be modelled. The details of how to do this should be determined by the Agency to meet their needs.
4.7.3.1 Situations where uncertainty analysis may be required
Whether uncertainty analysis is required is a matter for the Agency for whom the risk analysis is being carried out.
Reclamation practice is to not require uncertainty analysis for Comprehensive Facility Reviews (CFR) , except that the Senior Engineer doing the analysis may assign a range to the estimate based on his/her experience in estimating uncertainty in more detailed risk analyses. The USACE equivalent to a Reclamation CFR is the Periodic Assessment (PA).
For Issue Evaluation Risk Analysis (IERA) and Risk Reduction Risk Analysis (RRRA) uncertainty analysis will typically be carried out by Reclamation.
USACE does not require an uncertainty analysis. Instead a sensitivity analysis may be required as for Australian practice as detailed below.
Australian practice as discussed in ANCOLD (2003) is to carry uncertainties through the analysis and/or do sensitivity testing on important event tree nodes where the data available makes the assessment of that probability difficult.
4.7.3.2 Modelling uncertainty for event tree nodes where relative importance factors and likelihood factors tables are used to estimate conditional probabilities.
This covers the probability versus (RF)x(LF) tables in Sections 5 2 and 5.3, Sections 6.2 to 6.4.4, Sections 8.2 to 8.9, Section 9.7, Section 12.3, and Sections 13.3 to 13.5.
In these tables there is:
i) Uncertainty in the historic data “anchor” probabilities, and in the minimum and maximum probabilities (e.g. negligible, [0.005], and 0.2 in Table 5.4). These in turn affect the values in the tables in between. Where there are no historic data to “anchor” the probabilities there is uncertainty in the estimates based on the expert judgement of the Toolbox development team.
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ii) Uncertainty in the ability of these tables and the factors they are based on to model the relative probabilities.
iii) Uncertainty in the analysis and laboratory testing data upon which the methods may be based. An example would be the numerical analysis upon which Table 5.3 is largely based.
iv) Uncertainty resulting from limitations of the available investigations, design, construction and monitoring data relating to the probability being assessed. An example would be limitations of knowledge of the degree of compaction and borrow area variability in Table 6.1.
(a) Model uncertainty Uncertainties (i) (ii) and (iii) are model uncertainties.
Table 4.7 shows best estimate, and equivalent likely low and likely high probabilities. This can be used to develop likely minimum and likely maximum probability versus (RF)x(LF) tables. Table 4.7 is based on a dissection of the basis upon which the historic probabilities anchor points and the minimum and maximum values were determined. Details of how this was done are given in Section S4.7 of the Supporting Document. If the probability for (RF)x(LF) =6 is less than or equal to 0.0001, then the likely low probability should equal the best estimate.
Table 4.7 allows definition of the anchor point, minimum and maximum probability values. The risk analyst should then interpolate to determine the intermediate values on the (LF)x(RF) table. An example is given in the Supporting Document Section S4.6.
Reclamation Risk Analysis Methodology –Appendix T, Handling Uncertainty, use the terms “Reasonable Low” to represent the 10th percentile bound, and “reasonable high” to represent the 90th percentile bound. The range of 0.2x (likely low) to 5x (likely high) represents more stringent percentiles, possibly < 1% to >99%. It is for the agency doing the uncertainty analysis to judge what range the model uncertainty represents and to decide what range to adopt.
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Table 4.7 – Best estimate, likely high and likely low equivalence table
Best Estimate Probability Likely High Probability Likely Low Probability
0.0001 0.0005 0.0001
0.001 0.005 0.0002
0.01 0.05 0.002
0.02 0.1 0.004
0.05 0.2 0.01
0.1 0.4 0.02
0.2 0.6 0.04
0.3 0.8 0.07
0.5 0.95 0.15
0.9 0.999 0.4
Note. Likely high probabilities are assumed to be 5 times best estimate, and likely low probabilities 0.2 times best estimate. See Section S4.7 for details of the calculations to develop the values in the table.
(b) Data uncertainty The uncertainty in the probability estimate resulting from limitations in the data (factor (iv) above) should be assessed by assessing the likely low and likely high (RF)x(LF) values from the table, and using these in the Probability versus (RF)x(LF) tables to estimate the range of probabilities resulting from data uncertainty.
(c) Combining the model and data uncertainty. To combine the model and data uncertainty, use the likely low, best estimate and likely high probability from the relevant probability versus (RF)x(LF) table. An example is given in the Supporting Document, Section S4.6.
This is a severe test of overall uncertainty and Agencies will need to develop their policy on how to combine these components of uncertainty.
4.7.3.3 Modelling uncertainty for event tree nodes where scenarios and examples are described, and a range of probabilities provided.
This covers the Tables where scenarios are described, examples are given, and a range of probabilities provided from which the risk analyst makes a selection based on the available information, and the analysts degree of belief.
Examples are Tables 10.13, 11.1, 11.2, 11.3, 12.8 and 13.6.
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For these cases it is recommended that:
• The risk analysis team estimate is taken as the best estimate.
• The likely low and likely high probability is estimated by the analysis team, within the range shown in the table.
Where the Toolbox table indicates a probability of 1.0, this should generally be adopted for best estimate and likely low and likely high estimates. These are only used in the Toolbox where there is very high degree of confidence based on physical factors that a probability of 1.0 is applicable.
In cases where the information available to the risk analysis team strongly supports adopting best estimate and/or likely low or likely high probabilities outside the range in the tables, the risk analysis team may adopt this value, but it would not be expected that this would result in probabilities greatly different to those estimated by the Toolbox.
The factors leading to this probability estimate should be described and the reasoning for the revised estimate provided in the risk analysis report.
4.7.3.4 Modelling uncertainty for event tree nodes where single value estimates of probability are provided.
This covers tables where analysis has been carried out to combine a number of input variables, and the Toolbox development team have allowed for uncertainty in the input variables to allow for uncertainty. This includes Tables 5.29 to 5.35, 6.26, 6.27, and 7.4, 7.5.
i) Probability of initiation of erosion in concentrated leaks, Tables 5.29 to 5.35
As described in Sections S5.4.2.4 these tables have been developed allowing for:
• Probability distributions in the maximum crack width and crack width at depth versus crack width at the surface.
• The initial shear stress of the soil.
• Using these to run Monte Carlo analyses.
The values in Tables 5.29 to 5.35 are median values. Tables in Supporting Document Section S5.4.2.4 have the equivalent tables for the 10% and 90% values, representing the likely minimum and likely maximum probabilities.
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ii) Probability of initiation of erosion and progression in cohesionless soils, Tables 6.26, 6.27, and 7.4, 7.5
As described in Section S6.6.2.7 these probabilities are obtained by comparing the actual average seepage gradient to that required to initiate and progress backward erosion. The probabilities were assessed by expert judgement allowing for the uncertainty in the method used to assess whether backward erosion would initiate and progress.
Tables 6.26, 6.27, and 7.4, 7.5 are best estimate values. Tables in Supporting Document Section S6.6.2.7, S7.3.2 and S7.3.3 have the equivalent tables for the likely minimum and likely maximum probabilities. These have been developed by expert judgement.
4.7.3.5 Selection of the Probability Distribution
The risk analysis team should select the probability distribution they believe best fits their best estimate, likely low and likely high probability estimates. The alternatives which may be considered are explained in Reclamation (2001b). For many cases a triangular distribution is likely to be suitable.
4.8 Summarizing (Making the case)
Once a risk estimate is prepared with the use of this toolbox, the analyst needs to make summary of the key factors that generated the estimates of probability of failure. An exercise of ‘making the case’ is important so that reviewers and decision makers can quickly focus on the story being told. This can be done relatively easily by reviewing each of the components of the estimate and select those that drive most of the final estimate. Once these are determined, they should be reviewed and the main factors that contribute most to the actual estimate of this component should be brought forward into an engineering summary of the failure mode. This engineering summary should normally only focus on those factors key to the overall estimate.
By doing this the redundancy, or lack thereof, in the design can be demonstrated. In the case with much redundancy, i.e. dams with many components that contribute to the overall risk being low, it is important to highlight this. For example, dams with a low chance for concentrated leakage; a non-erodible core; some filtering components should be viewed as an overall robust situation with reasonable redundancy. In contrast, a homogenous dam with an erodible core where the risk is low due almost solely to a low probability of a concentrated leak is a case with little redundancy. It is important to summarize this situation for reviewers and decision makers.
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4.9 Combining Probabilities
Risk is computed by finding the product of probabilities and consequences for each path of the event tree.
The principles for combining the probabilities on the event trees and for the different failure paths is as follows;
• For mutually exclusive failure paths, as occurs on a specific event tree, the conditional probabilities of failure should be added.
• For failure paths that are not mutually exclusive, the total probabilities of failure from the event trees should be calculated using De Morgan’s rule;
P = 1 – (1-PIM1) x (1-PIM2) x (1-PIM3)…etc.
The method for presenting the probabilities of failure will depend on which method is intended to be used for computing the risk.
• If the risk is to be calculated for static, hydrological and seismic loading events separately, then refer to Section 4.9.1.
• If the risk is to be calculated using fragility curves, then refer to Section 4.9.2.
4.9.1 Adding Probabilities for Static, Hydrological and Seismic Loads
The following guidelines are provided for computing the annual probabilities of failure for the static, hydrological and seismic load cases.
Annual Probability of Failure for the Static Load Condition;
The annual probability of failure for the static load case is as follows;
• For each static reservoir level partition, combine the response probabilities of failure for each failure mode using De Morgan’s rule.
P = 1 – (1-PIM1) x (1-PIM2) x (1-PIM3)…etc.
Section 3.5 gives guidance on selecting the reservoir level partitions that correspond to the static load case.
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• The annual probability of failure for the static load case is then calculated by summing the product of the total response probability of failure for each load partition by the annual probability of the loading condition.
Annual Probability of Failure for the Hydrological Load Condition;
The annual probability of failure for the hydrological load case is as follows;
• For each hydrological reservoir level partition, combine the response probabilities of failure for each failure mode using De Morgan’s rule.
P = 1 – (1-PIM1) x (1-PIM2) x (1-PIM3)…etc.
Section 3.5 gives guidance on selecting the reservoir level partitions that correspond to the hydrological load case.
• The annual probability of failure for the hydrological load case is then calculated by summing the product of the total response probability of failure for each load partition by the annual probability of the loading condition.
Annual Probability of Failure for the Seismic Load Condition;
The annual probability of failure for the seismic load case is as follows;
• For each seismic load partition, combine the response probabilities of failure for each failure mode using De Morgan’s rule.
P = 1 – (1-PIM1) x (1-PIM2) x (1-PIM3)…etc.
Section 3.6 gives guidance on selecting the seismic level partitions.
• The annual probability of failure for the seismic load case is then calculated by summing the product of the total response probability of failure for each load partition by the annual probability of the loading condition.
4.9.2 Development of Fragility Curves
The following guidelines have been developed for users who intend to use fragility curves to quantify the risk. The probabilities of failure estimated for each of the reservoir level and earthquake loading partitions can be used as point estimates for developing fragility curves. Separate fragility curves should be developed for each of the potential failure modes identified in the screening process.
SECTION 4 Application of Tables for Estimating Conditional Probabilities
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The process to develop fragility curves for reservoir level loading is summarized as follows;
• Select the reservoir level partition points as described in Section 3.5.
• Estimate the conditional probabilities of failure for each of the three modes of internal erosion and for each reservoir level. The conditional probabilities for each failure path should be added as follows;
P = 1 – (1-PIM1) x (1-PIM2) x (1-PIM3)…etc.
• Plot the conditional probabilities vs reservoir level on a log-linear scale. Join the individual point estimates using straight lines. An example is shown in Figure 4.1.
1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
80 100 120 140 160 180 200 220 240 260
Reservoir Level (ft)
Con
ditio
nal p
roba
bilit
y of
failu
re
Internal erosion in theembankment
Internal erosion in thefoundation
Internal erosion from theembankment into thefoundation
Emba
nkm
ent c
rest
leve
Top
of A
ctiv
e C
onse
rvat
ion
Min
imum
Poo
l Lev
e
Floo
d of
Rec
ord
Leve
l
Figure 4.1 – Example fragility curve
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5 Probability of Initiation of Erosion in Transverse Cracks in the Embankment
5.1 Overall Approach
a) Estimate the probability of a transverse crack for normal and hydrologic loading for each of the initiating mechanisms that can lead to cracking and low stress zones in which hydraulic fracture can occur. These are:
Upper parts of the embankment (Section 5.2)
• Differential settlement cross valley (IM1)
• Differential settlement adjacent to a cliff (IM2)
• Differential settlement cross valley arching (IM3)
• Differential settlement as a result of cross section settlement (IM4)
• Differential settlement in the foundation beneath the core (IM5)
• Differential settlements due to embankment staging (IM6)
• Desiccation cracking (IM7, IM8)
Lower and middle parts of the embankment (Section 5.3)
• Differential settlement cross valley (IM9)
• Differential settlement as a result of cross section settlement due to arching (IM10)
• Differential settlement due to soil in the foundations (IM11)
• Differential settlement due to small scale irregularities in the foundation profile (IM12)
This is done using Tables 5.1 to 5.15 in Section 5.2 for cracking in the upper part of the dam, and Tables 5.16 to 5.21 in Section 5.3 for cracking in the middle and lower parts. The embankment is split into the upper and middle and lower parts to take into account the likely locations for each of the crack initiating mechanisms. The inputs to these tables are modified by observed settlements or cracking using Tables 5.22 and 5.23 in Section 5.3.5.
For most dams not all mechanisms will be present and those mechanisms are assigned a zero probability. The details for screening the mechanisms are described in Section 3.4.
b) Estimate the maximum likely crack width at the surface of the core for each of the initiating mechanisms which apply as described in Section 5.4. Then estimate the likely crack width at the reservoir level being considered.
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c) Estimate the probability of initiation of erosion for this mechanism given this estimated crack width, seepage gradient across the core, and the properties of the soil in the core (P IC ) using Section 5.4.
d) Estimate the probability of initiation of erosion (P I ) = (P C ) x (P IC ) for each initiating mechanism.
The probability estimates for initiation of erosion for each initiating mechanism are not added together, but are carried through the event trees for each failure path.
5.2 Estimating the Probability of Transverse Cracking (P C ) in the Upper Part of the Dam
5.2.1 Likelihood of a Transverse Crack Due to Cross Valley Differential Settlement (IM1)
Table 5.1 - Factors influencing the likelihood of cracking or hydraulic fracturing in the upper part of embankment dams - Cross Valley Differential Settlement (IM1)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Cross valley profile under embankment core(1)
(3) Uniform abutment profile without benches
Narrow bench very low in the abutment
b/h2 <0.5,
h2/h1 >1.5
Refer to Note (a)
Wide bench low in the abutment
b/h2 > 1; h2/h1 > 1
Wide bench in upper half to one third of the abutment
b/h2 > 1; 0.5 < h2/h1 < 1
or narrow bench in upper half to one third of the abutment, b/ h2 > 0.5; h2/h1 < 0.25
Wide bench near the crest in the abutment
b/h2 > 1.
0 < h2/h1 < 0.5
Slope of abutments under embankment core(1)
(2)
Gentle abutment slope
β 1 < 30o
Moderate abutment slopes
30o < β 1 < 45o
Steep abutments
45o < β 1 < 60o
Very steep abutments,
β 1 > 60o
Height of embankment
(1) Dams less than 50 ft (15 m) high
Dams 50 ft to 100 ft (15 m to 30 m) high
High dams 100 ft to 200 ft (30 m to 60 m)
Very high dams >200 ft (60 m) Refer to Note (b)
Notes: (a) See Figure 5.1 for definitions of b, h1, h2, β. (b) For dams higher than 400 ft (120 m) assign a likelihood factor of 5. (c) The method of applying this type of table is described in Section 4.4.
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Table 5.2 - Probability of a cracking or hydraulic fracture in the upper part of embankment dams-Cross Valley Differential Settlement versus ∑ (Relative importance factor (RF) x
(Likelihood factor(LF))
0.00001 0.00005 0.00015 [0.0005] 0.005 0.02 Below POR
0.0001 0.0005 0.002 [0.007] 0.05 0.2 Above POR
6 9 11 13 18 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
Figure 5.1 - Definition of terms used to describe cross valley geometry
bH
h2
h1
β1
β2
Valley Centerline
Dam crest
Abutment
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Table 5.3 - Factors influencing the likelihood of cracking or hydraulic fracturing in the upper part of embankment dams-Differential settlement adjacent a cliff at the top of the
embankment (IM2)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Cross valley profile under embankment core(a) (b)
(3) Wide bench Wb/Hw > 2.5 Note. If this condition is present, probability=zero
Bench adjacent to cliff 1.0 < Wb/Hw <2.5
Narrow bench adjacent to cliff 0.25 < Wb/Hw < 1.0
No or very narrow bench adjacent to cliff. Wb/Hw < 0.25
Slope of abutments under embankment core(a)
(2) Gentle abutment slope
β 1 < 25o
Note. If this condition is present, probability=zero
Moderate abutment slopes
25o < β 1 < 45o
Steep abutments
45o < β 1 < 60o
Very steep abutments,
β 1 > 60o
Height of embankment
(1) Dams less than 50 ft (15 m) high
Dams 50 ft to 100 ft (15 m to 30 m) high
High dams 100ft to 200 ft (30 m to 60 m)
Very high dams >200 ft (60 m)
Note: (a) See Figure 5.2 for definitions of Wb, Hw, β1 (b) This mechanism only applies for Wb/Hw< 2.5
Table 5.4 - Probability of a cracking or hydraulic fracture in the upper part of embankment-Differential settlement adjacent a cliff at the top of the embankment versus ∑ (Relative
importance factor (RF)) x (Likelihood factor(LF))
negligible negligible negligible negligible [0.0005] 0.002 0.02 Below POR
negligible negligible negligible negligible [0.005] 0.02 0.2 Above POR
6 9 11 13 14 19 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
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Figure 5.2 - Cracking or hydraulic fracture adjacent cliffs due to differential settlement of the embankment. Note that this mechanism only applies for Wb/Hw< 2.5.
β1
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Table 5.5 - Factors influencing the likelihood of cracking or hydraulic fracturing in embankment due to cross valley arching (IM3)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Slope of abutments under embankment core(a)
(3) Moderate abutment slope
β 1 ,β 2 < 45o
Moderate steep abutment slopes
45o<β2, β2<60o
Steep abutments
60o < β 1 ,β 2 < 75o
Very steep abutments,
β 1 ,β 2 > 75o
β 1 near vertical,
β 2 60o
Cross valley geometry under embankment core(a)
(2) W v /H > 0.75
Note.
If W v /H > 2,
Exclude this failure mode
0.4< W v /H<0.75
Narrow deep valley
0.25< W v /H< 0.4
Very narrow deep valley
W v /H < 0.25
Height of embankment
(1) Dams less than 50 ft (15 m) high
Dams 50 ft to 100 ft (15 m to 30 m) high
High dams 100 ft to 200 ft (30 m to 60 m)
Very high dams >200 ft (60 m)
Note: (a) See Figure 5.3 for definitions of W v , H, β 1 and β 2
(b) If the soil in the lower part of the core is poorly compacted or subject to collapse compression on saturation, and the upper part is not, increase weighted factor (LF x RF) by 1 or 2.
Table 5.6 - Probability of cracking or hydraulic fracturing in embankment due to cross valley arching versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF))
negligible negligible 0.00005 0.0001 0.0005 0.004 0.02 Below POR
negligible negligible 0.0005 0.001 0.007 0.05 0.2 Above POR
6 9 10 13 17 21 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
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Figure 5.3 – Longitudinal profiles of the dam showing the definition of terms for cross valley arching.
β1
β1 β1
β1
β2 β2
β2 β2
SECTION 5 Probability of Initiation of Erosion in Transverse Cracks in the Embankment
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5.2.2 Likelihood of Transverse Cracking Resultant on Cross Section Settlement due to Poorly Compacted Shoulders (IM4)
Table 5.7 – Factors influencing the likelihood of cracking or hydraulic fracturing in the upper part of embankment - cross section settlement resulting from poorly compacted shoulders
(IM4)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
EITHER Embankment zoning and Compaction of outer zone Excluding sloping core earth and rockfill dams
(3) Zoned earthfill, earthfill with filter drains or homogeneous (all materials similar modulus) Note: if have evidence from relative settlements of core and shoulders that the materials have a similar modulus, then probability = 0
Zoned earthfill, earthfill with filter drains, modulus of outer zones lower than core. Central core earth and rockfill (or “gravel fill”), with well compacted shoulders and core.
Central core earth and rockfill (or “gravel fill”), rockfill or gravel” fill compacted by dozer tracking or by small rollers in thick layers
Central core earth and rockfill, uncompacted (dumped) rockfill
OR Embankment zoning and Compaction of outer zone, sloping core earth and rockfill dams
(3) Core sloped steeper than 45o but within limits of sloping core embankment. Rockfill (or “gravel fill”), and core .well compacted, and with similar moduli.
Core sloped flatter than 45o Rockfill (or “gravel fill”), and core .well compacted.
Core sloped flatter than 45o. Rockfill (or “gravel fill”), rockfill or gravel” fill compacted by dozer tracking or by small rollers in thick layers
Core sloped flatter than 45o. Construction staged with rockfill in the lower part of the dam compacted to a higher modulus than the upper part.(a) OR uncompacted (dumped) rockfill
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Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Core geometry Width (W)/ Height (H)(b)
(2) W/H>3 1.5<W/H<3 0.5< W/H<1.5 W/H<0.5
Height of embankment
(1) Dams less than 50 ft (15 m) high
Dams 50 ft to 100 ft (15 m to 30 m) high
High dams 100 ft to 200 ft (30 m to 60 m)
Very high dams>200 ft (60 m)
Note. (a) If there is a large difference in moduli, a probability of cracking between 0.02 and 0.2 may be applied. (b) See Figure 5.4 for definition of width W and Height H. Width should be taken at the base of the core.
Table 5.8 - Probability of a transverse crack or hydraulic fracture resultant on cross section
settlement resulting from poorly compacted shoulders versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF))
0.00001 0.00002 0.00005 0.0002 [0.0005] 0.002 Below POR
0.0001 0.0002 0.0005 0.002 [0.007] 0.02(1) Above POR
6 9 11 13 18 24 RF x LF
Note: (1) If there is a large difference in modulus between the core and shoulders, a probability of cracking between 0.02 and 0.2 may be applied.
Note: “POR” refers to the Pool of Record level + 1 foot
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Figure 5.4 - Sloping core dam (a) Definitions of terms. (b) Limit of what constitutes a sloping core dam.
core slope β1
SECTION 5 Probability of Initiation of Erosion in Transverse Cracks in the Embankment
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5.2.3 Likelihood Of Transverse Cracking Due To Differential Settlements In Soil In The Foundation Beneath The Core (IM5)
Table 5.9 – Factors influencing the likelihood of cracking or hydraulic fracturing in the upper part of embankment dams- settlement resulting from differential settlements in soil in the
foundation (IM5)
Likelihood Factor (LF) Factor
Relative Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely (4)
Foundation geology and geometry (c)
(3) Rock foundations or uniform soil foundations(a)
Shallow soils or soils with gradual variation in depth and compressibility sufficient to cause differential settlement of less than 0.2% of the embankment height
Moderate depth of compressible soil in the foundation sufficient to cause differential settlement of 0.2% to 0.5% of the embankment height
Deep compressible soil in the foundation(b) sufficient to cause differential settlement of >0.5% of embankment height
Slope of the sides of the compressible zones (d)
(2) Gentle
α < 30o
Moderate
30o <α < 45o
Steep
45o <α < 60o
Very steep
α > 60o
Height of embankment
(1) Dams less than 50 ft (15 m) high
Dams 50 ft to 100 ft (15 m to 30 m) high
High dams 100 ft to 200 ft (30m to 60 m) high
Very high dams > 200 ft (60m) high
Notes: (a) If there is no compressible soil in the foundation this mode does not apply (b) Including soils which collapse on saturation and which have not been treated or removed during construction. (c) See Figure 5.5 for typical scenarios which may lead to differential settlement. (d) See Figure 5.5 for definition of slope α
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Table 5.10 - Probability of a crack or hydraulic fracture due to differential settlement in the foundation versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF))
negligible negligible 0.00005 0.0002 [0.0005] 0.003 0.02 Below POR
negligible negligible 0.0005 0.002 [0.007] 0.03 0.2 Above POR
6 8 9 11 13 18 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot. Note: (1) This mode does not apply if there is no compressible soil in the foundation beneath the core.
Figure 5.5 – Typical scenarios which may lead to differential settlement in the foundation.
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5.2.4 Likelihood Of Transverse Cracking Due To Differential Settlements Due To Embankment Staging (IM6)
This situation arises where the embankment has been staged during construction. There is a potential for differential settlement to occur if the “existing” (first stage) embankment is a significantly higher modulus than the remainder of the embankment. If this is the situation, use the method described in Section 5.2.1 to assess the likelihood a crack or hydraulic fracture will result. If however there is no or little difference in the modulus, this mode may be ignored. In most cases the latter will apply.
Figure 5.6 - Longitudinal section through staged embankment
5.2.5 Likelihood of Transverse Cracking due to Desiccation (IM7, IM8)
Desiccation In The Crest Of The Dam (IM7)
FIRST Consider the maximum likely depth of desiccation cracking for the soil in the core of the dam, and the climate using Table 5.13. If the reservoir stage being considered is below the likely depth of desiccation cracking, the probability of a crack due to desiccation cracking can be assumed to be zero.
SECOND For cases where the reservoir stage is above the base of potential desiccation cracking, follow the procedure below.
Final embankment crest level
b
h1
h2
Existing Embankment
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Table 5.11 – Factors influencing the likelihood of cracking in the upper part of embankment dams- cracking in the crest due to desiccation by drying (IM7)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Crest zoning and surface layer over core
(3) Road pavement cover(a) with base layer 300 mm or more thick, and/or Rock fill or non plastic granular layer at least 3 ft (1 meter) thick
No road pavement cover(a), with non-plastic granular material, 6 inches to 12 inches (150 mm to 300 mm) thick.
Thin ( less than 3 inches (75 mm)) surface gravel layer with no pavement cover(a) or Low plasticity granular transition layer over core
No surface layer. Dam core extends to crest level
Climate (2) Temperate climate, uniform rainfall throughout the year
Seasonal climate with annual rainfall greater than 20 inches (500 mm) and no prolonged hot dry periods
Monsoonal or other distinct wet and dry periods in the year. Summer maximum temperatures>85°F (>30°C)
Arid climate, less than 10 inches (250 mm) rainfall, High summer temperatures
Plasticity of core material
(1) Low plasticity to non plastic
Medium to low plasticity
Medium to high plasticity
High plasticity
Note: (a) Road pavement cover may comprise concrete, asphalt or bitumen seal.
Table 5.12 - Probability of a transverse crack, cracking in the crest due to desiccation by drying versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF))
0.0001 0.001 0.01 0.1 0.5 0.9
6 9 11 16 20 24 RF x LF
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Table 5.13 – Screening Tool. Maximum likely depth of desiccation cracking for a gravel surface layer with no road pavement cover based on climate
Maximum likely depth with gravel layer with no road
pavement cover(a)
Maximum likely depth with no surface layer (dam core extends to
crest level) Climate
(feet) (meters) (feet) (meters)
Arid climate, less than 10 inches (250mm ) rainfall, high summer temperatures
15 4.5 23 7
Monsoonal or other distinct wet and dry periods in the year. Summer maximum temperatures >85°F (>30°C )
13 4 20 6
Seasonal climate with annual rainfall greater than 20 inches (500 mm) and no prolonged hot dry periods
10 3 16 5
Temperate climate, uniform rainfall throughout the year
6 2 15 4.5
Note: (a) Road pavement cover may comprise concrete, asphalt or bitumen seal.
Desiccation Cracking On Seasonal Shutdown Layers And On The Surface Of Staged Embankments (IM8)
FIRST (a) This mechanism only applies above the level of saturation of the core. Below that any desiccation cracks should have swelled and closed. If the seasonal shutdown layer is below the Pool of Record, use the “Below POR” probabilities in Table 5.15.
(b) This mechanism only applies where there has been a seasonal shutdown during construction, or the embankment has been staged. The descriptions in Table 5.14 are to be assessed according to the conditions across the width of the core.
SECOND Where the mechanism applies, estimate the probability of desiccation cracking using Table 5.14 and Table 5.15, and multiply this probability by the assessed likelihood the layer will be continuous across the core.
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Table 5.14 - Factors influencing the likelihood of cracking on seasonal shutdown layers during construction and staged construction surfaces due to desiccation by drying (IM8)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Construction practices regarding clean-up of desiccated layers after construction shutdowns or the surface of the earlier stage of the dam
(4)
Very good control and clean-up practices. Desiccated layers removed from embankment and replaced with new soil or adequately reworked to specified moisture content. If this condition is present, probability=0, regardless of the other factors
Good control and practices, surfaces scarified, moisture adjusted to specified range, surface re-compacted.
Moderate control. Attempts to scarify desiccated layers, but depth of scarifying insufficient or difficulties with moisture control
Poor control. No attempt to scarify or remove desiccated layers, poor moisture control practices
Climate (2) Temperate climate, uniform rainfall throughout the year
Seasonal climate with annual rainfall greater than 20 inches (500 mm) and no prolonged hot dry periods
Monsoonal or other distinct wet and dry periods in the year. Summer maximum temperatures >85°F
(>30°C )
Arid climate, less than 10 inches (250 mm ) rainfall, High summer temperatures
Plasticity of core material
(1) Low plasticity to non plastic (LL < 20%)
Medium to low plasticity (20% < LL < 40%)
Medium to high plasticity (40% < LL < 50%)
High plasticity (LL > 50%)
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Table 5.15 - Probability of a transverse crack on seasonal shutdown layers during construction and staged construction surfaces due to desiccation by drying versus
∑ (Relative importance factor (RF)) x (Likelihood factor(LF))
negligible negligible negligible 0.0001 0.001 0.01 0.1 Below POR
negligible negligible negligible 0.001 0.01 0.1 0.9 Above POR
7 10 12 13 18 22 28 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
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5.3 Estimating The Probability Of Transverse Cracking Or Hydraulic Fracture (P C ) In The Middle And Lower Parts Of The Dam
5.3.1 Likelihood of Transverse Cracking or Hydraulic Fracture Due To Cross Valley Differential Settlement (IM9)
Table 5.16 - Factors influencing the likelihood of cracking or hydraulic fracture in the middle and lower parts of embankment dams-cross valley differential settlements (IM9)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely(1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Cross valley profile under embankment core
(3) Uniform abutment profile without benches
Minor bench in lower half of the abutment, not persistent across the core
Bench in lower half of the abutment b/h2 > 0.5; 1.5 < h2/h1 < 2
Wide bench in lower half of the abutment b/h2 > 1; 1 < h2/h1 < 1.5
Slope of the abutments under embankment core
(2) Gentle abutment slope, β2 < 30o
Moderately abutment slopes, 30o < β2 < 45o
Steep abutments, 45o < β2 < 60o
Very steep abutments, β2 > 60o
Height of embankment
(1) Dams less than 50 ft (15 m) high
Dams 50 ft to 100 ft (15 m to 30 m) high
High dams 100 ft to 200 ft (30 m to 60 m)
Very high dams >200ft (60 m)
Note: See Figure 5.1 for definitions of b, h1, h2, β2.
Table 5.17 - Probability of a transverse crack or hydraulic fracture in the middle and lower parts of embankment dams due to cross valley differential settlements versus ∑ (Relative
importance factor (RF)) x (Likelihood factor (LF))
negligible negligible negligible [0.0001] 0.001 0.005 Below POR
negligible negligible negligible [0.001] 0.01 0.05 Above POR
6 9 12 13 18 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
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5.3.2 Likelihood Of Transverse Cracking Or Hydraulic Fracture Due To Differential Settlement Causing Arching Of The Core Onto The Shoulders Of The Embankment (IM10)
This mode is applicable to central core earth and rockfill (or gravel shells) dams and puddle core earthfill dams. It is not applicable to all other the following dam types (including dams with a sloping core).
Table 5.18 – Factors influencing the likelihood of cracking or hydraulic fracturing in the middle and lower parts of embankments - settlement resulting from arching of the core onto
the shoulders (IM10)
Likelihood Factor (LF)
Factor
Relative Import-
ance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely(4)
Core geometry Width (W)/Height (H)
(3) W/H>1.0 (c)
0.5<W/H<1.0 Narrow core, 0.25< W/H<0.5
Very narrow core, W/H<0.25
Relative stiffness of core and shells
(2) Core has higher modulus than shells.
Shoulders poorly compacted or dumped. Core compacted >98% SMDD (c)
Modulus of core same or marginally lower than shoulders. Shoulders well compacted and high modulus. Core compacted to >98% SMDD at a moisture content between -2% and +1% of standard OWC
Core lower modulus than outer stiffness.
Shoulders well compacted and high modulus. Either core compacted 0% to 2% wet of OWC and between 95% and 98% SMDD or 2% to 3% dry of OWC and < 95% SMDD (b)
Core much lower modulus than outer shoulders or subject to collapse compression. Shoulders well compacted and high modulus Either core compacted > 2% wet of OWC, or more than 3% dry of OWC and < 95% SMDD (b)
Height of embankment
(1) Dams less than 50 ft (15 m) high
Dams 50 ft to 100 ft (15 m to 30 m) high
High dams 100 ft to 200 ft (30 m to 60 m)
Very high dams> 200 ft (60 m)
Notes: (a) The most likely location for arching to occur is in the upper to middle part of the dam. (b) In core materials compacted dry of optimum moisture and to a density ratio less than about 95%, collapse
compression of the core may occur. This may lead to arching and low stresses. It may also lead to softened zones and even a crack in the vicinity of the contact between the saturated and unsaturated parts of the core, i.e. at the phreatic surface.
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(c) The likelihood of arching is negligible for embankments with these characteristics (d) The mechanism is considered to be significant only for reservoir levels above the pool of record. (e) W = width of the core at depth H below the crest of the embankment. (f) Finite element analyses which properly model the history of the dam, and its properties including collapse on
saturation may be used to assess the likelihood of cracking or hydraulic fracture.
Table 5.19 - Probability of a transverse crack or hydraulic fracture in the middle and lower parts of embankment dams- settlement resulting from arching of the core onto the
shoulders of the embankment versus∑ (Relative importance factor (RF)) x (Likelihood factor (LF))
negligible negligible negligible negligible [0.001] 0.01 0.05 Above POR
6 9 11 12 13 18 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot. The probability for this initiating mechanism is assumed to be negligible for the Below POR cases.
5.3.3 Likelihood Of Transverse Cracking or Hydraulic Fracture Due To Differential Settlement In The Foundation Under The Core (IM11)
Refer to Section 5.2.3 which covers this mode as well as cracking and hydraulic fracture in the upper part of the embankment.
5.3.4 Likelihood of Transverse Cracking Or Hydraulic Fracture At The Foundation Contact Due To Small Scale Irregularities In The Foundation Profile Under The Core (IM12)
Small scale irregularities in the foundation profile under the core may comprise steps, benches or depressions in the foundation rock. Small scale irregularities include those features which have heights less than 10% of the embankment height. Larger scale features are covered in Section 5.3.2.
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Table 5.20 – Factors influencing the likelihood of cracking or hydraulic fracturing in the middle and lower parts of embankment dams due to small scale irregularities in the
foundation profile under the core (IM12)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Persistence of the irregularity across the core
(3) Persistent across less than 50% of the core (b)
Persistent 50% to 75% across the core width
Persistent 75% to 90% across the core
Persistent 90% to 100% across the core
Small scale irregularities in abutment profile
(2) Uniform abutment profile, or irregularities treated by slope modification
Steps, benches, depressions in rock foundations less than 3% of the embankment height
Steps, benches, depressions in rock foundations 3% to 5% of the embankment height
Steps, benches, depressions in rock foundation 5% to 10% of the embankment height (a)
Core geometry Width (W)/Height (H)
(1) Wide core, W/H>1.5
0.5<W/H<1.5 Narrow core, 0.25< W/H<0.5
Very narrow core, W/H<0.25
Notes: (a) Larger irregularities are covered in Section 5.3.2. (b) An irregularity with less than 50% persistence across the core is assumed to have a negligible contribution to the
probability of a transverse crack.
Table 5.21 - Probability of a transverse crack or hydraulic fracture in the middle and lower parts of embankment dams due to small scale irregularities in the foundation profile under
the core versus∑ (Relative importance factor (RF)) x (Likelihood factor (LF))
Negligible negligible negligible 0.0002 [0.0007] 0.002 0.01 Below POR
Negligible negligible negligible 0.002 [0.005] 0.02 0.1 Above POR
6 9 11 12 13 18 24 RF x LF
Notes: (1) Larger irregularities are covered in Section 5.3.2. (2) The probability of a transverse crack across the core is negligible for persistence less than 50%
Note: “POR” refers to the Pool of Record level + 1 foot
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5.3.5 Probability Of Transverse Cracking or Hydraulic Fracture - Factors To Account For Observations And Measured Settlements
Settlement Factors
Where there are settlement observations for the dam these can be used to modify the results of Sections 5.2.1 to 5.2.3, and Sections 5.3.1 to 5.3.3. The probability from the relevant table is multiplied by the factor from Table 5.22. For dams which have experienced settlements larger than the averfage population of that classof dam the probabilities of cracking or hydraulic fracture will be increased, and for those which haveexperienced settlements smaller than the average population of that class of dams the probability ofcracking or hydraulic fracture will be reduced. The multiplication factor should be selected taking accountof what data is available, allowing for the quantity and quality of the data and the relative improtance of theobservations. Table 5.22 applies to the assessment of transverse cracking in the upper part, and middle andlower part of the embankment, but lower corrections apply for the latter.
Select the likelihood column in Table 5.22 which corresponds to the maximum settlement measuredanywhere in the embankment expressed as a ratio of the maximum embankment height. Then obtain thesettlement multiplication factors for the upper and middle and lower parts from the corresponding bottomfour rows of Table 5.22 depending on whether the dam has poorly compacted rockfill shells or not.
If there are significant differential settlements across the valley greater than expected from the mechanisms present, an additional increase in probabilities may be applied. The maximum multiplier should be less than 10 times and should not “double up” on the factors listed in Table 5.22.
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Table 5.22 - Settlement multiplication factors versus observed settlements
Influence on Likelihood Factor
Less Likely Neutral More Likely Much More Likely
Observed maximum settlements as percentage of embankment height
- Core settlement during construction
< 1.5% 1.5% to 3% 3% to 4% > 4%
- Post construction crest settlement at 10 years after construction dams with poorly compacted shoulders
<0.5% 0.5% to 1.0%
1.0% to 1.5%
> 1.5%
- Post construction crest settlement at 10 years after construction other dams
<0.25% 0.25% to 0.5%
0.5% to 1% > 1%
- Long term settlement rates(% per log time cycle in years) dams with poorly compacted shoulders
< 0.15% 0.15% to 0.4%
0.4% to 0.7%
> 0.7%
- Long term settlement rates(% per log time cycle in years)-other dams
< 0.1% 0.1% to 0.25%
0.25% to 0.5%
> 0.5%
Dams with poorly compacted rockfill (b)
0.05 to 0.2 0.2 to 0.5 1.0 2 to 5 Settlement multiplication factors for cracking or hydraulic fracture in the upper part (a) of the embankment based on observed maximum settlements
All other dams
0.2 to 0.5 1.0 2 to 10 10 to 20
Dams with poorly compacted rockfill (b)
0.2 0.2 to 0.5 1.0 2 to 5 Settlement multiplication factors for cracking or hydraulic fracture in the middle and lower parts (c)(d) of the embankment All other
dams 0.5 1.0 2 to 5 5 to 10
Notes: (a) Multiplication factors to be applied to Probabilities from Sections 5.2.1, 5.2.2 and 5.2.3. (b) Includes dumped rockfill, and rockfill and other granular zones compacted by tracking with bulldozers and by small
rollers in thick layers (c) To be applied to probabilities from Sections 5.3.1, 5.3.2 and 5.3.3 (d) Multiplication factors assumed to be half those for cracking in the upper part.
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Observation of cracking factor
Where there are observations of cracking for the dam these can be used to modify the results of Sections 5.2.1 to 5.2.5. The probability is multiplied by the factor from Table 5.23.
Table 5.23 - Cracking observation factors (applies to upper embankment only)
Influence on Likelihood Factor
Less Likely Neutral More Likely Much More Likely
Cracking observed in test pits to the top of or into the core
No cracking observed when large areas of the top of the core are exposed.
No test pits Transverse cracks persistent across the top of the core and/or, extensive, open longitudinal cracking
Transverse cracks which pits show persist across the core, and extend below reservoir water level in the reservoir level partition being considered
Cracking Factor (A)
0.5 to 0.1 depending on the extent of exposure and how relevant the exposure is to the possible mechanism of cracking
1.0 5 to 100 depending on width(2) of cracking and whether they are in locations in which cracking might be expected
Probability of transverse crack = 1.0
Cracking in the surface of the crest, no test pits
No cracking observed, core exposed on the surface, careful inspection for cracking
No cracking observed, core covered with road pavement or other granular material
Narrow (<10mm) transverse cracks persistent across the crest and/or, extensive, narrow longitudinal cracking
Transverse cracks which persist across the crest and/or, extensive, wide longitudinal cracking.
Cracking Factor (B)
0.5 to 0.2 depending on the quality of exposure and whether they are in locations in which cracking might be expected
1.0 2 to 5 depending on and whether they are in locations in which cracking might be expected
2 to 20 depending on the width(2) of cracking and whether they are in locations in which cracking might be expected
Notes: (1) Apply either Cracking Factor (A) or Cracking Factor (B), whichever gives greatest probability of cracking (2) The greater the crack width the more likely it represents cracking in the core.
Evaluate the Cracking Factors (A) and (B) from Table 5.23 and then multiply the largest value of (A) or (B) tothe probabilities of transverse cracking in the upper part of the dam. For dams which display cracking theprobabilities will be increased. For those which do not display cracking the probabilities may remain the same,or are reduced depending on how extensive the investigations to locate cracking have been. The multiplication factor should be selected taking account of what data is available, allowing for the relative importance of theobservations. This factor only applies to the assessment of transverse cracking in the upper part of the embankment.Cracking in the middle and lower parts will generally not be observed.
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5.4 Estimation Of The Probability Erosion Will Initiate In A Crack Or Hydraulic Fracture In An Embankment (P IC ).
5.4.1 Overall Approach
(a) For cracking in the upper part of the dam the method to be followed is:
• Estimate maximum likely width of cracking at the top of the core from Table 5.24.
• Estimate likely crack width at the reservoir level stage under consideration using Table 5.25 and Figure 5.7. The width required is the width at the mid level of the flow path for the reservoir stage under consideration. In Figure 5.7 it is the average of C 1d and C 2d .
The width C 1d at depth d1 = C max ((D- d 1 )/D). That is, the crack is assumed to be uniformly tapered
from the dam crest to the base of the crack.
• Estimate the likely crack width from hydraulic fracture at the reservoir level stage under consideration using Table 5.26 .
• Estimate the gradient of flow through the crack using Figure 5.7. The gradient required is the average gradient at the mid level of the flow path for the reservoir stage under consideration. In Figure 5.7 it is (d 2 - d1 )/L.
• Assess the soil classification and whether the soils are dispersive. Dispersive soils are soils with Sherard Pinhole test D1 or D2. While reservoir water salinity will affect dispersion, the salt content of the reservoir water will in most cases reduce with flood inflows and unless laboratory testing is carried out to assess the initial shear stress with the same reservoir water salts content it should be assumed soils which test dispersive in the laboratory will be so in the dam. Where there are signs of dispersive soils in field performance, e.g. severe gully erosion, sinkholes and tunnelling, soils should be assumed dispersive regardless of laboratory test results.
• Based on the soil classification, dispersivity, and estimated crack width (the larger of the estimates from Table 5.25, and Table 5.26), estimate the probability of initiation of erosion in the crack and/or hydraulic fracture (P IC ) using Table 5.29 to Table 5.35, depending on the gradient of flow through the crack. Use
approximate interpolation between values where necessary. These tables assume the relationship between erosion rate index and soil classification shown in Table 5.27.
These tables only apply to soil compacted to 95% to 98% of Standard Proctor maximum dry density at a moisture content between -1% to +2% of optimum moisture content. For saturated soils, soils
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significantly dry of optimum moisture content, and poorly compacted soils, Hole Erosion Tests should be carried out to determine the initial shear stress, and the method detailed in (c) below followed.
• If there are Hole Erosion Tests available use the method detailed in (c) below
(b) For cracking in the middle and lower parts of the dam
The method to be followed is:
• Estimate maximum likely width of cracking in the middle or lower part of the dam from Table 5.28. This includes hydraulic fracture.
• Assess the soil classification and whether the soils are dispersive. Dispersive soils are soils with Sherard Pinhole test D1 or D2. While reservoir water salinity will affect dispersion, the salt content of the reservoir water will in most cases reduce with flood inflows and unless laboratory testing is carried out to assess the initial shear stress with the same reservoir water salts content it should be assumed soils which test dispersive in the laboratory will be so in the dam. Where there are signs of dispersive soils in field performance, e.g. severe gully erosion, sinkholes and tunnelling, soils should be assumed dispersive regardless of laboratory test results.
• Based on the soil type and estimated crack width, estimate the probability of initiation of erosion in the crack and/or hydraulic fracture (P IC ) using Table 5.29 to Table 5.35, depending on the gradient across
the crack. If there are hole erosion tests available assess which classification should apply to best reflect this value when using Table 5.29 to Table 5.35. Use approximate interpolation between values where necessary. These tables only apply to soil compacted to 95% to 98% of Standard Proctor maximum dry density at a moisture content between -1% to +2% of optimum moisture content. For saturated soils, soils significantly dry of optimum moisture content, and poorly compacted soils, Hole Erosion Tests should be carried out to determine the initial shear stress, and the method detailed in (c) below followed.
(c) Procedure to be followed where Hole Erosion Test data is available
In cases where Hole Erosion tests are available for the dam core soil, the following procedure should be followed:
• Estimate the crack width and hydraulic flow gradient as detailed in (a) or (b), whichever is applicable.
• EITHER Calculate the hydraulic shear stress in the crack for the reservoir stage under consideration using Table 5.36.
• AND Compare this hydraulic shear stress to the initial shear stress of the soil at the compaction and moisture conditions it exists in the core. Based on this comparison estimate the probability of initiation
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of erosion. In doing this calculation take account of the uncertainty in the crack width, and initial shear stress detailed in Section S5.4.2.4.
• OR/AND Use Table 5.37 to determine which of Tables 5.29 to 5.35 best fits the initial shear stress of the soil tested in the HET and use that table to estimate the probability of initiation of erosion.
5.4.2 Details Of The Method
Table 5.24 - Maximum likely width of cracking at the dam crest versus ∑ (Relative importance factor) x (Likelihood factor) for cracking in the upper part of the dam
Maximum likely crack width at the dam crest in millimeters (inches)relative to (relative importance factor) x (likelihood factor) Crack formation mechanism
6 to 9 9 to 11 11 to 13 13 to 18 18 to 24
Cross valley differential settlement Table 5.1
1 20 50(2) 75(3) 100(4)
Differential settlement adjacent to a spillway or other wall or cliff Table 5.3 Table 6.21
1 10 25(1) 37(1.5) 50(2)
Cross section settlement due to poorly compacted shoulders Table 5.7
1 20 50(2) 75(3) 100(4)
Differential settlements in the soil foundation
Table 5.9
1 20 50(2) 100(4) 150(6)
Desiccation cracking at the crest by drying Table 5.11
2 5 20 50(2) 75(3)
Desiccation cracking on seasonal shutdown layer Table 5.14
2 5 20 50(2) 75(3)
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Table 5.25 - Likely crack width at the depth shown versus maximum crack width at the dam crest determined from Table 5.24 for cracking in the upper part of the dam.( Depths in feet
and meters)
Likely crack width at depth shown, crack width in millimeters (inches) )1( Maximum crack width at dam crest
Inches Millimeters
5 feet 1.5 meters
10 feet 3 meters
15 feet 4.5 meters
20 feet 6 meters
25 feet 7.5 meters
30 feet 10 meters
0.5 10 1
1 25 2 1
2 50 20 5 1
3 75 40(1.6) 20 5 2
4 100 60(2.4) 35(1.4) 15 7 3 1
10 250 210(8) 180(7) 140(5.4) 110(4.4) 90(3.5) 60(2.4) Note. (1) Check potential crack width resulting from hydraulic fracture and use the larger of the crack widths from this table and Table 5.26 .
Table 5.26 – Examples of estimated maximum depths below the dam crest and widths of cracks formed by potential hydraulic fracture for cracking in the upper part of the dam
(A) Embankment abutment
Abutment slope
degrees
Ratio of bench width to
embankment height
Ratio of depth of zero stress to
embankment height at the
abutment
Ratio of approximate maximum depth at which
hydraulic fracture may occur to embankment height at the abutment
Likely width of crack formed by hydraulic
fracture in millimeters
15 0.67 <0.01 0.05 2
25 No bench 0.02 0.05 2
45 No bench 0.12 0.3 5
45 0.2 0.12 0.3 5
45 0.4 0.09 0.25 5
45 1.0 0.10 0.25 5
60 No bench 0.35 0.5 10
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(B) Adjacent to walls and cliffs in the upper part of the embankment
∑ (Relative importance factor (RF)) x
(Likelihood factor (LF)) from Table 5.3
Likely width of crack formed by hydraulic fracture in millimeters
14 to 19 5
>19 10
(C) Cross valley arching in the upper part of the embankment
∑ (Relative importance factor (RF)) x
(Likelihood factor (LF)) from Table 5.5
Likely width of crack formed by hydraulic fracture in millimeters
10 to 13 2
14 to 19 5
>19 10
(D) Over low stress zones over irregularities in the foundation
Assume that hydraulic fracture may persist from the crest to the foundation level, and the width is 5 mm.
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Table 5.27 Representative erosion rate index (IHET) versus soil classification for non dispersive soils based on Wan and Fell (2002, 2004)
Representative Erosion Rate Index (IHET) Soil Classification
Likely Minimum Best Estimate Likely Maximum
SM with <30% fines 1 <2 2.5
SM with > 30% fines <2 2 to 3 3.5
SC with < 30% fines <2 2 to 3 3.5
SC with >40% fines 2 3 4
ML 2 2 to 3 3
CL-ML 2 3 4
CL 3 3 to 4 4.5
CL-CH 3 4 5
MH 3 3 to 4 4.5
CH with Liquid Limit <65% 3 4 5
CH with Liquid Limit > 65% 4 5 6
Note.
(1) Use best estimate value for best estimate probabilities. Check sensitivity if the outcome is strongly dependent on the results. (2) For important decisions carry out Hole Erosion Tests, rather than relying on this table which is approximate (3) The Representative Erosion Rate index is for soils compacted to 95% standard (Proctor) maximum dry density at optimum
moisture content. (4) See Supporting Information Report for information regarding the Representative Erosion Rate index for soils which are
significantly drier than optimum moisture content or saturated.
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Table 5.28 - Maximum likely width of cracking in the dam versus ∑ (Relative importance factor) x (Likelihood factor) for cracking in the middle and lower parts of the dam
Maximum likely crack width in millimeters relative to (relative importance factor) x (likelihood factor) Crack formation
mechanism 6 to 9 9 to 11 11 to 13 13 to 18 18 to 24
Cross valley differential settlement Table 5.16
0 0 1 to 2 2 to 10 10 to 20
Differential settlement causing arching of the core onto the shoulders
Table 5.18
0 0 0 to 1 1 to 2 2 to 10
Differential settlement over small scale irregularities in the foundation Table 5.20
0 0 0 to 1 1 to 2 2 to 10
Differential settlements due to settlements in the foundation Table 5.9
0 0 0 to 2 2 to 10 10 to 20
Differential settlement causing arching of the core in the cut off trench Table 9.3
0 0 0 to 1 1 to 2 2 to 10
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Figure 5.7 Example of the estimation of crack width and flow gradient in the crack.
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Table 5.29 - Estimation of probability of initiation in a crack for ML or SM with <30% fines soil types
Probability of initiation of erosion for different seepage gradients
Average Hydraulic Gradient
Estimated likely crack width in core for Reservoir
stage being considered (mm) 0.1 0.25 0.5 1.0 2.0 5.0
1 0.05 0.2 0.6 0.95 1.0 1.0
2 0.1 0.6 0.9 1.0 1.0 1.0
5 0.6 1.0 1.0 1.0 1.0 1.0
10 0.9 1.0 1.0 1.0 1.0 1.0
25 1.0 1.0 1.0 1.0 1.0 1.0
50 1.0 1.0 1.0 1.0 1.0 1.0
75 1.0 1.0 1.0 1.0 1.0 1.0
100 1.0 1.0 1.0 1.0 1.0 1.0
Note. (1) The gradient is the average hydraulic gradient from the upstream to the downstream of the core at the level of the assumed crack under the reservoir level under consideration. No allowance is made for seepage head losses in the zones upstream or downstream of the core.
Table 5.30 - Estimation of probability of initiation in a crack for SC with <40% fines, or SM with >30% fines soil types
Probability of initiation of erosion for different seepage gradients
Average Hydraulic Gradient
Estimated likely crack width in core for Reservoir
stage being considered (mm) 0.1 0.25 0.5 1.0 2.0 5.0
1 0.02 0.2 0.6 0.9 0.95 1.0
2 0.1 0.6 0.9 0.95 1.0 1.0
5 0.6 0.95 0.99 1.0 1.0 1.0
10 0.9 1.0 1.0 1.0 1.0 1.0
25 0.95 1.0 1.0 1.0 1.0 1.0
50 1.0 1.0 1.0 1.0 1.0 1.0
75 1.0 1.0 1.0 1.0 1.0 1.0
100 1.0 1.0 1.0 1.0 1.0 1.0
Note. (1) The gradient is the average hydraulic gradient from the upstream to the downstream of the core at the level of the assumed crack under the reservoir level under consideration. No allowance is made for seepage head losses in the zones upstream or downstream of the core.
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Table 5.31 - Estimation of probability of initiation in a crack for SC with >40% fines, or CL-ML soil types
Probability of initiation of erosion for different seepage gradients
Average Hydraulic Gradient
Estimated likely crack width in core for Reservoir
stage being considered (mm) 0.1 0.25 0.5 1.0 2.0 5.0
1 0.02 0.1 0.4 0.8 0.9 0.95
2 0.1 0.5 0.7 0.9 0.95 1.0
5 0.4 0.8 0.9 0.95 1.0 1.0
10 0.7 0.9 0.95 1.0 1.0 1.0
25 0.9 0.95 1.0 1.0 1.0 1.0
50 0.95 1.0 1.0 1.0 1.0 1.0
75 1.0 1.0 1.0 1.0 1.0 1.0
100 1.0 1.0 1.0 1.0 1.0 1.0
Note. (1) The gradient is the average hydraulic gradient from the upstream to the downstream of the core at the level of the assumed crack under the reservoir level under consideration. No allowance is made for seepage head losses in the zones upstream or downstream of the core.
Table 5.32 - Estimation of probability of initiation in a crack for CL or MH soil types
Probability of initiation of erosion for different seepage gradients
Average Hydraulic Gradient
Estimated likely crack width in core for Reservoir
stage being considered (mm) 0.1 0.25 0.5 1.0 2.0 5.0
1 0.01 0.03 0.1 0.2 0.3 0.7
2 0.02 0.1 0.2 0.5 0.6 0.9
5 0.1 0.3 0.5 0.7 0.9 1.0
10 0.2 0.5 0.7 0.95 1.0 1.0
25 0.4 0.7 0.95 1.0 1.0 1.0
50 0.7 1.0 1.0 1.0 1.0 1.0
75 0.9 1.0 1.0 1.0 1.0 1.0
100 0.95 1.0 1.0 1.0 1.0 1.0
Note. (1) The gradient is the average hydraulic gradient from the upstream to the downstream of the core at the level of the assumed crack under the reservoir level under consideration. No allowance is made for seepage head losses in the zones upstream or downstream of the core.
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Table 5.33 - Estimation of probability of initiation in a crack for CL-CH or CH with LL<65% soil types
Probability of initiation of erosion for different seepage gradients
Average Hydraulic Gradient
Estimated likely crack width in core for Reservoir
stage being considered (mm) 0.1 0.25 0.5 1.0 2.0 5.0
1 0.005 0.02 0.05 0.1 0.2 0.6
2 0.01 0.05 0.1 0.3 0.5 0.9
5 0.05 0.2 0.3 0.6 0.8 1.0
10 0.1 0.3 0.6 0.9 0.95 1.0
25 0.3 0.6 0.9 1.0 1.0 1.0
50 0.6 0.95 1.0 1.0 1.0 1.0
75 0.8 1.0 1.0 1.0 1.0 1.0
100 0.9 1.0 1.0 1.0 1.0 1.0
Note. (1) The gradient is the average hydraulic gradient from the upstream to the downstream of the core at the level of the assumed crack under the reservoir level under consideration. No allowance is made for seepage head losses in the zones upstream or downstream of the core.
Table 5.34 - Estimation of probability of initiation in a crack for CH with LL>65% soil types
Probability of initiation of erosion for different seepage gradients
Average Hydraulic Gradient
Estimated likely crack width in core for Reservoir
stage being considered (mm) 0.1 0.25 0.5 1.0 2.0 5.0
1 0.001 0.002 0.005 0.01 0.05 0.1
2 0.002 0.005 0.01 0.02 0.1 0.4
5 0.005 0.01 0.05 0.1 0.3 0.95
10 0.01 0.04 0.1 0.4 0.6 1.0
25 0.02 0.1 0.4 0.8 0.95 1.0
50 0.1 0.5 0.95 1.0 1.0 1.0
75 0.3 0.8 1.0 1.0 1.0 1.0
100 0.4 0.95 1.0 1.0 1.0 1.0
Note. (1) The gradient is the average hydraulic gradient from the upstream to the downstream of the core at the level of the assumed crack under the reservoir level under consideration. No allowance is made for seepage head losses in the zones upstream or downstream of the core.
SECTION 5 Probability of Initiation of Erosion in Transverse Cracks in the Embankment
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Table 5.35 - Estimation of probability of initiation in a crack for dispersive soils (CL, CH, CL-CH)
Probability of initiation of erosion for different seepage gradients
Average Hydraulic Gradient
Estimated likely crack width in core for Reservoir
stage being considered (mm) 0.1 0.25 0.5 1.0 2.0 5.0
1 0.02 0.1 0.3 0.6 0.8 1.0
2 0.05 0.3 0.6 0.9 1.0 1.0
5 0.3 0.7 1.0 1.0 1.0 1.0
10 0.5 1.0 1.0 1.0 1.0 1.0
25 1.0 1.0 1.0 1.0 1.0 1.0
50 1.0 1.0 1.0 1.0 1.0 1.0
75 1.0 1.0 1.0 1.0 1.0 1.0
100 1.0 1.0 1.0 1.0 1.0 1.0
Note. (1) The gradient is the average hydraulic gradient from the upstream to the downstream of the core at the level of the assumed crack under the reservoir level under consideration. No allowance is made for seepage head losses in the zones upstream or downstream of the core.
Table 5.36 – Estimated hydraulic shear stress (N/m2) from water flowing in an open crack, versus crack width and flow gradient
Flow Gradient in Crack Crack Width Millimeters 0.1 0.25 0.5 1.0 2.0 5.0
1 0.5 1.25 2.5 5 10 25
2 1 2.5 5 10 20 50
5 2.5 6 12 25 50 125
10 5 12 25 50 100 250
20 10 25 50 100 200 500
50 25 60 125 250 500 1250
100 50 125 250 500 1000 2500
SECTION 5 Probability of Initiation of Erosion in Transverse Cracks in the Embankment
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Table 5.37 – Initial Shear Stress assumed for Tables 5.29 to 5.35
Table Number Soil Types Initial Shear Stress Assumed for
Assessing Probabilities of Initiation of Erosion
5.29 ML and SM with < 30% fines 2 Pa
5.30 SC with ,< 40% fines, SM with >30% fines
2 Pa
5.31 SC with > 40% fines, and CL-ML 4 Pa
5.32 CL and MH 5 Pa
5.33 CL-CH and CH with LL < 65% 25 Pa
5.34 CH with LL > 65% 60 Pa
5.35 Dispersive soils 2 Pa
5.5 Estimation Of The Probability Of Transverse Cracks In The Embankment Caused By Earthquake (IM13)
• First - Determine the earthquake hazard for the site (refer to Section 3.6 for details).
• Second - Estimate the likely damage class which the embankment may experience as a result of the from the earthquake and peak ground acceleration on bedrock at the dam site using Figure 5.8 for earthfill dams or Figure 5.9 for earth and rockfill dams. Do this for each earthquake load partition. The earthquake load partition ranges should be selected such that they coincide with the damage class contours shown in Figure 5.8 for earthfill dams or Figure 5.9 for earthfill and rockfill dams.
• Third - Estimate the probability of transverse cracking and likely maximum crack width from the damage class and Table 5.39.
• Fourth - Estimate the likely crack depth and assess the probability erosion will initiate using the method described in Section 5.4.
This procedure applies to situations where liquefaction does not occur in the dam or its foundations. If flow liquefaction occurs assume the damage is class 4. For cases where liquefaction occurs but it is not flow liquefaction, assume damage class 3.
SECTION 5 Probability of Initiation of Erosion in Transverse Cracks in the Embankment
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Table 5.38 – Damage classification system (Pells and Fell, 2002, 2003)
Damage Class Number
Description
Maximum Longitudinal Crack Width (1) mm
Maximum Relative Crest Settlement (2)
%
0 No or Slight < 10 mm <0.03
1 Minor 10 - 30 0.03 - 0.2 2 Moderate 30 - 80 0.2 - 0.5
3 Major 80 - 150 0.5 - 1.5 4 Severe 150 - 500 1.5 - 5
5 Collapse > 500 > 5
(1) Maximum crack width is taken as the maximum width, in millimeters, of any longitudinal cracking that occurs.
(2) Maximum relative crest settlement is expressed as a percentage of the structural dam height.
Figure 5.8 - Incidence of transverse cracking versus seismic intensity and damage class contours for earthfill dams (Pells and Fell 2002, 2003)
SECTION 5 Probability of Initiation of Erosion in Transverse Cracks in the Embankment
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Figure 5.9 - Incidence of transverse cracking versus seismic intensity and damage class contours for earthfill and rockfill dams (Pells and Fell 2002, 2003)
Table 5.39 – Estimation of the probability of transverse cracking from the damage class
For cases where cross valley or cross section cracking assessment is in lower three “boxes i.e. RFxLF ≤ 12 in Tables
5.2, 5.4 and 5.10
For cases where cross valley or cross section cracking assessment is in upper two “boxes” i.e. RF x LF > 13 in Tables
5.2, 5.4 and 5.10 Damage class Probability of
transverse cracking ”
Maximum likely crack width mm (inches)
Probability of transverse cracking
Maximum likely crack width at crest
mm (inches)
0 0.001 5 0.01 20
1 0.01 20 0.05 50(2)
2 0.05 50(2) 0.10 75(3)
3 0.2 100(4) 0.25 125(5)
4 0.5 150(6) 0.6 175(7)
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
6.1 Overall Approach
a) Estimate the probability of a continuous poorly compacted or high permeability zone (P P ) for each of the mechanisms which can lead to a poorly compacted or high permeability zone. These are:
• Poor compaction or high permeability layer during construction within the core (Section 6.2.1);
• Poor compaction or high permeability layer on the foundation contact (Section 6.2.2);
• Poor compaction or high permeability layer due to freezing (Section 6.2.3);
• Poor compaction or high permeability layer around a conduit or other structure penetrating the core (Sections 6.3 and 6.4).
Adjust this estimate to account for observations (Section 6.5).
b) Assess the erosion mechanism(s) which will apply. This will be one or more of the following:
• Backward erosion
• Suffusion
• Erosion in a crack or flaw resulting from the poor compaction.
Backward erosion and suffusion will apply to cohesionless soils and as discussed in Section 6.6.1, to soils with a plasticity index ≤ 7. For cohesive soils, erosion will occur in cracks or continuous open flow paths formed by collapse of the soil on saturation, or between aggregated particles of the soil, and can be considered as equivalent to erosion in a crack. Even low plasticity soils may form a crack so soils with a plasticity index between zero and 7 should be considered for both erosion in a crack and backward erosion and suffusion and the highest probability of initiation carried forward in the analysis.
c) Assess the probability of erosion in the poorly compacted or high permeability zone (P IP ) for the mechanism using the relevant method described in Section 6.6.
d) Estimate the probability of initiation of erosion (P I ) = (P P ) x (P IP ) for each poorly compacted or high permeability zone. For many dams one or more of the mechanisms will not be present.
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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6.2 Estimation Of The Probability Of A Continuous Poorly Compacted or High Permeability Zone In The Embankment Or On The Core-Foundation Contact
6.2.1 Poorly Compacted or High Permeability zone within the core (IM14)
The scenarios which may lead to poorly compacted or high permeability zones in the core of an embankment include:
• Poorly compacted layers in the core.
• A segregated layer in the core due to the presence of coarser particles and poor construction practices.
• Coarser soil layers in the core due to variability in particle size and soil type in the borrow areas. This can result in a cohesionless layer within a cohesive core, or a coarser cohesionless layer within a finer cohesionless soil.
The effect of these factors on the likelihood of a poorly compacted or high permeability zone is different for cohesive and cohesionless soils so they are treated separately. For these purposes a cohesionless soil is non plastic.
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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Table 6.1 – Factors influencing the likelihood of poorly compacted or high permeability zones in the embankment-cohesive soils (IM14)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
METHOD BASED ON COMPACTION EQUIPMENT, LAYER THICKNESS AND MOISTURE CONTENT (a)
Compaction equipment
(3) (a)
As for “neutral” but with good documentation and records )2(
Soil compacted by suitable rollers in suitable layer thicknesses
Soil placed and compacted by bulldozer, no compaction by rollers, or rolled in thick layers beyond the capability of the roller
Soil placed with, no formal compaction (e.g. by horse and cart in old dams, or by pushing into place by excavator or bulldozer or in very thick layers)
and Layer thickness
Layer thickness 6 to 10 inches (150mm to 250mm) after compaction
Layer thickness at or beyond the limit of compaction equipment (e.g. > 12 to 18 inches (300 mm to 450 mm) after compaction)
No control on layer thickness, often > 18 to 24 inches (450 mm to 600 mm) loose
and moisture content
Around optimum moisture content )1(
Dry of optimum moisture content )1(
Well dry of optimum moisture content. )1(
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
METHOD BASED ON COMPACTION EQUIPMENT, LAYER THICKNESS AND MOISTURE CONTENT(a)
AND/OR (a) Measured or estimated compaction density ratio and moisture content (COHESIVE SOILS)
(3) (a)
All very well compacted to e.g. ≥ 98% standard dry density ratio, moisture content 2% dry of optimum to 1% wet of standard OWC (b)
Well compacted to e.g. 95-98% standard dry density ratio, moisture content 2% dry of optimum to 1% wet of standard OWC
Layers poorly compacted, dry of standard optimum moisture content e.g. < 93% standard dry density ratio, 2% to 3% dry of standard OWC
Layers very poorly compacted, dry of standard optimum moisture content e.g. < 90% standard dry density ratio, 3% dry of standard OWC
FACTORS APPLYING TO BOTH ALTERNATIVES
Borrow area variability,
(2) Uniform soils in the borrow areas,
Uniform or minor variability in the borrow areas,
Variable soils in the borrow areas
Very variable soils in borrow areas including gravely soils;
Site supervision
Good site supervision documented with laboratory tests,
Good site supervision
Moderate site supervision
Poor site supervision,
Core geometry Width (W)/Height (H)
(1) Wide core, W/H>1.5
0.5<W/H<1.5 Narrow core, 0.25< W/H<0.5
Very narrow core, W/H<0.25
Notes: (a) Make an assessment based on a combination of available data (b) If soils are well compacted this mechanism will not apply
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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Table 6.2 – Factors influencing the likelihood of poorly compacted or high permeability zones in the embankment-non cohesive soils (IM14)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
EITHER (a) Compaction equipment
(3) (a)
As for “neutral” but with good documentation and records (b)
Soil compacted by suitable rollers in suitable layer thicknesses
Soil placed and compacted by bulldozer, no compaction by rollers, or rolled in thick layers beyond the capability of the roller
Soil placed with, no formal compaction ( e.g. by horse and cart in old dams, or by pushing into place by excavator or bulldozer or in very thick layers
and Layer thickness
Layer thickness 8 to 12 inches (200 mm – 300 mm) after compaction
Layer thickness at or beyond the limit of compaction equipment (e.g. > 12 to 18 inches (300 mm to 450 mm) after compaction)
No control on layer thickness, often > 24 to 36 inches (600 mm to 900 mm) loose
and moisture content
Around optimum moisture content (a)
Dry of optimum moisture content(a)
Well dry of optimum moisture content(a)
AND/OR(a) Measured or estimated compaction density ratio and moisture content (NON-COHESIVE SOILS)
(3) (a)
All very well compacted
e.g. very dense, >85% relative density with good documentation and records (b):
SPT (N 1 ) 60 > 42
All well compacted e.g. dense, 66% to 85% relative density :
SPT (N 1 ) 60 26 to 42
Layers moderately compacted, e.g. medium dense, 36% to 65% relative density:
SPT (N 1 ) 60 9 to 25
Layers very poorly compacted, e.g. very loose to loose, <35% relative density,
SPT (N 1 ) 60 < 8
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Borrow area variability,
(2) Uniform soils in the borrow areas,
Uniform or minor variability in the borrow areas,
Variable soils in the borrow areas
Very variable soils in borrow areas including gravely soils;
Site supervision
Good site supervision documented with laboratory tests,
Good site supervision
Moderate site supervision
Poor site supervision,
Core geometry Width (W)/Height (H)
(1) Wide core, W/H>1.5
0.5<W/H<1.5 Narrow core, 0.25< W/H<0.5
Very narrow core, W/H<0.25
Notes: (a) Make an assessment based on a combination of available data (b) If soils are well compacted this mechanism will not apply.
Table 6.3 - Probability of a poorly compacted or high permeability layer in the embankment
versus∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) (applies to upper, middle and lower parts of the embankment)
negligible 0.00003 0.0001 [0.0004] 0.005 0.01 Below POR
negligible 0.0003 0.001 [0.005] 0.05 0.5 Above POR
6 9 11 13 18 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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6.2.2 Poorly Compacted or High permeability layer on the core-foundation contact (IM15)
Table 6.4 – Factors influencing the likelihood of poorly compacted or high permeability zones on the core-foundation/abutment contact (IM15)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
EITHER Foundation preparation below the core, rock foundations,
(3) Uniform rock surface or surface treated with shotcrete, or concrete to correct slope irregularities (c)
Regular rock surface, or rock surface treated with shotcrete or concrete to correct slope irregularities (b)
Irregular rock surface, with minimal slope correction or treatment or irregular or benched soil with no compaction
Very irregular rock surface, overhangs with no slope correction, shotcrete or concrete treatment
OR Foundation preparation below the core, soil foundations
(3) Uniform well compacted soil foundation (c)
Compacted soil foundation (b)
Irregular or benched soil with no compaction
Poor stripping of soil foundation leading to poor compaction of first lift
Compaction methods for contact zone
(2) As for “neutral” but with good documentation and records (d)
Soil compacted using special compaction methods (rubber tyres, use more plastic materials, compaction wet of OWC)
Soil placed and compacted by bulldozer, no compaction by rollers Layer thickness at the limit of compaction equipment (e.g. > 12 inches (300 mm) or 18 inches (450 mm) after compaction) (a)
Poor compaction methods used, soil poorly compacted or allowing segregation against foundation surface. Thick layer thickness, often > 18 inches (450 mm) or 24 inches (600 mm) loose
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Continuity of features, Core geometry Width (W)/Height (H)
(1) Wide core, W/H>1.5 Core wall cutoff or grout cap cutoff present
0.5<W/H<1.5 Narrow core, 0.25< W/H<0.5
Very narrow core, W/H<0.25
Notes: (a) Smaller thicknesses are for cohesive soil, larger thicknesses for cohesionless soil. (b) For most cases this mechanism may be judged as of negligible likelihood and assigned zero probability. (c) For this foundation preparation the probability of this mechanism is negligible (d) Even situations where soil is well compacted can soften or loosen if the contact is irregular. (e) For homogeneous earthfill dams, assess foundation preparation and compaction methods for the central portion of
the section.
Table 6.5 - Probability of a poorly compacted or high permeability layer on the core foundation contact versus∑ (Relative importance factor (RF)) x (Likelihood factor (LF))
Negligible 0.0001 0.0002 [0.0004] 0.005 0.01 Below POR
Negligible 0.0005 0.002 [0.005] 0.05 0.1 Above POR
6 9 11 13 18 24 RF x LF
Notes: (1) This and some other combinations which involve contradictory compaction scenarios are quite unlikely to occur (2) If soils are well compacted they this mechanism will not apply
Note: “POR” refers to the Pool of Record level + 1 foot.
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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6.2.3 Poorly Compacted or High Permeability Layer in the Embankment due to Freezing (IM16, IM17)
6.2.3.1 At the crest of the embankment (IM16)
Freezing conditions can result in frost heave and formation of ice lenses in the crest of dams. When the ice thaws, loosened and/or cracked soil may be present in which internal erosion may initiate if the reservoir rises sufficiently high. This section describes how to assess the probability of the presence of such features and the depth to which they may exist. The procedure is:
FIRST Consider the maximum likely depth of freezing for the soil in the core of the dam, and the climate using Table 6.8. If the reservoir stage being considered is below the likely depth of freezing, the probability of a crack or poorly compacted zone due to freezing can be assumed = zero.
SECOND For cases where the reservoir stage is above the base of potential freezing, follow the procedure below to estimate the probability of frost action affecting the dam and the depth of the frost action.
The method for estimating the maximum width of flaw which may result from the frost action is detailed in Section 6.6.6.
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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Table 6.6 – Factors influencing the likelihood of cracking and poorly compacted zones in the upper part of embankment dams due to freezing (IM16)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Climate (3) Other climates where temperatures do not fall below freezing point except possibly overnight or for a day or two. (a)
Temperate climate where temperatures may remain below freezing point for up to 1 month
Sub arctic or alpine climates where temperatures remain below freezing point for 1 to 3 months
Sub arctic or alpine climates where temperatures remain below freezing point for 3 months or more
Classification of core material
(2) Clean gravel (GP,GW) and sand (SP,SW), less than 3% finer than 0.02mm
Gravely (GP,GW) and sandy (SP,SW), soils with between 3% and 6% finer than 0.02mm High plasticity clays (CH)
Silty gravely (GM,GW-GM,GP-GM) and silty sandy soils (SM, SW-SM, SP-SM) with 6% to 15% finer than 0.02mm Clayey sands and gravels (SC, GC) and clays with plasticity index < 12
Silts (ML, MH), silty sands (SM) with > 15% finer than 0.02mm, And clayey silts (ML-CL)
Crest zoning-surface layer over core
(1) Greater than 6 ft (2 meters) of rockfill over the core
Gravely material or rockfill 3 ft to 6 ft (1m to 2m) thick over the core
Gravel material or rockfill 18 inches to 3 ft (0.45m to 1m) thick over the core
No surface layer with dam core extending to crest level or thin ( less than 3 inches (75 mm)) road pavement or gravely material
Note (a) If climatic conditions are as described here this mode does not apply
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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Table 6.7 - Probability of cracking or poorly compacted zones in the crest due to freezing versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF))
negligible negligible 0.0001 0.001 0.1 0.3 0.9
6 10 11 12 16 21 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
Table 6.8– Maximum likely depth of freezing induced flaws based on climate
Climate Maximum likely depth
(feet) (meters)
Sub arctic or alpine climates where temperatures remain below freezing point for 3 months or more
6 1.8
Sub arctic or alpine climates where temperatures remain below freezing point for 1 to 3 months
4 1.3
Temperate climate where temperatures may remain below freezing point for up to 1 month
2 0.6
Other climates where temperatures do not fall below freezing point except possibly overnight or for a day or two.
0 0
6.2.3.2 On Seasonal Shutdown Layers And On The Surface Of Staged Embankments (IM17)
FIRST This mechanism only applies where there has been a seasonal shutdown during construction, or the embankment has been staged.
SECOND Where the mechanism applies estimate the probability of a freezing layer using Table 6.9, and multiply this probability by the assessed likelihood the layer will be continuous across the core. This likelihood is to be assessed by the risk analysis team based on the information available and their judgement.
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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Table 6.9 - Factors influencing the likelihood of high permeability layer on seasonal shutdown layers during construction and staged construction surfaces due to freezing
(IM17)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Construction practices regarding clean-up of frozen layers after construction shutdowns or the surface of the earlier stage of the dam
(4)
Very good control and clean-up practices.
Frozen layers removed from embankment and replaced with new soil or adequately reworked to specified moisture content. If this condition is present, probability=zero
Good control and practices, surfaces scarified, moisture adjusted to specified range, surface re-compacted.
Moderate control. Attempts to scarify frozen layers, but depth of scarifying insufficient or difficulties with moisture control on re-compacting the soil
Poor control. No attempt to scarify or remove frozen layers, poor moisture control on re-compacting the soil
Climate (2) Other climates where temperatures do not fall below freezing point except possibly overnight or for a day or two.
Temperate climate where temperatures may remain below freezing point for up to 1 month
Sub arctic or alpine climates where temperatures remain below freezing point for 1 to 3 months
Sub arctic or alpine climates where temperatures remain below freezing point for 3 months or more
Classification of core material
(1) Clean gravel (GP,GW) and sand (SP, SW), less than 3% finer than 0.02mm
Gravely (GP, GW) and sandy (SP,SW) soils with between 3% and 6% finer than 0.02mm
High plasticity clays (CH)
Silty gravely (GM, GW-GM, GP-GM) and silty sandy soils (SM, SW-SM, SP-SM) with 6% to 15% finer than 0.02mm
Clayey sands and gravels (SC, GC) and clays with plasticity index < 12
Silts (ML, MH), silty sands (SM) with > 15% finer than 0.02mm,
And clayey silts (ML-CL)
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Table 6.10 - Probability of a high permeability layer on seasonal shutdown layers during construction and staged construction surfaces due to freezing versus ∑ (Relative
importance factor (RF)) x (Likelihood factor(LF))
negligible negligible negligible 0.0001 0.001 0.01 0.1 Below POR
negligible negligible negligible 0.001 0.01 0.1 0.9 AbovePOR
7 10 12 13 18 22 28 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
SECTION 6 Probability of Initiation of Erosion in Poorly Compacted and High Permeability Zones in the Embankment
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6.3 Probability Of A Poorly Compacted or High Permeability Zone Around A Conduit or Features Allowing Erosion Into the Conduit
6.3.1 Poorly Compacted or High Permeability Zone Around A Conduit Through The Embankment (IM18)
Assess the probability of a poorly compacted or high permeability zone around the conduit using Table 6.11 and Table 6.12.
Table 6.11 – Factors influencing the likelihood of poorly compacted or high permeability zones along outside of a conduit. (IM18)
Likelihood Factor (LF) Factor
Relative Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely(4)
Conduit type and surround
(3) Concrete encased round pipe, concrete precast or cast in situ, sloping sides.
Concrete encased round pipe, concrete precast or cast in situ, vertical sides. Flowable fill (CLSM)
Masonry, brick, Any round pipe (including corrugated metal pipe), not concrete encased
Cut off collars
(2) No cut off collars
Well detailed cut off collars, USBR design
Poorly detailed cut off collars, widely spaced
Poorly detailed cut off collars, close spacing
Compaction of earthfill around the conduit
(2)
Compaction by rollers to>98% standard maximum dry density at OWC-1% to OWC+2%
Compaction by hand and mechanical equipment to >95% standard maximum dry density at OWC-1% to OWC+2%
Compaction by hand equipment, thick layers, dry of optimum moisture content
No formal compaction, or poor compaction practices used adjacent to conduits (e.g. thick layers inappropriate for equipment)
Conduit trench details
(2)
Trench totally in non-erodible rock, backfilled to the surface with concrete (a)
Wide, slopes flatter than 1H:1V, base width not less than conduit width plus 2 meters either side.
No desiccation of sides of trench
Medium width, depth, and slope; and/or sides of trench desiccated and cracked
Narrow, deep, near vertical sides in soil or rock, backfilled with soil; and/or sides of trench highly desiccated and cracked
Note: (a) If the conduit is totally embedded in a trench totally in non-erodible rock, backfilled to the surface with concrete it should not be considered as a conduit through the embankment (probability = zero)
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Table 6.12 - Probability of a poorly compacted or high permeability zone associated with a conduit versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF))
0.0001 0.0002 0.0005 [0.0009] 0.005 0.02 Below POR
0.0003 0.0006 0.0015 [0.003 0.02 0.1 > 20% Above POR
0.001 0.002 0.005 [0.01] 0.05 0.5 First Fill (untested)
9 12 16 20 26 36 RF x LF
Note: (1) If the conduit is totally embedded in a trench totally in non-erodible rock, backfilled to the surface with concrete it should not be considered as a conduit through the embankment (probability = negligible)
(2) Above POR probabilities apply where the reservoir rise is greater than 20% increase in previously recorded hydraulic head (e.g. for flood protection dams).
Note: “POR” refers to the Pool of Record level + 1 foot
Figure 6.1 Example of poor detailing of seepage collars around a conduit (from FEMA 2005).
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6.3.2 Features Allowing Erosion into a Conduit (IM19)
Assess the probability of a feature being present in the conduit which would allow erosion of the surrounding soil into the conduit.
a) If the internal condition of the conduit is regularly inspected and there is good documentation of the inspections, then estimate the probability of erosion into a conduit using Table 6.13.
b) If the internal condition of the conduit is not known, then use Table 6.14.
It should be noted that this mechanism can apply for erosion into the conduit from the foundation and from the embankment.
Erosion into a conduit may be followed by development of erosion along the conduit in the progression stage. This should be considered when assessing the likelihood of breach. The likelihood of development of piping along the conduit given erosion initiates into the conduit should be estimated from Table 6.16, with the
∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) taken from Table 6.11. The two potential
failure paths should be considered in progression, detection and intervention, and breach.
Table 6.13 – Factors influencing the likelihood of initiation of erosion into a non-pressurized conduit when internal condition is known.
Observed Condition Probability of initiation for Erosion
into the Conduit )1( Careful inspection showing no evidence of open joints or cracks Negligible Careful inspection showing no evidence of open joints, but hairline cracks in concrete are present
0.001 to 0.005
Open joints or cracks present, no evidence of seepage 0.05 to 0.3 Corroded corrugated metal, or cast iron or steel with advanced stages of corrosion )2(
0.1 to 0.9
Open joints or cracks present, evidence of seepage through joint/crack
0.3 to 0.9
Open joints or cracks present, evidence of erosion of soil into the conduit
1.0
Notes (1) Select best estimate taking account of the width of joint openings, the type of joints, the width of cracks, and the quantity of seepage through the crack or joint.
(2) Select best estimate accounting for the extent of corrosion, and whether it penetrates through the conduit. Consider the conduit in its current condition. If corrosion is in progress consider time effects on the estimated probability and report this.
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Table 6.14 – Factors influencing the likelihood of initiation of erosion into a non-pressurized conduit when the internal condition is not known (IM19)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Either Conduit type Concrete, masonry, brick OR
(3)
Cast in-situ concrete. Precast concrete pipes with high quality joints with water stops.
Concrete pipe with bell and spigot joints.
Precast concrete culverts Cast in-situ concrete culvert with poor or no water stops
Masonry, brick.
Steel/Cast Iron Pipe
New steel or cast iron with extensive corrosion protection. Concrete encased steel or iron.
“New” cast iron or steel pipe (“New” < 20 years cast iron, 10 years steel)
“Old” cast iron or steel pipe, not encased (“old” > 60 years cast iron, 30 years steel) Corrugated metal pipe < 5 years
“Old” corrugated metal pipe (>10 years).
Conduit operation
(2)
Dry conduit, inspected regularly
Wet conduit, with low velocity (<5 ft/sec ( 1.5 meters/sec)) flows, dewatered regularly for inspection, or dry
Wet conduit, medium to high velocity flows
Wet conduit, high velocity (> 15ft/sec (3 meters/sec)) or surging flows
Settlement of the conduit
(1) Rock foundation or measured small settlements
Shallow compressible foundation soils, calculated small settlements
Deep compressible foundation soils calculated large settlements
Measured significant settlement and differential settlement; junction of shaft and conduit within the embankment
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Table 6.15 - Probability of initiation of erosion into a conduit versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF))
0.0001 0.0003 0.0005 [0.001] 0.02 0.1 Below POR
0.001 0.003 0.005 [0.01] 0.1 0.5 First wetting
6 9 11 13 18 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
.
Table 6.16 - Probability of the development of piping along the conduit given erosion initiates into the conduit versus ∑ (Relative importance factor (RF)) x (Likelihood
factor(LF)) from Table 6.11
0.01 0.02 0.05 0.1 0.5 1.0
9 12 16 20 26 36 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
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6.4 Poorly Compacted or High Permeability Zone or Gap Associated With A Spillway Or Abutment Wall
6.4.1 Approach
• Assess the probability of a poorly compacted or high permeability zone or gap for each of the three mechanisms for a spillway or abutment wall;
1) Poorly compacted or high permeability zone associated with the wall (using Table 6.17 in Section 6.4.2).
2) Crack/gap adjacent to the wall (using Table 6.19 in Section 6.4.3).
3) Differential settlement adjacent to the wall (using Table 6.21 in Section 6.4.4)
• Adopt the maximum probability of the three mechanisms.
• For mechanisms (2) and (3) estimate the probability erosion will initiate in the crack or gap using the methods detailed in Section 5.4.
• For mechanism (1) estimate the probability erosion will initiate in the high permeability zone using the methods detailed in Section 6.6.
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6.4.2 Poorly Compacted or High Permeability Zone Associated with a Spillway Or Abutment Wall (IM20)
Table 6.17 – Factors influencing the likelihood of a poorly compacted or high permeability zone associated with a spillway or abutment wall (IM20)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Compaction of earthfill adjacent to the wall
(3)
Compaction by rollers to >98% standard maximum dry density at OWC-2% to OWC+2%
Compaction by hand and mechanical equipment to >95% standard maximum dry density at OWC-2% to OWC+2%
Compaction by hand equipment, thick layers, dry of optimum moisture content
No formal compaction, or poor compaction practices (e.g. placed in very thick lifts or allowing segregation against wall)
Concrete buttresses
(2) None
Single but with good compaction around the buttress
Single with poor details such as vertical sides, little evidence of good compaction
Several close together preventing good compaction
Finish on wall
(1) Smooth planar coupled with flat slope (flatter than 0.5H:1V)
Smooth, planar Rough and irregular
Vertical and horizontal steps (e.g. masonry/ brick walls)
Table 6.18 - Probability of a high permeability zone associated with a spillway or abutment wall versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF))
0.00005 0.0001 0.0002 [0.0003] 0.002 0.02 Below POR
0.001 0.002 0.005 [0.01] 0.05 0.5 Above POR
6 9 11 13 18 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
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6.4.3 Crack/Gap Adjacent to a Spillway or Abutment Wall (IM21)
Table 6.19 – Factors influencing the likelihood of a crack or gap adjacent to a spillway or abutment wall (IM21)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Slope of wall (3) Sloping, flatter than 0.5H to 1V
Sloping, 0.1H to 1V to 0.5H to 1V
Vertical, or Vertical with flatter slope on lower part
Overhanging over the core width.
Wall type, wall stiffness
(2) Very stiff gravity wall or counterfort wall
Thin gravity wall Counterfort wall subjected to cyclic reservoir level conditions
Cantilever wall not normally subjected to cyclic reservoir level conditions
Cantilever wall, subject to cyclic reservoir level conditions. Poor freeze /thaw details
Concrete buttresses
(1) Single or multiple with good details and proven good compaction around the buttress
None
or Single with probably good to reasonable compaction around the buttress
Single with poor details such as vertical sides, little evidence of good compaction
Several close together preventing good compaction
Notes: (a) See Figure 6.2(a) (b) See Figure 6.2(b) (c) Select the factor which best describes the worse of the two conditions
Table 6.20 - Probability of a gap or crack associated with a spillway or abutment wall versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF))
0.00005 0.0001 0.0002 [0.0004] 0.002 0.02 Below POR
0.001 0.002 0.005 [0.01] 0.05 0.3 Above POR
6 9 11 13 18 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
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Figure 6.2 - Situations where a gap may form between the dam fill and spillway wall (a) Steep foundation adjacent spillway wall;
(b) Change in slope of the retaining wall (Fell et al 2004).
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6.4.4 Differential Settlement Adjacent to a Spillway or Abutment Wall (IM22)
Table 6.21 - Factors influencing the likelihood of cracking or hydraulic fracturing due to differential settlement adjacent a spillway or abutment wall (IM22)
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Cross valley profile under embankment core(1)
(3)
Wide bench Wb/Hw > 2.5
Note. If this condition is present, probability=zero
Bench adjacent to wall 1.0 < Wb/Hw <2.5
Narrow bench adjacent to wall 0.25 < Wb/Hw < 1.0
No or very narrow bench adjacent to wall. Wb/Hw < 0.25
Slope of abutments under embankment core(1)
(2)
Gentle abutment slope
β 1 < 25o
Note. If this condition is present, probability=zero
Moderate abutment slopes
25o < β 1 < 45o
Steep abutments
45o < β 1 < 60o
Very steep abutments,
β 1 > 60o
Height of embankment
(1) Dams less than 50 ft (15 m) high
Dams 50 ft to 100 ft (15 m to 30 m) high
High dams 100ft to 200 ft (30 m to 60 m)
Very high dams >200 ft (60 m)
Note: (a) See Figure 5.2 for definitions of Wb, Hw, β1 (b) This mechanism only applies for Wb/Hw< 2.5
Table 6.22 - Probability of cracking or hydraulic fracture due to differential settlement adjacent a spillway or abutment wall versus ∑ (Relative importance factor (RF)) x
(Likelihood factor(LF))
negligible negligible negligible negligible [0.0005] 0.002 0.02 Below POR
negligible negligible negligible negligible [0.005] 0.02 0.2 Above POR
6 9 11 13 14 19 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
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6.4.5 Wrap around details for connection of embankment dam to concrete gravity dam (IM23)
Figure 6.3 shows typical details of the connection of an embankment dam to a concrete gravity dam. There is a potential seepage path along PQRS. The path length and hence the gradient varies with the reservoir level.
There is a potential for the embankment to move away from the concrete dam at PQ and particularly at RS due to settlement of the embankment dam during construction, and usually to a lesser extent after construction. It is recommended that this situation be assessed as follows:
• The primary control on seepage and initiation of erosion is considered to be along QR. The likelihood of a crack or gap being present, and if so, the probability erosion will initiate should be assessed as for an embankment abutting a very stiff retaining wall (refer to Section 6.4.3).
• When assessing the seepage gradient along QR, the likelihood there will be gaps or poorly compacted soil along PQ and RS should be assessed taking account of the factors in Table 6.23. For the worst scenarios, there will be no benefit from the seepage path on PQ and RS if there is a gap there which can be seen on inspection.
• The effect is likely to be most important for reservoir level stages nearing dam crest level.
Table 6.23 - Factors to be considered in assessing seepage gradients on wrap-around
Factors which make it likely there is a good seepage contact along PQ and RS, and gradients
will be lower )1(
Factors which make it likely there is a poor seepage contact along PQ and RS, and gradients
will be higher )1(
Uniform slope with no overhangs Well compacted embankment shoulders or zoning with all materials having a similar and high modulus Uniform concrete slopes with at least 0.1H to 1V slope
Low embankments Reservoir level at least 20 feet below dam crest level so there is a lesser likelihood a crack will persist to reservoir level
Overhangs in the concrete Poorly compacted shoulders leading to large settlements during and post construction Change in slope of concrete such as shown in Figure 6.2 allowing a gap to form as the embankment settles
High embankment Reservoir level approaching dam crest level
Notes. (1) See Figure 6.3 for definition of terms
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Figure 6.3 – Wrap around details for connection of embankment dam to concrete gravity dam
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6.5 Probability Of Poorly Compacted or High Permeability Zone - Factors To Account For Observations
Observation of seepage factor
Where there are observations of seepage for the dam these can be used to modify the results of Sections 6.2, 6.3 and 6.4. The probabilities obtained from Sections 6.2, 6.3 and 6.4 are multiplied by the factor from Table 6.24. The multiplication factor should be selected taking account of what data is available, allowing for the relative importance of the observations.
This factor applies to the assessment of poorly compacted or high permeability zones in the embankment, around conduits and adjacent walls
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Table 6.24 - Seepage observation factors
Influence on Likelihood Factor Less Likely
(1) Neutral
(2) More Likely
(3) Much More Likely
(4)
Observed Seepage No seepage observed for dams where there is no potential for seepage to be hidden, careful inspection for seepage
Seepage observed at toe of dams with permeable downstream zone or internal drainage systems, or potential for hidden seepage
Wet areas on the downstream slope
Concentrated seepage is present on the downstream slope
Seepage Adjustment Factor (A)
Multiplier = 0.9 to 0.5
Multiplier = 1.0
Probability of high permeability zone = 0.5 to 1.0
Probability of high permeability zone = 1.0
Observations in drill holes/CPT in the core
Multiple drill holes or CPT tests indicate no evidence of high permeability or softened zones
No drill holes or CPT tests in core
Drill holes or CPT tests indicate softened zones in the core
Multiple drill holes or CPT tests indicate persistent high permeability zones are likely to be present
Drill hole/CPT Adjustment Factor (B)
Multiplier = 0.1 to 0.5 depending on quantity and quality of the investigations
Multiplier = 1.0
Multiplier = 5 to 10
Probability of high permeability zone = 0.5 to 1.0
Drilling/Grouting Practices Inducing Defects in the Core
No water drilling or pressure grouting through the core
Drilling through the core with water causing excessive water losses in the core
High pressure grouting was carried out through the core
Adjustment Factors for Induced Core Defects (C)
Multiplier = 1.0 Multiplier = 2 to 5 Multiplier = 5 to 10
Notes: (1) Apply either Seepage Factor (A), Drill hole/CPT Factor (B) or Induced Defect Factor (C), whichever gives greatest probability of high permeability zones. (2) Use multipliers towards the lower of the range for reservoir level below POR and towards the upper of the range for reservoir levels above POR.
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6.6 Estimation Of The Probability Of Initiation Of Erosion In A Poorly Compacted or High Permeability Layer In The Embankment, Adjacent A Wall Or Around A Conduit
6.6.1 Screening Check On Soil Classification
Is the soil cohesive or cohesionless?
If the soil is cohesionless or has a Plasticity Index ≤ 7, follow the procedures in Sections 6.6.2 and 6.6.3 to assess the probability of backward erosion and suffusion.
If the soil is cohesive with a Plasticity Index > 7, then the likelihood of backwards erosion and suffusion is negligible under the seepage gradients which occur in a conventional dam. Consider if erosion may occur through a crack in the soil using the procedure detailed in Sections 6.6.4 and 6.6.5. If the seepage gradients are >4, consider suffusion for soils with a Plasticity Index ≤ 12.
6.6.2 Assessment Of The Probability Of Initiation Of Backward Erosion In A Layer Of Cohesionless Soil or Soil with Plasticity Index ≤ 7
The steps to be followed are:
• Estimate the average seepage gradient (i av ) through the core at the level of the high permeability layer
for the reservoir stage under consideration.
• Estimate the time it will take to develop a seepage gradient in the layer from the estimated permeability of the soil, allowing for potential collapse of the layer on saturation if the soil is not well compacted. Use Table 6.25 to assist in this estimate. From this and the time the reservoir will be above this stage assess whether there is sufficient time to develop the seepage gradient in the layer. For layers below the normal operating pool level the layer will be saturated and the seepage gradient will develop as the reservoir rises.
• From the particle size distribution of the core material estimate a representative uniformity coefficient Cu = D 60 /D 10 .
• Estimate the average gradient (i pmt ) required to initiate and progress backward erosion from Figure 6.4.
This is the gradient that is required to initiate backward erosion at the downstream end of the layer and also to progress the pipe by backward erosion to the upstream end of the layer.
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• Correct this average gradient for the geometry, horizontal to vertical permeability ratio of the zone subject to backward erosion, and grain size as detailed in the Supporting Information Section C6.6.2.4.
This gives (i pmt ) Corrected where
( )R
pmtzKSLDCorrectedpmt C
iCCCCCCCi αγ=)( (6.9)
where i pmt = Maximum point seepage gradient needed for complete piping in the flume test based
on the soil coefficient of uniformity Cu (from Figure 6.4)
CD = Correction factor for (D/L)
CL = Correction factor for total pipe length L
CS = Correction factor for grain size
CK = Correction factor, for permeability anisotropy. This is for the anisotropy of the soil layer subject to backward erosion, not the embankment core as a whole.
Cz = Correction factor for high-permeability under layer
Cγ = Correction factor for density
Cα = Adjustment for pipe inclination
CR = Correction factor for dam axis curvature
D = Depth of piping sand layer, in direction perpendicular to α (m)
L = Direct (not meandered) length between ends of a completed pipe path, from downstream to upstream exit, measured along the pipe path (m)
• For Cu> 6.0, also estimate the critical gradient (i cr ) from i cr = ( satγ - wγ ) / wγ . Adopt this gradient if it
is smaller than (i pmt ) Corrected .
• Estimate the probability of initiation and progression of backward erosion from Table 6.26 for well
compacted layers and Table 6.27 for poorly compacted layers. Use i av and (i pmt ) Corrected or (i cr ) as
inputs. The table allows for gradients potentially being higher than the average at the downstream side as has been observed on many dams, and case study data from Sweden which shows erosion may occur at average gradients less than 1.0, at least if the layers are poorly compacted. It also allows for application of corrections recommended by Schmertmann (2000) which for a thin layer of permeable soil indicate
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gradients higher than those from Figure 6.4 are required to initiate erosion. These probabilities apply for reservoir levels up to and above the pool of record.
• For poorly compacted silt/sand/gravel soils which are subject to collapse settlement on saturation, assess the likelihood of initiation of erosion using Section 6.6.4.
Table 6.25 - Time to develop seepage gradient in cohesionless soils
Method of compaction (see Tables 6.1 and 6.2 for detailed descriptions
Time for developing seepage gradient with
collapse settlement
Time for developing seepage gradient if there is
no collapse settlement
No formal compaction Minutes Not applicable. Collapse settlement is highly likely
Tracking by dozer or rolled in layers too thick for the equipment
Minutes to a few hours Not applicable. Collapse settlement is highly likely
Compacted by rollers in suitable layer thicknesses to normal compaction standards
Not applicable Hours to days for silty sands and sands.
Compacted by rollers in suitable layer thicknesses to normal compaction standards with well documented compaction records
Not applicable Hours to days for silty sands and sands.
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Figure 6.4 - Maximum point gradient, ipmt, needed for complete piping (initiation and progression for an unfiltered exit) versus uniformity coefficient of soil (Schmertmann 2000).
This relationship applies for Cu between 1 and 6.
For Cu>6, calculate the critical gradient icr = ( satγ - wγ ) / wγ
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Table 6.26 - Estimation of the probability of initiation and progression of backward erosion P IP in cohesionless soils and soils with PI ≤ 7 for well compacted layers
Average seepage gradient across embankment core (iav) Average seepage gradient required to initiate & progress backward erosion (ipmt)Corrected or (icr)
0.05 0.1 0.25 0.5 1.0 2.0
0.05 0.9 0.95 0.99 0.99 0.99 0.99
0.1 0.2 0.9 0.95 0.99 0.99 0.99
0.25 0.01 0.2 0.9 0.95 0.99 0.99
0.5 0.001 0.01 0.2 0.9 0.95 0.99
1.0 0.0001 0.001 0.01 0.2 0.9 0.95
Table 6.27 - Estimation of the probability of initiation and progression of backward erosion P IP in cohesionless soils and soils with PI ≤ 7 for uncompacted layers
Average seepage gradient across embankment core (iav) Average seepage gradient required to initiate & progress backward erosion
(i pmt ) Corrected or (icr) 0.05 0.1 0.25 0.5 1.0 2.0
0.05 0.9 0.95 0.99 0.99 0.99 0.99
0.1 0.5 0.9 0.95 0.99 0.99 0.99
0.25 0.2 0.5 0.9 0.95 0.99 0.99
0.5 0.05 0.2 0.5 0.9 0.95 0.99
1.0 0.02 0.05 0.2 0.5 0.9 0.95
6.6.3 Probability Of Initiation Of Erosion By Suffusion In A Layer Of Cohesionless Soil or Soil with Plasticity Index ≤ 7 (PI ≤ 12 for seepage gradients >4)
Check if the soil is potentially internally unstable
Check if the proportion of the finer fraction is less than 40% of the total mass of the soil. The finer fraction is defined by the point of inflection of broadly graded or gap graded soils. This is a check on whether the
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coarser particles will form a matrix into which the finer particles will fit. If the answer is yes, continue to assess the likelihood of the soil being internally unstable as described in the following steps. If not (there are more than 40% finer particles) the coarse particles will “float” in the finer particles and suffusion is not possible. These soils may experience backward erosion.
Assess the probability the soil is internally unstable (P IUS )
From the particle size distribution for the soil, determine the d15, d60 and d90 sizes (the particle size for which 15%, 60% and 90% are finer). The grading curve is not adjusted for this procedure. Then estimate the probability the soil is internally unstable (PIUS) from Figure 6.5 for soils with more than 10% fines passing 0.075 mm (#200 sieve), and Figure 6.6 for soils with less than 10% fines passing 0.075 mm.
1 10 100 1000
2
4
6
8
10
[woSUNBD2.GRF]
h' =
d90
/d60
h" = d90 /d15
1 10 100 1000 4000
D1
Data source:Kenney et al. (1983)Kenney et al. (1984)Kenney & Lau (1984, 85)Lafleur et al. (1989)Burenkova (1993)Skempton & Brogan (1994)Chapuis et al. (1996)UNSW
Internally stable soil samples arerepresented by hollow symbols(e.g. , , etc.), andinternally unstable soil samples arerepresented by solid symbols(e.g. , , etc.).
Data point (447, 17.2)plotted out of range
B10.050.100.300.500.70
0.900.95
is the probability, predicted by logisticregression, that a soil is internally unstableif it is plotted along the respectivedotted line .
P
P = exp(Z)/[1 + exp(Z)]Z = 2.378 LOG(h") - 3.648 h' + 3.701
Sun (1989) data and UNSW data points B1,D1 not included in the logistic regression.
P
Figure 6.5 - Contours of the probability of internal instability for silt-sand-gravel soils and clay-silt-sand-gravel soils of limited clay content and plasticity, Plasticity
Index ≤ 12. (Wan and Fell 2004)
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1 10 100
2
4
6
8
10h'
= d
90 /d
60
h" = d90 /d15
1 10 100 200
0.950.90
0.700.500.30
0.100.05
4R
A3C1
Data source:Kenney et al. (1983)Kenney et al. (1984)Kenney & Lau (1984, 85)Lafleur et al. (1989)Burenkova (1993)Skempton & Brogan (1994)Chapuis et al. (1996)
Internally stable soil samples arerepresented by hollow symbols(e.g. , , etc.), andinternally unstable soil samples arerepresented by solid symbols(e.g. , , etc.).
UNSW (only data points 4R,A3 and C1)
is the probability, predicted by logisticregression, that a soil is internally unstableif it is plotted along the respectivedotted line .
P
P = exp(Z)/[1 + exp(Z)]Z = 3.875 LOG(h") - 3.591 h' + 2.436
Sun (1989) data are not included inthe logistic regression.
P
Figure 6.6 - Contours of the probability of internal instability for sand-gravel soils with less than 10% non-plastic fines passing 0.075 mm (Wan and Fell 2004).
Assess the probability that given the soil is internally unstable erosion by suffusion will begin (PSI)
Assess the probability that given the soil is internally unstable suffusion will begin under the seepage gradient in the highly permeable layer using Table 6.28. The probability of suffusion and backward erosion should both be assessed and carried forward in the analysis.
Table 6.28 - Seepage gradients at which suffusion may occur
Average seepage gradient across embankment core (i) Porosity (volume of voids/total volume of
soil) 0.05 0.1 0.25 0.5 1.0 2.0
<0.20 0.01 0.02 0.05 0.2 0.9 0.99
0.20 to 0.25 0.02 0.05 0.1 0.5 0.95 0.99
0.25 to 0.30 0.05 0.1 0.2 0.9 0.99 0.99
0.30 to 0.35 0.1 0.2 0.5 0.95 0.99 0.99
>0.35 0.2 0.5 0.9 0.99 0.99 0.99
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6.6.4 Probability Of Initiation Of Erosion In A Poorly Compacted or High Permeability Cohesive Soil Layer and in silt-sand-gravel soils in which collapse settlement may form a crack or flaw
It is well documented that internal erosion and piping occurs in poorly compacted cohesive soils. This is particularly so for dispersive soils. The mechanism is potentially of two types:
• The soil behaves as a series of clods with openings between the clods in which water passes.
• The soil collapses on saturation forming a crack or flaw in which the water flows. This is most likely where there is poorly compacted soil against a pipe but is possible within layers of soil.
To model this it is most practical to assume a crack is formed and to assess the likelihood of erosion initiating in the crack.
The procedure is:
• Assess the thickness of the layer of soil which is poorly compacted (T p ). There may be a single layer or
several layers. The minimum layer thickness adopted should be 300 mm (12 inches).
• Estimate the amount by which the layer may collapse (C F ) using Table 6.29. Then estimate the height
of the gap which could result (G) from G = (T p ) x (C F ). This represents the scenario with the weight of
the soil above being supported on non-collapsed soil adjacent.
• Assume G is the height of the crack which is formed, and use the method outlined in Section 5.4 to estimate the probability of initiation of erosion given this width crack, the average gradient through the core at the level of the high permeability layer, and the soil properties.
The mechanism applies to such zones within the embankment, on the embankment/foundation contact, around conduits, and adjacent to walls.
This method should be also applied to silty sands, and silty sandy gravel soils which may be subject to collapse settlement even if the soils are non plastic, since they will erode rapidly in a crack.
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Table 6.29 - Amount of collapse settlement which may occur on saturation versus compaction properties
Description of the method and degree of compaction of the core
Amount of collapse settlement as a
proportion of the layer thickness
Soil placed with, no formal compaction ( e.g. by horse and cart in old dams, or by pushing into place by excavator or bulldozer or in very thick layers)
No control on layer thickness,
Well dry of optimum moisture content.
Layers very poorly compacted, dry of standard optimum
moisture content e.g. < 90% standard dry density ratio, 3%
dry of standard OWC
0.02 to 0.05
Soil placed and compacted by bulldozer, no compaction by rollers, or rolled in thick layers beyond the capability of the roller
Layer thickness at or beyond the limit of compaction equipment
Dry of optimum moisture content
Layers poorly compacted, dry of standard optimum moisture
content e.g. < 93% standard dry density ratio, 2% to 3% dry of
standard OWC
0.01 to 0.02
Soil rolled in layers near the limit of the capability of the rollers, at moisture contents dry of standard OWC
Compacted to e.g. 93-95% standard dry density ratio,
moisture content 2% to 3% dry of standard OWC
0.005
Soil compacted by suitable rollers in suitable layer thickness
Around optimum moisture content
Well compacted to e.g. 95-98% standard dry density ratio, moisture content 2% dry of
optimum to 1% wet of standard OWC
Will not collapse, but for the poorly compacted layer
within
0.005
As above but with good documentation and records. All very well compacted to e.g. ≥ 98% standard dry density ratio, moisture content 2% dry of optimum to 1% wet of standard OWC
Will not collapse, but for the poorly compacted layer
within
0.005
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6.6.5 Probability Of Initiation Of Erosion In A Poorly Compacted or High Permeability Cohesive Soil Layer Around A Conduit
The method assumes that the critical case is where poorly compacted soil surrounding the conduit collapses on saturation and a gap is formed.
The procedure is:
• Assess the thickness of the layer of soil which is poorly compacted. (T p ). There may be a single layer or
several layers.
• Estimate the amount by which the layer may collapse (C F ) using Table 6.29 as a guide. Then estimate
the height of the gap which could result (G) from G = (T p ) x (C F ). To do this take account of the
dimensions of the conduit and the trench in which it is placed.
• For cases where it appears that the soil around the pipe is well compacted assume and where crack widths <5 mm are calculated, assume a crack width of 5 mm to allow for possible shrinkage of the soil from the pipe during construction or in service.
• Assume G is the height of the crack which is formed, and use the method outlined in Section 5.4 to estimate the probability of initiation of erosion given this width crack, the average gradient through the core at the level of the high permeability layer, and the soil properties.
6.6.6 Probability Of Initiation Of Erosion In A High Permeability Soil Due to Frost Action
The procedure is:
• Assess the width of the frost induced crack or flaw using the procedure detailed below.
• Use the method outlined in Section 5.4 to estimate the probability of initiation of erosion given this width crack or flaw, the average gradient through the core at the level of the high permeability layer, and the soil properties.
The effects of frost action are complex and include formation of cracks due to heave, and formation of ice lenses. The latter may melt in summer months and leave pathways in which erosion may initiate. Where there is specific information about frost effects for the dam being assessed, that information should be used by the risk analysis team to assess likely defect widths. In the absence of such data Table 6.30 should be used. These widths may be applied to the full depth of penetration of frost from Table 6.8 as the evidence is the ice lenses may be as thick at the base of freezing as at the surface.
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Table 6.30 - Width of frost induced flaw versus (RFxLF)
(RFxLF) from Table 6.7 (RFxLF) from Table 6.10 Width of flaw -mm
24 28 20
21 22 10
16 18 5
12 13 2
10 12 Zero
6.7 Allowance for the Presence of Unknown and Unpredictable Flaws in the Core of the Embankment
6.7.1 Background
Even with well designed and constructed dams, for which there is good record of construction, it is possible that there are unknown and unpredictable flaws in the core which may, under some circumstances, lead to initiation of erosion.
In the opinion of the development team, the unknown and unpredictable flaws are most likely to be a poorly compacted layer or a layer that was allowed to crack or soften during construction. For reasons of continuity the flaw is probably more likely to be in the upper part of the dam where the core width is smaller. The flaw could also be due to unpredictable cracking or to a pathway created by installation of instrument cables or tubes.
The likelihood of an unknown flaw is greater above the reservoir pool levels that the dam has been tested. Below the POR there is a greater chance that the flaw has been detected and addressed as a known issue.
The probability of these unknown flaws should be low as the risk analysis has already considered the more predictable modes of initiation. In most cases they should not contribute significantly to the probability of failure because other more predictable flaws will have a greater probability.
If a dam does not have filters or a transition zone (e.g. a homogeneous dam), the probability of failure approaches that of the probability of the presence of a flaw, and the probability given there is a flaw, erosion initiates. In these cases if the dam has a high consequence of failure, even a very small probability of a flaw can be significant contributor to risk as there are little other defensive measures in place.
The potential for unknown or unpredictable flaws in dams is always a possibility. It is therefore considered important that the responsible dam safety decision makers be aware of this when assessing the safety of the dam.
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This section provides advice on what to do in these situations.
The development team has strived to address all failure modes that, in their experience, occur in embankment dams. Procedures are also suggested to handle failure modes not well covered in this methodology. However, in the end, as pointed out by the late Ralph Peck in his paper “The Risk of the Oddball”, there remains the potential that even with the “… efforts of even the most experienced engineers the most significant potential failure mode may occasionally be overlooked.” As Peck summarizes, the only recourse is continuing surveillance. Surveillance should always be part of the monitoring program for the dam and all dam owners should be aware of this. The risk analyst should remind the owner of this in the preparation of the report. Armed with possibly a fresh look at potential failure modes, a review of the surveillance program at the end of the risk analysis is always a good idea.
6.7.2 Recommended Procedure
For dams which do not have filters or transition zones protecting all or part of the core, and the assessed probability of a flaw for the initiation modes described in Sections 5 and 6 give very low probability of a flaw being present (≤ 10-4 for reservoir levels above POR and ≤ 10-5 for reservoir levels below POR) and the consequences of failure are high, it is recommended that the procedure detailed below be followed to check the effect on the risk analysis of the presence of unknown and unpredictable flaws.
6.7.3 Suggested size and location of the flaw and the probability of occurrence
It is suggested that:
• A 2mm wide flaw is assumed to be present in a location that is critical for each reservoir level under consideration. This can be where the gradient of flow through the flaw will be greatest, where there is no filter or transition zone, or the filter or transition zone is so coarse that there is a significant probability of being in the continuing erosion range.
• Develop a failure path for this scenario.
• Assign a probability of the presence of the flaw of 10-4 for reservoir levels above POR and 10-5 for reservoir levels below POR.
• Complete the evaluation of the event tree for this failure path.
See the Supporting Document for the rationale behind these suggestions.
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6.7.4 Assessing the Probability of Failure if the Flaw Were to Exist and Reporting the Outcome of the Analysis
Assess the probability of failure for each of the reservoir stages affected by the flaw by assuming the flaw is as described in Section 6.7.3.
Report this separately to the other failure modes. Make the case in the report of how likely (or unlikely) the dam has such a flaw. This discussion could focus on the amount and quality of construction control information, the climatic conditions at the dam site that may have been present during construction, and other factors considered relevant.
Whether or not this probability of failure is combined with the other failure modes to assess the overall probability of failure is for the Agency for whom the risk analysis is being carried out to decide.
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7 Probability of Initiation of Erosion in a Soil Foundation
7.1 Screening Check on Soil Classification
Is the soil cohesive or cohesionless?
If the soil is cohesionless or has a Plasticity Index ≤ 7, then follow the procedures in Sections 7.2 and 7.3 to assess the probability of backward erosion and Section 7.4 for suffusion.
If the soil is cohesive with a Plasticity Index > 7, then the likelihood of backwards erosion and suffusion is zero under the seepage gradients which occur in foundations of a conventional dam. Consider if erosion may occur through a crack in the soil using the procedure detailed in Section 7.5. If the seepage gradients are >4, consider suffusion for soils with a Plasticity Index ≤ 12.
7.2 Assessment Of The Probability Of Initiation Of Backward Erosion In A Layer Of Cohesionless Soil or Soil with Plasticity Index ≤ 7 In The Foundation (IM24)
7.2.1 Description of Method
The steps to be followed are:
a) Estimate the probability (P cl ) there is a continuous layer of cohesionless soil or soil with PI ≤ 7 from
upstream of the embankment, to downstream of the embankment. The layer does not have to be exposed to the ground surface downstream of the embankment. That is, it may be overlain by a layer of cohesive soil.
b) If there is no continuous layer such as shown in Figure 7.1, then backward erosion is not possible and the probability of backward erosion may be taken as zero. In some situations there will be some uncertainty and the probability of a continuous layer should be assessed from the geotechnical borehole data, understanding of the depositional conditions in which the soils were and deposited, piezometer data, including response of the piezometers to changes in reservoir level. P cl is likely to be between 0.1 and
1.0 for most situations
c) Assess the probability of “heave” (P H ) or reaching the critical gradient (i cr ) which is a zero effective
stress condition, at the toe of the embankment for the reservoir stage under consideration. This assessment should consider the potential for localised areas of a thinner confining layer within a distance of 2 x dam height downstream of the dam toe (e.g. a toe ditch). This should be done using local gradients at the toe of the embankment from piezometer readings, and/or finite element seepage flow modelling as
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described in Section 7.2.2 and Table 7.1, or more approximately using the method shown in Section 7.2.3 and Table 7.2 and Table 7.3.
d) Estimate the probability of initiation and progression of backward erosion given heave has occurred (P IH ) using Section 7.3. For situations where sand boils have been observed, the probability of initiation and progression for the reservoir level at which sand boils have been observed and above is assumed to be 1.0
e) Given that backwards erosion may initiate and progress without a heave condition being present, estimate the probability of initiation and progression of backward erosion given heave has not occurred (P INH ) using Section 7.3.3.
f) Estimate the probability of initiation and progression of backward erosion (P I ) from the results of the
assessments above. (P I ) = (P cl ) x [(P H ) x (P IH ) + (1-(P H ) x (P INH )].
Figure 7.1 - An example of a situation where there is no continuous layer of cohesionless soil in the foundation and backward erosion cannot occur.
SAND
CLAY
CLAY
3 1 3
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7.2.2 Estimation of the probability of heave or reaching the critical gradient (P H ) from piezometer data and/or seepage flow net models.
(a) Calculate the factor of safety against heave or reaching the critical gradient from the following equations:
FUT = uvσ (1)
Where σv = total vertical stress at any point in the foundation – kN/m2
u = pore pressure at the same point – kN/m2
or
FUT = wp
sathh
γγ (2)
where γsat = unit weight of saturated foundation soil – kN/m3
γw = unit weight of water – kN/m3
hp = piezometric head – meters
Figure 7.2 - Cross section of an embankment and dam foundation showing seepage flow net and definition of terms
The alternative method for estimating the factor of safety is to consider the gradient of the flow net. If the gradient approaches the critical gradient, liquefaction and heave can be expected to occur.
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FUC = gradientactualgradientcritical (3)
For vertically up seepage, the critical gradient i cr can be calculated from (Terzaghi 1960)
i cr = (G – 1)/(1 + e) (4)
where G = soil particle density (specific gravity) in tonnes/m3
e = void ratio
or from
• i cr = ( satγ - wγ ) / wγ (5)
Where there is a layer of cohesive or other low permeability soil overlying the soil which may be subject to backward erosion, the most critical gradient usually occurs from the base of the lower permeability layer to the ground surface.
(b) Estimate the probability of heave from FUT or/and FUC from Table 7.1.
Table 7.1 – Estimation of the probability of heave or reaching the critical gradient (P H ) from the calculated factor of safety against heave.
Estimated factor of safety against heave
FUT FUC
Seepage gradient at toe of embankment as a
ratio of icr
Probability of heave (PH)
1.3 2.0 0.50 0.005 to 0.05
1.23 1.7 0.59 0.02 to 0.2
1.12 1.3 0.77 0.05 to 0.5
1.05 1.15 0.87 0.1 to 0.9
1.0 1.0 1.00 0.9 to 0.99
0.92 0.85 1.20 0.99
0.80 0.66 1.50 0.999
The selected probability should take account of the quality of the data on which the factors of safety are based.
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7.2.3 An approximate method for assessing the probability of heave
An approximate estimate of the probability of heave (P H ) can be obtained from Table 7.2 and Table 7.3. The approach is to assess which of the embankment and foundation arrangements shown in Figure 7.3 to Figure 7.6 best models the dam under consideration. The table is based on finite element seepage modelling. Note that the seepage pressures are determined by the shape of the geometry, and the results apply to similar geometries regardless of scale. The relative thickness of the foundation to embankment height does not significantly affect the results. The results for the approximate method apply for the condition where the reservoir level is 0.5 m below the crest level.
Table 7.2 – Estimation of the probability of heave from embankment geometry and the foundation permeability ratio kh/ kv for situations where there is no confining layer in the
foundation
Seepage Model Foundation
permeability ratio (kh/ kv)
Factor of safety against heave from seepage
analyses (FUT )
Probability of heave
(PH)
A 1 1.6 0.001 to 0.009
10 1.2 0.02 to 0.2
100 0.9 0.99
B 1 1.45 0.005 to 0.05
10 1.05 0.1 to 0.9
100 0.8 0.999
Table 7.3 – Estimation of the probability of heave from embankment geometry and the foundation permeability ratio kh/ kv for situations where there is a confining layer in the
foundation
Seepage Model Foundation
permeability ratio
(kh/ kv)
Factor of safety against heave from seepage
analyses (FUT )
Probability of heave
(PH)
C 1 0.4 1.0
10 0.3 1.0
100 0.3 1.0
D 1 0.4 1.0
10 0.3 1.0
100 0.3 1.0
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Figure 7.3 - Seepage model A of embankment dam and foundation (Maniam 2004).
Figure 7.4 - Seepage model B of embankment dam and foundation (Maniam 2004).
Figure 7.5 - Seepage model C where foundation is overlain by low permeability clay (Maniam 2004)
Figure 7.6 - Seepage model D used to represent the cracked downstream clay (Maniam 2004).
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7.3 Estimating the probability of backward erosion given heave has occurred
7.3.1 Probability of initiation and progression of backward erosion if sand boils have been observed.
If sand boils have been observed it should be assumed that the probability of initiation and progression of backward erosion = 1.0 for reservoir levels at or above the level at which sand boils have been observed. For lower reservoir levels use the procedure in Section 7.3.2. This applies to sand boils with moving sand but not pin boils.
In these sections the probability of progression only covers whether the backwards erosion process will progress within the developing pipes. It does not include assessment of whether a roof will form and whether flow limitation may occur. These are covered in Section 11.
7.3.2 Estimating the probability of initiation and progression of backward erosion where heave or reaching the critical gradient is predicted or sand boils have been observed at higher reservoir levels (P IH )
If heave or reaching the critical gradient is predicted for the reservoir level under consideration it may be assumed that the probability of initiation of backwards erosion = 1.0.
However whether backwards erosion will then progress to develop a pipe all the way from the downstream toe to upstream of the dam is related to the gradients under the main part of the dam. For practical purposes in most cases this can be taken as the average seepage gradient (i avf ) in the foundation layer beneath the dam at
the reservoir stage under consideration.
The average seepage gradient (i avf ) is defined as the hydraulic head difference divided by the seepage path
length. However if there is upstream blanketing with lower permeability soil much of the head may be lost in seepage through this “blanket”. If in doubt neglect the blanketing effect. In practical terms this gradient may be estimated as (H2 – H3)/L in Figure 7.7. This allows for the head losses through the upstream clay layer.
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Figure 7.7 - Section through embankment and foundation showing definition of terms to estimate the average gradient in the foundation sand.
If there is a sheet pile, soil bentonite or concrete cut-off wall the gradient of interest is the average gradient in the soil subject to backward erosion from downstream of the cut-off wall to the toe of the embankment allowing for the effectiveness of the cut-off wall. This is discussed further in the Supporting document Section S 7.3.2.
The other factors are the particle size characteristics and permeability of the soil, and the geometry of the embankment and the foundation. In the absence of more definite methods it is proposed that the Schmertmann (2000) method be used to make this assessment as follows:
• Estimate the average seepage gradient (i avf ) through the cohesionless soil layer in the foundation
beneath the central part of the dam (not at the toe where there are likely to be locally higher gradients) for the level for the reservoir stage under consideration.
• From the particle size distribution of the foundation material estimate the uniformity coefficient Cu = D 60 /D 10 .
• Estimate the point seepage gradient required to progress backward erosion using Figure 6.4 from Schmertmann (2000).
• Correct this average gradient for the geometry, horizontal to vertical permeability ratio of the zone subject to backward erosion, and grain size as detailed in the Supporting Information Section C6.6.2.4. This gives (i pmt ) Corrected .
L
H1
Reservoir level Piezometric surface at base of clay layer
Sand
ClayH2
Piezometric surface at base of clay layer
H3 T
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• For Cu> 6.0, also estimate the critical gradient (i cr ) from i cr = ( satγ - wγ ) / wγ . Adopt this gradient if it
is smaller than (i pmt ) Corrected .
Estimate the probability of initiation and progression from Table 7.4. Use i av and (i pmt ) Corrected as inputs. The
table allows for the assumption that for cases where heave is predicted to have occurred initiation has also occurred, so higher probabilities are assigned than for the case where heave has not occurred. For this latter case see Section 7.3.3.
Table 7.4 – Estimation of the probability of initiation and progression of backward erosion in the foundation given heave is predicted (P IH )
Average seepage gradient in the foundation (iavf) Average seepage gradient required
to initiate backward erosion (ipmt)Corrected from
Figure 6.4
0.05
0.1
0.25
0.5
0.75
1.0
2.0
0.05 1.0 1.0 1.0 1.0 1.0 1.0 1.0
0.1 0.5 1.0 1.0 1.0 1.0 1.0 1.0
0.25 0.2 0.5 1.0 1.0 1.0 1.0 1.0
0.5 0.05 0.2 0.5 1.0 1.0 1.0 1.0
0.75 0.01 0.05 0.2 0.5 1.0 1.0 1.0
1.0 0.001 0.01 0.05 0.2 0.5 1.0 1.0
7.3.3 Estimation of the probability of initiation and progression of backward erosion (P INH ) for cases where heave is not predicted.
The testing by Schmertmann (2000) and at Delft and field experience is that soils with uniformity coefficients (Cu) <6 experience initiation and progression of backward erosion at average seepage gradients lower than the critical gradient. They recognise that the critical gradient is experienced at the toe, but their testing did not have a confining layer which is virtually a pre-requisite for heave to occur as required for situations satisfying the requirements of Section 7.3.2. To allow for these situations the following is suggested:
• Estimate the average seepage gradient (i avf ) through the cohesionless soil layer in the foundation
beneath the center of the dam at the level for the reservoir stage under consideration.
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• From the particle size distribution of the foundation material estimate the representative uniformity coefficient Cu = D 60 /D 10 .
• Estimate the point seepage gradient required to initiate and progress backward erosion from Figure 6.4. The maximum point gradient (i pmt ).
• Correct this average gradient for the geometry, horizontal to vertical permeability ratio of the zone subject to backward erosion, and grain size as detailed in the Supporting Information Section C6.6.2.4. This gives (i pmt ) Corrected .where
( )R
pmtzKSLDCorrectedpmt C
iCCCCCCCi αγ=)(
where i pmt = Maximum point seepage gradient needed for complete piping in the flume test based
on the soil coefficient of uniformity Cu (from Figure 6.4)
CD = Correction factor for (D/L)
CL = Correction factor for total pipe length L
CS = Correction factor for grain size
CK = Correction factor, for permeability anisotropy
Cz = Correction factor for high-permeability under layer
Cγ = Correction factor for density
Cα = Adjustment for pipe inclination
CR = Correction factor for dam axis curvature
D = Depth of piping sand layer, in direction perpendicular to α (m)
L = Direct (not meandered) length between ends of a completed pipe path, from downstream to upstream exit, measured along the pipe path (m)
• For Cu> 6.0, also estimate the critical gradient (i cr ) from i cr = ( satγ - wγ ) / wγ . Adopt this gradient if it
is smaller than (i pmt ) Corrected .
• Estimate the probability of initiation from Table 7.5. Use i avf and (i pmt ) Corrected as inputs. The table
allows for application of corrections recommended by Schmertmann (2000) which for many typical
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situations for a dam on a relatively thin layer of erodible soil compared to the dam height indicate gradients significantly higher than those from Figure 6.4 are required to initiate erosion.
Table 7.5 – Estimation of the probability of initiation of backward erosion for cases where heave is not predicted (P INH )
Average seepage gradient in the foundation beneath the center of the dam ( iavf) Point seepage gradient
required to initiate
backward erosion
(ipmt)Corrected from Figure 6.4
0.05
0.1
0.25
0.5
0.75
1.0
2.0
0.05 0.5 0.9 0.95 0.99 0.995 0.999 0.9999
0.1 0.2 0.5 0.9 0.95 0.97 0.99 0.999
0.25 0.01 0.2 0.5 0.9 0.93 0.95 0.99
0.5 0.001 0.05 0.2 0.5 0.7 0.9 0.95
0.75 0.003 0.01 0.05 0.35 0.5 0.7 0.93
1.0 0.0001 0.001 0.01 0.2 0.35 0.5 0.9
7.3.4 Estimation of the total probability of initiation and progression for this reservoir stage
Estimate the probability of initiation and progression of backward erosion (P I ) from the results of the
assessments above. (P I ) = (P cl ) x [(P H ) x (P IH ) + (1-(P H ) x (P INH )].
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7.4 Estimation Of The Probability Of Initiation Of Suffusion In A Cohesionless Layer In The Foundation (IM25)
First Estimate the probability (P cl ) there is a continuous layer of cohesionless soil from upstream of the
embankment, to downstream of the embankment.
Second Use the method outlined in Section 6.6.3 to estimate the probability of suffusion. Multiply this value with the probability there is a continuous layer subject to suffusion in the foundation.
7.5 Estimation Of The Probability Of Initiation Of Erosion In A Crack In Cohesive Soil In The Foundation (IM26)
7.5.1 Overall Approach
First: Estimate the probability (P cl ) there is a layer of soil beneath the embankment in which a continuous
crack or interconnected pattern of cracks may exist. Cracking may be the result of differential settlement in the foundation, or desiccation cracks in the foundation soil which was not stripped from the foundation. The question is best put in terms of the width of the crack. For example “what is the probability of a continuous crack or pattern of cracks 5mm wide”. It may be useful to consider the question for 1mm, 5 mm, and say 10mm wide cracks, as there may be a significantly high likelihood of narrow cracks, and much lower likelihood of wider cracks.
Second: Estimate the probability erosion will initiate in the cracks (P IC ) using Section 5.4.
The probability of initiation = (P cl ) x (P IC ).
7.5.2 Some Factors To Consider In This Assessment And Suggested Method For Estimating The Probability Of A Continuous Crack
(a) For Cracking Due to Differential Settlement
The situations which are likely to result in cracking in the foundation soils are essentially the same as those causing cracking low in the embankment due to differential settlement in the foundation. An example is shown in Figure 5.5 (b). Given this, it is suggested that if in using Section 5.2.3 to assess the probability of cracking in the embankment due to differential settlement in the foundation, the presence of cracking in the
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embankment is likely to be on the foundation/embankment contact, then this probability also be assigned to the probability of cracking in the cohesive soil in the foundation beneath the embankment.
If the assessment of cracking in Section 5.2.3 is for features such as those in Figure 5.5 (a) and (c) which will cause cracking near the crest of the dam, then cracking in the foundation due to differential settlement may be assumed to be negligible.
(b) For Cracking Due to Desiccation
Some factors to consider in assessing the likelihood of continuous or interconnected cracking include:
• Whether the soils in the foundation on which the dam was built are susceptible to desiccation in the climatic conditions at the site. This can be assessed using Section 5.2.5 and Tables 5.11 and 5.12 considering the foundation soil as the “core material”.
• Whether desiccation cracking is evident in the soil surrounding the dam.
• Whether the cracking is likely to persist below the level of the cut-off for the dam. This can be assessed using observed desiccation crack depths for the site, or using Tables 5.24 and 5.25 to estimate the depth and width of cracking, and knowing the depth of the cut-off below the ground surface.
• The continuity is likely to be linked to the width of the cut-off, with wide cut-offs being less likely to have continuous cracking than narrow cut-offs.
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8 Probability of the Presence of Open or In Filled Defects in Rock Foundations
8.1 Overall Approach
The framework considers the geological processes which can lead to the formation of open or in filled defects or solution features in rock. The geological processes considered are:
• Defects related to stress relief effects in valley sides (Section 8.2).
• Defects related to stress relief effects in the valley floor – valley bulge and rebound (Section 8.3).
• Solution features for rock subject to solution such as limestone, dolomite, gypsum and salt (Section 8.4).
• Defects associated with landslides and faults and shear zones.(Section 8.5)
Tables have been produced to evaluate the probabilities for assessing the presence of continuous open or in filled defects and solution features caused by these geological processes.
An outline of the overall approach is summarized in the flow chart shown in Figure 8.1.
The steps to assess the probability such defects and solution features exist in the dam foundation below the core are as follows;
• Assess the probability of one or more continuous in filled or open defects or solution features in the rock in the foundation beneath the core of the embankment for each of the types of geological features.
For each type of geological feature, there are two parts to the assessment; the first is based on the geology and topography of the dam site. This information will be available for all dam sites. The second is based on observations and site investigation data of which there will be greatly varying amounts for different dams. It is anticipated that for some older dams there may be virtually no such data.
The two estimates are combined by a weighted average depending on the detail of the investigation and construction data that is available with greater weighting to the second method where there is good quality data available (Section 8.12).
The relative importance factors are selected taking account of the data which is likely to be available. While continuity of these features is very important it is unlikely there will be good quality information on this for many dams so the weighting given to it is not high for these cases.
• Assess the width of the open or in filled defects or solution features, how far these occur into the foundation, and how their widths vary with depth in the foundation (Section 8.6).
• Assess the probability that the defects are in filled (Section 8.7).
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Figure 8.1 – Flow chart for estimating the probability, width, depth and spatial distribution of continuous open defects and solution features in rock foundations.
Is the defect open or in filled?
Probability of one or more continuous open or in filled defects (stress relief valley sides, valley bulge, solution features, and other geological
feature)
Make estimates based on; • Geologic/topographic factors (stress relief defects); and • Observations and investigation factors.
Probabilities are estimated for three widths at ground surface level 5mm to 25mm, 25mm to 100mm and >100mm) Combine the estimates using a weighted average
For open defects, is grouting ineffective?
For in filled defects, grouting is generally assumed to be ineffective.
Does erosion of the infill initiate?
Does erosion of the infill continue?
Combine the probability estimates for open defects and in filled defects that have eroded
Prepare a summary of the probability of occurrence of open defects and solution features categorized by width, depth and spatial occurrence in the embankment foundation.
Prepare sketches showing the defects in relation to the cut-off foundation beneath the core, general foundation under the shoulders, foundation grouting and cut-off foundation surface treatment.
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• Assess the probability that grouting has not been effective in cutting off the open defects (Section 8.8). For in filled defects, it is assumed that grouting is not effective.
• Assess the probability of cut-off walls not being effective in cutting off open or in filled defects or solution features. (Section 8.9)
• Assess the probability that erosion of the infill will initiate given grouting and cut-off walls are not effective (Section 8.10).
• Assess the probability that erosion of the infill in defects or solution features will continue (Section 8.11).
• Combine the probabilities for open defects and in filled defects which will potentially erode. (Section 8.12)
• Describe the open and in filled defects and solution features, their width, depth, spatial distribution in the foundation, and how these relate to the cut-off and general foundation of the embankment beneath the core. In particular identify features which will be in contact with the core at the base of the cut-off and in the sides of the cut-off trench.
Given the defects or solution features occur below the core of the embankment, identify the potential failure paths, and potential breach modes due to the open defects and solution features. Possible failure paths are;
a) Gross enlargement of the defect – this can release the storage but is usually not capable of breaching the dam unless the feature is large relative to the size of the dam
b) Slope instability of the embankment due to increased pore pressures caused by seepage up into the downstream shell;
c) Unravelling of the embankment due to seepage exiting into the downstream shell;
d) Initiation of internal erosion of the embankment at or into the foundation by backward erosion piping or scour followed by gross enlargement, slope instability, unravelling or sinkhole development in the embankment.
This is the end product of what is covered in this Section.
Then for each potential failure path and breach mechanism, assess:
a) The probability of initiation of erosion of the core into the open defect or scour of the core at the defect-core interface.(Section 9).
b) The probability of progression (Section 11).
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c) The probability of detection, intervention and repair (Section 12).
d) The probability of breach (Section 13).
8.2 Probability of one or more continuous in filled or open defects in the rock in the foundation beneath the embankment (IM27)
8.2.1 Overview of method
This section assesses the probability of an open or in filled defect such as a joint or joint set or bedding surface being continuous in the dam foundation from upstream of the core of the embankment to downstream of the core. It does not consider whether these are cut off by the foundation excavation, grouting or other treatment. That is considered in subsequent steps (Sections 8.8 and 8.9).
The probabilities are estimated for features of 3 different widths, as follows;
• 5mm to 25 mm
• 25mm to 100mm
• >100mm
Open or in filled defects of each width may all be present and each should be considered. These have been determined because of their likely impact on the probability of breach of the embankment. The widths for stress relief features are at the ground surface not accounting for the depth of the cut-off of the embankment. For solution features it is the maximum width which may be at the surface or at depth.
This is done in two ways:
• Based on the geology and topography of the site. This data will be available for all dams.
• Based on observations, drilling, and water pressure tests and grouting during site investigations and construction. There will be varying amounts of this data for each dam.
The weighted average of these estimates is carried forward in the analysis. The weighting relates to the detail of the investigations and construction data available.
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8.2.2 Estimation of the probability of one or more continuous in filled or open defects in the rock foundation beneath the embankment based on geologic and topographic data
The defects are stress relief joints, sheet joints and bedding surface partings.
The major variables affecting the likelihood of these being in the dam foundation, and their relative importance are;
• Geological environment. It is known that inter-bedded weak and strong rocks such as inter-bedded shale and sandstone commonly result in open joints due to differential strains due to stress relief on valley formation, and these strains being concentrated in bedding surface shears in the weaker rock. The other geological environments where stress relief defects are common are massive rocks such as granite. These are commonly called sheet joints.
• Topography. The topography which is likely to lead to stress relief features. This is dependent on the depth of valley and steepness of valley sides.
• Continuity and orientation of mapped defects in the exposure of rock in the abutments. It does not rely on mapping of the dam foundation during investigations and construction.
Use Tables 8.1 to 8.3 to estimate the probability of a continuous in filled or open defect in the rock in the foundation beneath the embankment. Note that in Table 8.3 the probabilities for each size defect are independent of each other because all defect sizes may be present. The probabilities may total > 1.0 because they are not conditional probabilities.
Where the geology of the site is not covered in Table 8.1, the risk analysis team should assess which of the descriptions in Table 8.1 best suits the geology of the site.
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Table 8.1 - Factors influencing the likelihood of a continuous in filled or open defect in the rock in the foundation beneath the embankment
Influence on Likelihood
Factor Relative
Importance of Factor
Less Likely
(1)
Neutral
(2)
More Likely
(3)
Much More Likely
(4)
Geological environment likely to give open or in-fill continuous features
(3) Shale not containing other rocks (sub-horizontal bedded) Uniform sandstone (sub-horizontal bedded)
Schistose, steeply dipping
Granite
Basalt(a) columnar Rhyolite, ignimbrite(a) Schistose parallel to abutment Thinly inter-bedded sedimentary
Sedimentary – inter-bedded thin beds of mud rocks and thick beds of sandstone or limestone/dolomite or conglomerate Volcanics, inter-bedded thin beds of tuff or other soft rocks, with thick beds of hard rocks
Topography of the dam site (Steepness and valley depth)
(2)
LL from Table 8.2 matrix
N from Table 8.2 matrix
ML from Table 8.2 matrix
MML from Table 8.2 matrix
Continuity and orientation of defects from surface mapping of the dam abutments
(1) Discontinuous, oblique to valley
Discontinuous, sub-parallel to valley
Interconnected defects, sub-parallel to valley
Continuous defects, sub-parallel to valley
Notes. (a) Some basalts (e.g. if inter-bedded with weak tuff, and some ignimbrites) may classify as “Much more likely”
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Table 8.2 - Factors influencing likelihood for topography
Average Abutment Slope (degrees) (a) (b) Valley Depth
<20 20-45 45-60 >60
< 30m (<100 ft)
LL LL N ML
30 – 100m (100-300 ft)
LL N ML MML
100 – 300m (300-1000 ft)
LL ML MML MML
>300m (> 1000 ft)
N ML MML MML
Notes (a) Use average overall slope except for slopes with large colluvium deposits overlying the rock surface, in which case use the slope of the rock surface.
(b) For slopes with more than 6m (20 ft) high cliffs, adopt a category not lower than ML.
Table 8.3 - Probability of a continuous in filled or open feature in the rock foundation beneath the embankment versus ∑ (Relative importance factor (RF) x (Likelihood factor
(LF))
Defect width
5-25 mm 0.001 0.005 0.01 0.05 0.5 0.9
25-100 mm 0.0005 0.001 0.005 0.01 0.1 0.5
>100 mm 0.0001 0.0002 0.001 0.005 0.02 0.2
RF x LF 6 9 11 13 18 24
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8.2.3 Estimation of the probability of one or more continuous in filled or open defects in the rock foundation beneath the embankment based on site investigations and construction data
The defects are stress relief joints, sheet joints and bedding surface partings.
Estimate the probability of one or more continuous in filled or open defect from Tables 8.4 and 8.5. Do this for:
• 5mm to 25 mm defects
• 25mm to 100mm defects, and
• >100mm defects
It is expected that there will be different probabilities for each defect size. Note that in Table 8.5 the probabilities for each size defect are independent of each other because all defect sizes may be present. The probabilities may total > 1.0 because they are not conditional probabilities.
8.2.4 Effects Of Blasting On The Foundation
The potential for blasting of the rock foundation for the cut-off or, for example to form a trench into which the diversion conduit is placed, to lead to open defects should be assessed. This can only be assessed on a case by case approach. Construction photographs are the best guide as to whether such features may exist, and their likely continuity and opening.
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Table 8.4 - Factors influencing the likelihood of a continuous in filled or open defects in the rock in the foundation beneath the embankment
Influence on Likelihood Factor
Relative Importance of Factor
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely(4)
Spatial continuity of the open or in the foundation (c)
(3) Data shows no open or in filled defects aligning spatially in upstream-downstream direction
Data shows isolated and/or discontinuous open or in filled defects aligning in upstream-downstream direction, or a tortuous path
Data shows some features or single continuous open or in filled defects partially aligning upstream-downstream direction
Data shows many or a single open or in filled continuous defects spatially aligning upstream – downstream
Site investigation and construction data indicating open or in filled defects of this size are/are not present
(2)
Good quality site investigation and construction data indicates open or in filled defects of this size are very unlikely to be present
Site investigation and construction data indicates circumstantial evidence of open or in filled defects of this size are unlikely to be present
Site investigation and construction data (b) indicates circumstantial evidence open or in filled defects of this size are present
Good quality site investigation and construction data(a) indicates open or in filled defects of this size are present
Geological environment likely to give open or in-fill continuous features
(1) Shale not containing other rocks (sub-horizontal bedded) Uniform sandstone (sub-horizontal bedded)
Schistose, steeply dipping
Granite Basalt(d) Rhyolite, ignimbrite(d) Schistose parallel to abutment Thinly inter-bedded sedimentary
Sedimentary – inter-bedded thin beds of mud rocks and thick beds of sandstone or limestone/dolomite or conglomerate Volcanics, inter-bedded thin beds of tuff or other soft rocks, with thick beds of hard rocks
Notes (a) For example records/photographs from excavations, tunnels, down hole imaging, high water losses in drilling, very high grout takes, drill rods dropping
(b) For example, high water losses in drilling, high leakage rate in dam foundation, very high grout takes, drill rods dropping, low piezometric levels in the abutments.
(c) Data would include the information noted in Notes (a) and (b). Spatial alignment is likely to be able to be related to geologic features such as stress relief joints, shears, etc
(d) Some basalts (e.g. if inter-bedded with weak tuff, and some ignimbrites may classify as “Much more likely”.
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Table 8.5 - Probability of a continuous in filled or open features in rock in the foundation beneath the embankment versus ∑
(Relative importance factor (RF) x (Likelihood factor (LF))
Defect width
5-25 mm 0.001 0.01 0.1 0.2 0.5 0.9
25-100 mm 0.0005 0.001 0.005 0.01 0.1 0.5
>100 mm 0.0001 0.0002 0.001 0.005 0.02 0.2
RF x LF 6 9 11 13 18 24
8.3 Probability of one or more continuous open or in filled valley bulge or rebound features in the rock in the foundation beneath the embankment
8.3.1 Overview of method
This section assesses the probability of an open or in filled valley bulge or rebound feature such as a joint or joint set, thrust fault, or bedding surface being continuous in the foundation from upstream of the core of the embankment to downstream of the core. It does not consider whether these are cut off by the foundation excavation, grouting or other treatment. That is considered later.
The probabilities are estimated for features of 3 different widths. These have been determined because of their likely impact on the probability of breach of the embankment. The widths are at the ground surface not accounting for the depth of the cut-off of the embankment. The widths are:
• 5mm to 25 mm
• 25mm to 100mm
• >100mm
This is done in two ways:
• Based on the geology and topography of the site. This data will be available for all dams.
• Based on observations, drilling, and water pressure tests and grouting during site investigations and construction. There will be varying amounts of this data for each dam.
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The weighted average of these estimates is carried forward in the analysis. The weighting relates to the detail of the investigations and construction data available.
8.3.2 Estimation of the probability of one or more continuous in filled or open valley bulge or rebound features in the rock foundation beneath the embankment based on geologic and topographic data
The major variables and their relative importance are;
• Geological environment. Valley bulge or rebound features only occur in near horizontally bedded rocks sedimentary rocks, and in particular where there are inter-beds of strong rock such as sandstone, with weaker rocks such as shale or claystone on which differential movements due to stress relief are concentrated. For other geological environments assume the probability of valley bulge or rebound defects is negligible.
• Potential for buckling or strut shear. The presence of beds of stronger rock underlain by weaker rock in the valley floor and the slenderness of the strut as characterised by the relative thickness of the strong rock bed compared to the valley width.
• Topography. The topography which is likely to lead to stress relief features. This is dependent on the depth of valley and steepness of valley sides.
These assessments do not rely on mapping of the dam foundation during site investigations and construction.
Use Tables 8.6 and 8.7 to estimate the probability a continuous in filled or open valley bulge or rebound feature in the rock in the foundation beneath the embankment. Note that in Table 8.7 the probabilities for each size defect are independent of each other because all defect sizes may be present. The probabilities may total > 1.0 because they are not conditional probabilities.
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Table 8.6 - Factors influencing the likelihood of a continuous in filled or open valley bulge or rebound feature in the rock in the foundation beneath the embankment
Influence on Likelihood
Factor Relative
Importance of Factor
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Geological environment likely to give valley bulge or rebound features
(3) Shale or siltstone not containing other rocks
Uniform sandstone (a)
Thick beds of siltstone or shale inter-bedded with massive beds of sandstone, limestone, dolomite or conglomerate
Thin beds of siltstone inter-bedded with massive beds of sandstone, limestone, dolomite or conglomerate
Thin beds of claystone or shale inter-bedded with massive beds of sandstone, limestone, dolomite or conglomerate
Potential for buckling or strut failure relating to slenderness of the strut
(2)
(Valley floor width) / (strut thickness) <1
(Valley floor width) / (strut thickness) >2
(Valley floor width) / (strut thickness) >4
(Valley floor width) / (strut thickness) >8
Topography of the dam site (Steepness and valley depth)
(1) LL from Table 8.2 matrix
N from Table 8.2 matrix
ML from Table 8.2 matrix
MML from Table 8.2 matrix
Notes (a) Likelihood of valley bulge feature is negligible in these geological environments.
Table 8.7 - Probability of a continuous in filled or open valley bulge or rebound feature in rock in the foundation beneath the embankment versus ∑ (Relative importance factor (RF)
x (Likelihood factor (LF))
Feature width
5-25 mm 0.001 0.01 0.1 0.2 0.5 0.9
25-100 mm 0.0005 0.001 0.005 0.02 0.2 0.5
>100 mm 0.0001 0.0002 0.001 0.005 0.05 0.2
RF x LF 6 9 11 14 18 24
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8.3.3 Estimation of the probability of one or more continuous in filled valley bulge or rebound feature in the rock foundation beneath the embankment based on site investigations and construction data
Estimate the probability of one or more continuous in filled or open defect from Tables 8.8 and 8.9. Do this for:
• 5mm to 25 mm defects
• 25mm to 100mm defects, and
• >100mm defects
It is expected that there will be different probabilities for each defect size. Note that in Table 8.9 the probabilities for each size defect are independent of each other because all defect sizes may be present. The probabilities may total > 1.0 because they are not conditional probabilities.
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Table 8.8 - Factors influencing the likelihood of a continuous in filled or open valley bulge or rebound feature in the rock in the foundation beneath the embankment
Influence on Likelihood
Factor Relative
Importance of Factor
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Spatial continuity of the valley bulge or rebound features (c)
(3) Data shows no open or in filled features aligning spatially in upstream-downstream direction
Data shows isolated and/or discontinuous open or in filled feature aligning in upstream-downstream direction
Data shows some features or single open or in filled continuous feature partially aligning upstream-downstream direction
Data shows many or a single open or in filled continuous feature spatially aligning upstream – downstream
Site investigation and construction data indicating open or in filled features are/are not present
(2)
Good quality site investigation and construction data indicates open or in filled defects of this size are very unlikely to be present
Site investigation and construction data indicates circumstantial evidence of open or in filled defects of this size are unlikely to be present
Site investigation and construction data (b) indicates circumstantial evidence open or in filled defects of this size are present
Good quality site investigation and construction data(a) indicates open or in filled defects of this size are present
Geological environment in relation to the presence/absence of valley bulge or rebound features
(1) Shale or siltstone not containing other rocks Uniform sandstone (a)
Thick beds of siltstone or shale inter-bedded with massive beds of sandstone, limestone, dolomite or conglomerate
Thin beds of siltstone inter-bedded with massive beds of sandstone, limestone, dolomite or conglomerate
Thin beds of claystone or shale inter-bedded with massive beds of sandstone, limestone, dolomite or conglomerate
Notes (a) For example records/photographs from excavations, tunnels, down hole imaging, high water losses in drilling, very high grout takes, drill rods dropping
(b) For example, high water losses in drilling, high leakage rate in dam foundation, very high grout takes, drill rods dropping, low piezometric levels in the abutments.
(c) Data would include the information noted in Notes (a) and (b). Spatial alignment is likely to be able to be related to geologic features such as stress relief joints, shears, etc.
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Table 8.9 - Probability of a continuous in filled or open valley bulge feature in rock in the foundation beneath the embankment versus ∑ (Relative importance factor (RF) x
(Likelihood factor (LF))
Feature width
5-25 mm 0.001 0.01 0.1 0.2 0.5 0.9
25-100 mm 0.0005 0.001 0.005 0.02 0.2 0.5
>100 mm 0.0001 0.0002 0.001 0.005 0.05 0.2
RF x LF 6 9 11 14 18 24
8.4 Probability of one or more continuous open or in filled solution features in the rock in the foundation beneath the embankment
8.4.1 Overview of method
Screening
This Section applies only to rock foundations subject to solution such as limestone, dolomite, gypsum and salt.
Approach
This section assesses the probability of an open or in filled solution feature in the dam foundation continuous from upstream of the core of the embankment to downstream of the core.
The probabilities are estimated for solution features of 3 different widths as follows:
• 5mm to 100mm
• 100mm to 300mm
• >300mm
These widths have been determined because of their likely impact on the probability of breach of the embankment. The widths are the maximum which may not be at the ground surface. They do not consider whether these are cut off by the foundation excavation, grouting or other treatment. That is considered later.
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The probabilities are estimated in two ways:
• Based on the geology and topography of the site. This data will be available for all dams.
• Based on observations, drilling, and water pressure tests and grouting during site investigations and construction. There will be varying amounts of this data for each dam.
The weighted average of these estimates is carried forward in the analysis. The weighting relates to the detail of the investigations and construction data available.
8.4.2 Estimation of the probability of one or more continuous in filled or solution features in the rock foundation beneath the embankment based on geologic and topographic data
The major variables and their relative importance are;
• Geological environment. The presence or absence in the region and dam site of karst and solution features.
• The topography which is likely to lead to stress relief defects such as joints and bedding partings along which solution is likely to initiate. This is dependent on the depth of valley and steepness of valley sides; and the presence or absence of regional defects such as joints and faults.
• Continuity and orientation of mapped valley stress relief or regional defects in the exposure of rock in the dam abutments.
These assessments do not rely on mapping of the dam foundation during investigations and construction.
Use Tables 8.10 to 8.11 to estimate the probability a continuous in filled or open solution feature in the rock in the foundation beneath the embankment. Note that in Table 8.11 the probabilities for each size defect are independent of each other because all defect sizes may be present. The probabilities may total > 1.0 because they are not conditional probabilities.
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Table 8.10 - Factors influencing the likelihood of a continuous in filled or open solution feature in the rock in the foundation beneath the embankment
Influence on Likelihood
Factor Relative
Importance of Factor
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Geological environment relating to development of solution features
(3) Regional and dam site geology indicates solution features are very unlikely (e.g. caves and sinkholes are absent)
Low leakage in the foundation
Regional and dam site geology indicates solution features are unlikely (e.g. only isolated caves and sinkholes).
Low leakage in the foundation
Regional and dam site geology indicates solution features are likely (e.g. a few caves and sinkholes
Moderate to high leakage in the foundation
Regional and dam site geology and observations in outcrop indicates solution features are very likely (e.g. many caves and sinkholes).
High leakage in the foundation
Presence of stress relief defects based on the topography of dam site And/or Regional Defects
(2) LL from Table 8.2 matrix
Regional defects not evident on good quality air photographs and surface geological mapping
N from Table 8.2 matrix
Regional defects not evident on poor quality air photographs and surface geological mapping
ML from Table 8.2 matrix
Regional defects evident on poor quality air photographs and surface geological mapping
MML from Table 8.2 matrix
Regional defects evident on good quality air photographs and surface geological mapping
Continuity and Orientation of the stress relief and/or regional defects from surface mapping of the dam abutments in which solution features may develop
(1) Discontinuous, oblique to valley
Discontinuous, sub-parallel to valley
Interconnected defects, sub-parallel to valley
Continuous defects, sub-parallel to valley
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Table 8.11 - Probability of a continuous in filled or open solution features in rock in the foundation beneath the embankment versus ∑ (Relative importance factor (RF) x
(Likelihood factor (LF))
Solution feature width or diameter.
5-100mm 0.01 0.05 0.1 0.2 0.5 0.9
100-300 mm 0.005 0.02 0.05 0.1 0.3 0.5
>300 mm 0.001 0.005 0.01 0.02 0.05 0.1
RF x LF 6 9 11 14 18 24
8.4.3 Estimation of the probability of one or more continuous in filled or open solution features in the rock foundation beneath the embankment based on site investigations, construction and monitoring data
Estimate the probability of one or more continuous in filled or open solution features from Tables 8.12 and 8.13. Do this for:
• 5mm to 100 mm solution feature
• 100mm to 300mm solution feature, and
• >300mm solution feature
It is expected that there will be different probabilities for each solution feature size. It is important to consider continuous features, not isolated caves.
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Table 8.12 - Factors influencing the likelihood of a continuous in filled or open solution feature in the rock in the foundation beneath the embankment
Influence on Likelihood
Factor Relative
Importance of Factor
Less Likely
(1)
Neutral
(2)
More Likely
(3)
Much More Likely
(4)
Site investigation, monitoring and construction data indicating open or in filled solution features are/are not present
(3)
Good quality site investigation and construction data indicates open or in filled defects of this size are very unlikely to be present.
High piezometric levels in the abutments. Low leakage in the foundation
Site investigation and construction data indicates circumstantial evidence of open or in filled defects of this size are unlikely to be present.
Moderate piezometric levels in the abutments. Low leakage in the foundation
Site investigation and construction data(b) indicates circumstantial evidence open or in filled defects of this size are present.
Low piezometric levels in the abutments. Moderate to high leakage in the foundation
Good quality site investigation and construction data(a) indicates open or in filled defects of this size are present.
Low piezometric levels in the abutments. High leakage in the foundation
Spatial continuity of solution features (c)
(2) Data shows no open or in filled solution features aligning spatially in upstream-downstream direction
Data shows isolated open or in filled solution features aligning in upstream-downstream direction
Data shows some features or single open or in filled solution features partially aligning upstream-downstream direction
Data shows many or a single open or in filled solution features spatially aligning upstream – downstream
Geological environment relating to development of solution features
(1) Regional and dam site geology indicates solution features are very unlikely (e.g. caves and sinkholes are absent)
Regional and dam site geology indicates solution features are unlikely (e.g. only isolated caves and sinkholes)
Regional and dam site geology indicates solution features are likely (e.g. a few caves and sinkholes)
Regional and dam site geology indicates solution features are very likely (e.g. many caves and sinkholes)
Notes (a) For example records/photographs from excavations, tunnels, down hole imaging, high water losses in drilling, very high grout takes, drill rods dropping
(b) For example, high water losses in drilling, high leakage rate in dam foundation, very high grout takes, drill rods dropping, low piezometric levels in the abutments.
(c) Data would include the information noted in Notes (a) and (b). Spatial alignment is likely to be able to be related to geologic features such as stress relief joints, shears, etc.
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Table 8.13 - Probability of a continuous in filled or open solution features in rock in the foundation beneath the embankment versus ∑ (Relative importance factor (RF) x
(Likelihood factor (LF))
0.001 0.005 0.02 0.1 0.3 0.9
6 9 11 14 18 24 RF x LF
8.5 Probability of one or more continuous open or in filled features associated with other geological features such as landslides, faults and shears
8.5.1 Overview of method
This section assesses the probability of an open or in filled feature associated with geological processes other than stress relief or solution features being present in the foundation of the dam and continuous from upstream of the core to downstream of the core. These include defects related to landslides in rock, such as joints and bedding surface partings, and fault or shear zones. It does not consider whether these are cut off by the foundation excavation, grouting or other treatment. That is considered later.
The probabilities are estimated for features of 3 different widths as follows:
• 5mm to 25mm
• 25mm to 100mm
• >100mm
These have been determined because of their likely impact on the probability of breach of the embankment. The widths are at the ground surface not accounting for the depth of the cut-off of the embankment.
The assessment is based on the evidence that such features are present based on observations, drilling, and water pressure tests and grouting during site investigations and construction.
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8.5.2 Estimation of the probability of one or more continuous in filled or open other geological features in the rock foundation beneath the embankment based on site investigations and construction data
Estimate the probability of one or more continuous in filled or open defect from Tables 8.14 and 8.15. Do this separately for each defect size; 5mm to 25mm features, 25mm to 100mm features, and >100mm features. It is expected that there will be different probabilities for each defect size. It is important to consider continuous features relative to the width of the embankment, and not isolated features.
Table 8.14 - Factors influencing the likelihood of a continuous in filled or open geological feature in the rock in the foundation beneath the embankment
Influence on Likelihood
Factor
Relative Import-ance of Factor
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Site investigations. monitoring and construction data indicating open or in filled geological features are/are not present
(2)
Good quality site investigation and construction data indicates open or in filled defects of this size are very unlikely to be present
Site investigation and construction data indicates circumstantial evidence of open or in filled defects of this size are unlikely to be present
Site investigation and construction data(b) indicates circumstantial evidence open or in filled defects of this size are present
Good quality site investigation, monitoring and construction data(a) indicates open or in filled defects of this size are present
Spatial continuity of the geological features(c)
(2) Data shows no open or in filled defects aligning spatially in upstream-downstream direction
Data shows isolated open or in filled defects aligning in upstream-downstream direction
Data shows some features or single open or in filled defects partially aligning upstream-downstream direction
Data shows many or a single open or in filled defects spatially aligning upstream – downstream
Geological environment relating to development of such features
(2) Regional and dam site geology indicates the geological features are very unlikely
Regional and dam site geology indicates the geological features are unlikely to be present
Regional and dam site geology indicates the geological features are likely to be present
Regional and dam site geology indicates the geological features are known or very likely to be present
Notes (a) For example records/photographs from excavations, tunnels, down hole imaging, high water losses in drilling, very high grout takes, drill rods dropping
(b) For example, high water losses in drilling, high leakage rate in dam foundation, very high grout takes, drill rods dropping, low piezometric levels in the abutments.
(c) Data would include the information noted in Notes (a) and (b). Spatial alignment is likely to be able to be related to geologic features such as stress relief joints, shears, etc.
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Table 8.15 - Probability of a continuous open or in filled features in the rock foundation beneath the embankment versus ∑ (Relative importance factor (RF) x
(Likelihood factor (LF))
0.001 0.005 0.02 0.1 0.3 0.9
6 9 11 14 18 24 RF x LF
8.6 Width and extent of open or in filled defects or solution features in the embankment foundation
This section estimates the extent that the open or in-filled defects or solution features extend into the foundation beneath the embankment and the relation between the width of the defects and features to the distance from the original ground surface at the dam site.
The size of the defects given in the preceding sections are for the widths measured at the original ground surface (i.e. before construction of the dam) or for solution features, the maximum width, which may be below the ground surface. The assessment depends on the type of defect.
The issue of whether the extent of the excavation for the foundation and cut-off trench was sufficient to remove these features from the foundation beneath the core of the dam or whether they exist in the sides of the cut-off trench is covered in Section 8.12.
8.6.1 Extent of occurrence and width of defects associated with stress relief defects in the valley sides
For stress relief defects in valley sides, estimate the width of the open or in filled defects below the original ground surface based the available site investigations data, and construction mapping and grouting records. If there is little or no such data make the assessment based on the assumed geometry of stress relief defects shown in Figure 8.2. This may also be used to supplement the site investigations and construction data. Assume that the defect openings for the jointed rocks in Figures 8.2 (a) and (b) and similar conditions vary linearly with depth and horizontal distance from the ground surface. Assume that the maximum opening is for the first joint from the natural surface.
For massive rocks subject to sheet jointing the sheet joints may be associated with weathering to soil strength to a width of up to 300mm (12 inches) but are seldom open more than 50mm (2 inches).
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(a) Horizontally bedded sedimentary rocks.
Figure 8.2 – Assumed distribution of defect depths for defects related to stress relief effects in the valley sides – (a) for interbedded sedimentary rock.
(Figures from Fell et al 2004).
Stress relief joints open for 3 or 4 joints or for a width of up to 30% of valley depth whichever is larger
Stress relief joints open for 3 or 4 joints or for a width of up to 30% of valley depth whichever is larger
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(b) Uniform jointed rock such as thinly bedded sandstone, jointed granites and basalt (see supporting document for explanation of numbers).
(c) Massive rocks such as some granite.
Figure 8.2 – Assumed distribution of defect depths for defects related to stress relief effects in the valley sides – (b) Jointed rocks such as thinly bedded sandstones, granite or basalt,
and (c) for massive rocks (e.g. some granite). Figures from Fell et al 2004).
Stress relief joints to a distance normal to the ground surface of up to 30% of the valley depth.
Stress relief joints (sheet joints) to a distance normal to the slope of up to 30% of the valley depth
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8.6.2 Width and extent of features associated with stress relief effects in the valley floor – valley bulge or rebound
For stress relief effects associated with valley bulge or rebound, the extent and depth to which the features may occur should be assessed based on the available information from construction and investigations.
The assessment of the size of the defects is considered in the assessment of probability of open or in-filled defects (Section 8.3).
In the absence of other information it should be assumed these features exist to below the level of the strut (massive stronger bed). It should be noted that these features are known to have occurred to depths of up to 15 meters (50ft) below the valley floor.
8.6.3 Width and extent of solution features
For solution defects, the assessment of the size of the defects is already considered in the assessment of probability of open or in-filled defects. The depth and spatial distribution of solution features should be assessed based on the following factors;
• How the solution features were formed – stress relief effects or regional effects and the extent these can be expected to occur .
• The geological history of the valley, particularly in relation to the historical groundwater levels which may have been lower in the geological history of the valley.
• Observational data – observations from boreholes including in-filled features, voids, water losses and water pressure testing and grouting records.
It is not practical to develop any general rules for these assessments, except to say that for solution on stress relief defects, the information given in Section 8.6.2 can be used as a guide.
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8.7 Likelihood of Defects or Solution Features being in filled
Given there are defects below the level of the core it is necessary to assess the probability these are open or in filled. Table 8.16 should be used to assist in making this assessment.
Table 8.16 – Probability of Defects or Solution Features being open or in filled
Probability Scenarios
Open In Filled
Very small leakage in dam foundations, coring or down-hole imaging shows in fill, mapping of foundations during construction shows infill; water pressure testing shows scour of infill.
0.01 to 0.1 0.99 to 0.9
Moderate leakage in dam foundations but no identifiable single or few sources, coring or down-hole imaging, mapping of foundations during construction shows a mix of in filled and open defects and solution features; water pressure testing shows scour of in fill.
0.05 to 0.5 0.95 to 0.5
Localised large leakage in dam foundations, coring or down-hole imaging, mapping of foundations during construction shows a mix of in filled and open defects and solution features.
0.5 to 0.9 0.5 to 0.1
Large leakage in dam foundations, coring or down-hole imaging, mapping of foundations during construction shows open defects or solution features; complete loss of drill water in boreholes.
0.95 to 1.0 0.05 to 0
8.8 Likelihood of Grouting Not Being Effective in cutting off open or in filled defects or solution or other features
Evaluate the likelihood of grouting not being effective in cutting off the potential open or in filled defect or solution features is as follows;
• For open defects, assess the likelihood of grouting not being effective using Tables 8.17 and 8.18. Note that there are three probability scales on Table 8.18; the upper scale is for defects 5mm to 25 mm, the middle scale for 25 mm to 100 mm, and the lower scale is for defects >100 mm.
• For in filled defects, grouting is assumed to be ineffective and assign a probability for grouting not being effective = 1.0.
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Table 8.17 - Factors influencing the likelihood of grouting not being effective for continuous open defects and solution features
Influence on Likelihood
Factor Relative
Importance of Factor
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4) Orientation of grout holes compared with the open defects(1)
(3) (c)
Grout holes at a wide angle to the dip of the open defect (45 to 90 degrees)
Grout holes at an acute angle to dip of open defects (30 to 45 degrees)
Grout holes at an acute angle to dip of open defects (10 to 30 degrees)
Grout holes parallel or near parallel to dip of open defects (<10 degrees)
Quality of grouting (,closure, number of lines, spacing, grout takes, w/c ratio)
(2)
Three or more lines of grout curtain, with primary holes 6m (20ft) or less spacing, secondary, tertiary etc holes to close to < 10 lugeons or <25 kg cement /meter (15lb/ft) take, W/C ratio < 3
Single line grout curtain with primary holes 6m (20ft) or less spacing, secondary, tertiary etc holes to close to < 10 lugeons or <25 kg cement /meter (15lb/ft) take, W/C ratio < 3
Single line curtain 5m to 6m (15 ft to 20 ft) spacing, no check of closure, high (>5:1 ) W/C ratio
Single line curtain, > 10m (30ft) spacing, single stage, no secondary holes to check closure, high (>10:1 ) W/C ratio
Performance (pore pressures and leakage) (b)
(1) (c)
Significant reduction in foundation pore pressures across the grout curtain (Δhp/hp >60%) Very low leakage in the foundation(c)
Moderate reduction in pore pressures across grout curtain (Δhp/hp = 30% to 60%). Low leakage in the foundation
Minor reduction in pore pressures across grout curtain (Δhp/hp = 10% to 30%). Moderate to high leakage in the foundation
No or very little reduction in pore pressures across grout curtain (Δhp/hp <10%). High leakage in the foundation OR No performance data available at all
Notes (a) The dip of the open defect will depend on the type of defect;
• For stress relief defects in the valley wall in inter-bedded sedimentary rock, these defects are likely to be near vertical and parallel to the valley walls (refer to Figure 8.2a). For stress relief defects associated with massive rocks, these are likely to be parallel to the valley slopes (refer to Figure 8.2b).
• Defects associated with valley bulge are likely to be horizontal or near horizontal. • Solution features are more likely to develop along the predominant defects sets.
(b) Refer to Figure 8.3 for definition of Δhp and hp. When making this assessment takes account of the amount and quality of the instrumentation, the duration and range of reservoir levels of the observations. I
(c) If there is very good instrumentation which can measure the effectiveness of the grouting to a high degree of confidence, and there is a large drop in pore pressure across the grouting, the weighting for Performance may be taken as (3), and the weighting of Orientation taken as (1)
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Figure 8.3 – Definition of Δhp and hp.
Table 8.18 - Probability of grouting not being effective for continuous open defects or solution features versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF))
5-25mm 0.001 0.01 0.05 0.2 0.5 0.9
25-100mm 0.002 0.02 0.1 0.3 0.6 0.95
>100mm 0.005 0.05 0.2 0.5 0.8 0.99
RF x LF 6 9 11 13 18 24
8.9 Likelihood of Cut-off Walls Not Being Effective in cutting off open or in filled defects or solution or other features
Where a cut-off has been excavated and backfilled in the rock foundation to intercept the continuous open defect or solution feature, use Tables 8.19 and 8.20 to assess the probability the cut-off has not been successful and a continuous open defect or solution feature remains. In assigning the weightings it is assumed that for such cut-offs there will be good quality monitoring of the pore pressure drop across the cut-off.
hp Δhp
Piezometer Rock Foundation
Grout curtain
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Table 8.19 - Factors influencing the likelihood of a cut-off in the foundation not being effective for continuous open defects and solution features
Influence on Likelihood
Factor Relative
Importance of Factor
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Width and depth of the cut-off relative to the defects and solution features
(3) Width and depth of the defects and solution features well defined and cut-off extends sufficiently wide and deep
Width and depth of the defects and solution features not well defined cut-off may or may not extend sufficiently wide and deep
Width and depth of the defects and solution features not well defined and cut-off probably does not extend sufficiently wide and deep
Width and depth of the defects and solution features well defined and cut-off does not extend sufficiently wide and deep
Performance (pore pressures and leakage) (1)
(2) Significant reduction in foundation pore pressures across the cut-off wall (Δhp/hp >60%)
Very low leakage in the foundation
Moderate reduction in pore pressures across cut-off wall (Δhp/hp = 30% to 60%).
Low leakage in the foundation
Minor reduction in pore pressures across cut-off wall (Δhp/hp = 10% to 30%).
Moderate to high leakage in the foundation
No or very little reduction in pore pressures across cut-off wall (Δhp/hp <10%).
High leakage in the foundation
OR
No performance data
Quality of the cut-off
(1) Excavated open hole or under water, borehole camera inspection to confirm defects are intercepted,
And
Concrete, or bentonite, cement, sand gravel backfill
Excavated under bentonite, good clean-up of the base of the excavation, and overlap between panels or piers,
and/or
Concrete, or bentonite, cement, sand gravel backfill
Excavated under bentonite, moderate clean-up of the base of the excavation, and overlap between panels or piers,
and/or
Bentonite cement or poorly controlled concrete or cement, sand gravel backfill
Excavated under bentonite, poor clean-up of the base of the excavation, poor overlap between panels or piers,
and/or
Bentonite cement or soil bentonite backfill
Notes (1) Refer to Figure 8.3 for definition of Δhp and hp. When making this assessment taking into account of the amount and quality of the instrumentation, the duration and range of reservoir levels of the observations.
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Table 8.20 - Probability of a cut-off not being effective for continuous open defects or solution features versus ∑ (Relative importance factor (RF) x (Likelihood factor (LF))
0.001 0.005 0.02 0.1 0.5 0.9
6 9 11 14 18 24 RF x LF
8.10 Probability that erosion of infill in the defects or solution feature initiates
8.10.1 Overview of Method
This section considers the likelihood of erosion of the infill initiating due to seepage flow. An in-filled feature can be eroded by seepage flows through gaps within or along the sides of the infill material or due to seepage through adjoining open defects causing scour of the infill material. Figure 8.4 shows these potential mechanisms. Gaps in the infill material may form by collapse settlement of infill material upon saturation, incomplete filling of the defect, or hydraulic fracture through the infill.
Figure 8.4 – Potential mechanisms for erosion of infill within a defect or solution feature.
SOLUTION FEATURE
FLOW ALONG A CRACK OR GAP CAUSED BY COLLAPSE ON SATURATION
SCOUR DUE TO FLOW THROUGH AN ADJOINING OPEN JOINT
FLOW THROUGH A GAP ON THE SIDE OF THE INFILL
INFILL
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The assessment is based on two approaches:
• Based on performance, in terms of any evidence of changes in seepage and piezometric levels with time which would be indicative of erosion of in filled defects.
• Based on first principles, taking into account the opening width of the gap/crack in the infill, gradient and nature of the infill material.
The weighted average of the two estimates is then made using weightings judged by the risk analysis team based on the quality of the input data.
8.10.2 Estimation of the probability of erosion of in fill initiating based on performance data
Use Table 8.21 to estimate the probability of erosion initiating based on performance data.
Table 8.21 Probability of erosion initiating based on performance data
Scenario Probability for Erosion Initiates
Long term seepage and piezometric levels show no irregularities such as sudden increases or reductions in pressure or flow; For reservoir levels up to the Pool of Record – For reservoir levels above the Pool of Record –
0.005 to 0.1 depending on the
frequency and quality of seepage and piezometer data
Use first principles approach (Section
5.4) Long term seepage is irregular or showing long term upward trend. Piezometric levels showing irregular behaviour or long term changes (up or down)
1.0
No data on seepage or piezometric levels and seepage at toe is hidden (e.g. drowned, deep alluvium)
1.0
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8.10.3 Estimation of the probability of erosion of infill initiating using first principles
The method is as follows;
• Estimate the width of the gap or crack adjacent to the infill material wgap. Consider information from observations in excavations and other exposures (e.g. tunnels or adits). If no information is available then assume the gap width wgap is 5 mm. This allows for the potential for on-going opening of stress relief defects due to dam construction activities, tree roots, saturating of the infill causing settlement and leaving a gap.
• Estimate the average hydraulic gradient along the in filled defect. This is equal to the difference in elevation of the reservoir and the natural ground elevation at the downstream toe (or at the location of the exit point of seepage) divided by the seepage path length along the defect from the upstream toe to the downstream toe.
• Assess the soil classification of the infill material.
• Use Tables 5.29 to 5.35 to estimate the likelihood of erosion initiating, using the gap width wgap for the crack width values in the tables.
8.11 Probability that erosion of infill continues
8.11.1 Approach
The probability of erosion of infill continuing is estimated by:
i. Assessing the probability that the exit point of seepage through the open or in-filled defect is filtered or unfiltered.
ii. If the exit is unfiltered then the probability of erosion continuing will be 1.0.
iii. If the exit is filtered, then estimate the probability of erosion continuing using Section 10.1.4, considering the defect infill as the base soil.
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8.11.2 Probability of Filtered or Unfiltered Exit
The likelihood that the exit will be filtered or unfiltered will depend on the embankment zoning and the details of the foundation geology and the geometry of the in filled defect or solution feature. The steps are as follows;
• Estimate the probability that there will an unfiltered exit (Punf) using Table 10.13 to aid judgment. The conditional probability of continuation for this scenario is equal to (Punf) x 1.0.
• Calculate the probability that there will be a filtered exit (Pfe) = 1- Punf.. Assess the filter materials and materials being eroded in terms of the Continuing Erosion criteria as described using the procedure in Section 10.1.4.
• The probability of continuing erosion = (Punf x 1.0) + (Pfe x PCE).
Note that in situations where a foundation filter drain or toe drain system is present, there is still the possibility that seepage paths could bypass the filter drain system due to the geological conditions, compaction of soil foundations below foundation filters, or deteriorated toe drain systems. Examples of these scenarios are included in Table 10.13 and Figures 10.5, 10.6 and 10.7.
8.12 Combining probabilities for a continuous open defect in rock and describing the defects and solution features
8.12.1 Calculating weighted averages of estimates
In Sections 8.2 to 8.4 two estimates are made of the probability of the presence of open or in filled defects or solution features. The first is based on topographic and geologic information (P TG ) which should be available
for all dam sites. The second (P SC ) depends on having more detailed site investigations and construction
records, which for some dams will be not available, or there will be limited data.
The weighted estimate of the probability (P W ) should be estimated using:
P W = w P TG + (1-w) P SC
Where w = weighting factor to be assessed based on the quantity and quality of the available data. Table 8.22 provides some guidance in assessing the weighting factor.
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Table 8.22 - Weighting factors for assessing probabilities of open or in filled defects and solution features
Information Available Weighting Factor (w)
No site investigations or construction mapping or other records 1.0
Limited site investigations data (e.g. small number of boreholes, no or poor quality water pressure testing data, no mapping of the embankment cut-off foundation or grouting records, no foundation treatment information or photographs of foundations)
0.7 to 0.9
Some site investigations data (e.g. small number of boreholes or larger number but poor quality boreholes, Sparse or poor quality water pressure testing data, no mapping of the embankment cut-off foundation or grouting records, no foundation treatment information or photographs of foundations)
0.6 to 0.8
Some good quality site investigations data and water pressure testing, limited mapping of the embankment cut-off foundation, basic grouting records, no records of foundation treatment some photographs of foundations
0.4 to 0.6
Extensive good quality site investigations data and water pressure testing, reasonable quality mapping of the embankment cut-off foundation, and grouting records, some records of foundation treatment and photographs of foundations
0.2 to 0.4
Very detailed and good quality site investigations data, good quality mapping of the embankment cut-off foundation, grouting records, foundation treatment and photographs of foundations
0.1 to 0.2
8.12.2 Summing probabilities
A continuous open defect in the rock foundation could already be present or could be formed by erosion of an in filled defect.
Compute the probability of a continuous open defect in rock foundation below the embankment using the event tree shown in Figure 8.5. This is to be done for each defect or solution feature width using the weighted probabilities from Section 8.12.1 where weighting is applied.
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50.0% Open featureof X mm width
50.0% Is grouting ineffective?
50.0%
10.0% Is feature open or infilled?
Estimated width below cutoff trench X mm 50.0% Open featureof X mm width
50.0% Does erosion continue?
50.0%
50.0% Does erosion initiate?
50.0%
50.0% Is grouting ineffective?
50.0%
Continuous open or infilled feature present?
1.0% repeat tree
50.0%
Abutment stress relief features
>100mm
5-25mm
25-100mm
Open
Infilled
Yes
No
Yes
No
Yes
No
Yes
No
Figure 8.5 – Computation of probability of a continuous open defect or solution feature below the embankment.
8.13 Describing the defects and solution features and failure modes
8.13.1 Describing the defects and solution features in relation to the embankment details
It is essential that the risk analysis team document with sketch diagrams (plans and sections) of the spatial distribution of the open and in filled defects and solution features which have been assessed potentially present in the foundation. This should show the features superimposed on the foundation drawings and showing the cut-off and general foundations beneath the core of the embankment so the relationship between the defects and solution features and the base of the cut-off trench, and sides of the cut-off trench is clear. The extension of the defects and solution features upstream and downstream of the core, including under the shoulders of the embankment, and beyond the embankment should also be shown.
Any foundation grouting, surface treatment of the cut-off foundation, and cut-off walls (if constructed) should also be shown.
These are required so that the potential failure modes can be clearly visualised for the assessment of progression, detection, intervention and repair, and breach probabilities.
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8.13.2 Describing the failure paths
The potential failure paths due to internal erosion in rock foundations are;
i) Gross enlargement of the defect.
ii) Slope instability due to increased pore pressures caused by seepage from the defect or solution feature up into the downstream shell.
iii) Unravelling due to seepage exiting from the defect or solution feature into the downstream shell;
iv) Sinkhole development.
v) Initiation of internal erosion of the embankment at or into the foundation by backward erosion piping or scour followed by gross enlargement, slope instability, unravelling or sinkhole development in the embankment.
The potential failure paths arising from the defects and solution features should be assessed and sketches prepared to show them so the risk analysis team have a clear picture of the failure paths and their relation to the defects and solution features.
It should be expected that there will be more than one failure path. For example it is likely the potential stress relief defects may occur in one or both abutments, but not to the river section of the foundation. Valley bulge features are likely to be in the river section of the foundation.
SECTION 9 Probability of Initiation of Erosion from Embankment into Foundation
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9 Probability of Initiation of Erosion from Embankment into Foundation
9.1 General Principles
For erosion to initiate from the embankment into the foundation, requires open joints in rock or coarse soils in the base or sides of the cut off trench. For cases where a cut off trench is not present, then the issue is whether erosion can occur along the core-foundation contact.
Internal erosion may initiate by:
• Backward erosion or suffusion in a high permeability zone in the core or cut-off trench.
• Scour of the core at the core – foundation contact by water flowing in joints in the rock foundation.
• Erosion in a crack or hydraulic fracture across the cut off trench.
9.2 Overall Approach
The method to assess the probability of initiation of erosion into these features is:
(a) Assess from the available data the probability of a continuous pathway of open joints in rock or coarse grained soils (Ppath) in the base or sides of the core trench or core-foundation contact. In many cases it will become apparent at this stage that there is little or no likelihood of such features being present and the probability of piping into the foundation may be assessed as negligible. Refer to Section 9.3 for guidance on estimating the probability.
(b) Assess the probability of the initiation of internal erosion by backward erosion or suffusion (Pe) starting at the core-foundation contact given there is a continuous path. Refer to Section 9.5 for guidance on estimating the probabilities.
(c) Assess the probability of initiation of scour. Refer to Section 9.6 for guidance on estimating the probabilities.
(d) Assess the probability of erosion of the core following hydraulic fracture due to arching in a narrow core trench. Refer to Section 9.7 for guidance on estimating the probabilities.
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9.3 Probability of a continuous pathway for erosion of the core of the embankment into a rock foundation (Ppath) IM28
9.3.1 Probability of a continuous pathway of open defects and solution features in the rock foundation (PCR)
This should be assessed from the geology of the foundation, mapping and, photographs taken during construction, grouting records, the depth of general foundation and cut off excavation, treatment carried out on the walls and floor of the cut off trench (e.g. shotcrete, slush concrete, dental concrete). In many cases it will become apparent at this stage that there is little or no likelihood of such features being present and the probability of internal erosion into the foundation may be assessed as negligible.
The probability of continuous pathways should be assessed by:
• For defects and solution features wider than 5mm, use Section 8 to assess the probability of such defects and features, whether they persist to below the base of the cut-off trench beneath the core, and into the sides of the cut-off trench. This assessment will also determine the spatial distribution of such defects and features.
• This will result in a set of probabilities for the different width features, e.g. 5mm to 25mm, 25mm to 100mm, (PCR) 255− , (PCR) 10025− etc.
• For defects such as joints <5mm wide, it should be assumed that they are present (PCR = 1.0) unless there is very detailed mapping, photography, and written record to demonstrate with high confidence they are not present. It may be demonstrated that the maximum width defect left in the cut-off foundation was, for example, <2mm, while wider features may occur in the sides of the cut-off trench.
9.3.2 Likelihood treatment of the embankment cut-off foundation does not prevent contact of the core with open defects or solution or other features (PTI)
Use Table 9.1 to assess the probability the foundation treatment fails to prevent contact of the core with open defects or solution features. Do this for each defect width, for the base and the sides of the cut-off trench, and for the various parts of the foundation, e.g. each abutment and the river section.
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Table 9.1 - Probability of treatment of the cutoff foundation not preventing contact of the core with open defects or solution features
Scenarios Probability of the treatment not preventing contact
Well document evidence that there was no treatment of the cut-off foundation 1.0
No construction records available, the design and construction organisation not known or known but likely to have not paid much attention to inspecting foundations and carrying out surface treatment
0.3 to 0.9
No construction records available, but knowledge that the practice of the design and construction authority was to inspect foundations and carry out surface treatment
0.1 to 0.5
Evidence that the foundations were mapped, but not in detail. Some evidence that open and in-filled defects and solution features were covered with concrete or shotcrete.
0.05 to 0.2
Well documented evidence that the foundations were carefully mapped, and all open and in-filled defects and solution features were covered with at least 100mm (4 inches) of concrete or good quality shotcrete, or that they were cleaned out to at least 3 times the surface width and treated with slush grout.
0.01 to 0.001
9.3.3 Probability of a continuous pathway for erosion of the core into a rock foundation (Ppath)
Using the results from Sections 9.3.1 and 9.3.2, estimate the probability of a continuous pathway for erosion of the core into open defects and solution features from:
Ppath = (PCR)x (PTI)
Do this for each width of defect and feature as the likelihood of erosion initiating is related to the defect width.
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9.4 Probability of a continuous pathway of coarse grained layers in soil foundations (IM29)
This should be assessed from the geology of the foundation, mapping and, photographs taken during construction, the depth of general foundation and cut off excavation, and whether there are filters between the core and trench side. In many cases it will become apparent at this stage that there is little or no likelihood of such features being present and the probability of internal erosion into the foundation may be assessed as negligible.
Guidance on estimating the probability is given for a range of scenarios for soil foundations in Table 9.2.
Table 9.2 – Probability of a continuous pathway for erosion into soil foundation (IM29)
Scenarios Examples Range of Probabilities for Continuous Pathway of Coarse Grained Soils
Adequate treatment of soil foundation contact
Filter protection provided on downstream side of cut-off trench
Negligible
Assume probability = 0
Site investigations indicate continuous coarse grained foundation soil layers are very unlikely to be present
No evidence of openwork gravel layers Negligible
Assume probability = 0
Site investigation data is not available, but circumstantial evidence indicates coarse grained foundation soils are unlikely to be present.
Circumstantial evidence might include;
Observations of cuts in foundation soil;
Geological environments where coarse grained soils are unlikely to be present (e.g. residual soils, aeolian, lacustrine, volcanic ash).
0.0001 to 0.001
Depending on the quality of the available data. In some cases
negligible.
Site investigation data is not available, but circumstantial evidence indicates coarse grained foundation soils maybe present.
Circumstantial evidence might include;
Observations of cuts in foundation soil;
Geological environments where coarse grained soils maybe present (e.g. alluvium, colluvium, glacial, lateritic profiles).
0.001 – 0.01
Depending on level of confidence in assessment and degree of continuity of features
Site investigation or construction data indicates coarse grained foundation soils are likely to be in contact with the core, no or inadequate treatment
Evidence from drill holes, excavation logs, construction photographs
0.05 – 0.5
Depending on extent and degree of continuity of soils
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9.5 Probability of the initiation of internal erosion by backward erosion or suffusion starting at the core-foundation contact.
This considers the likelihood of initiation of internal erosion by backward erosion or suffusion due to seepage through the core exiting into an unprotected continuous pathway in a rock or soil foundation.
The steps in the assessment are as follows;
• Estimate the probability of a continuous pathway for erosion into the foundation (Ppath) from Sections 9.3 and 9.4.
• Estimate the probability of backward erosion or suffusion initiating at the core-foundation contact (Pe) using the methods described in Section 6.6.
• The probability of internal erosion by backward erosion or suffusion = Ppath x Pe.
• Do this for each of the potential defect openings and soil particle sizes and take these estimates forward into the assessment of continuation, progression, detection, intervention and repair, and breach.
If the embankment is well instrumented, the seepage gradients will be the gradients determined from piezometers upstream and downstream of the cutoff trench and/or from the flow net derived from piezometers in the embankment and foundation. Otherwise the gradients should be estimated using flow nets modeling the embankment and foundation, or from simplified calculations of the likely gradient across the core. For cases where there are defects of varying widths the head loss will occur mainly in the narrow defects as discussed in Section 9.6.2. This should be accounted for when estimating the seepage gradients through the core.
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9.6 Probability of initiation of scour at the core-foundation contact
9.6.1 The Steps to be followed
This considers the likelihood that seepage flows within a continuous pathway in a rock or soil foundation may initiate erosion of the core material at the core-foundation contact.
The steps in the assessment are as follows;
• Estimate the probability of a continuous pathway for erosion at the core-foundation contact (Ppath) from Sections 9.3 and 9.4.
• Estimate the probability of erosion of the core material at the core-foundation contact (Pic) using the method for erosion in a crack in the core as described in Section 5.4. The hydraulic gradient used in the assessment should be based on the estimated seepage gradient on the core-foundation contact. Guidance is given in Section 9.6.2. Assume that the hydraulic shear stresses imposed on the core by the water flowing in the open joints is equivalent to those for an equivalent crack width.
• The probability of internal erosion by scour = Ppath x Pic.
• Do this for each of the potential defect openings and soil particle sizes and take these estimates forward into the assessment of continuation, progression, detection, intervention and repair, and breach.
9.6.2 How to model scour into defects of varying width and persistence
Section 8 is modeled around assessing the probability of defects being present in the foundation which are continuous from upstream to downstream of the core, and are a constant width. There may be foundations where the information available from construction and site investigations indicates that there will be continuous open defects in the foundation but they are of varying width. Figure 9.1 shows some examples of this.
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Figure 9.1 – Examples of foundations with continuous open defects of varying width
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The following equations can be used to estimate the hydraulic shear stress on the surface of a cylindrical pipe, or parallel sided transverse crack.
The assumptions are:
• Linear head loss from upstream to downstream
• Steady uniform flow along the crack
• Zero pressure head at the downstream end
• Uniform frictional resistance along the surface of the crack or cylindrical pipe
• Driving force = frictional resistance.
(a) Cylindrical pipe:
L
gH fw 4
φρτ =
where τ = Hydraulic shear stress in N/m2
wρ = Density of water in kg/m3
g = Acceleration due to gravity = 9.8m/s2
fH = Head loss in pipe due to friction in meters
L = Length of pipe in meters
φ = Diameter of the pipe in meters
(b) Vertical transverse crack
LWH
WgH
f
fw
)(2
2
+=
ρτ
where τ = Hydraulic shear stress in N/m2
wρ = Density of water in kg/m3
g = Acceleration due to gravity = 9.8m/s2
fH = Head loss in crack due to friction in meters
L = Length of crack base in meters
W = Width of crack in meters.
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Hence for narrow cracks and cylindrical pipes the hydraulic shear stress τ ∝ ( fH /L, and W or d)
The gradient in a cylindrical pipe is given by
g
VfL
H f
24 2
φ= (i.e. Darcy-Weisbach equation)
4
2πφVq =
μφρ VR w
e =
where f is the friction loss factor for pipe flow.
φ is the diameter of the pipe.
V is the mean velocity of flow along the pipe.
Q is the rate of discharge.
eR is the Reynold’s number.
μ is the coefficient of dynamic viscosity of water (10-3 kg/ms at 20oC).
From these equations it can be seen that the hydraulic gradient ∝ (1/ 3φ ) whereas the imposed hydraulic
shear stress ∝ φ , so the gradient is most affected by the defect width or diameter. Hence in the situations shown in Figure 9.1 erosion will initiate in the narrow defects where gradients are high in preference to the wider sections of defect. Within the accuracy of the calculations, it is sufficient to assume that all the head loss occurs in the narrow defects.
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9.7 Probability of erosion of the core following hydraulic fracture due to arching in a narrow cut-off trench
The steps in the assessment are as follows;
• Estimate the probability of a continuous pathway for erosion at the core-foundation contact (Ppath) from Sections 9.3 and 9.4. The hydraulic fracture in the cut-off trench needs to coincide with an open joint or coarse grained soil layer to find an unfiltered exit and hence the assessed probability should consider the likelihood of this coincidence.
• Estimate the probability of a hydraulic fracture occurring across the cut-off trench (Phf) using Table 9.3 and Table 9.4.
• Estimate the probability of erosion through the hydraulic fracture across the cutoff trench (Pic) using the method for erosion in a crack in the core as described in Section 5.4. The hydraulic gradient used in the assessment should be based on the estimated seepage gradient across the cut-off trench. Assume that the hydraulic fracture is 5 mm wide.
• Probability of internal erosion by hydraulic fracture across the cutoff trench = Ppath x Phf x Pic.
• Do this for each of the potential defect openings and soil particle sizes and take these estimates forward into the assessment of continuation, progression, detection, intervention and repair, and breach.
Figure 9.2 - Definition of terms for arching across a cut-off trench.
W
β D
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Table 9.3 - Factors influencing the likelihood of hydraulic fracturing within the cutoff trench due to arching
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Slope of side slopes of cutoff trench (a)
(3)
Moderate slope
β ≤ 45o
Note. If this condition is present, probability is negligible
Moderate steep slope
45o < β < 60o
Steep slope
60o ≤ β < 75o
Very steep slope
β ≥ 75o
Geometry of cutoff trench(1)
(2)
Wide trench W/D > 0.75
0.4< W/D<0.75
Narrow deep trench 0.25< W/D< 0.4
Very narrow deep trench W/D < 0.25
Depth of cutoff trench
(1) < 6 ft (2m) deep
6 ft to 13 ft (2 m to 4 m)
13 ft to 20 ft (4 m to 6 m)
> 20 ft (6 m)
Note: (a) See Figure 9.2 for definitions of W, D, and β.
Table 9.4 - Probability of hydraulic fracturing in cut off trench due to arching versus ∑ (Relative importance factor (RF)) x (Likelihood factor(LF))
negligible negligible 0.00005 0.0001 0.0005 0.005 0.01 Below POR
negligible negligible 0.0005 0.001 0.005 0.05 0.1 Above POR
6 9 10 13 17 21 24 RF x LF
Note: “POR” refers to the Pool of Record level + 1 foot
SECTION 10 Probability of Continuation
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10 Probability of Continuation
10.1 Probability of Continuation for Internal Erosion in the Embankment
10.1.1 Internal Erosion Through the Embankment – Overall Approach
Step 1: Assess which of the following five scenarios is most applicable to the dam section and failure path that is under consideration:
• Scenario 1: Homogeneous zoning with no fully intercepting filter.
• Scenario 2: Downstream shoulder of fine grained cohesive material which is capable of holding a crack/pipe. Soils which are capable of holding a crack or pipe are:
– well compacted shoulder (shell), containing > 5% plastic fines; or
– poorly compacted shoulder (shell), containing >15% plastic fines
– well compacted shoulder, containing > 30% non plastic fines
– poorly compacted shoulder, >30% non plastic
• Scenario 3: Filter/transition zone is present downstream of the core or a downstream shoulder zone which is not capable of holding a crack/pipe. This includes earthfill dams with a chimney filter.
• Scenario 4: Erosion into a crack or open joint (e.g. open joint or crack in a conduit or adjoining concrete structure).
• Scenario 5: Erosion into a toe drain.
The example sketches shown in the navigation table (Table A7 in Appendix A) can be used to help evaluate the most applicable scenario.
Step 2: For Scenarios 1 and 2, estimate the probability for Continuing Erosion based on the guidance given in the applicable section (Sections 10.1.2 or 10.1.3).
For Scenario 3, a four way split for filtering behaviour is recommended in the event trees:
• Seals with No Erosion – the filtering material stops erosion with no or very little erosion of the material it is protecting. The increase in leakage flows is so small that it is unlikely to be detectable. The No Erosion branch on the event tree is a “No Breach” branch.
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• Seals with Some Erosion – the filtering materials initially allow erosion from the soil it is protecting, but it eventually seals up and stops erosion. Leakage flows due to piping can be up to 3 cfs (100 l/s), but are self healing.
• Seals with Excessive Erosion – the filter material allows erosion from the material it is protecting, and in the process permits large increases in leakage flow (up to 35 cfs), but the flows are self healing. The extent of erosion is sufficient to cause sinkholes on the crest and erosion tunnels through the core.
• Continuing Erosion – the filtering material is too coarse to stop erosion of the material it is protecting and continuing erosion is permitted. Unlimited erosion and leakage flows are likely.
For Scenario 3, estimate the probability for Some Erosion, Excessive Erosion and Continuing Erosion based on the guidance given in Section 10.1.4.
For Scenario 4, estimate the probability for Some Erosion, Excessive Erosion and Continuing Erosion based on the guidance given in Section 10.1.5.
The maximum leakage flows for the various filter erosion categories described above are used to assess the potential for unravelling and instability in the Breach Mechanism phase.
10.1.2 Probability for Continuation – Scenario 1 (Homogeneous zoning)
There is no potential for filtering action for this scenario. Adopt a probability of Continuing Erosion = 1.0.
10.1.3 Probability for Continuation – Scenario 2 (Downstream shoulder can hold a crack or pipe)
The issue for this scenario is whether the crack/high permeability feature that is present through the core is continuous through the downstream shoulder, or if not, whether it can find an exit. This depends on the following factors:
• The mechanism causing the concentrated leak, in particular whether it also causes cracking in the shoulder.
• The material characteristics and width of the downstream shoulder zone.
Use Table 10.1 to evaluate the conditional probability of continuing erosion.
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Table 10.1 Conditional Probability Ranges for Continuation (Scenario 2)
Predominant Mode of Concentrated Leak
Characteristics of downstream shoulder zone
Range of Conditional Probabilities for
Continuing Erosion Well compacted, cohesive materials. Material likely to hold a crack.
1.0 Cracking due to differential settlement (cross valley, foundation, embankment staging). Mechanism causing cracking in the core is also likely to cause cracking of the downstream shell (e.g. common cause cracking).
Poorly compacted, low plasticity materials. Material may collapse on wetting.
0.5 – 0.9
Similar plasticity to core 0.5 - 1.0 Desiccation cracking near crest, or on construction layer Lower plasticity than core, less prone to
desiccation cracking 0.1 – 0.5
High permeability feature also likely to be present across the shoulder zone (e.g. shutdown surface)
0.5 - 1.0
Leak unlikely to find an exit through the shoulder (i.e. very wide downstream shoulder, well compacted, low gradients, low erodibility, different compaction methods and lift thicknesses used in core and downstream shoulder)
0.01 – 0.1
High permeability zone in the core or along the foundation contact, or
Cracking due to differential settlement, features causing cracking in the core are not present below the downstream shell.
Leak likely to find an exit through the shoulder (e.g.. narrow downstream shoulder, high gradient across shoulder, high erodibility, similar compaction methods and lift thicknesses used in core and downstream shoulder, materials placed in upstream/downstream orientation, feature extends part way through the shoulder)
0.1 – 0.5
Along outside of conduits passing through the dam
Leak also likely to be common cause through downstream shoulder (e.g. desiccation cracking on sides of excavation, poor compaction, arching in trench backfill)
0.5 - 1.0
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10.1.4 Probability for Continuation – Scenario 3 (Filter/transition zone is present downstream of the core or a downstream shoulder zone which is not capable of holding a crack/pipe)
The method of assessing the probability for continuation depends on the information that is available on the particle size distributions of the core and filter/transition/shoulder materials. The two approaches are as follows:
• If particle size distribution information is available for the core and filter/transition/shoulder materials (either from construction, specifications and/or borrow area investigations), then use the approach described in 10.1.4 (a).
• If particle size distribution information is not available for the core and filter/transition/shoulder materials, then use the approach described in 10.1.4 (b).
(a) Particle Size Distribution Information is Available
The recommended procedure is shown as a flowchart in the navigation tables (Table A7 in Appendix A) and involves the following steps:
Step 1: Adjust and select base soil gradings. Plot the particle size distributions for the core material and the filters or transitions which are protecting the core. If the maximum particle size of the core material is >4.75 mm, then regrade the core grading such that the maximum size is 4.75 mm. If the base soil is gap graded, then regrade the base soil grading on the particle size that is missing (i.e. at the point of inflection of the grading curve). Select representative gradings of the regraded base soil which are indicative of the finer 5% of the base soil gradings (fine base soil grading), the average grading (average base soil grading) and the coarser 5% of the base soils (coarse base soil grading). Figure 10.1 shows an example.
Step 2: Check for the blow out condition. In cases where there is limited depth of cover over the filter/transition zone, assess the potential for blow out by comparing the seepage head at the downstream face of the core to the weight of soil cover. This is calculated as the ratio of the total stress from the vertical depth of soil (and rockfill) over the crack exit to the potential reservoir head. If the factor of safety is greater than about 0.5 three dimensional effects will be sufficient to make this a non-issue. If the factor of safety is less than about 0.1 it should be assumed the filter/transition will not be effective and probability of continuation PCE = 1.0. Between these limits a probability of continuation between 0.1 and 0.9 should be applied. If the factor of safety for blow out is greater than 0.5, then follow the proceeding steps,
Step 3: Check if the filter/transition zone will hold an open crack. If the filter/transition zone contains an excess of silty or clayey fines, assess the potential for them to hold an open crack using Table 10.2. If the probability of the filter/transition holding a crack from Table 10.2 is ≥ 0.1, then evaluate the remaining steps by
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considering the ‘cracked’ filter/transition zone as the base soil and the zone downstream of the cracked filter as the filter material. This assumes the cracked filter zone will also erode. If the filter is cemented, then the ‘cracked’ filter zone should be ignored and the core evaluated against the zone downstream of the cracked filter.
Step 4: Check if the filter/transition zone is segregated. Assess the potential for segregation of the filter/transition/shoulder materials using Table 10.3, Table 10.4 and Table 10.5. If a continuous segregated layer is likely to be present, then estimate the grading of the segregated layer assuming that 50% of the finer soil fraction is segregated out leaving the remaining 50% of coarser fraction. Figure 10.2 shows a graphical method for adjusting the gradation curve to allow for segregation. Use the DF15 values from the adjusted grading curves for estimating the conditional probabilities of No Erosion, Some Erosion, Excessive Erosion and Continuing Erosion in the remaining steps.
Step 5: Check if the filter/transition zone is internally unstable. Evaluate the probability that the filter or transition zone materials are internally unstable (PIUS) using Figure 6.5 for materials with >10% fines or Figure 6.6 for materials with <10% fines. If the probability of internal instability (PIUS) is ≥ 0.3, then adjust the grading curve assuming that 50% of the unstable soil fraction is washed out. Figure 10.2 shows a graphical method for adjusting the gradation curve to allow for suffusion. Use the DF15 values from the adjusted filter grading curves for assessing the probability of No Erosion, Some Erosion, Excessive Erosion and Continuing Erosion in Step 7. If the probability of internal instability is < 0.3, then do not adjust the filter grading curves.
Step 6: Evaluate the DF15 values for the No, Excessive and Continuing Erosion boundaries using Table 10.6 and Table 10.7 for the fine base soil grading, the average base soil grading and the coarse base soil grading. Plot the DF15 values for these boundaries on the grading curve limits of the filter/transition material (see Figure 10.4 for an example). Use the adjusted grading curves for the filter/transition zone if required to do so by the preceding steps 4 or 5.
Step 7: Estimate the probabilities for No Erosion, Some Erosion, Excessive and Continuing Erosion for each representative base soil grading. Estimate the proportion of the filter/transition gradings that fall into each of the particular erosion categories based on the plot of filter/transition grading curves versus Filter Erosion Boundaries (an example is shown in Figure 10.4). If there are no filter/transition gradings that fall into the Continuing Erosion category, then use Table 10.8 to aid judgement in assigning probabilities for Continuing Erosion. This allows for the possibility of the gradations being coarser than indicated by the available information and depends on how much finer the gradings are to the Continuing Erosion boundary. The suggested approach is to estimate the proportions for the Some, Excessive and Continuing Erosion categories first (PSE, PEE and PCE ) and then calculate PNE = 1- (PSE + PEE + PCE). Do this for each of the representative base soil gradings (fine, average and coarse gradings) as follows;
• For the fine base soil grading; PNE fine, PSE fine, PEE fine, and PCE fine.
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• For the average base soil grading; PNE ave, PSE ave, PEE ave, and PCE ave.
• For the coarse base soil grading; PNE coarse, PSE coarse, PEE coarse, and PCE coarse.
Make an initial estimate of the probabilities of the No Erosion, Some Erosion, Excessive Erosion and Continuing Erosion branches by the sum-product of the % of base soil gradings and the % of NE, SE, EE and CE for each representative base soil grading. The calculations are as follows;
• PNE = (5% x PNE fine) + (90% x PNE ave) + (5% x PNE coarse).
• PSE = (5% x PSE fine) + (90% x PSE ave) + (5% x PSE coarse).
• PEE = (5% x PEE fine) + (90% x PEE ave) + (5% x PEE coarse).
• PCE = (5% x PCE fine) + (90% x PCE ave) + (5% x PCE coarse).
An example of summing of the probabilities is shown in Table 10.9 for the example shown in Figure 10.4.
Use judgement to adjust the calculated percentages to take into account the effects of other factors such as the distribution of the core and filter gradations in the fill, borrow area variability and selective placement of materials.
(b) Simplified Approach – Particle Size Distribution Information is Not Available
• Estimate the particle size distribution of the core materials based on the likely source of materials. The gradation of the soils may be able to be estimated based on the likely geological origin of the materials (e.g. decomposed granitic soils, residual soils, alluvial fine clays and silts, etc).
• Estimate the particle size distribution of the filter/transition/shoulder materials based on the likely source of the materials and whether they were processed or not (e.g. run-of-pit alluvial sands and gravels, unprocessed quarry fines or tunnel spoil, processed sand and gravels, etc). Estimate the DF15 of the filter/transition/downstream shoulder materials.
• Evaluate the DF15 values for the No, Excessive and Continuing Erosion boundaries for the estimated gradation of the core materials using Table 10.6 and Table 10.7.
• Estimate the probabilities for No Erosion, Some Erosion, Excessive and Continuing Erosion based on the estimated proportion of the filter/transition gradings that is likely to fall into each of the particular filter erosion categories. The suggested approach is to estimate the probabilities for Some, Excessive and Continuing Erosion (PSE, PEE and PCE) and calculate PNE = 1- (PSE + PEE + PCE).
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(c) Estimate Potential Leakage Flows
Assess the potential leakage flows that could develop if piping were to initiate if piping were to initiate in the core based on the following guidance;
• Information from case histories of poor filter performance suggest the potential maximum leakage flows that could develop due to piping are as follows:
– Filters falling into the Some Erosion category – up to 3 cfs (100 l/sec):
– Filters falling into the Excessive Erosion category – 3 to 35 cfs (100 to 1000 l/sec).
– Filters falling into the Continuing Erosion category – flows of 35 cfs (1000 l/sec) and increasing.
It is recommended that the maximum leakage flows listed above be used in the assessment of the probability of a breach mechanism developing. Lower leakage flows are likely if upstream flow limitation occurs, but the factors would need to be carefully considered and justified if they were to be relied on in the assessment.
Figure 10.1 – Example of the selection of representative grading curves (fine, average and coarse) for the assessment of filter compatibility.
Particle Size (mm)
Envelope of Base Soil Gradings
Average Grading
Representative Fine Grading Curve
Representative Coarse Grading Curve
% P
assi
ng
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Figure 10.2 – Approximate method for estimating DF15 after washout of the erodible fraction from a suffusive soil or for soils susceptible to segregation.
Table 10.2 - Likelihood for Filters with Excessive Fines Holding a Crack
Probability of holding a crack Fines Plasticity
Fines Content
% Passing 0.075 mm Compacted Not compacted
5% 0.001 0.0002
7% 0.005 0.001
12% 0.05 0.01
15% 0.1 0.02
Non plastic (and no cementing present)
>30% 0.5 0.1
5% 0.05 0.02
7% 0.1 0.05
12% 0.5 0.3
Plastic (or fines susceptible to cementing)
≥ 15% 0.9 0.7
Note: Fines susceptible to cementing for filters having a matrix predominately of sand sized particles (e.g. filters derived from crushed limestone).
15%
(1) Select the point of maximum inflexion of the grading curve (2) Locate the mid point below the point of inflexion
% P
assi
ng
Particle size
Original gradation
Estimated gradation curve after washout or segregation
Equal distance
(4) Estimate the D15 after washout or segregation
(3) Estimate the shape of the gradation curve passing through the mid point
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Table 10.3 - Potential for Segregation of Filtering Materials
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Construction practices
(3) Good construction and stockpiling practices used
Fair construction and stockpiling practices
Poor construction or stockpiling practices
Very poor construction and stockpiling practices with no regard for segregation effects
Placed in thin lifts < 2 feet (< 0.6 m), careful control during construction.
End dumping from trucks, spread by dozer in thin lifts < 2 feet (< 0.6 m)
End dumping from trucks, spread by dozer in thick lifts > 2 feet (> 0.6 m)
Filters/transitions constructed by pushing material over the edge of the core
Gradation – Comparison to USBR/US Corps filter criteria,
(2) Meets segregation criteria in Table 10.4.
Borderline segregation criteria in Table 10.4.
Fails segregation criteria in Table 10.4
Significant departure from segregation criteria in Table 10.4.
and % sand >50% passing 4.75 mm sieve
>40% passing 4.75 mm sieve
25 – 40% passing 4.75 mm sieve
<25% passing 4.75 mm sieve
Width of zone
(1) Wide zone, > 20 foot wide (>6 m)
10 – 20 foot wide zone (3 – 6 m)
Narrow zone, 5 – 10 foot wide (1.5 – 3 m)
Narrow zone, <5 foot (<1.5 m)
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Table 10.4 – Gradation Limits to Prevent Segregation (USDA SCS 1994, USBR 1987, US Corps of Engineers 1994)
Minimum D10 (mm) Maximum D90 (mm)
<0.5 20
0.5 – 1.0 25
1.0 – 2.0 30
2.0 – 5.0 40
5.0 – 10 50
10 – 50 60
Table 10.5 – Susceptibility of filter/transition zones to segregation versus weighted score (Relative importance factor (RF)) x (Likelihood factor(LF))
Weighted Score from Table 10.3 Segregation Assessment Consideration of Segregation Effects for
Filter/Transition Assessment
6 – 10 Low potential for segregation Segregation of filter/transition materials do not need to be considered
11 – 17 Moderate potential for segregation Segregation of filter/transition materials should be considered, unless investigations show otherwise.
18 – 24 High potential for continuous segregated layers
Segregation should be assumed to be present, unless investigations show otherwise.
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Table 10.6 – No erosion boundary for the assessment of filters of existing dams (after Foster and Fell 2001).
Base Soil Category
Fines content
(1)
Design Criteria of Sherard and Dunnigan
(1989)
Range of DF15 for No Erosion Boundary From
Tests
Criteria for No Erosion Boundary
1 ≥ 85% DF15 ≤ 9 DB85 6.4 - 13.5 DB85 DF15 ≤ 9 DB85 (2)
2 40 - 85% DF15 ≤ 0.7 mm 0.7 - 1.7 mm DF15 ≤ 0.7 mm (2)
3 15 - 40% DF15 ≤ (40-pp% 0.075 mm) x (4DB85-0.7)/25 +
0.7
1.6 - 2.5 DF15 of Sherard and Dunnigan design
criteria
DF15 ≤ (40-pp% 0.075 mm) x (4DB85-0.7)/25 + 0.7
4 < 15% DF15 ≤ 4 DB85 6.8 - 10 DB85 DF15 ≤ 4 DB85
Notes: (1) The fines content is the % finer than 0.075 mm after the base soil is adjusted to a maximum particle size of 4.75 mm.
(2) For highly dispersive soils (Pinhole classification D1 or D2 or Emerson Class 1 or 2), it is recommended to use a lower DF15 for the no erosion boundary. For soil group 1 soils, suggest use the lower limit of the experimental boundary, i.e. DF15 ≤ 6.4 DB85. For soil group 2 soils, suggest use DF15 ≤ 0.5 mm. The equation for soil group 4 would be modified accordingly.
Table 10.7 – Excessive and Continuing erosion criteria (Foster 1999; Foster and Fell 1999, 2001).
Base Soil Proposed Criteria for Excessive Erosion Boundary
Proposed Criteria for Continuing Erosion Boundary
Soils with DB95<0.3 mm DF15 > 9 DB95
Soils with 0.3<DB95<2 mm DF15 > 9 DB90
Soils with DB95>2 mm and fines content >35%
DF15 > the DF15 value which gives an erosion loss of 0.25g/cm2 in the CEF test (0.25g/cm2 contour line in Figure 10.3)
For all soils: DF15 > 9DB95
Soils with DB95>2 mm and fines content <15%
DF15 > 9 DB85
Soils with DB95>2 mm and fines content 15-35%
DF15 > 2.5 DF15 design,
where DF15 design is given by: DF15 design=(35-pp%0.075 mm)(4DB85-0.7)/20+0.7
Notes: Criteria are directly applicable to soils with DB95 up to 4.75 mm. For soils with coarser particles determine DB85 and DB95 using grading curves adjusted to give a maximum size of 4.75 mm.
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0
5
10
15
0 5 10 15 20 25 30 35 40 45 50 55 60Core material % fine - medium sand (0.075 - 1.18mm)
Filte
r D
F15
(mm
)
No Erosion Boundaryfor Soil Group 2DF15=0.7mm
0.25g/cm2
Contour of Erosion Loss
EXCESSIVE EROSION
SOME EROSION
Figure 10.3 – Criteria for Excessive Erosion Boundary.
Table 10.8 – Aid to judgement for estimation of probability for Continuing Erosion (PCE) when the actual filter grading is finer than the Continuing Erosion Boundary
Comparison of Actual DF15 of the Filter/transition Zone to the Continuing Erosion boundary Probability for Continuing Erosion (PCE)
DF15 in dam < 0.1x DF15CE 0.0001
DF15 in dam < 0.2 x DF15CE 0.001
DF15 in dam < 0.5 x DF15CE 0.01 – 0.05
Notes: DF15CE = DF15 for Continuing Erosion Boundary from Table 10.7.
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Assessment of Zone 1 core against no erosion, excessive erosion and continuing erosion criteriaNo Erosion Excessive
ErosionContinuing
Erosion
DB85 (mm) DB95 (mm)% passing 0.075mm
% fine-medium sand (0.075 - 1.18mm) DF15 (mm) DF15 (mm) DF15 (mm)
Fine Grading 1.9 3.3 50 25 0.7 2 30Average 2.4 4 41 29 0.7 2.5 36Coarse Grading 2.5 4.2 35 30 0.7 2.6 38
Base soil sizes (mm)Core Gradation
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10 100 1000
Seive Size (mm)
Perc
ent P
assi
ng
Filter erosion boundaries for the Average core grading
Filter erosion boundaries for the Fine core grading
Filter erosion boundaries for the Coarse core gradingZone 1 - Core Materialre-graded to maximum size of 4.75 mm
Zone 3- FilterTransition
0.7 2.5 36
No Erosion
SomeErosion
Excessive Erosion
ContinuingErosion
0.7 2.0 30
Zone 1- Fine Grading
Zone 1 - Average Grading
Zone 1 - Coarse Grading
38
Figure 10.4 - Example of plot showing filter/transition gradings compared to Filter Erosion Boundaries. Evaluate the filter erosion boundaries for the representative fine, average and coarse gradings of the core material.
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Table 10.9 Example of Estimating Probabilities for No, Some, Excessive and Continuing Erosion for the example shown in Figure 10.4
Estimated Proportion of Filter Gradings falling into each Filter Erosion category (from Figure 10.4) Representative
Base Soil Grading No Erosion (NE) Some Erosion
(SE) Excessive
Erosion (EE) Continuing
Erosion (CE) Sum PXX
Fine Base Soil Grading (represents 5% of finest grading curves)
PNE fine = 20%
PSE fine = 60%
PEE fine = 20%
PCE fine = 0%
100%
Average Base Soil Grading (represents 90% of grading curves)
PNE ave = 20%
PSE ave = 70%
PEE ave = 10%
PCE ave = 0%
100%
Coarse Base Soil Grading (represents 5% of coarsest grading curves)
PNE coarse = 20%
PSE coarse = 70%
PEE coarse = 10%
PCE coarse = 0%
100%
Calculation of Probabilities for No, Some, Excessive and Continuing Erosion (Pxx)
PNE = (5% x PNE fine) + (90% x PNE ave) + (5% x PNE coarse)
PSE = (5% x PSE fine) + (90% x PSE ave) + (5% x PSE coarse)
PEE = (5% x PEE fine) + (90% x PEE ave) + (5% x PEE coarse)
PCE = (5% x PCE fine) + (90% x PCE ave) + (5% x PCE coarse)
Calculation Result
20% 69.5% 10.5% 0% 100%
Assigned Probabilities
PNE = 0.20 PSE = 0.69 PEE = 0.11 PCE = 0.0001(a) 1.000
Notes: (a) Even though there are no filter gradings falling into the Continuing Erosion category in this example, a probability of 0.0001 was assigned for Continuing Erosion based on the guidance given in Table 10.8. This takes into account the possibility of the materials in the dam being coarser than indicated by the gradation curves. In this example, the filter gradation envelope is significantly finer than the Continuing Erosion boundary, and hence a very low probability is assigned based on Table 10.8.
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10.1.5 Probability for Continuation – Scenario 4 (Internal erosion into an open defect, joint or crack in the foundation, in a wall or conduit)
For erosion to continue through an open defect, the defect needs to be sufficiently open to allow the soil surrounding the defect to pass through it. The recommended procedure is as follows:
• Evaluate the opening size that would allow Continuing Erosion (JOSCE) of the surrounding soil using Table 10.10.
• Estimate the conditional probability for Continuing Erosion by estimating the proportion of soil gradations that are coarser than the Continuing Erosion category and using Table 10.11.
Table 10.10 - Continuing Erosion criteria for erosion into an open defect,
Comparison of Soil Gradation to Joint/Defect opening size (JOS) Erosion condition
All Soils
Continuing erosion (CE) JOSCE = D95 surrounding soil
Notes: • JOSCE = Joint/defect opening size that would allow continuing erosion of the surrounding soil.
• D95 should be based on the average soil grading after regrading on 4.75mm particle size.
Table 10.11 – Aid to judgement for estimation of probability for continuation for open defects/joints/cracks
Comparison of joint opening in the dam (JOS) to the Continuing Erosion criteria
Joint Opening in the dam Probability for Continuing Erosion (PCE)
JOS < 0.1x JOSCE 0.0001
JOS < 0.2 x JOSCE 0.001
JOS < 0.5 x JOSCE 0.01
JOS > JOSCE 0.1 – 0.9
Estimate based on the proportion of gradings finer than CE
Notes: JOSCE = Joint Opening for Continuing Erosion Boundary = D95 of the surrounding soil
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10.1.6 Probability for Continuation – Scenario 5 (Erosion into a toe drain)
This scenario is applicable if the failure path under consideration involves a seepage path that exits into a toe drain which could lead to continuing erosion of the embankment or foundation materials.
The assessment of erosion into a toe drain considers the observed condition of the toe drain (from video or external inspections) and the design and construction details of the toe drain. Estimate the probability of continuing erosion for erosion into a toe drain using Table 10.12.
Table 10.12 – Probability of continuation for erosion into toe drains
Drain Inspection Design and Construction Details Probabilities for
Continuing Erosion into Toe Drains
Video inspections indicate no deterioration or damage to the pipes
Good design and construction details (e.g. filter surround present, proper pipe)
0.0001 to 0.0005
Poor design and construction details (e.g. thin plastic pipe, geotextile surround)
0.0005 to 0.005
No video inspection of drain, and no external evidence of poor performance (i.e. clear outflow, no sinkholes)
Good design and construction details (e.g. filter surround present, good joint details) and deterioration unlikely (metal pipe <20 years)
0.0005 to 0.005
Poor design and construction details (e.g. thin plastic pipe, geotextile wrap of drainage gravel). Or deterioration likely to be present (e.g. metal pipe > 30 years, old tile drains, nearby source of tree roots)
0.005 to 0.05
Video inspection of drain shows. broken pipe, open joints, materials found in drain) Or external evidence of sinkholes over drain, evidence of internal erosion in outflow)
0.1 – 0.9 depending on severity of damage
0.1 to 0.5 if some damage but no actual surrounding material has moved into
pipes 0.5 to 0.95 if large openings
in pipe and surrounding material has moved into
pipe.
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10.2 Probability for Continuation for Internal Erosion Through the Foundation
10.2.1 Approach
The probability of continuation of erosion should be estimated by:
a) Assessing the probability that the exit will be a filtered or unfiltered exit.
4) Given the exit is unfiltered the probability of continuation will be 1.0.
5) Given the exit is filtered, estimate the probability for Continuing Erosion using the method described in Section 10.1.4.
The probability of continuation will be the product of the probability of an unfiltered exit and the probability assessed considering the filters.
10.2.2 Probability of Filtered or Unfiltered Exit
The likelihood that the exit will be filtered or unfiltered will depend on the failure path being considered, the embankment zoning and the details of the foundation geology. The steps are as follows;
• Estimate the probability that there will an unfiltered exit (Punf) using Table 10.13 to aid judgment. The conditional probability of continuation for this scenario is equal to (Punf) x 1.0.
• Calculate the probability that there will be a filtered exit (Pfe) = 1- Punf.. Assess the filter materials and materials being eroded in terms of the Continuing Erosion criteria using the procedure in Section 10.1.4.
• The probability of continuing erosion PCE = (Punf x 1.0) + (Pfe x PCE).
Note that in situations where a foundation filter drain or toe drain system is present, there is still the possibility that seepage paths could bypass the filter drain system due to the geological conditions, compaction of soil foundations below foundation filters, or deteriorated toe drain systems. Examples of these scenarios are included in Table 10.13 and illustrated in Figures 10.5 to 10.7).
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Table 10.13 – Probability of by-passing the foundation filter for piping through the foundation or piping from the embankment into the foundation
Scenarios Examples Range of Probabilities of the Seepage Path Bypassing the
Foundation Filter
Foundation filter fully penetrates the foundation material that is erodible
Filter drain has adequate discharge capacity
Filter trench completely penetrates through the foundation sand/silt layer, in filled defects in rock or desiccated foundation clay and into a non-erodible material (Figure 10.5a)
Negligible
Assume probability unfiltered exit = 0
Foundation filter partially penetrates the foundation material that is erodible
Filter drain has adequate discharge capacity
Filter trench penetrating through foundation sand/silt layer, in filled defects in rock or desiccated foundation clay but erodible soil or in filled defects in rock remains beneath the filter trench (Figure 10.5b)
0.01 to 0.001
Foundation filter partially penetrates the foundation material that is erodible
Filter drain has adequate discharge capacity
Filter trench partially penetrating through foundation sand/silt layer, or desiccated foundation clay but some of this soil or in filled defects in rock remains beneath the filter trench (Figure 10.5b)
0.1 to 0.01
Foundation filter partially penetrates the foundation material that is erodible
Filter drain has inadequate discharge capacity
Filter trench partially penetrating through foundation sand/silt layer, or desiccated foundation clay (Figure 10.5b)
0.1 to 0.9 depending on the degree to which filter drain
capacity is exceeded
Foundation filter blanket drain directly overlying the foundation material that is erodible, clean-up of the foundation allows seepage into the filter drain
Filter drain overlying a foundation sand/silt layer, desiccated foundation clay (Figure 10.5c) or in filled defects in rock.
0.01 – 0.001
depending on the width and discharge capacity of the filter
drain. For very narrow widths the probability could be as high as 0.1
Foundation filter blanket drain directly overlying the foundation material that is erodible, filter drain has inadequate discharge capacity and or clean-up of the foundation hinders flow of seepage into the filter drain
Filter drain overlying a foundation sand/silt layer, desiccated foundation clay (Figure 10.5c) or in filled defects in rock.
0.5 – 0.01
depending on the width of the filter drain, clean-up of the foundation to allow seepage to flow into the filter
drain and discharge capacity of filter drain
Low permeability layer is present below the foundation filter drain.
Filter drain has adequate discharge capacity
Low permeability soil layer between the foundation filter/toe drain and the foundation material that is being eroded (e.g. Figure 10.6)
Residual soil left over jointed bedrock below the foundation filter
0.1 – 0.5
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Scenarios Examples Range of Probabilities of the Seepage Path Bypassing the
Foundation Filter
Scarifying and rolling the foundation below the foundation filter in soils with macrostructure,
Filter drain has adequate discharge capacity
Foundation soils or highly weathered rocks containing relict defects, root holes, desiccation cracks, or lateritic soils.
0.1 – 0.5
High permeability soil or rock has an unprotected exit downstream
Soil layer that can be piped daylights downstream of the dam
Continuous open jointed rock daylights downstream of the dam (Figure 10.7)
0.5 – 0.9
Discharge capacity of foundation filter drainage system is not sufficient
Thin sand filter layer on high permeability soil or rock foundation
Filter materials contain excess of fines (>5% fines passing 0.075mm)
0.1 – 0.9
Blocked or collapsed toe drains HDPE corrugated pipes, collapsed tile drains, biological growth in pipes
0.1 – 0.9
No foundation filter or toe drain system provided, cohesive shell materials
1.0
It needs to be recognized that low permeability strata beneath horizontal drains may prevent them working effectively, Figure 10.6 shows an alluvial foundation where the lower permeability strata (A and E) will prevent the seepage in the most permeable sand and gravel strata (B, and D) from flowing into a filtered exit in the horizontal drain.
For the situation of backward erosion piping within a foundation sand layer which has an overlying low permeability layer, the likelihood of finding an unfiltered exit is already considered in the assessment of initiation of backward erosion. An unfiltered exit is implicit if a heave condition or a sand boil is present.
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(a) Example of fully penetrating filter drain
(b) Example of partially penetrating filter drain
(c) Example of horizontal filter drain directly overlying erodible foundation material
Figure 10.5 – Examples of scenarios of fully penetrating and partially penetrating foundation filter drains.
NON-ERODIBLE ROCK
SAND
1
2A 2B
SAND
1
2B
NON-ERODIBLE ROCK
2A
SAND
1 FOUNDATION FILTER DRAIN
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Figure 10.6 - Example of an embankment where much of the seepage flow will be to an unfiltered exit.
Foundation filter
Sand layer
Unfiltered exit
Figure 10.7 - Example of an embankment where there is an unfiltered exit due to day lighting of the foundation sand layer downstream of the dam.
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10.3 Probability of Continuation for Internal erosion of the embankment at or into the foundation
10.3.1 Erosion into open joints in rock foundation
Evaluate the probability of the joint openings being sufficiently open and continuous to allow erosion of the core materials based on the outcomes of the assessment in Sections 8 and 9. Use the method described in Section 10.1.5 to evaluate the probability of continuing erosion.
If the geological conditions of the rock mass are such that the open joints at the core-foundation contact are unlikely to daylight at an unfiltered exit, or need to exit via an interconnected path of another joint set which are less open, then reduce the probability for continuing erosion using the judgment probability mapping tables in Appendix E.
If the geological conditions are such that the seepage through the rock mass needs to exit through an overlying soil layer (e.g. alluvium overlying a jointed rock mass), then evaluate the probability of continuing erosion at both the contact with the rock defects and also at the contact with the overlying soils. The assessment of continuation at the soil layer contact needs to consider the potential volume of embankment material that may be stored within the open jointed rock mass before filtering takes place..
10.3.2 Erosion into coarse grained soil foundation
Evaluate the probability of the coarse grained soil foundation layer being sufficiently open and continuous to allow erosion of the core materials. Evaluate the probability of the foundation soils permitting Continuing Erosion of the core materials using the methods described in Section 10.1.4.
If the geological conditions of the soil layering are such that the open soil layers at the core-foundation contact are unlikely to daylight at an unfiltered exit, or need to exit via an interconnected path of another soil layer which is capable of acting as an effective filtering medium, then reduce the probability for continuing erosion using the judgment probability mapping tables in Appendix E.
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11 Probability of Progression
11.1 Overall Approach
Step 1: Estimate the probability that the soil will “hold a roof” over a pipe (Section 11.2).
Step 2: Estimate the probability that “crack filling” action will not stop the erosion process (Section 11.3).
Step 3: Estimate the probability that flow in the developing pipe will not be restricted by an upstream zone (or for example a concrete face slab) so the erosion process continues to develop (Section 11.4).
11.2 Probability of Forming a Roof
11.2.1 Internal Erosion Through the Embankment
For internal erosion and piping through the dam or piping from the embankment into a rock foundation, the core must be capable of holding the roof of a pipe. Assess the probability of the soil forming a roof of a pipe using Table 11.1.
11.2.2 Internal Erosion through a Soil Foundation
For internal erosion and piping through a soil foundation, the roof of a pipe will be formed by layers of soil in the foundation which are cohesive or have high fines content, or by the core of the embankment. Other geological conditions which may form a roof within a soil foundation include where basalts overly the soil layer.
Assess the probability of the embankment and foundation materials supporting the roof of a pipe in the foundation using Table 11.1.
In most cases the core of the embankment is capable of providing a roof to a developing pipe in the foundation. However, if there are upstream or downstream zones of non plastic granular material in the embankment that are not capable of supporting a roof of a pipe (e.g. rockfill or gravel shells), then a pipe through the foundation may not be able to fully develop. Figure 11.1b shows an example of this.
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(a) Homogeneous earthfill dam
(b) Dam with gravel or rockfill shells
Figure 11.1 Scenarios for holding a roof of a pipe for internal erosion through the foundation
SAND
1
SAND
1 3
2 2
3
ROCKFILL OR GRAVEL SHELLS
PIPE COLLAPSE LEADING TO SINKHOLE
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Table 11.1 – Probability of a soil being able to support a roof to an erosion pipe
Soil Classification Percentage Fines
Plasticity of the Fines Moisture Condition Likelihood of
Supporting a Roof
Clays, sandy clays (CL, CH, CL-CH)
> 50% Plastic Moist or saturated 1.0
ML or MH >50% Plastic or non-plastic
Moist or saturated 1.0
Sandy clays, Gravely clays, (SC, GC)
15% - 50% Plastic Moist or Saturated 1.0
Silty sands,
Silty gravels, Silty sandy gravel (SM, GM)
> 15% Non plastic Moist
Saturated
0.7 to 1.0
0.5 to 1.0
Granular soils with some cohesive fines (SC-SP, SC-SW, GC-GP, GC-GW)
5% to 15% Plastic Moist Saturated
0.5 to 1.0 0.2 to 0.5
Granular soils with some non plastic fines (SM-SP, SM-SW, GM-GP, GM-GW)
5% to 15% Non plastic Moist
Saturated
0.05 to 0.1
0.02 to 0.05
Granular soils, (SP, SW, GP, GW)
< 5% Non plastic
Plastic
Moist and saturated
Moist and saturated
0.0001
0.001 to 0.01
Notes: (1) Lower range of probabilities is for poorly compacted materials (i.e. not rolled), and upper bound for well compacted materials.
(2) Cemented materials give higher probabilities than indicated in the table. If soils are cemented, use the category that best describes the particular situation.
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11.3 Probability of Crack Filling Action Not Being Effective
11.3.1 Internal Erosion the Embankment
Estimate the probability of crack filling action not stopping pipe enlargement using Table 11.2.
For piping through the dam or piping from the dam into a rock foundation, crack filling from an upstream zone can limit the extent of erosion in the core if the materials washed into the crack or pipe are capable of filtering against the downstream filter or transition zone. The washed in materials aid in the filtering action against the downstream zone. This will be of greatest benefit in cases where there is poor filter compatibility between the core and downstream filter due to a lack of sand size particles in the core. In these cases, the probability of continuation may be high, but the washed in materials may be capable of filtering against the downstream filter zone and this reduces the potential for the pipe enlarging. There is less benefit where the materials that are washed in are of similar sizes to those already in the core, hence the probabilities for crack filling in Table 11.2 are higher for a well graded core material compared to those for a core which is deficient in sand sizes. There is very little benefit where there is no downstream filter/transition zone.
11.3.2 Internal Erosion Through the Foundation
The potential for crack filling action for internal erosion in the foundation depends on the zoning of the embankment and the geological features in the foundation.
If the eroding foundation soil layer is located immediately below the embankment, and the embankment forms the roof of the pipe, then evaluate the probability for crack filling action as for erosion in the dam using Table 11.2.
If the eroding foundation soil layer is located further below the embankment, then consider the potential for the overlying soil layers to wash into the developing pipe. There needs to be a filtering material at the downstream end of the flow path for crack filling action to be effective. The filtering material may be a naturally occurring layer in the foundation, or the embankment filter.
11.3.3 Internal Erosion of the Embankment into or at the Foundation
The issues are the same as for internal erosion through the embankment. Estimate the probability of crack filling action not stopping pipe enlargement using Table 11.2.
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Table 11.2 – Probability for crack filling action not stopping pipe enlargement – internal erosion through the embankment
Embankment Zoning Upstream Granular Zone
Downstream Filter or Transition or other granular
material
Likelihood of Piping Progressing – Crack Filling
Action Not Effective
Homogeneous, earthfill with toe drain, earthfill with horizontal drain, concrete face earthfill, puddle core earthfill, earthfill with corewall, hydraulic fill
None except for rip rap and filters under these
None or none effective 1.0
Earthfill with vertical and horizontal drain, zoned earthfill None Present 1.0
Central and sloping core earth and rockfill (or gravel shoulders) Present Present
0.1 to 0.9
If the core is well graded and has fine to coarse sand sizes
(0.075 – 4.75 mm) already present (1)
0.01 to 0.1 If the core is deficient in sand sized particles, and washed in sand material aids in sealing
the downstream zone (2).
Notes: (1) Crack filling is more likely to stop pipe enlargement when the core zone is deficient in sand size particles and these particles can be provided by washing in from the upstream zone. This aids in sealing of the downstream filter zone. If the core is well graded and has sand sizes present, then the potential benefits of crack filling are less as the sand size particles are already present.
(2) Probability dependent on compatibility of particle sizes of granular soils upstream of the core and in the downstream filter transition.
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11.4 Probability for Limitation of Flows
11.4.1 Flow limitation by upstream zone
Estimate the probability that flow in the developing pipe will not be restricted by an upstream zone using Table 11.3. This considers the potential for flow limitation due to zoning within the dam or cutoff walls or other structural elements within the dam or foundation.
11.4.2 Flow into/out of open joint in conduits
Limitation of flows is not applicable to these failure modes and a probability of no flow limitation of 1.0 should be used.
Erosion into open defects in a conduit may lead to the development of a sinkhole on the embankment, and this is considered under the breach node of the event tree (refer to Section 13.5).
Leakage out of a pressurised conduit is likely to be limited by the defect in the pipe. Estimate the potential flows out of the defects in the conduit pipe and this is used in Section 13.3 to estimate the likelihood for it to cause slope instability.
11.4.3 Flow into jointed bedrock
The possible scenarios are;
• Erosion initiating at the core-foundation contact where there is no or a shallow cut off trench. This is likely to lead to the pipe forming through the embankment. For this case, estimate the probability that flow in the developing pipe will not be restricted by an upstream zone use Table 11.3.
• Erosion initiating within a deep cutoff trench into open joints in a rock foundation. The extent of erosion may become limited by the opening width of the rock defects. This is embedded in the system for estimating the likelihood of breach due to the flow through the open joints in the rock foundation (Section 13). The limitation of flows is therefore not applicable to this scenario and a probability of no flow limitation of 1.0 should be used.
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Table 11.3 – Probability that flow in the developing pipe will not be restricted by an upstream zone, cut-off wall or a concrete element in the erosion path
Characteristics of Upstream Zone/Concrete Element/Cut-off
Likelihood for No Flow Restriction
Flow Limitation by an Upstream Zone; No zone upstream of core (e.g. Homogeneous, earthfill with toe drain, earthfill with filter drains) 1.0
High permeability zone (e.g. clean rockfill) 1.0
Fill with > 15% cohesive fines, highly likely to support a roof, Mechanism causing cracking or flaw in the core is also likely to affect the upstream zone (e.g. common cause cracking).
0.8 to 1.0
Fill with > 15% cohesive fines, highly likely to support a roof, features causing cracking or flaw in the core are not present below the upstream shell.
0.01 to 0.1 depending on the confidence that there is not a common cause defect
Fill with 5% to 15% cohesive fines, likely to support a roof. (1) Mechanism causing cracking or flaw in the core is also likely to affect the upstream zone (e.g. common cause cracking).
0.5 to 0.7
Fill with 5% to 15% cohesive fines, likely to support a roof (1), features causing cracking or flaw in the core are not present below the upstream zone.
0.05 to 0.3 depending on the confidence that there is not a common cause defect
and fines content
Fill with <15% cohesionless fines, unlikely to support a roof (1) Mechanism causing cracking or flaw in the core is also likely to affect the upstream zone (e.g. common cause cracking).
0.4 to 0.9 if gradient across upstream zone is > 1
0.1 to 0.4 if gradient across upstream zone is < 1
Fill with <15% cohesionless fines, unlikely to support a roof (1), features causing cracking or flaw in the core are not present below the upstream zone.
0.01 to 0.1 if gradient across upstream zone is <1. Assign probability depending
on the confidence that there is not a common cause defect
0.05 to 0.2 if gradient across upstream zone is > 1
Fill with 15% to 30% cohesionless fines, may support a roof, Mechanism causing cracking or flaw in the core is also likely to affect the upstream zone (e.g. common cause cracking).
0.2 to 0.8
Fill with 15% to 30% cohesionless fines, may support a roof, features causing cracking or flaw in the core are not present below the upstream shell.
0.01 to 0.1 depending on the confidence that there is not a common cause defect
Fill with > 30% cohesionless fines, may support a roof, Mechanism causing cracking or flaw in the core is also likely to affect the upstream zone (e.g. common cause cracking).
0.8 to 1.0
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Characteristics of Upstream Zone/Concrete Element/Cut-off
Likelihood for No Flow Restriction
Fill with > 30% cohesionless fines, may support a roof, features causing cracking or flaw in the core are not present below the upstream shell.
0.01 to 0.1 depending on the confidence that there is not a common cause defect
Upstream low permeability blanket (for internal erosion in the foundation)
0.01 to 0.1 depending on the extent of coverage of the piping soil layer
Flow Limitation by a Concrete Element in the embankment; Concrete slab on upstream slope 0.1 to 0.5
Soil cement wave protection 0.05 to 0.2
Partially penetrating concrete core wall in dam (for internal erosion and piping along foundation contact)
0.01 to 0.001 for piping along the core-foundation contact (depending on height
of the wall)
Flow Limitation by cut-off walls in the foundation (for internal erosion and piping in the foundation); Sheet pile walls Extruded – 0.01 to 0.5
Cold rolled – 0.1 to 0.9. If have good piezometers data to show wall is integral may use low end figure or possibly even lower
Concrete core wall within embankment (1920’s-1930’s), 0.01 to 0.001(2)
Modern diaphragm walls:
Cementitious walls – conventional concrete, plastic concrete, cement bentonite
0.0001 well constructed, 0.001 serious defects suspected
Non-cementitious walls – soil bentonite 0.001 to 0.01 Soil cement bentonite wall 0.01 to 0.1
Column walls – jet grouting, soil mixing 0.01 to 0.1
Open joint, water stop, crack or other defect in the conduit 0.05 to 0.2
Notes: (1) Need to check whether the upstream zone materials are susceptible to suffusion and backward erosion. If so, fines can wash out and lead to higher permeability and /or a pipe may develop. At gradients > 1.0, backward erosion is likely.
(2) Need to consider potential size of pipe and ability of downstream shoulder to handle flows. (3) For these walls the soil is excavated by excavator or dragline, and the bentonite mixed with the excavated
soil using earth moving equipment.
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12 Probability of Detection, Intervention and Repair
12.1 General Principles
The likelihood that a particular failure path can be detected, and if so, whether it is possible to intervene (e.g. by lowering the reservoir level), or carry out repairs to prevent the dam breaching is usually best considered as two questions:
1. Will this failure path be detected?
2. Will intervention and repair be possible?
A probability is assigned to each of these questions. The overall probability of detection, intervention and repair is the product of these two probabilities.
The likelihood of detection and successful intervention and repair is dependent on a number of factors including:
a) The category of internal erosion and piping. i.e. internal erosion in the embankment, the foundation or embankment to foundation.
b) The mechanism of initiation of internal erosion – erosion in a crack, suffusion or backward erosion.
c) The breach mode – gross enlargement of a pipe, instability of the downstream slope, unravelling or sloughing of the downstream slope, settlement of the foundation, sinkhole development.
d) The nature of and the geometry of the materials in the foundation.
e) The zoning of the embankment, and the materials in the embankment.
f) The reservoir level at the time of the piping incident, and how rapidly it can be drawn down.
g) The type and frequency of monitoring and surveillance at the dam and the training of the staff to recognize a developing internal erosion and piping incident.
h) The ability to get trained personnel out to the site in the event of a piping incident.
i) The ability of those responsible to be able to direct emergency release of the reservoir
j) The availability of materials and equipment to intervene and carry out repair works.
It is necessary to use judgement to assess these probabilities.
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12.2 Some Information on the Rate of Internal Erosion and Piping
The likelihood of detection and successful intervention or repair depends on the time from when the internal erosion process may be detected to when breach begins.
Fell et al (2001, 2003) studied case histories of failures and accidents for piping in the embankment, foundation, and embankment to foundation. Based on the case histories and an understanding of the physical processes they provided guidance on the time for progression beyond when a concentrated leak is first observed, and development of a breach. Table 12.1 to Table 12.3 are based on that study.
Table 12.1 should be used to estimate the approximate likely time to dam failure after a concentrated leak is first observed. Tables 11.1, 12.2, 11.3 and 12.3 are used in Table 12.1 working from left top right.
Table 12.3 replaces an original table to assess the likely rate of erosion of the core of the embankment or the soil in the foundation. Table 11.1 and Table 11.3 should be used to assess the ability to support a roof and upstream flow limitation respectively.
In these tables the terms for rates are defined as shown in Table 12.4. Dual descriptors are used to describe intermediate terms e.g. very rapid – rapid for 6 hours. The terms are applied to part (e.g. progression) or the whole process.
Most of the cases studied were for breach by gross enlargement, so the method is applicable to cases where the mechanism is gross enlargement. It is considered to be reasonably applicable to cases where the final breach is by slope instability, following development of a pipe. It will probably underestimate the time for breach by sloughing. Sloughing is a slowly developing breach mode which should take days or weeks to lead to breach.
Breach by sinkhole development is potentially a rapid process in the final stages when the sinkhole emerges into the reservoir. We would expect breach to occur in a small number of hours but do not have case data to support a more refined estimate.
Table 12.1 is used by assigning the values to the first four columns, and selecting the likely time for progression and breach which best fits the data.
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Table 12.1 – A method for the approximation estimation of the time for progression of piping and development of a breach, for breach by gross enlargement, and slope instability linked
to development of a pipe (Fell et al 2001, 2003).
Factors Influencing the Time for Progression and Breach
Ability to Support a Roof
From Table 11.1
Rate of Erosion
From Table 12.2
Upstream Flow Limiter
From Table 11.3
Breach Time
From Table 12.3
Approximate Likely Time- Qualitative
Approximate Likely Time
Yes R or VR No VR or R-VR Very Rapid < 3 hours
Yes R No R Very Rapid to Rapid 3-12 hours
Yes R-M No VR
Yes R No R-M Rapid 12-24 hours
Yes R No M or S
Yes R or R-M No M or M-S
Yes M or R-M Yes R or R-M
Rapid to Medium 1-2 days
Yes M or R-M No S
Yes R-M or M Yes S Medium 2-7 days
Yes M Yes or No S Slow Weeks – even months or years
Note: , VR = Very Rapid; R – Rapid; M = Medium; S = Slow.
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Table 12.2 - Rate of Erosion of the core or soil in the foundation
Time for erosion in the core of the embankment or in the foundation Soil Classification
Best Estimate Erosion Rate Index
(IHET) Gradient along pipe 0.2 Gradient along pipe 0.5
SM with <30% fines <2 Very Rapid Very Rapid
SM with > 30% fines 2 to 3 Very Rapid Very Rapid
SC with < 30% fines 2 to 3 Very Rapid Very Rapid
SC with >40% fines 3 Rapid Very Rapid
ML 2 to 3 Very Rapid to Rapid Very Rapid
CL-ML 3 Rapid Very Rapid
CL 3 to 4 Rapid Very Rapid to Rapid
CL-CH 4 Rapid Rapid
MH 3 to 4 Rapid Very Rapid to Rapid
CH with Liquid Limit <65% 4 Rapid to Medium Rapid
CH with Liquid Limit > 65% 5 Medium to Slow Medium
Table 12.3 – Influence of the material in the downstream zone of the embankment on the likely time for development of a breach.
Material Description Likely Breach Time
Coarse grained rockfill Slow – medium
Soil of high plasticity (plasticity index > 50%) and high clay size content including clayey gravels
Medium – rapid
Soil of low plasticity (plasticity index < 35%) and low clay size content, all poorly compacted soils, silty sandy gravels
Rapid – very rapid
Sand, silty sand, silt Very rapid
Table 12.4 – Qualitative terms for times of development of internal erosion, piping and breach (Fell et al 2001, 2003).
Qualitative Term Equivalent Time
Slow (S) Medium (M)
Rapid (R) Very Rapid (VR)
Weeks or months, even years Days or weeks
Hours (> 12 hours) or days < 3 hours
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Note that the dispersivity of the soil does not significantly affect the rate of erosion so is not listed as a factor in Table 12.2. For a homogeneous dam the whole of the embankment is the same soil, so in Table 12.2 the soil is considered as the core, and in Table 12.3 as the downstream zone.
Fell et al (2001,2003) show that the method gives a reasonable estimate of the time for progression beyond where a concentrated leak is observed and breach and the times are acceptably accurate for the purpose here which is to assess the likelihood of detection, intervention and repair. Fell et al (2001, 2003) caution however, against over-reliance of these figures for life loss estimates where the estimates are sensitive to the assumed warning times. The times estimated in Table 12.1 are only approximate, and hidden or unknown details within a dam or its foundation may give shorter or longer times.
12.3 Detection
12.3.1 Some General Principles
Detection may be possible in the continuation or early progression phase, or more likely, in the advanced stages of progression and breach formation. Detection is likely to be by:
1. Observation of increased seepage out of the downstream face of the embankment or in the foundation. This may be by visual observation, or by seepage measurement, or more sophisticated methods such as thermal monitoring of the foundation or the downstream slope.
2. Measured higher pore pressures in the foundation and/or embankment.
3. Settlements, deformation and cracking in the embankment or area downstream of the dam.
Whether detection is likely depends on:
1. The rate at which the internal erosion and piping, and associated processes, such as instability of the downstream face, occurs.
2. The frequency of inspections, and measurement of monitoring equipment.
3. The dam zoning and the location of the concentrated leak and whether the leak will be visible to those doing the inspection.
For example if a process may go from initiation or first presence of a concentrated leak to breach in say 6 hours, and the dam is only inspected or monitored weekly, it is very unlikely that a piping incident will be detected before breach occurs. However if the dam is visible by the general population, there is some chance the leak may be noticed non-the-less.
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Detection early in the internal erosion process is usually difficult, particularly for erosion initiating along a crack, or by backwards erosion because the amount of leakage is very small at the start. Fell et al (2001, 2003) record that most piping incidents are first identified as a concentrated leak in the progression phase. Suffusion is more likely to be detected by piezometers because the process is slower to develop. The presence of conditions potentially leading to heave and backward erosion in the foundation may also be detected by piezometers provided they are correctly positioned and read as reservoir levels rise.
Visual inspection is a vital tool in detecting internal erosion and piping, whether it is successful is dependent on the factors discussed above, but also on such practical issues as:
• Inspections are seldom practical at night, so there is 30% to 50% of the time (varying throughout the year) when detection will not be effective, particularly for rapidly developing piping mechanism. Many dams are not inspected on weekends, further reducing the likelihood of detection.
• Dense vegetation, runoff from rainfall, snow cover can all hide the presence of a concentrated leak. However it can be the case that melted snow is a good indicator of areas affected by seepage.
• For very long embankments, it is not practical to walk to inspect, so it is less likely small leaks are detected.
It is known that most internal erosion and piping failures occur at reservoir levels close to or above historic high, and the physical processes are driven by the reservoir water. Hence a good monitoring and surveillance program will have a greatly increased frequency of inspections and reading of critical instruments under such reservoir conditions.
12.3.2 Assessing the Probability of Not Detecting Internal Erosion
The probability of not detecting internal erosion is determined by
• Assess the probability of not observing the concentrated leak (P nol ) allowing for the location of the
leak for the failure mode under consideration and factors which may mean the leak cannot be observed. This is done using Tables 9.5 and 9.6.
Assess the probability that given the leak is observable (1- P nol ), it is not detected (P nd ) allowing for the time
between the first appearance of the concentrated leak, and the frequency of inspections and/or reading of monitoring instruments. This is done using
• Table 12.7.
• The probability of not detecting the internal erosion P nol + [(1- P nol ) x (P nd )].
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When using these tables, take account of:
• The location of the potential leak when assessing the probabilities. For example there might be a dam where leaks in the abutment area may be readily observed because the foundations are low permeability, and the vegetation is clear, while they may be difficult to observe in the river section because the foundation is high permeability alluvium and the toe overgrown with vegetation.
• The toe of the embankment being drowned out by another reservoir or is in the river, which may make it virtually impossible to detect leaks in this part of the dam.
• The internal erosion mechanism. It may be easier to detect some such mechanisms than others e.g. backward erosion piping in the foundation because sand boils will form.
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Table 12.5 – Factors influencing the likelihood of not observing a concentrated leak (Pnol)
Influence on Likelihood of Not Observing
Factor Relative Import-
ance Less Likely
(1) Neutral
(2) More Likely
(3)
Much More Likely
(4)
Can a concentrated leak be observed at toe?
(3) Foundation low permeability soil or rock, so leaks will emerge at the toe.
and No vegetation or only mown grass at toe, observation of leakage is easy.
Foundation low permeability soil or rock so leaks will emerge at the toe.
or/and Vegetation at toe may preclude observation of seepage.
Foundation medium permeability soil or rock so leaks may remain in the foundation and not emerge at the toe.
or/and
Dense vegetation at toe makes observation of seepage difficult.
Tail-water drowns part or all of toe, or foundation permeable alluvium so leaks may not emerge at the toe.
and Dense vegetation at toe makes observation of seepage difficult.
Dam Zoning which affects whether leaks emerge on the downstream face of the embankment
(2) Homogeneous, earthfill with core wall, concrete face earthfill
Earthfill with toe drain, Zoned earthfill dam, Puddle core,
Earthfill with horizontal and chimney drains, zoned earth and rockfill
Central core earth and rockfill dams, concrete face rockfill, rockfill with core wall.
Seepage instrumentation weirs, etc.
(1) Seepage collected to flow to readily observed measuring weir or real time monitored
Seepage partly collected to flow to measuring weir
Seepage partly collected to flow to measuring weir but masked by rainfall effects
No seepage collection system.
Table 12.6 - Probability of not observing a concentrated leak (P nol ) versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) for internal erosion in an embankment
0.05 0.1 0.2 0.3 0.5 0.9
6 9 12 15 18 24 RF x LF
SECTION 12 Probability of Detection, Intervention and Repair
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Table 12.7 – Probability that given the leak is observable it is not detected given the time between the first appearance of the concentrated leak, and the frequency of inspections
and/or reading of monitoring instruments
Probability of Not Detecting the Internal Erosion (Pnd) Given the Time for Development of Concentrated Leak to Initial Breach From Table 12.1 Frequency of
Inspection and /or Monitoring
< 3 hrs 3 to 12 hrs 12 to 24 hrs 1 to 2 days 2 to 7 days Weeks or
months
Monthly, no public nearby
0.999 0.99 0.95 0.9 0.6 0.1
Monthly, public nearby
0.999 0.8 0.5 0.25 0.1 0.05
Weekly, no public nearby
0.99 0.95 0.9 0.7 0.2 0.1
Weekly, public nearby
0.99 0.75 0.5 0.2 0.1 0.05
Daily, no public nearby
0.9 0.6 0.5 0.1 0.05 0.01
Daily, public nearby
0.8 0.5 0.4 0.1 0.05 0.01
Daily with real time monitoring of leakage
0.2 0.15 0.1 0.1 0.05 0.01
SECTION 12 Probability of Detection, Intervention and Repair
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12.4 Assessing the likelihood of Intervention and Repair
Intervention and repair to prevent the progression of internal erosion and piping and breach can take several forms including:
(i) Drawing down the reservoir level using spillway gates or outlet valves.
(ii) Installing pressure relief wells in the foundation of the embankment.
(iii) Building reverse filters over “boils” or areas where eroding material is emerging from the foundation of the embankment.
(iv) Building a weighting berm to reduce the likelihood of heave, or slope instability, or unravelling.
(v) Dumping granular material (sand/gravel/rockfill) into the upstream side of sinkholes to try to block them.
More than one of these measures may be used together. Which is applicable or feasible will depend on the particular circumstances of the dam.
It should be recognised that there may be reluctance on the part of the reservoir owner or operator to release water given the lost revenue that may result, or if release of reservoir water is likely to result in property damage and loss of life, for example if levee banks downstream of the dam are likely to be overtopped by the flood resulting from release of the water.
Table 12.8 should be used to assess the probability that given the concentrated leak is detected, intervention and repair is not successful. This is done for each pool (reservoir) level partition. It is not practical to cover all the possible scenarios and those doing the risk analysis are required to make their assessment within the range of probabilities shown. In making this assessment consideration should be made for the failure mode and location of the developing pipe.
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Table 12.8 – Assessment of the probability that given the concentrated leak is detected, intervention and repair is not successful (P ui )
Time for Development of Concentrated Leak to Initial
Breach
What can be done Probability of
Not Intervening
< 3 hrs There is too little time to successfully intervene regardless of the failure mode
0.99
3 to 12 hrs In most cases it will be impractical to intervene successfully in this amount of time. Only in cases where there is a straight forward method of intervention, and there are personnel, equipment and materials available will intervention be successful.
0.9 to 0.99
12 to 24 hrs In many cases it will be impractical to intervene successfully in this time. Only in cases where there is a straight forward method of intervention, and there are personnel, equipment and materials available will intervention be successful; or it is a small storage which can be drawn down to stop the failure mode.
0.85 to 0.99
1 to 2 days In many cases it will be impractical to intervene successfully in this time. Only in cases where there is a straight forward method of intervention, and there are personnel, equipment and materials available will intervention be successful; or it is a small storage or medium storage with large gate discharge capacity which can be drawn down to stop the failure mode.
0.7 to 0.95
2 to 7 days In some cases it will be practical to intervene successfully in this time. In cases where there is a straight forward method of intervention, and there are personnel, equipment and materials available; or it is a small storage or medium storage with large gate discharge capacity allowing the reservoir to be drawn down to stop the failure mode.
0.2 to 0.9 (a)
Weeks or months In some cases it will be practical to intervene successfully in this time. Where there is a straight forward method of intervention, and there are personnel, equipment and materials available and large resources intervention has a fair chance of being successful; or it is a small or medium storage with large gate discharge capacity allowing the reservoir to be drawn down to stop the failure mode
0.1 to 0.8 (a)
Note: (a) Use values less than 0.5 only if there is a high degree of confidence in the assessed value.
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12.5 Calculation of Probability of Not Detecting and Not Intervening
The probability of not detecting and not intervening is calculated as follows;
Probability that intervention fails = [Probability of not observing the concentrated leak because it is not observable] + [(Probability it is observable) x (Probability it is not detected in the time between concentrated leak and breach) x (Probability that intervention and repair is not successful)],
Or
Probability that intervention fails = P nol + [(1- P nol ) x P nd x P ui ]
This calculation is represented by the sub-event tree structure shown in Figure 12.1.
Probability of Not Intervening
0.1 0.1 0.1No Intervention
Internal Erosion is Not Able to be Detected
0.5 0.45 0.45No Intervention
0.9 Not Detected in Time
0.5 0.225 0.225 No Intervention
0.5 Intervention and Repair is Not Successful
0.5 0.225Intervention is Successful
Probability of Not Intervening = 0.775
Not Intervene Tree
Yes
No
Yes
No
Yes
No
Figure 12.1 – Sub-event tree for calculating the probability of not intervening.
SECTION 13 Probability of Breach
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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13 Probability of Breach
13.1 Overall Approach and Screening
For each general failure mode including internal erosion in the embankment, in soil or rock foundations, and from embankment to foundation:
Step 1: Screen the breach mechanisms depending on the dam zoning type using Table 13.1.
Step 2: Estimate the probability of breach by gross enlargement of the pipe using Section 13.2.
Step 3: Estimate the probability of breach by instability of the downstream slope using Section 13.3. This involves estimating the probability of slope instability occurring and the probability of loss of freeboard given instability.
Step 4: Estimate the probability of breach by unravelling or sloughing of the downstream slope of the embankment using Section 13.4.
Step 5: Estimate the probability of breach by sinkhole development using Section 13.5.
Step 6: Estimate the overall probability of breach by adding the probabilities for each of the four mechanisms, using the appropriate statistical summation Pbreach = 1 – [(1 - Pge) x (1 - Psi) x (1 - Psu) x (1 - Psd)].
In most cases the probability of breach will be 1.0 when it is on the continuing erosion branch of the event tree. Exceptions to this will be if the pool level drops below the inlet of the developing pipe before a breach mechanism has time to develop. This is considered in Section 13.2.
The probability of breach is often less than 1.0 when on the some or excessive erosion branches of the event tree. For these cases, the seepage flows that develop through the dam or foundation will be limited by the filtering material. The probability of breach will depend on how well the dam can cope with the leakage flows that may occur. Section 10.1.4 provides guidance on the possible magnitude of leakage flows that may develop for the some and excessive erosion conditions.
13.1.1 Screening of Breach Mechanisms
For most dam types and failure modes, the likelihood for breach development will be dominated by one or two of the potential breach mechanisms. Breach mechanisms will not necessarily be applicable to some dam zoning types or modes of piping and can be ignored.
Table 13.1 lists those breach mechanisms which should be considered in the assessment depending on the dam zoning type and mode of internal erosion for internal erosion in the embankment due to a crack or poorly compacted zone. Table 13.1 also applies to internal erosion in a soil foundation. Figure 1.1 in Section 1 showsthe dam zoning types.
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Table 13.1 – Screening of breach mechanisms for internal erosion through the embankment, internal erosion in soil foundations, and from embankment into foundation
Breach Mechanisms Dam Zoning Type Gross
Enlargement Slope Instability Sloughing or Unravelling
Sinkhole Development
Homogeneous earthfill * Exclude, except if downstream fill is
cohesionless
Earthfill with filters * Exclude, except if downstream fill is
cohesionless
Earthfill with rockfill toe * Exclude, except if downstream fill is
cohesionless
Zoned earthfill Exclude, except if downstream fill can
support a roof
Exclude, except if downstream fill is
cohesionless
Zoned earthfill and rockfill
Exclude, except if downstream fill can
support a roof
*
Central core earth and rockfill (or gravel shells)
Exclude, except if downstream fill can
support a roof
Exclude, except if existing dam has marginal stability
*
Concrete face earthfill * Exclude, except if downstream fill is
cohesionless
Concrete face rockfill (including gravel fill)
Exclude Exclude, except if dam is gravel or low
permeability
* Exclude
Puddle core earthfill * Exclude, except if downstream fill is
cohesionless
Earthfill with corewall Exclude * Exclude, except if downstream fill is
cohesionless
Rockfill with corewall Exclude Exclude, except if existing dam has marginal stability
*
Hydraulic fill Exclude, except if downstream fill can
support a roof
*
Key: Breach mechanism should be included for the probability estimate * Breach mechanism should be included for probability estimate, and usually is the more critical
mechanism
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Table 13.1 does not apply to failure modes involving open or in filled defects and solution features in rock foundations because the leakage flows may exceed the capacity of even free draining rockfill.
Internal erosion by the process of suffusion is very unlikely to lead to the formation of a pipe through the dam or its foundation, and hence the probability of breach by gross enlargement where the mode of erosion is suffusion can be excluded. Breach by slope instability or sloughing/unravelling are usually the more critical mechanisms for suffusion, although the probabilities for breach are usually relatively low for this mode internal erosion.
13.2 Estimation of the Probability of Breach by Gross Enlargement
13.2.1 Screening for internal erosion in the embankment, soil foundation, and embankment into foundation;
• Breach by gross enlargement of the pipe requires a continuing erosion condition. Breach by gross enlargement of the pipe can be considered to be negligible when on the “Some Erosion” and “Excessive Erosion” branches of the event tree.
• For internal erosion through the embankment, breach by gross enlargement can be considered negligible in cases where the downstream shell is unable to support a roof of a pipe. Use Table 13.2 to assess if this applicable.
• If applicable, estimate the probability of breach by gross enlargement using Table 13.3. This considers whether the reservoir will drop below the level of the pipe before the enlarging pipe develops into a breach.
Table 13.2 – Probability of breach by gross enlargement of the pipe – Ability to support a pipe (Screening)
Downstream shell/zone Ability to Support a Roof
Probability of Breach by Gross Enlargement
Downstream shell comprises free draining rockfill, or coarse sandy gravel Downstream shell comprises sand and gravel, <5% plastic fines or <15% non plastic fines
Very unlikely for piping through dam
Not a likely mode of breach for piping through the dam. Breach by slope instability or unravelling/sloughing are likely to be more critical. Assign probability of breach by gross enlargement Pge = 0.
All other cases Likely Assess using Table 13.3
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13.2.2 Screening for internal erosion in a rock foundation;
Breach by gross enlargement is only possible for internal erosion through rock foundations if the in-filled defect is sufficiently large such that the embankment may collapse into the void and lowers the crest to below the reservoir level.
Ignore this failure mode unless the size of the in filled defect is very large (e.g. in-filled caverns or caves in karst > 2m).
13.2.3 Assessment for internal erosion in the embankment, soil foundation and from embankment into foundation
For breach to occur by gross enlargement of a pipe; the pipe must stay open until it is so large that the settlement of the crest due to the pipe, or collapse of the embankment into the pipe lowers the crest to below the reservoir level.
If there is no intervention, the process can only stop if one or more of the following occurs:
a) The hydraulic shear stresses in the pipe reach an equilibrium condition with the erosion resistance of the soil. This will not happen unless the reservoir level drops giving a lower gradient, as the hydraulic shear stress increases with hole diameter for a constant gradient.
6) The reservoir empties or falls below the entrance of the pipe before a breach mechanism is able to develop. This is a common consideration where internal erosion may develop in the upper part of the dam under short duration flood loading conditions.
Table 13.3 provides guidance on the probability of breach by gross enlargement assuming there is no restriction on flows, and no intervention to lower the reservoir level.
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Table 13.3 – Probability of breach by gross enlargement of the pipe
Characteristics of Core Material
Soil Classification Hole Erosion Index
Time for Reservoir Level to Fall Below the
Invert of the Pipe
Probability of Breach by Gross Enlargement
SM, SC, ML, dispersive soils <=3
2 to 3
1.0
CL, CL-CH, MH or CH with Liquid Limit <65%
4 3 to 5
>2 days 1-2 days <1 day
0.8 to 0.95 0.6 to 0.8 0.3 to 0.6
CH with Liquid Limit > 65% 5
4 to 6
> 2 weeks
1 – 2 weeks <1 week
0.8 to 0.95
0.3 to 0.8 0.1 to 0.3
CH with Liquid Limit <65%
Or CH with Liquid Limit > 65% HET carried out
6 Likely to self limit 0.05 to 0.1
Notes: (1) Assuming there is no restriction on flows and no intervention to lower the reservoir level (2) IHET from Hole Erosion Tests. (3) The basis for the judgemental probabilities is given in the supporting information document.
13.2.4 Assessment for internal erosion in a rock foundation
• Estimate the probability that the roof over the void collapses and causes the crest to subside.
• Estimate the probability that the amount of crest subsidence is sufficient to cause loss of freeboard.
This needs to be considered on a case by case basis using the methods described in Appendix E.
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13.3 Estimation Of The Probability Of Breach By Slope Instability
13.3.1 Approach
• For internal erosion in embankments, soil foundations and from embankment to foundation, estimate the probability of slope instability occurring due to the increased seepage flows (Psi-i) using Table 13.4 and Table 13.5.
• For internal erosion in rock foundations, use Section 13.3.3 and Tables 13.6 to 13.9.
• Estimate the probability of loss of freeboard due to instability (Psi-lf) using Table 13.10 and Table 13.11.
• The probability of breach by slope instability is equal to (Psi-i) x (Psi-lf).
13.3.2 Estimation of the probability of slope instability initiates for internal erosion in the embankment, soil foundation, and from embankment into foundation
The assessment considers whether internal drainage measures in the dam are able to prevent pore pressures rising in the dam and/or foundation and whether the factor of safety of the dam falls below 1.0 if pore pressures do increase.
Estimate the probability of a downstream slide initiating using Table 13.4 and Table 13.5. It is assumed that seepage in a soil foundation will exit under the embankment.
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Table 13.4 – Factors which influence likelihood of breaching by instability of the downstream slope – Slide Initiates for internal erosion in the
embankment, in soil foundations, and from embankment into foundation.
Likelihood Factor (LF)
Factor
Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Internal drainage measures in dam
(3) Good
Filter drains with good discharge capacity
Or free draining rockfill or clean sandy gravel in the downstream zones
Moderate
Single stage filter zones
Or sandy gravel, or moderate fines rockfill in the downstream zones
Limited
Filter drain with excessive fines, poor discharge capacity,
Or silty sandy gravel, or high fines content weathered rockfill in the downstream zones
None
No or limited zoning of materials and no filter drains
Downstream Slope
For dams with an earthfill downstream zone (a)
(2)
3H:1V or flatter
2.5H:1V
2H:1V
Steeper than 1.8H:1V
OR
For dams with a free draining rockfill downstream zone (b)
Flatter than 1.75H: 1V
1.5H: 1V Steeper than 1.4H: 1V
Steeper than 1.3H: 1V
Downstream shell materials
(1) Sandy gravel <5% fines,
Coarse grained, free draining rockfill
Sandy gravel 5-20% fines
‘Dirty’ rockfill
Cohesive soils,
Fine grained rockfill
Silty sand, silty sandy gravel, 20-50% fines
Notes: (a) Applies to the following dam types; homogeneous earthfill, earthfill with filter, earthfill with rock toe, zoned earthfill, concrete face earthfill, puddle core earthfill, earthfill with core wall and hydraulic fill.
(b) Applies to the following dam types; zoned earth and rockfill, central core earth and rockfill, concrete face rockfill and rockfill with core wall.
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Table 13.5 - Estimation of the probability of breach by slope instability – slide initiates for internal erosion in the embankment, in soil foundations, and from embankment into
foundation versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF))
0.001 0.003 0.005 0.02 0.1 0.9 (CE)
0.0001 0.0005 0.002 0.01 0.05 0.5 (EE)
negligible negligible 0.00001 0.001 0.005 0.05 (SE)
6 9 11 13 18 24
Note: Select the probability scale corresponding to the filter erosion condition being considered on the event tree. CE = Continuing Erosion branch, EE = Excessive Erosion branch, and SE = Some Erosion branch.
13.3.3 Estimation of the probability of Slope Instability of the embankment initiates for internal erosion in a rock foundation
• Estimate the probability that leakage through the rock foundations exits into the downstream shell PS using Table 13.6.
• Estimate the probability of slope instability initiating due to the increased leakage flows (Psi-i) using Table 13.7, Table 13.8 and Table 13.9.
The assessment considers whether the internal drainage measures in the dam are able to prevent pore pressures rising in the dam and/or foundation and whether the factor of safety of the dam falls below 1.0 if pore pressures do increase.
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Table 13.6 – Probability of seepage exits from defects or solution features in a rock foundation into the downstream shell (PS)
Scenarios Probability of the Seepage
Path Exiting into the Downstream Shell
The open or in-filled defect in the rock foundation daylights downstream of the dam, and the defect is not in direct contact with the downstream shell, and there is very limited interconnectivity through other joint sets
Negligible. Adopt PS = 0
The open or in-filled defect in the rock foundation daylights downstream of the dam, and the defect is not in direct contact with downstream shell, but there is a likely connection into the downstream shell via an interconnected open joint set
0.1 to 0.5
The open or in-filled defect in the rock foundation daylights downstream of the dam, and the defect is likely to be in direct contact with downstream shell
0.5 to 1.0 (a)
The open or in-filled defect in the rock foundation does not daylight downstream of the dam, and the defect is in direct contact with downstream shell
1.0 (a)
Note (a) The geometry of the leakage flow path affects the flow rate. If the leakage path daylights downstream of the dam it is likely there will be less flow into the downstream shell of the dam.
Evaluate the relative discharge capacity of the foundation drains and downstream zone compared to the size of the defect in the rock foundation using Table 13.7.
Estimate the probability of a downstream slide initiating using Table 13.8 and Table 13.9.
SECTION 13 Probability of Breach
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Table 13.7 – Assessment of size of leak in defect or solution feature in a rock foundation relative to discharge capacity of foundation drains and downstream shell
Discharge capacity of foundation drain and downstream zone
Width of Defect or solution feature exiting into the
Downstream Zone
Poor No or limited zoning of materials and no
foundation filter drains
Limited Foundation filter
drain with excessive fines, poor discharge
capacity, Or silty sandy gravel, or high fines content
weathered rockfill in the downstream
zones
Moderate Single stage
foundation filter zone
Or sandy gravel, or moderate fines rockfill in the
downstream zones
Good Foundation filter drains with good
discharge capacity Or free draining rockfill or clean
sandy gravel in the downstream zones
<5mm N N LL Negligible
5 – 25mm ML ML N LL
25 – 100mm MML MML ML N
100 – 300mm MML MML MML ML
>300mm MML MML MML MML
Note: LL = Less Likely; N = Neutral; ML = More Likely; MML = Much More Likely
SECTION 13 Probability of Breach
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Table 13.8 – Factors which influence likelihood of breaching by instability of the downstream slope –- Slide Initiates for internal erosion in rock foundation
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely(1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Size of leak relative to discharge capacity of the foundation drains and downstream shell (from Table 13.7)
(3) LL
Refer to Table 13.7
N
Refer to Table 13.7
ML
Refer to Table 13.7
MML
Refer to Table 13.7
Downstream Slope
For dams with an earthfill downstream zone (a)
(2)
3H:1V or flatter
2.5H:1V
2H:1V
Steeper than 1.8H:1V
OR
For dams with a free draining rockfill downstream zone (b)
Flatter than 1.75H: 1V
1.5H: 1V Steeper than 1.4H: 1V
Steeper than 1.3H: 1V
Downstream shell materials (1) Sandy gravel <5% fines,
Coarse grained, free draining rockfill
Sandy gravel 5-20% fines
‘Dirty’ rockfill
Cohesive soils,
Fine grained rockfill
Silty sand, silty sandy gravel, 20-50% fines
Notes: (a) Applies to the following dam types; homogeneous earthfill, earthfill with filter, earthfill with rock toe, zoned earthfill, concrete face earthfill, puddle core earthfill, earthfill with core wall and hydraulic fill.
(b) Applies to the following dam types; zoned earth and rockfill, central core earth and rockfill, concrete face rockfill and rockfill with core wall.
Table 13.9 - Estimation of the probability of breach by slope instability – slide initiates (Psi-i) for internal erosion in rock foundations versus ∑ (Relative importance factor (RF)) x
(Likelihood factor (LF))
0.001 0.003 0.006 0.02 0.1 0.9
6 9 11 13 18 24
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A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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13.3.4 Loss of Freeboard due to Slope Instability
The assessment considers whether the resulting sliding deformations are sufficient to result in loss of freeboard so the reservoir overtops the dam crest. Estimate the probability of loss of freeboard using Table 13.10 and Table 13.11.
Table 13.10 – Factors which influence likelihood of breaching by instability of the
downstream slope – loss of freeboard
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Freeboard compared to dam height at the time of incident
(3) > 7% ≈ 5% < 3% < 1%
Presence of strain weakening soils in the embankment and foundation
(2) Sandy clays, low to medium plasticity, clay size content <20%, or medium dense to dense dilative non cohesive soils or rockfill.
Clays, sandy clays, clay size content 20% to 40%, or medium dense non cohesive soils.
Clays, sandy clays, high plasticity; clay size content (% passing 0.002 mm) > 40% or/and saturated, very loose sand, or loose silty sand contractive on shearing
As for more likely, but with very high clay size content or very loose contractive granular soil
Crest width (1) > 30 ft (9m) ≈ 20 ft (6m) < 13 ft (4m) ≤ 10 ft (3m)
Table 13.11 - Estimation of the probability of breach by loss of freeboard versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF))
0.001 0.005 0.02 0.1 0.5 1.0
6 9 11 13 18 24
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13.4 Estimation of the Probability of Breach by Sloughing or Unravelling
13.4.1 Approach
For sloughing to occur, the downstream face would have to be relatively steep, and the shoulder material a cohesionless soil, probably sandy gravel, or gravely sand, possibly with some silty fines. The process would have to be allowed to continue until it gradually eroded away the crest and allowed the reservoir to overtop the embankment.
Unravelling usually relates to the progressive removal of individual rocks by fairly large seepage flows flowing through the downstream rockfill.
The approach is:
• For internal erosion in rock foundations, Estimate the probability that seepage through the rock foundations exits into the downstream shell PS using Table 13.6.
• For internal erosion in the embankment, soil foundation and embankment into foundation, assume that the seepage will emerge into the downstream shell of the embankment, so PS = 1.0.
• For dams with a downstream zone of earthfill (i.e. clay, silt, sand or gravel) use Tables 13.12, 13.13 and 13.14 to estimate the probability of breach by sloughing Psl.
• For dams with a downstream zone of rockfill, use Tables 13.15, 13.16 and 13.17 to estimate the probability of breach by unravelling Pun.
• The probability of breach by sloughing or unravelling is equal to (PS) x (Psl) for dams with a downstream zone of earthfill or (PS) x (Pun) for dams with a rockfill shell.
For cases where a very coarse rockfill toe is present, the probabilities for breach by unravelling can be reduced from those in given in Table 13.16 if calculations indicate that unravelling is very unlikely to occur.
SECTION 13 Probability of Breach
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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Table 13.12 – Factors which influence likelihood of breaching by unravelling – dams with an earthfill downstream zone
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Material in downstream zone
(3) Cohesive soils Sandy gravel <20% fines,
Silty sand, silty sandy gravel, 20%-50% non plastic fines.
As for more likely, but uncompacted materials
Freeboard at the time of incident
(2) > 13 ft (4 m) ≈ 10 ft (3 m) < 6 ft (2 m) < 3 ft (1 m)
Downstream slope of the embankment
(1) 3H:1V or flatter 2.5H: 1V 2H: 1V Steeper than 1.8H: 1V
Table 13.12 applies to the following dam types; homogeneous earthfill, earthfill with filter, earthfill with rock toe, zoned earthfill, concrete face earthfill, puddle core earthfill, earthfill with core wall and hydraulic fill.
Table 13.13 - Estimation of the probability of breach by sloughing (earthfill)
versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) for internal erosion in the embankment, in soil foundations, and from embankment into foundation
1.0 1.0 1.0 1.0 1.0 1.0 (CE)
0.01 0.05 0.1 0.5 0.9 1.0 (EE)
0.001 0.003 0.01 0.05 0.1 0.5 (SE)
6 9 11 13 18 24
Note: Select the probability scale corresponding to the filter erosion condition being considered on the event tree. CE = Continuing Erosion branch, EE = Excessive Erosion branch, and SE = Some Erosion branch.
SECTION 13 Probability of Breach
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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Table 13.14 - Estimation of the probability of breach by sloughing (earthfill) versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) for internal
erosion in rock foundation
1.0 1.0 1.0 1.0 1.0 1.0 (>25mm)
0.01 0.05 0.1 0.5 0.9 1.0 (5-25mm)
0.001 0.003 0.005 0.05 0.1 0.5 (<5mm)
6 9 11 13 18 24
Note: Select the probability scale corresponding to the width of the open or in filled defect that exits into the downstream shell.
Table 13.15 – Factors which influence likelihood of breaching by unravelling – dams with a rockfill downstream zone
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Material in downstream zone
(3) Coarse grained free draining rockfill.
Medium grained “dirty” rockfill
Fine grained rockfill
As for more likely, but uncompacted materials
Downstream slope of the embankment
(2) Flatter than 1.75H: 1V
1.5H: 1V Steeper than 1.4H: 1V
Steeper than 1.3H: 1V
Freeboard at the time of incident
(1) > 13 ft (4 m) ≈ 10 ft (3 m) < 6 ft (2 m) < 3 ft (1 m)
This table applies to the following dam types; zoned earth and rockfill, central core earth and rockfill, concrete face rockfill and rockfill with core wall.
SECTION 13 Probability of Breach
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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Table 13.16 - Estimation of the probability of breach by unravelling (rockfill) versus∑ (Relative importance factor (RF)) x (Likelihood factor(LF)) for internal erosion in
the embankment, in soil foundations, and from embankment into foundation
0.5 0.6 0.7 0.8 0.9 1.0 (CE)
0.001 0.005 0.01 0.05 0.1 0.5 (EE)
0.0001 0.0005 0.001 0.005 0.01 0.05 (SE)
6 9 11 13 18 24
Note: Select the probability scale corresponding to the filter erosion condition being considered on the event tree. CE = Continuing Erosion branch, EE = Excessive Erosion branch, and SE = Some Erosion branch.
Table 13.17 - Estimation of the probability of breach by unravelling (rockfill) versus ∑ (Relative importance factor (RF)) x (Likelihood factor (LF)) for internal erosion
in rock foundation
0.5 0.6 0.7 0.8 0.9 1.0 (>300mm)
0.5 0.6 0.7 0.8 0.9 1.0 (100-300mm)
0.001 0.005 0.01 0.05 0.1 0.5 (25-100mm)
0.0001 0.0005 0.001 0.005 0.01 0.05 (5-25mm)
0.0001 0.0005 0.001 0.005 0.01 0.05 (<5mm)
6 9 11 13 18 24
This table applies to the following dam types; zoned earth and rockfill, central core earth and rockfill, concrete face rockfill and rockfill with core wall.
Note: Select the probability scale corresponding to the width of the open or in filled defect that exits into the downstream shell.
SECTION 13 Probability of Breach
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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13.5 Estimation of the Probability of Breach by Sinkhole Development
13.5.1 Approach
• Estimate the probability of a sinkhole developing as a result of the internal erosion (Ps-f).
• Estimate the probability that the sinkhole causes loss of freeboard (Ps-lf). Assume the sinkhole develops on the crest unless there is a specific reason to expect it to develop elsewhere on the embankment.
• The probability of breach by sinkhole development = probability of sinkhole (Ps-f) x probability of loss of freeboard due to the sinkhole (Ps-lf).
13.5.2 Probability of Sinkhole Formation
Estimate the probability of a sinkhole developing as a result of the internal erosion (Ps-f) using Table 13.18.
Table 13.18 – Probability of a sinkhole or crest settlement developing (Ps-f)
Mode of Internal Erosion Probability of Sinkhole or Crest
Settlement Developing given Internal Erosion has Initiated
Internal erosion in the embankment and into the foundation
0.6
Internal erosion in the foundation 0.3
13.5.3 Probability of Loss of Freeboard due to Sinkhole Formation
For breach to occur by sinkhole development into an erosion pipe in the embankment, the sinkhole or crest settlement would need to be sufficiently large to settle the crest to below reservoir level. For internal erosion in the foundation, loss of freeboard can also occur by excessive settlement of the embankment induced by the loss of foundation materials.
Estimate the probability of loss of freeboard due to sinkhole formation using Table 13.19 and Table 13.20.
SECTION 13 Probability of Breach
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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Table 13.19 – Factors which influence likelihood of breaching by sinkhole development – loss of freeboard given sinkhole develops
Likelihood Factor (LF)
Factor Relative
Importance Factor (RF)
Less Likely (1)
Neutral (2)
More Likely (3)
Much More Likely
(4)
Freeboard at the time of the incident
(3) > 13 ft (4 m) ≈ 10 ft (3 m) < 6 ft (2 m) < 3 ft (1 m)
Width of crest (2) > 30 ft (9 m) ≈ 20 ft (6 m) < 13 ft (4 m) ≤ 10 ft (3 m)
Material in the core of the embankment
(1) High plasticity clay, well compacted
Low to medium plasticity clays, and sandy clays
Non-cohesive, silty sand or silty sandy gravel
As for more likely, poorly compacted/loose.
Table 13.20 - Estimation of the probability of breach by sinkhole development – loss of freeboard given sinkhole develops versus ∑ (Relative importance factor (RF)) x
(Likelihood factor (LF))
0.0002 0.0005 0.001 0.005 0.02 0.2 (CE)
0.0001 0.0002 0.0005 0.002 0.01 0.1 (EE)
0.00005 0.0001 0.0002 0.001 0.005 0.01 (SE)
6 9 11 13 18 24
SECTION 14 References
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
14-1
14 References
Barneich, J., Majors, D., Moriwaki, Y., Kulkarni, R. and Davidson, R., Application of reliability analysis in the Environmental Impact Report (EIR) and design of a major dam project. Proceedings of Uncertainty 1996. Geotechnical Engineering Division, ASCE.
Fell, R., Wan, C.F., Cyganiewicz, J. and Foster, M. (2001). The time for development and detectability of internal erosion and piping on embankment dams and their foundations. UNICIV Report No. R-399, ISBN: 84841 366 3. School of Civil and Environmental Engineering, The University of New South Wales.
Fell, R., Wan, C.F., Cyganiewicz, J. and Foster, M. (2003). Time for development of internal erosion and piping in embankment dams. ASCE Journal of Geotechnical and GeoEnvironmental Engineering, Vol. 129, No.4, 307-314.
Fell, R., Wan, C.F. and Foster, M. (2004). Methods for estimating the probability of failure of embankment dams by internal erosion and piping – piping through the embankment. UNICIV Report No. R-428, The University of New South Wales, Sydney, Australia. ISBN 85841 395 7.
Fell, R. and Wan, C.F. (2005) Methods for estimating the probability of failure of embankment dams by internal erosion and piping in the foundation and from embankment to foundation. UNICIV Report No R-436, The University of New South Wales, Sydney, Australia 2052.ISBN: 85841 403 1.
FEMA (2005) Conduits through Embankment Dams, Best practices for design, construction, problem identification and evaluation, inspection, maintenance, renovation and repair, L-266, Federal Emergency Management Agency.
Foster, M.A. (1999). The probability of failure of embankment dams by internal erosion and piping. PhD thesis, School of Civil and Environmental Engineering, The University of New South Wales.
Foster, M.A. and Fell, R. (1999a). A Framework for Estimating the Probability of Failure of Embankment Dams by Piping Using Event Tree Methods. UNICIV Report No. R-377. School of Civil and Environmental Engineering, The University of New South Wales. ISBN: 85841 343 4.
Foster, M.A. and Fell, R. (1999b). Assessing Embankment Dam Filters Which Do Not Satisfy Design Criteria. UNICIV Report No. R-376, School of Civil and Environmental Engineering, University of New South Wales. ISBN: 85841 343 4, ISSN 0077-880X.
Foster, M. and Fell, R. (2000). Use of Event Trees to Estimate the Probability of Failure of Embankment Dams by Internal Erosion and Piping. 20th Congress on Large Dams, Beijing. Vol. 1, 237-260. ICOLD, Paris.
Foster, M. and Fell, R. (2001). Assessing embankment dams, filters which do not satisfy design criteria, J. Geotechnical and Geoenvironmental Engineering, ASCE, Vol.127, No.4, May 2001, 398-407.
SECTION 14 References
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
14-2
Maniam, M. (2004). Critical seepage gradients beneath embankment dams. Bachelor of Civil Engineering thesis, School of Civil and Environmental Engineering, The University of New South Wales, Sydney.
Pells, S. and Fell, R. (2002). Damage and Cracking of Embankment Dams by Earthquakes, and the Implications for Internal Erosion and Piping. UNICIV Report No. R-406, School of Civil and Environmental Engineering, The University of New South Wales, ISBN: 85841 375 2.
Pells, S. and Fell, R. (2003). Damage and Cracking of Embankment Dams by Earthquake and the Implications for Internal Erosion and Piping. Proceedings 21st Internal Congress on Large Dams, Montreal. ICOLD, Paris Q83-R17, International Commission on Large Dams, Paris.
Schmertmann, J.H. (2000). The non-filter factor of safety against piping through sands. ASCE Geotechnical Special Publication No. 111, Judgment and innovation. Edited by F. Silva and E. Kavazanjian, ASCE, Reston.
Sherard, J.L. and Dunnigan, L.P. (1989). Critical filters for impervious soils. J. Geotech. Eng. ASCE, Vol.115, No.7, 927-947.
Skempton A.W. and Brogan, J.M. (1994). Experiments on piping in sandy gravels. Geotechnique 44, No.3, 449-460.
Wan, C.F. and Fell, R. (2004). Experimental investigation of internal instability of soils in embankment dams and their foundations. UNICIV Report No.429, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, ISBN 85841 396 5.
Wan, C.F. and Fell, R. (2002). Investigation of internal erosion and piping of soils in embankment dams by the slot erosion test and the hole erosion test. UNICIV Report No. R-412, ISBN: 85841 379 5, School of Civil and Environmental Engineering, The University of New South Wales.
Wan, C.F. and Fell, R. (2004). Experimental investigation of internal instability of soils in embankment dams and their foundations. UNICIV Report No.429, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, ISBN 85841 396 5.
Wan, C.F. and Fell, R. (2004a). Investigation of rate of erosion of soils in embankment dams. ASCE Journal of Geotechnical and GeoEnvironmental Engineering, Vol. 130, No. 4, 373-380.
Wan, C.F. and Fell, R. (2004b). Laboratory tests on the rate of piping erosion of soils in embankment dams. Geotechnical Testing Journal, vol.27, No.3, 295-303.
Weijers, J.B.A and Sellmeijer, J.B. (1993). A new model to deal with the piping mechanism on “Filters in Geotechnical and Hydraulic Engineering. Brauns, Herbaum and Schuler (editors), Balkema, Rotterdam.
SECTION 15 List of Acronyms & Symbols
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
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15 List of Acronyms & Symbols
List of Acronyms & Symbols used in this Report
Acronym/Symbol Meaning Reference
α Slope of sides of compressible zone Section 5.2.3, Figure 5.5
β abutment slope Section 5.3.2, Figure 5.1
AEP Annual Exceedance Probability Section 3.4.3
CE Continuing Erosion Section 7.1
CF Amount of collapse compression as a proportion of the layer thickness
Section 6.6.4
CLSM Controlled low strength material Section 6.3
CPT Cone Penetration Test Section 6.5
EE Excessive Erosion Section 7.1
POR Pool of record Section 4.4
G Height of the gap/crack formed by collapse compression
Section 6.6.4
H Height of dam Section 5.2.1, Figure 5.3
Hw Height of wall/cliff Section 5.2.1, Figure 5.2
iav Average seepage gradient Section 6.6
iavf Average seepage gradient in the foundation Section 11.3
icr Critical seepage gradient Section 6.6
IHET Erosion Rate Index Section 5.4.2
ipmt Average gradient required to initiate backward erosion
Section 6.6
LF Likelihood factor Section 4.4
NE No Erosion boundary Section 7.1
OWC Optimum Water Content Section 6.2
Pc Probability of a transverse crack Section 5.1
PCE Probability of continuing erosion Section 7.2
Pcl Probability of continuous layer of cohesionless soil Section 11.2
Pdetect Probability of detection Section 9
Pe Probability of initiation of backward erosion or suffusion at the core-foundation contact
Section 12.2
Pfe Probability of filtered exit Section 7.2
PH Probability of heave Section 11.2
Phf Probability of hydraulic fracture across the cutoff Section 12.6
SECTION 15 List of Acronyms & Symbols
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
15-2
trench
PI Probability of initiation of erosion Section 5.1
PIC Probability of initiation of erosion in a crack Section 5.1
Pic Probability of scour erosion at the core-foundation contact
Section 12.4
PIH Probability of initiation and progression of backward erosion given heave
Section 11.3
PINH Probability of initiation and progression of backward erosion given no heave
Section 11.3
Pintervene Probability of intervention Section 9
PIP Probability of initiation and progression of backward erosion
Section 6.6
PIUS Probability soil is internally unstable Section 6.6
Ppath Probability of a continuous pathway of open joints in rock or coarse grained soil
Section 12.2
Punf Probability of unfiltered exit Section 7.2
RF Relative importance factor Section 4.4
SE Some Erosion Section 7.1
SPT(N1)60 Standard Penetration Test N value, corrected to 60% energy
Section 6.2
SMDD Standard Maximum Dry Density
TP Thickness of layer of poorly compacted soil Section 6.6.4
W/D Width to depth ratio of the cut-off trench Section 12.6
W/H Width to height ratio of the core Section 5.3.2, Figure 5.4
Wb Width of bench at base of wall/cliff Section 5.2.1, Figure 5.2
Wv Width of base of valley Section 5.2.1, Figure 5.3
Appendix A Navigation Table for Internal Erosion
Through the Embankment
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-1
Table A1. Probability of Failure by Internal Erosion Through the Embankment (Sheet 1)
Initiating Mechanism Sketch (1) Failure Path
Identification and Screening
(2) Evaluate the Probability of
Initiation of Erosion PI
(3) Probabilities for No, Some, Excessive
and Continuing Erosion PNE, PSE, PEE,
PCE
(4) Probability of Progression PP
(5) Probability of Unsuccessful Detection and
Intervention Pudi
(5) Probability of Breach Pbreach
(6) Calculate the Probability of Failure
Initiation of Erosion in Transverse Cracks in Upper Part of the Embankment
Cross SectionCrack in Upper Part
Upper 1/3rd
Cross SectionCrack in Upper Part
Upper 1/3rd
Use Table A2 to identify and screen potential crack mechanisms
Use Table A2 to evaluate the probability of initiation for each crack initiating mechanism.
PI (IMx)
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table A7.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table A8.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table A9.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table A10.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE
Calculate the probability of failure for each IM using the event tree.
Pfail = PI (IMx) x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
Pbreach-CE
Transverse Cracks in Upper Part of Embankment
Yes
No
Initiation
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI (IMx) PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-CE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE
Σ Pfail
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-2
Table A1. Probability of Failure by Internal Erosion Through the Embankment (Sheet 2)
Initiating Mechanism Sketch (1) Failure Path Identification and
Screening
(2) Evaluate the Probability of
Initiation of Erosion PI
(3) Probabilities for No, Some, Excessive
and Continuing Erosion PNE, PSE, PEE,
PCE
(4) Probability of Progression PP
(5) Probability of Unsuccessful Detection and
Intervention Pudi
(5) Probability of Breach Pbreach
(6) Calculate the Probability of Failure
Initiation of Erosion in Transverse Cracks in the Middle and Lower Parts of the Embankment
Cross SectionCrack in Middle and Lower Part
Lower 2/3rd
Cross SectionCrack in Middle and Lower Part
Lower 2/3rd
Use Table A3 to identify and screen potential crack mechanisms
Use Table A3 to evaluate the probability of initiation for each crack initiating mechanism.
PI (IMx)
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table A7.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table A8.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table A9.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table A10.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE
Calculate the probability of failure for each IM using the event tree.
Pfail = PI (IMx) x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
No
Pbreach-CE
Transverse Cracks in Middle and Lower Part of Embankment
Yes
Initiation
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI (IMx)
PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE Pfail-CE
Σ Pfail
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-3
Table A1. Probability of Failure by Internal Erosion Through the Embankment (Sheet 3)
Initiating Mechanism Sketch (1) Failure Path Identification and
Screening
(2) Evaluate the Probability of
Initiation of Erosion PI
(3) Probabilities for No, Some, Excessive
and Continuing Erosion PNE, PSE, PEE,
PCE
(4) Probability of Progression PP
(5) Probability of Unsuccessful Detection and
Intervention Pudi
(5) Probability of Breach Pbreach
(6) Calculate the Probability of Failure
Initiation of Erosion in Poorly Compacted or High Permeability Zones in the Embankment
Cross SectionPoorly Compacted or High Permeability Zone
Cross SectionPoorly Compacted or High Permeability Zone
Cross SectionPoorly Compacted or High Permeability Zone
Use Table A4 to identify and screen potential crack mechanisms
Use Table A4 to evaluate the probability of initiation for each initiating mechanism.
PI (IMx)
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table A7.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table A8.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table A9.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table A10.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE
Calculate the probability of failure for each IM using the event tree.
Pfail = PI (IMx) x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
Pbreach-CE
Poorly Compacted or High Permeability Zones in the Embankment
Yes
No
Initiation
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI (IMx)
PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE Pfail-CE
Σ Pfail
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-4
Table A1. Probability of Failure by Internal Erosion Through the Embankment (Sheet 4)
Initiating Mechanism Sketch (1) Failure Path Identification and
Screening
(2) Evaluate the Probability of
Initiation of Erosion PI
(3) Probabilities for No, Some, Excessive
and Continuing Erosion PNE, PSE, PEE,
PCE
(4) Probability of Progression PP
(5) Probability of Unsuccessful Detection and
Intervention Pudi
(5) Probability of Breach Pbreach
(6) Calculate the Probability of Failure
Initiation of Erosion in Poorly Compacted or High Permeability Zones Along a Conduit
Cross Section
Conduit
Cross Section
Conduit
Use Table A5 to identify and screen potential crack mechanisms
Use Table A5 to evaluate the probability of initiation for each initiating mechanism.
PI (IMx)
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table A7.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table A8.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table A9.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table A10.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE
Calculate the probability of failure for each IM using the event tree.
Pfail = PI (IMx) x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
Pbreach-CE
Poorly Compacted or High Permeability Zones Along a Conduit
Yes
No
Initiation Along Conduit
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI (IMx)
PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE Pfail-CE
Σ Pfail
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-5
Table A1. Probability of Failure by Internal Erosion Through the Embankment (Sheet 5)
Initiating Mechanism (1) Failure Path Identification and
Screening
(2) Evaluate the Probability of Initiation of Erosion PI
(3) Probability for Continuing Erosion
PCE
(3) Probability for Erosion into the Conduit to Develop into Internal Erosion Along the
Conduit P
(4) Probability of Progression PP
(5) Probability of Unsuccessful Detection and
Intervention Pudi
(5) Probability of Breach Pbreach
(6) Calculate the Probability of Failure
Initiation of Erosion into a Conduit Leading to Sinkhole or Crest Settlement
Use Table A5 to identify and screen potential crack mechanisms
Use Table A5 to evaluate the probability of initiation into the conduit.
PI (IMx)
Evaluate the probability for Continuing Erosion for erosion into the conduit using Table A7 (Scenario 4).
PCE
Evaluate the probability for erosion into the conduit to develop into internal erosion along the conduit using Table 6.16 with weighted score from Table 6.11.
PALONG
Not applicable to this failure path.
PP = 1.0
Estimate the probability for not detect and intervene using Table A9.
Pudi
Estimate the probabilities of breach for the Continuing Erosion branch using Table A10 (sinkhole/crest settlement breach mechanism only).
Pbreach-NE = 0. Pbreach-CE
Calculate the probability of failure for each IM using the event tree.
Pfail = PI (IMx) x PP x Pudi x
(PCE x Pbreach-CE)]
EVENT TREE STRUCTURE
Erosion into a Conduit Yes
No
Initiation Into Conduit
Continuing Erosion
No Erosion
Continuation PI (IMx)
PCE
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach-CE Pfail-CE
Σ Pfail
Yes
No
Develops into IE Along Conduit
PALONG This branch leads to Internal Erosion Along the Conduit (refer Table A1, Sheet 4)
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-6
Table A1. Probability of Failure by Internal Erosion Through the Embankment (Sheet 6)
Initiating Mechanism Sketch (1) Failure Path Identification and
Screening
(2) Evaluate the Probability of
Initiation of Erosion PI
(3) Probabilities for No, Some, Excessive
and Continuing Erosion PNE, PSE, PEE,
PCE
(4) Probability of Progression PP
(5) Probability of Unsuccessful Detection and
Intervention Pudi
(5) Probability of Breach Pbreach
(6) Calculate the Probability of Failure
Initiation of Erosion in Poorly Compacted or High Permeability Zones Adjacent to a Spillway or Abutment Wall
Use Table A6 to identify and screen potential crack mechanisms
Use Table A6 to evaluate the probability of initiation for each initiating mechanism.
PI (IMx)
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table A7.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table A8.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table A9.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table A10.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE
Calculate the probability of failure for each IM using the event tree.
Pfail = PI (IMx) x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
Pbreach-CE
Poorly Compacted or High Permeability Zones Adjacent to a Spillway or Abutment Wall
Yes
No
Initiation
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI (IMx)
PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE Pfail-CE
Σ Pfail
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-7
Table A2. Probability of Initiation of Erosion in Transverse Cracks – Upper Parts of the Embankment
Probability of Transverse Cracking in Upper Part of Embankment
Probability of Erosion in the Crack
Initiating Mechanism
(1) Screening of Failure Path (2) Assess the weighted
score (WS) and estimate Probability of a Crack
PC (un-factored)
(3) Multiplication Factor for Observations and Measured Settlement
(MOU) and calculate PCU
(4) Estimate maximum likely crack width at
the dam crest
(5) Estimate likely crack width at reservoir level stage being considered
(WC)
(6) Estimate probability of erosion (PIC)
(7) Calculate the Probability Initiation of Erosion (PI)
IM1 – Cross Valley Differential Settlement
Crack
Long Section
Crack
Long Section
No Exclusions Apply – Always Include
Assess weighted score from Table 5.1 and obtain probability from Table 5.2.
PC1 (un-factored)
Obtain multiplication factors from Table 5.22 and Table 5.23. Select the maximum factor (MOU.1).
PC1 = PC1 (un-factored) x MOU.1
Obtain from Row 1 of Table 5.24, using weighted score from Step (2)
Obtain width for cracking from Table 5.25 and width for hydraulic fracture from Table 5.26(A). Use the larger of the two values
WC1
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC1) determined in Step (5).
PIC.1
PI.1 = PC1 x PIC.1
IM2 – Differential Settlement Adjacent a Cliff
Crack/Gap
Long Section
Crack/Gap
Long Section
Check if applicable using Table 3.1.
Assess weighted score from Table 5.3 and obtain probability from Table 5.4.
PC2 (un-factored)
Multiplication factor same as for FM1 (MOU.1)
PC2 = PC2 (un-factored) x MOU.1
Obtain from Row 2 of Table 5.24, using weighted score from Step (2)
Obtain width of crack from Table 5.25 and width of hydraulic fracture from Table 5.26(B). Use the larger of the two values.
WC2
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC2) determined in Step (5)
PIC.2
PI.2 = PC2 x PIC.2
IM3 – Cross Valley Arching
Crack
Long Section
Crack
Long Section
Check if applicable using Table 3.1.
Assess weighted score from Table 5.5 and obtain probability from Table 5.6.
PC3 (un-factored)
Multiplication factor same as for FM1 (MOU.1).
PC3 = PC3 (un-factored) x MOU.1
Obtain from Table 5.26, using weighted score from Step (2)
Use crack width from Step (4).
WC3
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC3) determined in Step (5)
PIC.3
PI.3 = PC3 x PIC.3
IM4 – Cross section Settlement due to Poorly Compacted Shoulders
CrackingCross Section
Settlement of shoulders
CrackingCross Section
Settlement of shoulders
Check if applicable using Table 3.1.
Assess weighted score from Table 5.7 obtain probability from Table 5.8.
PC4 (un-factored)
Multiplication factor same as for FM1 (MOU.1).
PC4 = PC4 (un-factored) x MOU.1
Obtain from Row 3 of Table 5.24, using weighted score from Step (2)
Obtain width of crack from Table 5.25.
WC4
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC4) determined in Step (5).
PIC.4
PI.4 = PC4 x PIC.4
IM5 – Differential settlements in the foundation beneath the core
Long SectionLong Section
Check if applicable using Table 3.1.
Assess weighted score from Table 5.9 and obtain probability from Table 5.10.
PC5 (un-factored)
Multiplication factor same as for FM1 (MOU.1).
PC5 = PC5 (un-factored) x MOU.1
Obtain from Row 4 of Table 5.24, using weighted score from Step (2)
Obtain width of crack from Table 5.25.
WC5
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC5) determined in Step (5).
PIC.5
PI.5 = PC5 x PIC.5
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-8
Probability of Transverse Cracking in Upper Part of Embankment
Probability of Erosion in the Crack
Initiating Mechanism
(1) Screening of Failure Path (2) Assess the weighted
score (WS) and estimate Probability of a Crack
PC (un-factored)
(3) Multiplication Factor for Observations and Measured Settlement
(MOU) and calculate PCU
(4) Estimate maximum likely crack width at
the dam crest
(5) Estimate likely crack width at reservoir level stage being considered
(WC)
(6) Estimate probability of erosion (PIC)
(7) Calculate the Probability Initiation of Erosion (PI)
IM6 – Cracking due to differential settlements due to embankment staging.
Crack
Stage 2
Long Section
Stage 1
Crack
Stage 2
Long Section
Stage 1
Check if applicable using Table 3.1.
Assess weighted score from Table 5.1 and obtain probability from Table 5.2 (refer to Section 5.2.4 on how to apply).
PC6 (un-factored)
Obtain multiplication factor from Table 5.23 (MOU.6).
PC6 = PC6 (un-factored) x MOU.6
Obtain from Row 1 of Table 5.24, using weighted score from Step (2)
Obtain width of crack from Table 5.25.
WC6
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC6) determined in Step (5).
PIC.6
PI.6 = PC6 x PIC.6
IM7 – Cracking in the crest due to desiccation by drying.
Long SectionLong Section
Check if applicable using Table 3.1.
Assess weighted score from Table 5.11 and obtain probability from Table 5.12.
PC7 (un-factored)
Obtain multiplication factor from Table 5.23 (MOU.7).
PC6 = PC6 (un-factored) x MOU.7
Obtain from Row 5 of Table 5.24, using weighted score from Step (2)
Obtain width of crack from Table 5.25.
WC7
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC7) determined in Step (5).
PIC.6
PI.7 = PC7 x PIC.7
IM8 – Cracking on seasonal shutdown layers during construction and staged construction surfaces due to desiccation by drying
Crack
Stage 2 Stage 1
Long Section
Crack
Stage 2 Stage 1
Long Section
Check if applicable using Table 3.1.
Assess weighted score from Table 5.14 and obtain probability from Table 5.15.
PC8 (un-factored)
Multiplication factor not applicable (MOU.8 = 1.0).
PC8 = PC8 (un-factored)
Obtain from Row 6 of Table 5.24, using weighted score from Step (2)
Use crack width from Step (4).
WC8
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC7) determined in Step (5).
PIC.8
PI.8 = PC8 x PIC.8
IM13 – Cracking due to earthquake loading.
Crack
Long Section
Crack
Long Section
Check if applicable using Table 3.1.
Assess damage class from Figure 5.8 for earthfill dams or Figure 5.9 for earth and rockfill dams. Obtain probability from Table 5.39.
PC13 (un-factored)
Multiplication factor not applicable (MOU.13 = 1.0).
PC13 = PC13 (un-factored)
Obtain from Table 5.39, using damage class from Step (2)
Obtain width of crack from Table 5.25.
WC13
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC13) determined in Step (5).
PIC.13
PI.13 = PC13 x PIC.13
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-9
Table A3. Probability of Initiation of Erosion in Transverse Cracks – Middle and Lower Parts of the Embankment
Probability of Transverse Cracking in Middle and Lower Parts of the Embankment
Probability of Erosion in the Crack
Initiating Mechanism
(1) Screening of Failure Path (2) Assess the weighted
score (WS) and estimate Probability of a Crack
PC (un-factored)
(3) Multiplication Factor for Observations and Measured Settlement
(MOL) and calculate PC
(4) Estimate maximum likely crack width
(includes hydraulic fracture)
(5) Estimate likely crack width at reservoir level stage being considered
(WC)
(6) Estimate probability of erosion (PIC)
(7) Calculate the Probability Initiation of Erosion (PI)
IM9 – Cross Valley Settlement
Crack
Long Section
Crack
Long Section
Check if applicable using Table 3.2.
Assess weighted score from Table 5.16 and obtain probability from Table 5.17.
PC9 (un-factored)
Obtain multiplication factor from Table 5.22 (MOL.).
PC9 = PC9 (un-factored) x MOL.
Obtain from Row 1 of Table 5.28, using weighted score from Step (2)
Use crack width from Step (4).
WC9
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC9) determined in Step (5).
PIC.9
PI.9 = PC9 x PIC.9
IM10 – Differential settlement causing arching of the core onto the shoulders of the embankment.
Check if applicable using Table 3.2.
Assess weighted score from Table 5.18 and obtain probability from Table 5.19.
PC10 (un-factored)
Multiplication factor same as for FM9 (MOL)
PC10 = PC10 (un-factored) x MOL
Obtain from Row 2 of Table 5.28, using weighted score from Step (2)
Use crack width from Step (4).
WC10
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC10) determined in Step (5)
PIC.10
PI.10 = PC10 x PIC.10
IM11 – Differential settlement in the foundation under the core
Already considered in IM5
IM12 – Small scale irregularities in the foundation profiles under the core
Long SectionLong Section
Check if applicable using Table 3.2.
Assess weighted score from Table 5.20 obtain probability from Table 5.21.
PC12 (un-factored)
Multiplication factor not applicable (MOL = 1.0).
PC12 = PC12 (un-factored)
Obtain from Row 3 of Table 5.28, using weighted score from Step (2)
Use crack width from Step (4).
WC12
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC12) determined in Step (5).
PIC.12
PI.12 = PC12 x PIC.12
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-10
Table A4. Probability of Initiation of Erosion in a Poorly Compacted or High Permeability Zones in the Embankment
Probability of High Permeability Zone in the Embankment
Probability of Erosion in the High Permeability Zone (cohesionless soils) Probability of Erosion in the High Permeability Zone (cohesive soils)
Initiating Mechanism
(1) Screening of Failure
Path
(2) Assess the weighted score (WS) and estimate
Probability of a High Permeability Zone PP (un-factored)
(3) Multiplication Factor for
Observations of Seepage (MOS) and
calculate PP
(4) Assess whether there is time for seepage gradient
to develop
(5) Estimate average seepage gradient
required to initiate and progress backward erosion (iPMT or iCR)
(6) Estimate probability of erosion (PIP)
(7) Estimate the height of the gap due to
collapse settlement
(8) Estimate probability of erosion (PIC)
(7) Calculate the Probability Initiation of
Erosion (PI)
IM14 – Poorly compacted or high high permeability layer in the embankment
Cross Section
High Permeability Zone
Cross Section
High Permeability Zone
Check if applicable using Table 3.3.
Assess weighted score from Table 6.1 for cohesive soils or Table 6.2 for cohesionless soils. Obtain the probability from Table 6.3.
PP14 (un-factored)
Obtain multiplication factor from Table 6.24 (MOS.).
PP14 = PP14 (un-factored) x MOS.
For reservoir levels above the normal operating pool level, use Table 6.25 to estimate time for seepage gradient to develop in layer. Exclude if the reservoir level rise is insufficient for seepage gradient to develop.
Estimate the average gradient (iPMT)corrected required to initiate and progress erosion from Figure 6.4 – see Section 6.6.2. If Cu>6, estimate the critical gradient (iCR)
Obtain probability of erosion from Table 6.26 for well compacted layers and Table 6.27 for poorly compacted layers based on the average seepage gradient across the embankment core (iave) and iPMT (or iCR). PIP.14
Assess the thickness of the poorly compacted layer (TP.14). Estimate the amount by which the layer may collapse (CF) from Table 6.29. Estimate the height of the gap G14 = TP.14 x CF
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the gap height (G14) determined in Step (7). PIC.14
Cohesionless soils: PI.14 = PP14 x PIP.14
Cohesive soils: PI.14 = PP14 x PIC.14
IM15 – Poorly compacted or high permeability layer on the core-foundation contact
Long SectionPoorly compacted layer
Long SectionPoorly compacted layer
Check if applicable using Table 3.3.
Assess weighted score from Table 6.4 and obtain probability from Table 6.5.
PP15 (un-factored)
Obtain multiplication factor from Table 6.24 (MOS.).
PP15 = PP15 (un-factored) x MOS.
Repeat the above step for each of the postulated high permeability layer types
Same as IM14 Obtain probability of erosion from Table 6.26 for well compacted layers and Table 6.27 for poorly compacted layers based on the average seepage gradient across the embankment core (iave) and iPMT (or iCR). PIP.15
Repeat the above step for each of the postulated high permeability layer types
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the gap height (G15) determined in Step (7). PIC.15
Cohesionless soils: PI.15 = PP15 x PIP.15
Cohesive soils: PI.15 = PP15 x PIC.15
IM16 – Cracking in the crest due to desiccation by freezing
Long SectionLong Section
Check if applicable using Table 3.3.
Assess weighted score from Table 6.6 and obtain probability from Table 6.7. Check depth of freezing induced flaws using Table 6.8.
PP16 (un-factored)
Obtain multiplication factor from Table 6.24 (MOS.).
PP16 = PP16 (un-factored) x MOS.
Not applicable – consider as for cohesive soils
Not applicable – consider as for cohesive soils
Not applicable - refer to Steps (7) and (8).
Assess the width of the of the frost induced flaw using Table 6.30 (G16)
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the gap height (G16) determined in Step (7). PIC.16
Cohesionless soils: PI.16 = PP16 x PIP.16
Cohesive soils: PI.16 = PP16 x PIC.16
IM17 – Seasonal shutdown layers during construction and staged construction surfaces due to freezing.
Stage 1
Long Section
Stage 2 Stage 1
Long Section
Stage 2
Check if applicable using Table 3.3.
Assess weighted score from Table 6.9 and obtain probability from Table 6.10.
PP17 (un-factored)
Obtain multiplication factor from Table 6.24 (MOS.).
PP17 = PP17 (un-factored) x MOS.
Not applicable – consider as for cohesive soils
Not applicable – consider as for cohesive soils
Not applicable - refer to Steps (7) and (8).
Assess the width of the of the frost induced flaw using Table 6.30 (G17)
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the gap height (G17) determined in Step (7). PIC.17
Cohesionless soils: PI.17 = PP17 x PIP.17
Cohesive soils: PI.17= PP17x PIC.17
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-11
Table A5. Probability of Initiation of Erosion in a Poorly Compacted or High Permeability Zone Around or into a Conduit
Probability of High Permeability Zone in the Embankment
Probability of Erosion in the High Permeability Zone (cohesionless soils) Probability of Erosion in the High Permeability Zone (cohesive soils)
Initiating Mechanism
(1) Screening of Failure
Path (2) Assess the weighted
score (WS) and estimate Probability of a High
Permeability Zone PP (un-factored)
(3) Multiplication Factor for
Observations of Seepage (MOS) and
calculate PP
(4) Assess whether there is time for
seepage gradient to develop
(5) Estimate average seepage gradient required
to initiate and progress backward erosion (iPMT or
iCR)
(6) Estimate probability of erosion (PIP)
(7) Estimate the height of the gap due to
collapse settlement
(8) Estimate probability of erosion (PIC)
(7) Calculate the Probability Initiation of
Erosion (PI)
IM18 – Poorly compacted or high permeability layer around a conduit through the embankment
Long Section High Permeability Zone
Long Section High Permeability Zone
Check if applicable using Table 3.3.
Assess weighted score from Table 6.11 and obtain probability from Table 6.12.
PP18 (un-factored)
Obtain multiplication factor from Table 6.24 (MOS.).
PP18 = PP18 (un-factored) x MOS.
This step is not applicable to this situation.
Estimate the average gradient (iPMT) required to initiate and progress erosion from Figure 6.4. If Cu>6, estimate the critical gradient (iCR) – see Section 6.6.2.
Obtain probability of erosion from Table 6.26 for well compacted layers and Table 6.27 for poorly compacted layers based on the average seepage gradient across the embankment core (iave) and iPMT (or iCR). PIP.18
Assess the thickness of the poorly compacted layer (TP.18). Estimate the amount by which the layer may collapse (CF) from Table 6.29. Estimate the height of the gap G18 = TP.18 x CF
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the gap height (G14) determined in Step (7). PIC.18
Cohesionless soils: PI.18 = PP18 x PIP.18
Cohesive soils: PI.18 = PP18 x PIC.18
IM19 – Erosion into a (non-pressurised) conduit
Check if applicable using Table 3.3.
When the internal condition of the conduit is known, obtain probability from Table 6.13.
When the internal condition of the conduit is not known, assess the weighted score from Table 6.14 and obtain probability from Table 6.15.
PP19 (un-factored)
Not applicable.
PP19 = PP19 (un-factored).
This step is not applicable to this situation.
Same as FM18 This step is not applicable to this situation.
This step is not applicable to this situation.
This step is not applicable to this situation.
PI.19 = PP19
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-12
Table A6. Probability of Initiation of Erosion in a Poorly Compacted or High Permeability Zone Adjacent to a Spillway or Abutment Wall
Probability of High Permeability Zone in the Embankment
Probability of Erosion in the High Permeability Zone (cohesionless soils) Probability of Erosion in the High Permeability Zone (cohesive soils)
Initiating Mechanism
(1) Screening of Failure
Path (2) Assess the weighted
score (WS) and estimate Probability of a High
Permeability Zone PP (un-factored)
(3) Multiplication Factor for
Observations of Seepage (MOS) and
calculate PP
(4) Assess whether there is time for
seepage gradient to develop
(5) Estimate average seepage gradient required
to initiate and progress backward erosion (iPMT or
iCR)
(6) Estimate probability of erosion (PIP)
(7) Estimate the crack width or height of the
gap due to collapse settlement
(8) Estimate probability of erosion (PIC)
(7) Calculate the Probability Initiation of
Erosion (PI)
IM20 – Poorly compacted or high permeability zone associated with a spillway or abutment wall
Check if applicable using Table 3.3.
Assess weighted score from Table 6.17 and obtain probability from Table 6.18.
PP20 (un-factored)
Obtain multiplication factor from Table 6.24 (MOS.).
PP20 = PP20 (un-factored) x MOS.
For reservoir levels above the normal operating pool level, use Table 6.25 to estimate time for seepage gradient to develop in layer. Exclude if the reservoir level rise is insufficient for seepage gradient to develop.
Estimate the average gradient (iPMT) required to initiate and progress erosion from Figure 6.4. If Cu>6, estimate the critical gradient (iCR).
Obtain probability of erosion from Table 6.26 for well compacted layers and Table 6.27 for poorly compacted layers based on the average seepage gradient across the embankment core (iave) and iPMT (or iCR). PIP.20
Assess the thickness of the poorly compacted layer (TP.18). Estimate the amount by which the layer may collapse (CF) from Table 6.29. Estimate the height of the gap G20 = TP.20 x CF
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the gap height (G20) determined in Step (7). PIC.20
Cohesionless soils: PI.20 = PP20 x PIP.20
Cohesive soils: PI.20 = PP20 x PIC.20
IM21 – Crack/gap adjacent to a spillway or abutment wall
Check if applicable using Table 3.3.
Assess weighted score from Table 6.19 and obtain probability from Table 6.20.
PC21 (un-factored)
Obtain multiplication factors from Table 5.16 and Table 5.17. Select the maximum factor (MOU.1).
PC21 = PC21 (un-factored) x MOU.1
Not applicable to this failure path
Not applicable to this failure path
Refer to Steps (7) and (8). Obtain width of crack from Table 5.26(B).
WC21
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC21) determined in Step (7).
PIC.21
PI.21 = PC21 x PIC.21
IM22 – Differential settlement adjacent to a spillway or abutment wall
Crack/Gap
Long Section
Crack/Gap
Long Section
Check if applicable using Table 3.3.
Assess weighted score from Table 6.21 and obtain probability from Table 6.22.
PC22 (un-factored)
Obtain multiplication factors from Table 5.16 and Table 5.17. Select the maximum factor (MOU.1).
PC22 = PC22 (un-factored) x MOU.1
Not applicable to this failure path
Not applicable to this failure path
Refer to Steps (7) and (8). Obtain max likely width of crack at dam crest from Row 2 of Table 5.24, using weighted score from Step (2).
Obtain width of crack at the level of interest from Table 5.25 and width for hydraulic fracture from Table 5.26(B). Use the larger of the two values
WC22
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the crack width (WC22) determined in Step (7).
PIC.22
PI.22 = PC22 x PIC.22
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-13
Table A7. Probability of Continuation for Internal Erosion in the Embankment
Assess which Scenario is Applicable to the Failure Path under Consideration
Examples Probability of Continuation (PNE , PSE , PEE , PCE)
Scenario 1: Homogeneous zoning with no fully intercepting filter
1
HOMOGENEOUS EARTHFILL
3
2
13
INTERNAL EROSION ABOVE CORE AND FILTERS
1
EARTHFILL WITH TOE DRAIN, INTERNAL EROSION ABOVE TOE DRAIN
1
HOMOGENEOUS EARTHFILL
1
HOMOGENEOUS EARTHFILL
3
2
13
INTERNAL EROSION ABOVE CORE AND FILTERS
3
2
13
INTERNAL EROSION ABOVE CORE AND FILTERS
1
EARTHFILL WITH TOE DRAIN, INTERNAL EROSION ABOVE TOE DRAIN
1
EARTHFILL WITH TOE DRAIN, INTERNAL EROSION ABOVE TOE DRAIN
1
EARTHFILL WITH TOE DRAIN, INTERNAL EROSION ABOVE TOE DRAIN
No potential for filtering.
Probability for continuing erosion, PCE=1.0
PNE = PSE = PEE = 0
Scenario 2: Downstream shoulder of fine grained cohesive material which is capable of holding a crack/pipe.
See Section 7.1.3 for more details.
11A
ZONED EARTHFILL WITH COHESIVE SHELLS
1A2
1
INTERNAL EROSION ABOVE FILTER ZONE, COHESIVE DOWNSTREAM SHELL
1A1A11A
ZONED EARTHFILL WITH COHESIVE SHELLS
1A11A
ZONED EARTHFILL WITH COHESIVE SHELLS
1A2
1
INTERNAL EROSION ABOVE FILTER ZONE, COHESIVE DOWNSTREAM SHELL
1A1A 21
INTERNAL EROSION ABOVE FILTER ZONE, COHESIVE DOWNSTREAM SHELL
1A1A
Filtering does not occur if the crack/high permeability zone persists through the downstream shoulder zone.
Use Table 10.1 to estimate the probability for continuing erosion, PCE.
Calculate PNE = 1.0 – PCE
PSE = PEE = 0
Scenario 3: Filter/transition zone is present downstream of the core or a downstream shoulder zone which is not capable of holding a crack/pipe.
1
21 3
2
13
31
3
EARTHFILL WITH CHIMNEY FILTER ZONED EARTHFILL WITH CHIMNEY FILTER
ZONED EARTHFILL WITH GRANULAR SHELLS
1
21
1
21 3
2
13 3
2
13
31
3 31
3
EARTHFILL WITH CHIMNEY FILTER ZONED EARTHFILL WITH CHIMNEY FILTER
ZONED EARTHFILL WITH GRANULAR SHELLS
Follow the procedure outlined in Section 10.1.4 to estimate the probabilities of No Erosion (PNE), Some Erosion (PSE), Excessive Erosion (PEE) and Continuing Erosion (PCE).
Figure A1 shows a flow chart which summarizes the procedure.
Scenario 4: Piping into an open defect, joint or crack.
SOIL
CONDUIT
EROSION INTO OPEN JOINTS IN ROCK FOUNDATION
SOIL
OPEN JOINTED ROCK
EROSION INTO AN OPEN CRACK OR JOINT IN A CONDUIT OR WALL
SOIL
CONDUIT
EROSION INTO OPEN JOINTS IN ROCK FOUNDATION
SOIL
OPEN JOINTED ROCK
EROSION INTO AN OPEN CRACK OR JOINT IN A CONDUIT OR WALL
Step 1: Evaluate the joint/defect opening size that would allow Continuing Erosion (JOSCE) using Table 10.10.
Step 2: Estimate the conditional probability for Continuing Erosion (PCE) by estimating the proportion of soils that are coarser than JOSCE and using Table 10.11.
Scenario 5: Erosion into a toe drain
1
INTERNAL EROSION THROUGH THE EMBANKMENT INTO A TOE DRAIN
1
INTERNAL EROSION THROUGH THE FOUNDATION INTO A TOE DRAIN
1
INTERNAL EROSION THROUGH THE EMBANKMENT INTO A TOE DRAIN
1
INTERNAL EROSION THROUGH THE FOUNDATION INTO A TOE DRAIN
Estimate the probability of continuing erosion for erosion into a toe drain using Table 10.12. The assessment of erosion into a toe drain considers the observed condition of the toe drain (from video or external inspections) and the design and construction details of the toe drain.
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-14
Adjust base soil gradations.
If the maximum particle size of the base soil is >4.75 mm, then regrade the base grading such that the maximum size is 4.75 mm. If the base soil is gap graded, then regrade the base grading on the particle size that is missing.
Plot the particle size distributions for the base material.
Select representative gradings of the regraded base soil which are indicative of the finer 5% of the base soil gradings (fine base), the average grading (average base) and the coarser 5% of the base soils (coarser base).
Yes (PIUS ≥ 0.3)
No (PIUS < 0.3)
Adjust the gradation of the filter/transition materials using the graphical method in Figure 10.1.
Yes
No
Is the filter/transition material susceptible to segregation?
Evaluate weighted score using Tables 10.3 and 10.4, and assess whether segregation needs to be considered using Table 10.5.
Is the filter/transition material susceptible to suffusion?
Evaluate the probability the filter or transition zone materials are internally unstable (PIUS) using Figure 6.5 for materials with >10% fines or Figure 6.6 for materials with <10% fines. If the probability of internal instability (PIUS) is ≥ 0.3, then assume the filter/transition materials are susceptible to suffusion.
Will the filter/transition material hold a crack?
Evaluate the probability the filter/transition zone materials holding a crack PFC using Table 10.2. Assume the filter holds a crack if the probability of holding a crack PFC is ≥ 0.1.
No (PFC < 0.1)
Evaluate the DF15 values for the No Erosion, Some Erosion, and Continuing Erosion boundaries for the fine limit, average and coarse limit of the regraded core materials.
Use Tables 10.6 and 10.7 to evaluate the DF15 values.
Plot the DF15 values for these boundaries on the grading curve limits of the filter/transition material. Use the adjusted grading curves for the filter/transition if required by the preceding steps (i.e. for suffusion or segregation).
Estimate the probabilities for No, Some, Excessive and Continuing Erosion
1. Estimate the proportion of filter gradings that fall into the No Erosion, Some Erosion, Excessive Erosion and Continuing Erosion categories. Do this for each of the representative base soil gradings (fine base, average base and coarse base). If there are no gradations that fall into the Continuing Erosion category, then use Table 10.8 to aid judgement in assigning the probability for Continuing Erosion (this allows for the possibility of gradations being coarser than indicated by the available data). The suggested approach is to estimate the proportions for Some, Excessive and Continuing Erosion (PSE, PEE and PCE), and calculate PNE = 1- (PSE + PEE + PCE)
2. Make an initial estimate of the probabilities for the No Erosion, Some Erosion, Excessive Erosion and Continuing Erosion branches by calculating the sum-product of the % of base soil gradings and the % of NE, SE, EE and CE for each representative base soil grading (refer to Step 8 in Section 10.1.4a for the calculations).
3. Use judgement to adjust the calculated percentages to take into account the effects of other factors such as the distribution of the core and filter gradations in the fill, borrow area variability and selective placement of materials.
Yes (PFC ≥ 0.1)
Evaluate the remaining steps by considering the ‘cracked’ filter/transition zone as the base soil, and the zone downstream of the cracked filter as the filter material.
Will the filter/transition zone blow out due to a limited depth of cover?
Calculate the factor of safety of blow out, FSB = (total stress of material over the crack exit) / (reservoir head at the crack exit). Is the FSB value < 0.5?
Yes (FSB < 0.5)
If FSb < 0.1 then probability of continuing erosion PCE = 1.0. If FSb = 0.1 to 0.5, then assign a probability of continuing erosion PCE between 0.1 and 0.9.
No (FSB ≥ 0.5)
Use the adjusted filter/transition gradings in the remaining steps.
OUTPUT;
PSE
PEE
PCE
FIGURE A1 – FLOW CHART FOR EVALUATING THE PROBABILITIES FOR NO, SOME, EXCESSIVE AND CONTINUING EROSION FOR FILTER/TRANSITION ZONES
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-15
Table A8. Probability of Progression for Internal Erosion in the Embankment
Applicable Initiating Mechanism Probability of Forming a Roof (PPR) Probability that Crack Filling Action is Not Effective (PPC)
Probability that Upstream Zone Fails to Limit Flows (PPL)
All IE Embankment Failure Paths except IM19
(IM1 to IM18)
Assess the probability of the core material to form a roof of a pipe using Table 11.1.
PPR
Assess the probability of crack filling action not stopping pipe enlargement using Table 11.2.
PPC
Assess the probability that the upstream zone or concrete elements fail to limit flows using Table 11.3.
PPL
IM19 (Erosion into a conduit causing crest settlement/sinkhole)
Not applicable to this failure path
PPR = 1.0
Not applicable to this failure path
PPC = 1.0
Not applicable to this failure path
PPL = 1.0
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-16
Table A9. Probability of Unsuccessful Detection and Intervention for Internal Erosion in the Embankment
Probability of Not Detecting Probability of Not Intervening
Applicable Failure Path/Location
(1) Assess the Rate of Internal Erosion and Piping
(2) Assess the probability of the concentrated leak not being observable Pnol
(3) Assess the probability that given the leak is observable, that it is not detected Pnd
(4) Calculate the probability of not detecting the internal erosion Pndi
(5) Assess the probability that intervention and repair is not successful Pui
(6) Probability of Not Detect and Not Intervene
Pudi
All Failure Paths/Initiating Mechanisms
Estimate the approximate time for progression of piping and development of a breach using Tables 12.1, 12.2 and 12.3.
Assess the weighted score (WS) from Table 12.5 and obtain probability from Table 12.6.
Pnol
Assess the probability of not detecting the leak using Table 12.7.
Pnd
Calculate the probability of not detecting the internal erosion using Pnol from Step (2) and Pnd from Step (3);
= Pnol + [(1-Pnol) x Pnd]
Assess the probability that intervention and repair is not successful using Table 12.8.
Pui
Calculate the probability of unsuccessful detection and intervention using Pnol from Step (2), Pnd from Step (3) and Pui from Step (5);
Pudi = Pnol + [(1-Pnol) x Pnd x Pui]
(Refer to sub-event tree diagram below)
Probability of Not Intervening
0.1 0.1 0.1No Intervention
Internal Erosion is Not Able to be Detected
0.5 0.45 0.45No Intervention
0.9 Not Detected in Time
0.5 0.225 0.225 No Intervention
0.5 Intervention and Repair is Not Successful
0.5 0.225Intervention is Successful
Probability of Not Intervening = 0.775
Not Intervene Tree
Yes
No
Yes
No
Yes
No
Example sub-event tree for calculating the probability of not intervening
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version A-17
Table A10. Probability of Breach for Internal Erosion in the Embankment
Applicable Failure Path/Location
Branch on Event Tree (1) Screening of breach
mechanisms
(2) Probability of Breach by Gross Enlargement Pge
(3) Probability of Breach by Slope Instability Psi
(4) Probability of Breach by Sloughing or Unravelling
Psu
(5) Probability of Breach by Sinkhole Psd
(6) Calculate the Probability of Breach
All Failure Paths/Initiating Mechanisms
Evaluate the probabilities of breach for each branch of the event tree (i.e. No, Some, Excessive and Continuing Erosion branches)
Assess which breach mechanisms are relevant to the type of dam zoning and failure path being considered using Table 13.1.
Only consider the breach mechanisms that are included for estimating the probability of breach.
Excluded breach mechanisms are assigned a probability of breach = 0.
The probability of breach by gross enlargement Pge= 0 for the No, Some and Excessive Erosion branches.
Breach by gross enlargement is negligible in cases where the downstream shell is unable to support a roof of a pipe. Evaluate whether this is applicable using Table 13.2.
If this breach mechanism is applicable, estimate the probability of breach by gross enlargement using Table 13.3.
Pge
(a) Estimate the probability of slope instability occurring due to the increased seepage flows. Assess the weighted score from Table 13.4 and obtain the probability from Table 13.5. This is done for each branch of the event tree [Some Erosion (Psi-i SE), Excessive Erosion (Psi-i EE) and Continuing Erosion (Psi-i CE)].
(b) Estimate the probability of loss of freeboard due to instability (Psi-lf). Assess the weighted score from Table 13.10 and obtain the probability from Table 13.11.
(c) Calculate the probability of breach by slope instability for each branch of the tree;
(a) Probability seepage will emerge into the downstream shell PS = 1.0.
(b) For dams with a downstream zone of earthfill, assess the weighted score from Table 13.12 and obtain the probability for each branch of the tree from Table 13.13; Some Erosion (Psu-SE), Excessive Erosion (Psu-EE) and Continuing Erosion (Psu-CE).
(c) For dams with a downstream zone of rockfill, assess the weighted score from Table 13.15 and obtain the probability for each branch of the tree from Table 13.16; Some Erosion (Psu-SE), Excessive Erosion (Psu-EE) and Continuing Erosion (Psu-CE).
(a) Estimate the probability of a sinkhole developing as a result of the internal erosion (Ps-f) from Table 13.18.
(b) Estimate the probability that the sinkhole causes loss of freeboard. Assess the weighted score from Table 13.19 and obtain the probability for each branch of the event tree from Table 13.20. Some Erosion (Ps-lf SE), Excessive Erosion (Ps-lf EE) and Continuing Erosion (Ps-lf CE).
(c) Calculate the probability of breach by sinkhole development;
Calculate the probability of breach for each branch of the event tree (i.e. Some Erosion, Excessive Erosion and Continuing Erosion branches) by summing the probabilities using de Morgan’s rule as follows;
No Erosion Branch (NE) Pbreach = 0 for NE Pbreach-NE = 0
Some Erosion Branch (SE)
Pge-SE = 0 (Psi-SE) = (Psi-i SE) x (Psi-lf). (Psu-SE) (Psd-SE) = (Ps-f) x (Ps-lf SE) Pbreach-SE= 1 – [(1 - Pge-SE) x (1 - Psi-SE) x (1 - Psu-SE) x (1 - Psd-SE)].
Excessive Erosion Branch (EE)
Pge-EE = 0 (Psi-EE) = (Psi-i EE) x (Psi-lf). (Psu-EE) (Psd-EE) = (Ps-f) x (Ps-lf EE) Pbreach-EE= 1 – [(1 - Pge-EE) x (1 - Psi-EE) x (1 - Psu-EE) x (1 - Psd-EE)].
Continuing Erosion Branch (CE)
Pge-CE from Table 10.3 (Psi-CE) = (Psi-i CE) x (Psi-lf). (Pun-CE) (Psd-CE) = (Ps-f) x (Ps-lf CE) Pbreach-CE = 1 – [(1 - Pge-CE) x (1 - Psi-CE) x (1 - Psu-CE) x (1 - Psd-CE)].
E
Appendix B Navigation Table for Internal Erosion
Through a Soil Foundation
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version B-1
Table B1. Probability of Failure by Internal Erosion Through a Soil Foundation (Sheet 1)
Failure Path/Location Sketch (1) Failure Path
Identification and Screening
(2) Evaluate the Probability of
Initiation of Erosion PI
(3) Probabilities for No, Some, Excessive
and Continuing Erosion PNE, PSE, PEE,
PCE
(4) Probability of Progression PP
(5) Probability of Unsuccessful Detection and
Intervention Pudi
(5) Probability of Breach Pbreach
(6) Calculate the Probability of Failure
Initiation of Backward Erosion in a Layer of Cohesionless Soil in the Foundation
Use Table B2 to identify and screen potential failure paths.
Use Table B2 to evaluate the probability of initiation and progression of backward erosion for each failure path.
PI BEP
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table B5.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table B6.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table B7.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table B8.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE
Calculate the probability of failure using the event tree.
Pfail = PI BEP x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
Pbreach-CE
Backward Erosion in a Layer of Cohesionless Soil in the Foundation
Yes
No
Initiation & progression
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI (IMx) PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-CE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE
Σ Pfail
313
Backward erosion piping
313 313
Backward erosion piping
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version B-2
Table B1. Probability of Failure by Internal Erosion Through a Soil Foundation (Sheet 2)
Initiation of Suffusion in a Layer of Cohesionless Soil in the Foundation
Use Table B3 to identify and screen potential failure paths.
Use Table B3 to evaluate the probability of initiation of suffusion for each failure path.
PI suffusion
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table B5.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table B6.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table B7.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table B8.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE (Pge-CE = 0)
Calculate the probability of failure using the event tree.
Pfail = PI suffusion x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
Pbreach-CE
Suffusion in a Layer of Cohesionless Soil in the Foundation
Yes
No
Initiation
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI (IMx) PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-CE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE
Σ Pfail
313
Internally unstable soil
313 313
Internally unstable soil
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version B-3
Table B1. Probability of Failure by Internal Erosion Through a Soil Foundation (Sheet 3)
Initiation of Erosion in a Crack in Cohesive Soil in the Foundation
Use Table B4 to identify and screen potential failure paths.
Use Table B4 to evaluate the probability of initiation for each failure path.
PI crack
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table B5.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table B6.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table B7.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table B8.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE
Calculate the probability of failure using the event tree.
Pfail = PI crack x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
Pbreach-CE
Erosion in a Crack in Cohesive Soil in the Foundation
Yes
No
Initiation
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI (IMx) PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-CE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE
Σ Pfail
313
Desiccation cracks in clay
313
Desiccation cracks in clay
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version B-4
Table B2. Probability of Initiation of Backward Erosion in a Layer of Soil in the Foundation
Failure Path/Location (1) Screening of Failure Path
Probability of a Continuous Layer from Upstream to
Downstream PCL
Assess the Probability of Heave PH Estimate the Probability of Initiation and Progression of
Backward Erosion Given Heave has occurred P IH
Estimate Probability of Initiation and Progression of Backward Erosion where
Heave is not predicted P INH
Calculate the Total Probability of Initiation and Progression of
Backward Erosion
Identify potential failure paths for backward erosion in the soil foundations.
For each failure path, check if is applicable using Table 3.4
Estimate the probability there is a continuous layer of cohesionless soil from upstream of the embankment, to downstream of the embankment. Refer to Steps a) and b) in Section 7.2.1.
PCL
Assess the probability of heave for the reservoir stage under consideration.
Use the method described in Section 7.2.2 where piezometer data and/or seepage flow net models are available.
Otherwise, use the approximate method described in Section 7.2.3.
PH
Estimate the probability of backward erosion given heave has occurred as follows;
(1) If sand boils have been observed, the probability of initiation and progression of backward erosion = 1.0 for reservoir levels at or above the level at which sand boils have been observed. For lower reservoir levels use the procedure in Section 7.3.2.
(2) If sand boils have not been observed, the probability of initiation and progression of backward erosion is assessed as follows;
• Estimate the average seepage gradient (i avf )
through the cohesionless soil layer in the foundation beneath the central part of the dam (not at the toe where there are likely to be locally higher gradients) for the level for the reservoir stage under consideration.
• From the particle size distribution of the foundation material, estimate the uniformity coefficient Cu =
D 60 /D 10 .
• Estimate the point seepage gradient required to progress backward erosion using Figure 6.4 from Schmertmann (2000).
• Correct this average gradient for the geometry, horizontal to vertical permeability ratio of the zone subject to backward erosion, and grain size as detailed in the Supporting Information Section
C6.6.2.4. This gives (i pmt ) Corrected .
• For Cu> 6.0, also estimate the critical gradient
(i cr ) from i cr = ( satγ - wγ ) / wγ . Adopt this
gradient if it is smaller than (i pmt ) Corrected .
• Estimate the probability of initiation and
progression from Table 7.4. Use i av and
(i pmt ) Corrected as inputs.
Estimate the probability of backward erosion given heave has occurred as follows;
• Estimate the average seepage gradient
(i avf ) through the cohesionless soil layer
in the foundation beneath the centre of the dam at the level for the reservoir stage under consideration.
• From the particle size distribution of the foundation material estimate the representative uniformity coefficient Cu =
D 60 /D 10 .
• Estimate the point seepage gradient required to initiate and progress backward erosion from Figure 6.4.
• Correct this average gradient for the geometry, horizontal to vertical permeability ratio of the zone subject to backward erosion, and grain size as detailed in the Supporting Information Section C6.6.2.4. This gives
(i pmt ) Corrected .
• For Cu> 6.0, also estimate the critical
gradient (i cr ) from i cr = ( satγ - wγ ) /
wγ . Adopt this gradient if it is smaller
than (i pmt ) Corrected .
• Estimate the probability of initiation from
Table 7.5. Use i av and (i pmt ) Corrected as
inputs.
Estimate the probability of initiation and progression of backward erosion
(P I BEP) from the results of the
assessments in the preceding steps.
(P I BEP) = (P cl ) x [(P H ) x (P IH ) +
(1-(P H ) x (P INH )].
313
Backward erosion piping
313 313
Backward erosion piping
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version B-5
Table B3. Probability of Initiation of Suffusion in a Layer of Soil in the Foundation
Failure Path/Location (1) Screening of Failure Path
Probability of a Continuous Layer from Upstream to
Downstream PCL
Assess the Probability the Soil is Internally Unstable PIUS
Calculate the Probability of Initiation of Suffusion
PIsuffusion
Identify potential failure paths for suffusion in soil foundations.
For each failure path, check if is applicable using Table 3.4.
Check if soil is potentially internally unstable using Section 6.6.3.
Estimate the probability there is a continuous layer of cohesionless soil from upstream of the embankment, to downstream of the embankment. Refer to Steps a) and b) in Section 7.2.1.
PCL
From the particle size distribution for the soil, determine the d15, d60 and d90 sizes (the particle size for which 15%, 60% and 90% are finer). The grading curve is not adjusted for this procedure.
Then estimate the probability the soil is internally unstable (PIUS) from Figure 6.5 for soils with more than 10% fines passing 0.075 mm (#200 sieve), and Figure 6.6 for soils with less than 10% fines passing 0.075 mm
PIUS
Estimate the probability of initiation of
suffusion (P I suffusion) from the results of
the assessments in the preceding steps.
(P I suffusion) = PCL x PIUS
Table B4. Probability of Initiation of Erosion in a Crack in a Layer of Soil in the Foundation
Failure Path/Location (1) Screening of Failure Path
Probability of a Continuous Layer from Upstream to
Downstream PCL
Assess the Probability that Erosion will Initiate in the Crack PIC
Calculate the Probability of Initiation of Erosion in a Crack
PIcrack
Identify potential failure paths for erosion in cracks in soil foundations. Examples; differential settlement in the foundation, desiccation cracks in the foundation soil.
For each failure path, check if is applicable using Table 3.4.
Estimate the probability there is a layer of soil in which a continuous crack or interconnected pattern of cracks may exist. The question is best put in terms of the width of the crack. For example “what is the probability of a continuous crack or pattern of cracks 5mm wide.” Refer to Section 7.5 for further guidance.
PCL
Obtain the probability of erosion from the most appropriate table from Tables 5.29 to 5.35 in Section 5.4.2 based on the soil type containing the cracks in the foundation and for the crack width (WC) being considered.
PIC
Estimate the probability of initiation of
erosion in a crack (P I crack) from the
results of the assessments in the preceding steps.
(P I crack) = PCL x PIC
313
Internally unstable soil
313 313
Internally unstable soil
313
Desiccation cracks in clay
313
Desiccation cracks in clay
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version B-6
Table B5. Probability of Continuation for Internal Erosion in the Foundation
Assess the Probability that the Exit will be an Unfiltered Exit (Punf)
Probability of Continuation for an Unfiltered Exit (PCE)
Probability of Continuation for a Filtered Exit (PNE , PSE , PEE , PCE)
Sketch Probability of Continuation for a Filtered Exit (PNE , PSE , PEE , PCE)
Assess the probability that the exit will be an unfiltered exit for the failure path under consideration using Table 10.13.
An unfiltered exit is implicit if a heave condition or a sand boil is present.
Punf
The probability of continuation for an unfiltered exit PCE is;
PCE = Punf x 1.0
Assess which filtered exit scenario is most applicable to the failure path under consideration;
(Note: Scenarios 1 and 2 are not applicable to this failure mode)
Calculate the probability that there will be a filtered exit (Pfe). For all filtered exit scenarios;
Pfe = 1 – Punf
Scenario 3 – Exits into a filter/transition zone or other granular material which is not capable of holding a crack/pipe.
1
21
EARTHFILL WITH CHIMNEY FILTER
3
2
13
ZONED EARTHFILL WITH CHIMNEY FILTER
31
3
ZONED EARTHFILL WITH GRANULAR SHELLS
1
21
EARTHFILL WITH CHIMNEY FILTER
1
21
EARTHFILL WITH CHIMNEY FILTER
3
2
13
ZONED EARTHFILL WITH CHIMNEY FILTER
3
2
13
ZONED EARTHFILL WITH CHIMNEY FILTER
31
3
ZONED EARTHFILL WITH GRANULAR SHELLS
31
3
ZONED EARTHFILL WITH GRANULAR SHELLS
Follow the procedure outlined in Section 10.1.4 to estimate the probabilities of No Erosion (PNE), Some Erosion (PSE), Excessive Erosion (PEE) and Continuing Erosion (PCE).
Figure A1 shows a flow chart which summarizes the procedure.
Scenario 4 – Exits into an open defect, joint or crack.
SOIL
CONDUIT
EROSION INTO OPEN JOINTS IN ROCK FOUNDATION
SOIL
OPEN JOINTED ROCK
EROSION INTO AN OPEN CRACK OR JOINT IN A CONDUIT OR WALL
SOIL
CONDUIT
EROSION INTO OPEN JOINTS IN ROCK FOUNDATION
SOIL
OPEN JOINTED ROCK
EROSION INTO AN OPEN CRACK OR JOINT IN A CONDUIT OR WALL
Step 1: Evaluate the opening size for No Erosion, Some Erosion, Excessive Erosion and Continuing Erosion using Table 10.10.
Step 2: Estimate the conditional probabilities for No Erosion (PNE), Some Erosion (PSE), Excessive Erosion (PEE) and Continuing Erosion (PCE) by estimating the proportion of soils falling within each erosion category and using Table 10.11.
Scenario 5 – Erosion into a toe drain
1
SION THROUGH THE INTO A TOE DRAIN
1
INTERNAL EROSION THROUGH THE FOUNDATION INTO A TOE DRAIN
1
SION THROUGH THE INTO A TOE DRAIN
1
INTERNAL EROSION THROUGH THE FOUNDATION INTO A TOE DRAIN
Estimate the probability of continuing erosion for erosion into a toe drain using Table 10.12. The assessment of erosion into a toe drain considers the observed condition of the toe drain (from video or external inspections) and the design and construction details of the toe drain.
313
Backward erosion piping
313 313
Backward erosion piping
For backward erosion piping, an unfiltered exit is implicit if a heave condition or a sand boil is present.
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version B-7
Table B6. Probability of Progression for Internal Erosion in the Embankment
Applicable Failure Path/Location Probability of Forming a Roof (PPR) Probability that Crack Filling Action is Not Effective (PPC)
Probability that Upstream Zone Fails to Limit Flows (PPL)
All IE Foundation Failure Modes
Use Table 11.1 as a guide to estimating the probability of the embankment and foundation materials in supporting the roof of a pipe in the foundation.
PPR
If the eroding foundation soil layer is located immediately below the embankment, and the embankment forms the roof of the pipe, then evaluate the probability for crack filling action as for erosion in the dam using Table 11.2.
If the eroding foundation soil layer is located further below the embankment, then consider the potential for the overlying soil layers to wash into the developing pipe. There needs to be a filtering material at the downstream end of the flow path for crack filling action to be effective. The filtering material may be a naturally occurring layer in the foundation, or the embankment filter.
PPC
Assess the probability that an upstream soil layer, upstream zone or a concrete element fails to limit flows using Table 11.3.
PPL
Table B7. Probability of Unsuccessful Detection and Intervention for Internal Erosion in the Foundation
Probability of Not Detecting Probability of Not Intervening
Applicable Failure Path/Location
(1) Assess the Rate of Internal Erosion and Piping
(2) Assess the probability of the concentrated leak not being observable Pnol
(3) Assess the probability that given the leak is observable, that it is not detected Pnd
(4) Calculate the probability of not detecting the internal erosion Pndi
(5) Assess the probability that intervention and repair is not successful Pui
(6) Probability of Not Detect and Not Intervene
Pudi
All Failure Modes Estimate the approximate time for progression of piping and development of a breach using Tables 12.1, 12.2 and 12.3.
Assess the weighted score (WS) from Table 12.5 and obtain probability from Table 12.6.
Pnol
Assess the probability of not detecting the leak using Table 12.7.
Pnd
Calculate the probability of not detecting the internal erosion using Pnol from Step (2) and Pnd from Step (3);
= Pnol + [(1-Pnol) x Pnd]
Assess the probability that intervention and repair is not successful using Table 12.8.
Pui
Calculate the probability of unsuccessful detection and intervention using Pnol from Step (2), Pnd from Step (3) and Pui from Step (5);
Pndi = Pnol + [(1-Pnol) x Pnd x Pui]
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version B-8
Table B8. Probability of Breach for Internal Erosion in the Foundation
Applicable Failure Path/Location
Branch on Event Tree (1) Screening of breach
mechanisms
(2) Probability of Breach by Gross Enlargement Pge
(3) Probability of Breach by Slope Instability Psi
(4) Probability of Breach by Sloughing or Unravelling
Psu
(5) Probability of Breach by Sinkhole Psd
(6) Calculate the Probability of Breach
All Failure Modes
Evaluate the probabilities of breach for each branch of the event tree (i.e. No, Some, Excessive and Continuing Erosion branches)
Assess which breach mechanisms are relevant to the type of dam zoning and failure path being considered using Table 13.1.
Excluded breach mechanisms are assigned a probability of breach = 0.
The probability of breach by gross enlargement Pge= 0 for the No, Some and Excessive Erosion branches.
The probability of breach by gross enlargement Pge= 0 where the mode of erosion is suffusion.
If this breach mechanism is applicable, estimate the probability of breach by gross enlargement using Table 13.3.
Pge
(a) Estimate the probability of slope instability occurring due to the increased seepage flows. Assess the weighted score from Table 13.4 and obtain the probability from Table 13.5. This is done for each branch of the event tree [Some Erosion (Psi-i SE), Excessive Erosion (Psi-i EE) and Continuing Erosion (Psi-i CE)].
(b) Estimate the probability of loss of freeboard due to instability (Psi-lf). Assess the weighted score from Table 13.10 and obtain the probability from Table 13.11.
(c) Calculate the probability of breach by slope instability for each branch of the tree
(a) Probability seepage will emerge into the downstream shell PS = 1.0.
(b) For dams with a downstream zone of earthfill, assess the weighted score from Table 13.12 and obtain the probability for each branch of the tree from Table 13.13; Some Erosion (Psu-SE), Excessive Erosion (Psu-EE) and Continuing Erosion (Psu-CE).
(c) For dams with a downstream zone of rockfill, assess the weighted score from Table 13.15 and obtain the probability for each branch of the tree from Table 13.16; Some Erosion (Psu-SE), Excessive Erosion (Psu-EE) and Continuing Erosion (Psu-CE).
(a) Estimate the probability of a sinkhole developing as a result of the internal erosion (Ps-f) from Table 13.18.
(b) Estimate the probability that the sinkhole causes loss of freeboard. Assess the weighted score from Table 13.19 and obtain the probability for each branch of the event tree from Table 13.20. Some Erosion (Ps-lf SE), Excessive Erosion (Ps-lf EE) and Continuing Erosion (Ps-lf CE).
(c) Calculate the probability of breach by sinkhole development
Calculate the probability of breach for each branch of the event tree (i.e. Some Erosion, Excessive Erosion and Continuing Erosion branches) by summing the probabilities using de Morgan’s rule as follows;
No Erosion Branch (NE) Pbreach = 0 for NE Pbreach-NE = 0
0 Some Erosion Branch (SE)
Pge-SE = 0 (Psi-SE) = (Psi-i SE) x (Psi-lf). (Psu-SE) (Psd-SE) = (Ps-f) x (Ps-lf SE) Pbreach-SE= 1 – [(1 - Pge-SE) x (1 - Psi-SE) x (1 - Psu-SE) x (1 - Psd-SE)].
Excessive Erosion Branch (EE)
Pge-EE = 0 (Psi-EE) = (Psi-i EE) x (Psi-lf). (Psu-EE) (Psd-EE) = (Ps-f) x (Ps-lf EE) Pbreach-EE= 1 – [(1 - Pge-EE) x (1 - Psi-EE) x (1 - Psu-EE) x (1 - Psd-EE)].
Continuing Erosion Branch (CE)
Pge-CE from Table 10.3 (Psi-CE) = (Psi-i CE) x (Psi-lf). (Psu-CE) (Psd-CE) = (Ps-f) x (Ps-lf CE) Pbreach-CE = 1 – [(1 - Pge-CE) x (1 - Psi-CE) x (1 - Psu-CE) x (1 - Psd-CE)].
Appendix C Navigation Table for Internal Erosion
Through a Rock Foundation
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version C-1
Table C1. Probability of Failure by Internal Erosion Through a Rock Foundation (Sheet 1)
Failure Path/Location
Sketch
(1) Failure Path
Identification and Screening
(2) Evaluate the Probability of the Presence of Open
Defects or In Filled Defects that Have
Eroded Pd
(3) Probabilities for No, Some, Excessive
and Continuing Erosion PNE, PSE,
PEE, PCE
(4) Probability of Progression PP
(5) Probability of Unsuccessful Detection and
Intervention Pudi
(6) Probability of Breach Pbreach
(7) Calculate the Probability of Failure
Initiation of Erosion in Defects Related to Stress Relief Effects in the Valley Sides
Stress Relief Defects
Long Section
Stress Relief Defects
Long Section
Use Table C2 to identify and screen potential failure paths.
Use Table C2 to evaluate the probability of the presence of open defects or in filled defects that have eroded.
Pd valley side 5-25mm, 25-100mm and >100mm defects
The likelihood of continuation of the infill material is already considered in step (2).
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table C6.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table C7.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table C8.
Pbreach-5-25mm. Pbreach-25-100mm Pbreach->100mm
Calculate the probability of failure using the event tree.
Pfail = Pd-5-25mm x PP x Pudi x Pbreach-5-25mm + Pd-25-100mm x PP x Pudi x Pbreach-25-
100mm + Pd->100mm x PP x Pudi x Pbreach-
>100mm
Erosion in defects in a rock foundation related to stress relief effects in the valley sides
5-25mm
<5mm
Presence of open or in filled defects
Continuing Erosion
No Erosion
ContinuationPd
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach-5-25mm Pfail-5-25mm
EVENT TREE STRUCTURE
Σ Pfail
>100mm
25-100mm
Continuing Erosion
No Erosion
Continuation
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach-25-100mm Pfail-25-100mm
Continuing Erosion
No Erosion
Continuation
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach->100mm Pfail->100mm
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version C-2
Table C1. Probability of Failure by Internal Erosion Through a Rock Foundation (Sheet 2)
Initiation of Erosion in Defects Related to Stress Relief Effects in the Valley Floor – Valley Bulge and Rebound
Valley Bulge Features
Long Section
Valley Bulge Features
Long Section
Use Table C3 to identify and screen potential failure paths.
Use Table C3 to evaluate the probability of initiation for each failure path.
Pd valley floor 5-25mm, 25-100mm and >100mm defects
The likelihood of continuation of the infill material is already considered in step (2).
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table C6.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table C7.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table C8.
Pbreach-5-25mm. Pbreach-25-100mm Pbreach->100mm
Calculate the probability of failure using the event tree.
Pfail = Pd-5-25mm x PP x Pudi x Pbreach-5-25mm + Pd-25-100mm x PP x Pudi x Pbreach-25-
100mm + Pd->100mm x PP x Pudi x Pbreach-
>100mm
Erosion in defects in a rock foundation related to stress relief effects in the valley floor
5-25mm
<5mm
Presence of open or in filled defects
Continuing Erosion
No Erosion
ContinuationPd
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach-5-25mm Pfail-5-25mm
EVENT TREE STRUCTURE
Σ Pfail
>100mm
25-100mm
Continuing Erosion
No Erosion
Continuation
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach-25-100mm Pfail-25-100mm
Continuing Erosion
No Erosion
Continuation
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach->100mm Pfail->100mm
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version C-3
Table C1. Probability of Failure by Internal Erosion Through a Rock Foundation (Sheet 3)
Initiation of Erosion in Solution Features for Rock Subject to Solution
Solution Features
Long Section Limestone, dolomite
Solution Features
Long Section Limestone, dolomite
Use Table C4 to identify and screen potential failure paths.
Use Table C4 to evaluate the probability of initiation for each failure path.
Pd solution 5-100mm, 100-300mm and >300mm defects
The likelihood of continuation of the infill material is already considered in step (2).
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table C6.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table C7.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table C8. Pbreach-5-100mm. Pbreach-100-300mm Pbreach->300mm
Calculate the probability of failure using the event tree.
Pfail = Pd-5-100mm x PP x Pudi x Pbreach-5-100mm + Pd-100-300mm x PP x Pudi x Pbreach-100-
300mm + Pd->300mm x PP x Pudi x Pbreach-
>300mm
Erosion in solution features in a rock foundation
5-100mm
<5mm
Presence of open or in filled defects
Continuing Erosion
No Erosion
ContinuationPd
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach-5-25mm Pfail-5-100mm
EVENT TREE STRUCTURE
Σ Pfail
>300mm
100-300mm
Continuing Erosion
No Erosion
Continuation
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach-25-100mm Pfail-100-300mm
Continuing Erosion
No Erosion
Continuation
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach->100mm Pfail->300mm
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version C-4
Table C1. Probability of Failure by Internal Erosion Through a Rock Foundation (Sheet 4)
Initiation of Erosion in Features for Associated with Landslides and Faults and Shears
Fault or Shear ZoneLong Section
Defects associated with landslide
Fault or Shear ZoneLong Section
Defects associated with landslide
Use Table C5 to identify and screen potential failure paths.
Use Table C5 to evaluate the probability of initiation for each failure path.
Pd other 5-25mm, 25-100mm and >100mm defects
The likelihood of continuation of the infill material is already considered in step (2).
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table C6.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table C7.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table C8.
Pbreach-5-25mm. Pbreach-25-100mm Pbreach->100mm
Calculate the probability of failure using the event tree.
Pfail = Pd-5-25mm x PP x Pudi x Pbreach-5-25mm + Pd-25-100mm x PP x Pudi x Pbreach-25-
100mm + Pd->100mm x PP x Pudi x Pbreach-
>100mm
Erosion in defects in a rock foundation associated with landslides/faults/shears
5-25mm
<5mm
Presence of open or in filled defects
Continuing Erosion
No Erosion
ContinuationPd
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach-5-25mm Pfail-5-25mm
EVENT TREE STRUCTURE
Σ Pfail
>100mm
25-100mm
Continuing Erosion
No Erosion
Continuation
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach-25-100mm Pfail-25-100mm
Continuing Erosion
No Erosion
Continuation
Yes
No
Progression
PP Yes
No
Intervention Fails
Pudi Yes
No
Breach
Pbreach->100mm Pfail->100mm
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version C-5
Table C2. Probability of Initiation of Erosion in Defects Related to Stress Relief Effects in the Valley Sides in a Rock Foundation
Failure Path/Location Probability of Continuous Open or in
Filled Defects Based on Geology and Topography PTG
Probability of Continuous Open or in
Filled Defects Based on Investigation and
Construction Data PSC
Combine the Two Probability Estimates
for Continuous Open or in Filled Defects
Assess the Width and Extent of the Open or In Filled Defects
Assess the Probability that the Defects are Open or In Filled
Assess the Probability that Grouting or Cut-
off Walls Has Not Been Effective in Cutting Off the
Defects
Assess the Probability that Erosion of the Infill will Initiate
Assess the Probability that Erosion of the Infill in Defects will
Continue
Combine the probabilities for open defects and in filled defects which will
potentially erode Pd
Describe the Defects and Failure Modes
Identify potential failure paths for initiation of erosion in defects related to stress relief effects in the valley sides.
Estimate the probability of a continuous open or in filled defect in the rock foundation from upstream of the core to downstream of the core. This is done for three defect sizes; 5-25mm, 25-100mm and >100mm.
Assess the weighted score (WS) from Tables 8.1 and 8.2, and obtain the probabilities for each defect size from Table 8.3.
PTG-(5-25mm)
PTG-(25-100mm)
PTG-(>100mm)
Estimate the probability of a continuous open or in filled defect in the rock foundation from upstream of the core to downstream of the core. This is done for three defect sizes; 5-25mm, 25-100mm and >100mm.
Assess the weighted score (WS) from Tables 8.4, and obtain the probabilities for each defect size from Table 8.5.
PSC-(5-25mm)
PSC-(25-100mm)
PSC-(>100mm)
Obtain the weighting factor (w) based on the quantity and quality of the investigation and construction data using Table 8.22.
Calculate the weighted estimate of the probability of the presence of open or in filled defects. Do this for each defect size;
Pw(5-25mm) = w PTG(5-25mm) + (1-w) PSC(5-25mm)
Pw(25-100mm) = w PTG(25-
100mm) + (1-w) PSC(25-
100mm)
Pw(>100mm) = w PTG(>100mm ) + (1-w) PSC(>100mm )
Estimate the width and extent of the open or in filled defects below the original ground surface using Section 8.6.1.
Assess the probability that the defects below the level of the core are open or in filled using Table 8.16
For open defects, assess the likelihood of grouting not being effective using Tables 8.17 and 8.18.
For in filled defects, grouting is assumed to be ineffective and assign a probability for grouting not being effective = 1.0.
Use Tables 8.19 and 8.20 where a cut-off has been excavated and backfilled in the rock foundation to intercept the continuous open defect or solution feature.
Use Table 8.21 to estimate the probability of erosion initiating based on performance data.
Estimate the probability of erosion of infill initiating using first principles using Section 8.10.3.
Calculate the weighted average of the two probability estimates. Estimate the weighting factor based on the quality of the input data.
Estimate the probability that there will an unfiltered exit (Punf) using Table 10.13 to aid judgment.
Calculate the probability that there will be a filtered exit (Pfe) = 1- Punf.. Assess the filter materials and materials being eroded in terms of the Continuing Erosion criteria as described using the procedure in Section 10.1.4.
The probability of continuing erosion = (Punf x 1.0) + (Pfe x PCE).
Compute the probability of a continuous open defect in rock foundation below the embankment using the event tree shown in Figure 8.5 (see below). This is to be done for each defect or solution feature width using the weighted probabilities from Section 8.12.1 where weighting is applied.
Pd-(5-25mm) valley side
Pd-(25-100mm) valley side
Pd-(>100mm) valley side
Describe the defects in relation to the embankment details (refer to Section 8.13).
The potential failure modes arising from the defects should be assessed and sketches prepared to show them so the risk analysis team have a clear picture of the failure modes and their relation to the defects.
50.0% Open featureof X mm width
50.0% Is grouting ineffective?
50.0%
10.0% Is feature open or infilled?
Estimated width below cutoff trench X mm 50.0% Open featureof X mm width
50.0% Does erosion continue?
50.0%
50.0% Does erosion initiate?
50.0%
50.0% Is grouting ineffective?
50.0%
Continuous open or infilled feature present?
1.0% repeat tree
50.0%
Abutment stress relief features
>100mm
5-25mm
25-100mm
Open
Infilled
Yes
No
Yes
No
Yes
No
Yes
No
Sub-event tree structure to show computation of a continuous open defect below the embankment
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version C-6
Table C3. Probability of Initiation of Erosion in Defects Related to Stress Relief Effects in the Valley Floor – Valley Bulge and Rebound
Failure Path/Location Probability of Continuous Open or in
Filled Defects Based on Geology and Topography PTG
Probability of Continuous Open or in
Filled Defects Based on Investigation and
Construction Data PSC
Combine the Two Probability Estimates
for Continuous Open or in Filled Defects
Assess the Width and Extent of the Open or In Filled Defects
Assess the Probability that the Defects are Open or In Filled
Assess the Probability that Grouting or Cut-
off Walls Has Not Been Effective in Cutting Off the
Defects
Assess the Probability that Erosion of the Infill will Initiate
Assess the Probability that Erosion of the Infill in Defects will
Continue
Combine the probabilities for open defects and in filled defects which will
potentially erode Pd
Describe the Defects and Failure Modes
Identify potential failure paths for initiation of erosion in defects related to stress relief effects in the valley floor.
Estimate the probability of a continuous open or in filled defect in the rock foundation from upstream of the core to downstream of the core. This is done for three defect sizes; 5-25mm, 25-100mm and >100mm.
Assess the weighted score (WS) from Table 8.6 and obtain the probabilities for each defect size from Table 8.7.
PTG-(5-25mm)
PTG-(25-100mm)
PTG-(>100mm)
Estimate the probability of a continuous open or in filled defect in the rock foundation from upstream of the core to downstream of the core. This is done for three defect sizes;
5-25mm, 25-100mm and >100mm.
Assess the weighted score (WS) from Tables 8.8, and obtain the probabilities for each defect size from Table 8.9.
PSC-(5-25mm)
PSC-(25-100mm)
PSC-(>100mm)
Obtain the weighting factor (w) based on the quantity and quality of the investigation and construction data using Table 8.22.
Calculate the weighted estimate of the probability of the presence of open or in filled defects. Do this for each defect size;
Pw(5-25mm) = w PTG(5-25mm) + (1-w) PSC(5-25mm)
Pw(25-100mm) = w PTG(25-
100mm) + (1-w) PSC(25-
100mm)
Pw(>100mm) = w PTG(>100mm ) + (1-w) PSC(>100mm )
Estimate the width and extent of the open or in filled defects below the original ground surface using Section 8.6.2.
Assess the probability that the defects below the level of the core are open or in filled using Table 8.16.
For open defects, assess the likelihood of grouting not being effective using Tables 8.17 and 8.18.
For in filled defects, grouting is assumed to be ineffective and assign a probability for grouting not being effective = 1.0.
Use Tables 8.19 and 8.20 where a cut-off has been excavated and backfilled in the rock foundation to intercept the continuous open defect or solution feature.
Use Table 8.21 to estimate the probability of erosion initiating based on performance data.
Estimate the probability of erosion of infill initiating using first principles using Section 8.10.3.
Calculate the weighted average of the two probability estimates. Estimate the weighting factor based on the quality of the input data.
Estimate the probability that there will an unfiltered exit (Punf) using Table 10.13 to aid judgment.
Calculate the probability that there will be a filtered exit (Pfe) = 1- Punf.. Assess the filter materials and materials being eroded in terms of the Continuing Erosion criteria as described using the procedure in Section 10.1.4.
The probability of continuing erosion = (Punf x 1.0) + (Pfe x PCE).
Compute the probability of a continuous open defect in rock foundation below the embankment using the event tree shown in Figure 8.5 (see below). This is to be done for each defect or solution feature width using the weighted probabilities from Section 8.12.1 where weighting is applied.
Pd-(5-25mm) valley floor
Pd-(25-100mm) valley floor
Pd-(>100mm) valley floor
Describe the defects in relation to the embankment details (refer to Section 8.13).
The potential failure modes arising from the defects should be assessed and sketches prepared to show them so the risk analysis team have a clear picture of the failure modes and their relation to the defects.
50.0% Open featureof X mm width
50.0% Is grouting ineffective?
50.0%
10.0% Is feature open or infilled?
Estimated width below cutoff trench X mm 50.0% Open featureof X mm width
50.0% Does erosion continue?
50.0%
50.0% Does erosion initiate?
50.0%
50.0% Is grouting ineffective?
50.0%
Continuous open or infilled feature present?
1.0% repeat tree
50.0%
Abutment stress relief features
>100mm
5-25mm
25-100mm
Open
Infilled
Yes
No
Yes
No
Yes
No
Yes
No
Sub-event tree structure to show computation of a continuous open defect below the embankment
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version C-7
Table C4. Probability of Initiation of Erosion in Defects Related to Solution Features for Rock Subject to Solution
Failure Path/Location Probability of Continuous Open or in
Filled Solution Feature Based on
Geology and Topography PTG
Probability of Continuous Open or in
Filled Solution Feature Based on Investigation and
Construction Data PSC
Combine the Two Probability Estimates
for Continuous Open or in Filled Solution
Features
Assess the Width and Extent of the Open
or In Filled Solution Features
Assess the Probability that the Solution
Features are Open or In Filled
Assess the Probability that Grouting or Cut-
off Walls Has Not Been Effective in Cutting Off the
Solution Features
Assess the Probability that Erosion of the Infill will Initiate
Assess the Probability that Erosion of the Infill in Solution
Features will Continue
Combine the probabilities for open features and in filled features which will potentially erode Pd
Describe the Defects and Failure Modes
Identify potential failure paths for initiation of erosion in defects related to solution features.
Estimate the probability of a continuous open or in filled solution feature in the rock foundation from upstream of the core to downstream of the core. This is done for three sizes; 5-100mm, 100-300mm and >300mm.
Assess the weighted score (WS) from Table 8.10 and obtain the probabilities for each defect size from Table 8.11.
PTG-(5-100mm)
PTG-(100-300mm)
PTG-(>300mm)
Estimate the probability of a continuous open or in filled solution feature in the rock foundation from upstream of the core to downstream of the core. This is done for three sizes;
100mm, 100-300mm and >300mm.
Assess the weighted score (WS) from Tables 8.12, and obtain the probabilities for each defect size from Table 8.13.
PSC-(5-100mm)
PSC-(100-300mm)
PSC-(>300mm)
Obtain the weighting factor (w) based on the quantity and quality of the investigation and construction data using Table 8.22.
Calculate the weighted estimate of the probability of the presence of open or in filled solution feature. Do this for each defect size;
Pw(5-100mm) = w PTG(5-
100mm) + (1-w) PSC(5-100mm)
Pw(100-300mm) = w PTG(100-
300mm) + (1-w) PSC(100-
300mm)
Pw(>300mm) = w PTG(>300mm ) + (1-w) PSC(>300mm )
Estimate the width and extent of the open or in filled solution feature below the original ground surface using Section 8.6.3.
Assess the probability that the solution features below the level of the core are open or in filled using Table 8.16.
For open defects, assess the likelihood of grouting not being effective using Tables 8.17 and 8.18.
For in filled defects, grouting is assumed to be ineffective and assign a probability for grouting not being effective = 1.0.
Use Tables 8.19 and 8.20 where a cut-off has been excavated and backfilled in the rock foundation to intercept the continuous open defect or solution feature.
Use Table 8.21 to estimate the probability of erosion initiating based on performance data.
Estimate the probability of erosion of infill initiating using first principles using Section 8.10.3.
Calculate the weighted average of the two probability estimates. Estimate the weighting factor based on the quality of the input data.
Estimate the probability that there will an unfiltered exit (Punf) using Table 10.13 to aid judgment.
Calculate the probability that there will be a filtered exit (Pfe) = 1- Punf.. Assess the filter materials and materials being eroded in terms of the Continuing Erosion criteria as described using the procedure in Section 10.1.4.
The probability of continuing erosion = (Punf x 1.0) + (Pfe x PCE).
Compute the probability of a continuous open solution feature in rock foundation below the embankment using the event tree shown in Figure 8.5 (below). This is to be done for each solution feature width using the weighted probabilities from Section 8.12.1 where weighting is applied.
Pd-(5-100mm) solution
Pd-(100-300mm) solution
Pd-(>300mm) solution
Describe the solution features in relation to the embankment details (refer to Section 8.13).
The potential failure modes arising from the solution features should be assessed and sketches prepared to show them so the risk analysis team have a clear picture of the failure modes and their relation to the defects.
50.0% Open featureof X mm width
50.0% Is grouting ineffective?
50.0%
10.0% Is feature open or infilled?
Estimated width below cutoff trench X mm 50.0% Open featureof X mm width
50.0% Does erosion continue?
50.0%
50.0% Does erosion initiate?
50.0%
50.0% Is grouting ineffective?
50.0%
Continuous open or infilled feature present?
1.0% repeat tree
50.0%
Abutment stress relief features
>100mm
5-25mm
25-100mm
Open
Infilled
Yes
No
Yes
No
Yes
No
Yes
No
Sub-event tree structure to show computation of a continuous open defect below the embankment
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version C-8
Table C5. Probability of Initiation of Erosion in Defects Associated with Other Geological Features such as Landslides, Faults and Shears
Failure Path/Location Probability of Continuous Open or in Filled Defects
Based on Investigation and Construction Data PSC
Assess the Width and Extent of the Open or In
Filled Defects
Assess the Probability that the Defects are Open or In
Filled
Assess the Probability that Grouting or Cut-off Walls Has Not Been Effective in
Cutting Off the Defects
Assess the Probability that Erosion of the Infill will
Initiate
Assess the Probability that Erosion of the Infill in Defects will Continue
Combine the probabilities for open defects and in filled defects which will
potentially erode Pd
Describe the Defects and Failure Modes
Identify potential failure paths for initiation of erosion associated with landslides, faults and shears.
Estimate the probability of a continuous open or in filled defect in the rock foundation from upstream of the core to downstream of the core. This is done for three defect sizes;
5-25mm, 25-100mm and >100mm.
Assess the weighted score (WS) from Tables 8.14, and obtain the probabilities for each defect size from Table 8.15.
Pw-(5-25mm)
Pw-(25-100mm)
Pw-(>100mm)
Estimate the width and extent of the open or in filled defects below the original ground surface using Section 8.6.3 as a guide.
Assess the probability that the defects below the level of the core are open or in filled using Table 8.16.
For open defects, assess the likelihood of grouting not being effective using Tables 8.17 and 8.18.
For in filled defects, grouting is assumed to be ineffective and assign a probability for grouting not being effective = 1.0.
Use Tables 8.19 and 8.20 where a cut-off has been excavated and backfilled in the rock foundation to intercept the continuous open defect or solution feature.
Use Table 8.21 to estimate the probability of erosion initiating based on performance data.
Estimate the probability of erosion of infill initiating using first principles using Section 8.10.3.
Calculate the weighted average of the two probability estimates. Estimate the weighting factor based on the quality of the input data.
Estimate the probability that there will an unfiltered exit (Punf) using Table 10.13 to aid judgment.
Calculate the probability that there will be a filtered exit (Pfe) = 1- Punf.. Assess the filter materials and materials being eroded in terms of the No Erosion, Some Erosion, Excessive Erosion and Continuing Erosion criteria as described using the procedure in Section 10.1.4.
The probability of continuing erosion = (Punf x 1.0) + (Pfe x PCE).
Compute the probability of a continuous open defect in rock foundation below the embankment using the event tree shown in Figure 8.5. This is to be done for each defect width using the weighted probabilities from Section 8.12.1 where weighting is applied.
Pd-(5-25mm) other
Pd-(25-100mm) other
Pd-(>100mm) other
Describe the defects in relation to the embankment details (refer to Section 8.13).
The potential failure modes arising from the defects should be assessed and sketches prepared to show them so the risk analysis team have a clear picture of the failure modes and their relation to the defects.
50.0% Open featureof X mm width
50.0% Is grouting ineffective?
50.0%
10.0% Is feature open or infilled?
Estimated width below cutoff trench X mm 50.0% Open featureof X mm width
50.0% Does erosion continue?
50.0%
50.0% Does erosion initiate?
50.0%
50.0% Is grouting ineffective?
50.0%
Continuous open or infilled feature present?
1.0% repeat tree
50.0%
Abutment stress relief features
>100mm
5-25mm
25-100mm
Open
Infilled
Yes
No
Yes
No
Yes
No
Yes
No
Sub-event tree structure to show computation of a continuous open defect below the embankment
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version C-9
Table C6. Probability of Progression for Internal Erosion in a Rock Foundation
Applicable Failure Path/Location Probability of Forming a Roof (PPR) Probability of Crack Filling Action Not Effective (PPC) Probability that Upstream Zone Fails to Limit Flows (PPL)
All IE Foundation Failure Modes
The probability of the rock foundation materials in supporting the roof of a pipe in the foundation is assumed to be 1.0.
PPR = 1.0
Consider the potential for the overlying embankment or foundation soils to wash into the developing pipe. There needs to be a filtering material at the downstream end of the flow path for crack filling action to be effective. The filtering material may be a naturally occurring layer in the foundation, or the embankment filter.
PPC
Assess the probability that an upstream soil layer, upstream zone or a concrete element fails to limit flows using Table 11.3.
PPL
Table C7. Probability of Unsuccessful Detection and Intervention for Internal Erosion in a Rock Foundation
Probability of Not Detecting Probability of Not Intervening
Applicable Failure Path/Location
(1) Assess the Rate of Internal Erosion and Piping
(2) Assess the probability of the concentrated leak not being observable Pnol
(3) Assess the probability that given the leak is observable, that it is not detected Pnd
(4) Calculate the probability of not detecting the internal erosion Pndi
(5) Assess the probability that intervention and repair is not successful Pui
(6) Probability of Not Detect and Not Intervene
Pudi
All Failure Modes Estimate the approximate time for progression of piping and development of a breach using Tables 12.1, 12.2 and 12.3.
Assess the weighted score (WS) from Table 12.5 and obtain probability from Table 12.6.
Pnol
Assess the probability of not detecting the leak using Table 12.7.
Pnd
Calculate the probability of not detecting the internal erosion using Pnol from Step (2) and Pnd from Step (3);
= Pnol + [(1-Pnol) x Pnd]
Assess the probability that intervention and repair is not successful using Table 12.8.
Pui
Calculate the probability of unsuccessful detection and intervention using Pnol from Step (2), Pnd from Step (3) and Pui from Step (5);
Pndi = Pnol + [(1-Pnol) x Pnd x Pui]
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version C-10
Table C8. Probability of Breach for Internal Erosion in a Rock Foundation
Applicable Failure Path/Location
Size of Defects in the Rock
Foundation
(1) Screening of breach
mechanisms
(2) Probability of Breach by Gross Enlargement Pge
(3) Probability of Breach by Slope Instability Psi
(4) Probability of Breach by Sloughing or Unravelling Psu
(5) Probability of Breach by Sinkhole Psd
(6) Calculate the Probability of Breach
All Failure Modes
Evaluate the probabilities of breach for each defect size
Not applicable to this mode of internal erosion.
Ignore this failure mode unless the size of the in filled defect or solution feature is very large (e.g. in-filled caverns or caves in karst > 2m).
Pge
(a) Estimate the probability that leakage through the rock foundations exits into the downstream shell PS using Table 13.6.
(b) Estimate the probability of slope instability due to the increased flows Psi-
i. Assess the weighted score from Tables 13.7 and 13.8 and obtain the probability from Table 13.9. This is done for each defect size.
(b) Estimate the probability of loss of freeboard due to instability (Psi-lf). Assess the weighted score from Table 13.10 and obtain the probability from Table 13.11.
(c) Calculate the probability of breach by slope instability for each defect size.
(a) Estimate the probability that leakage through the rock foundations exits into the downstream shell PS using Table 13.6.
(b) For dams with a downstream zone of earthfill, assess the weighted score from Table 13.12 and obtain the probability for each defect size from Table 13.14. Psus
(c) For dams with a downstream zone of rockfill, assess the weighted score from Table 13.15 and obtain the probability for defect size from Table 13.17. Psus
(a) Estimate the probability of a sinkhole developing as a result of the internal erosion (Ps-f) from Table 13.18.
(b) Estimate the probability that the sinkhole causes loss of freeboard. Assess the weighted score from Table 13.19 and obtain the probability from Table 13.20.
(c) Calculate the probability of breach by sinkhole development;
Calculate the probability of breach for each branch of the event tree (i.e. for each of the defect sizes) by summing the probabilities using de Morgan’s rule as follows;
<5mm Pge = 0 (Psi<5mm) = PS x (Psi-i <5mm) x (Psi-lf). (Psu-<5mm) = PS x (Psus-<5mm) (Psd-<5mm) = 0 Pbreach-<5mm = 1 – [(1 - Psi-<5mm) x (1 - Psu-<5mm)].
5-25mm Pge = 0 (Psi-5-25mm) = PS x (Psi-i 5-25mm) x (Psi-lf). (Psu-5-25mm) = PS x (Psus-5-25mm) (Psd-5-25mm) = (Ps-f) x (Ps-lf SE)
Pbreach-5-25mm = 1 – [(1 - Psi-5-25mm) x (1 - Psu-5-25mm) x (1 - Psd-5-25mm)].
25-100mm Pge = 0 (Psi-25-100mm) = PS x (Psi-i-25-100mm) x (Psi-lf). (Psu-25-100mm) = PS x (Psus-25-100mm) (Psd-25-100mm) = (Ps-f) x (Ps-
lf EE) Pbreach-25-100mm = 1 – [(1 - Psi-25-100mm) x (1 - Psu-25-100mm) x (1 - Psd-25-
100mm)].
100-300mm Pge = 0 (Psi-100-300mm) = PS x (Psi-i-100-300mm) x (Psi-
lf). (Psu-100-300mm) = PS x (Psus-100-300mm) (Psd-100-300mm) = (Ps-f) x
(Ps-lf CE) Pbreach-100-300mm = 1 – [(1 - Pge-100-
300mm) x (1 - Psi-100-300mm) x (1 - Psu-
100-300mm) x (1 - Psd-100-300mm)].
>300mm Pge->300mm (Psi->300mm) = PS x (Psi-i->300mm) x (Psi-lf). (Psu->300mm) = PS x (Psus->300mm) (Psd->300mm) = (Ps-f) x (Ps-lf CE)
Pbreach->300mm = 1 – [(1 - Pge->300mm) x (1 - Psi->300mm) x (1 - Psu->300mm) x (1 - Psd->300mm)].
Appendix D Navigation Table for Internal Erosion of the
Embankment into or at the Foundation
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version D-1
Table D1. Probability of Failure by Internal Erosion of the Embankment at or into the Foundation (Sheet 1)
Failure Path/Location Sketch (1) Failure Path
Identification and Screening
(2) Evaluate the Probability of
Initiation of Erosion PI
(3) Probabilities for No, Some, Excessive
and Continuing Erosion PNE, PSE, PEE,
PCE
(4) Probability of Progression PP
(5) Probability of Unsuccessful Detection and
Intervention Pudi
(5) Probability of Breach Pbreach
(6) Calculate the Probability of Failure
Initiation of Erosion by Backward Erosion or Suffusion from a high permeability zone in the core or cut-off trench into the foundation
313
Backward erosion piping
313
Backward erosion piping
Use Table D2 to identify and screen potential crack mechanisms
Use Table D2 to evaluate the probability of initiation.
PI –BEP
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table D5.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table D6.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table D7.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table D8.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE
Calculate the probability of failure using the event tree.
Pfail = PI-BEP x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
Pbreach-CE
Backward Erosion or Suffusion from the Embankment into the Foundation
Yes
Initiation
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI-BEP PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-CE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE
Σ Pfail
No
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version D-2
Table D1. Probability of Failure by Internal Erosion of the Embankment at or into the Foundation (Sheet 2)
Initiation of Erosion by Scour at the Core-Foundation Contact
Erosion of core by water flowing in open rock defects
313
Erosion of core by water flowing in open rock defects
313 313
Use Table D3 to identify and screen potential crack mechanisms
Use Table D3 to evaluate the probability of initiation.
PI – scour
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table D5.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table D6.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table D7.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table D8.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE
Calculate the probability of failure using the event tree.
Pfail = PI –scour x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
Pbreach-CE
Erosion by Scour at the Core-Foundation Contact
Yes
Initiation
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI -scour PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-CE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE
Σ Pfail
No
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version D-3
Table D1. Probability of Failure by Internal Erosion of the Embankment at or into the Foundation (Sheet 3)
Initiation of Erosion in a Crack or Hydraulic Fracture Across the Cut-Off Trench
13
Hydraulic fracture in cut-off trench
311
3
Hydraulic fracture in cut-off trench
31
Use Table D4 to identify and screen potential crack mechanisms
Use Table D4 to evaluate the probability of initiation of the embankment at or into a rock foundation.
PI-crack
Evaluate the probabilities for No, Some, Excessive and Continuing Erosion for the failure path under consideration using Table D5.
PSE PEE
PCE
Estimate the probabilities for forming a roof (PPR), crack filling action not stopping pipe enlargement (PPC) and upstream zone fails to limit flows (PPL) for the failure path under consideration using Table D6.
PP = PPR x PPC x PPL
Estimate the probability for not detect and intervene using Table D7.
Pudi
Estimate the probabilities of breach for the Some, Excessive and Continuing Erosion branches using Table D8.
Pbreach-NE = 0. Pbreach-SE Pbreach-EE Pbreach-CE
Calculate the probability of failure using the event tree.
Pfail = PI -crack x PP x Pudi x
[(PSE x Pbreach-SE) +
(PEE x Pbreach-EE) +
(PCE x Pbreach-CE)]
Pbreach-CE
Erosion by in a Crack or Hydraulic Fracture Across the Cut-Off Trench
Yes
Initiation
Some Erosion
No Erosion
Continuation
Excessive Erosion
Continuing Erosion
PI -crack PSE
PEE
PCE
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Progression
PP
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Intervention Fails
Pudi
Yes
No
Breach
Yes
No
Breach
Yes
No
Breach
Pbreach-EE
Pbreach-SE
Pfail-CE
Pfail-EE
Pfail-SE
EVENT TREE STRUCTURE
Σ Pfail
No
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version D-4
Table D2. Probability of Initiation of Erosion by Backward Erosion from a high permeability zone in the core or cut-off trench into the foundation
Probability of Erosion in the High Permeability Zone (cohesionless soils)
Failure Path/Location (1) Assess the Probability of a Continuous
Pathway Ppath (2) Assess whether there is time for seepage gradient to develop
(3) Estimate average seepage gradient required to initiate
and progress backward erosion (iPMT or iCR)
(4) Estimate probability of erosion (PIP)
(5) Calculate the Probability Initiation of Erosion (PI)
Erosion into Open Joints in Rock
Estimate the probability of a continuous pathway of open joints in rock in the base or sides of the core trench or core-foundation contact. (a) Estimate the probability of a continuous pathway of open defects or solution features of different sizes >5mm from Section 8 (Tables C2, C3, C4 and C5). For defects <5mm, assume they are present (refer to Section 9.3.1). (b) Assess the probability the foundation treatment fails to prevent contact of the core with open defects or solution features (PTI) using Table 9.1. (c) Calculate the probability of a continuous pathway for each defect size.
Ppath = PCR x PTI
For reservoir levels above the normal operating pool level, use Table 6.25 to estimate time for seepage gradient to develop in layer. Exclude if the reservoir level rise is insufficient for seepage gradient to develop.
Estimate the average gradient (iPMT) required to initiate and progress erosion from Figure 6.4. If Cu>6, estimate the critical gradient (iCR) – see Section 6.6.2.
Obtain probability of erosion from Table 6.25 for well compacted layers and Table 6.26 for poorly compacted layers based on the average seepage gradient across the embankment core at the core-foundation contact (iave) and iPMT (or iCR). PIP
Cohesionless soils: PI-BEP. = Ppath x PP x PIP
This is done for each defect size
Erosion into Coarse Grained Soil
Estimate the probability of a continuous pathway of coarse grained soil in the base or sides of the core trench or core-foundation contact using Table 9.2.
Ppath
Same as above Same as above Same as above Same as above
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version D-5
Table D3. Probability of Initiation of Erosion by Scour at the Core-Foundation Contact
Failure Path/Location (1) Assess the Probability of a
Continuous Pathway Ppath (2) Estimate probability of erosion (PIC)
(3) Calculate the Probability of Initiation of Erosion (PI)
Scour Erosion due to Open Joints in Rock
Same as for Backward Erosion (Step 1 of Table D2)
Ppath
Estimate the probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and using the defect size as the “crack width”. Do this for each defect size (i.e. 5-25mm, 25-100mm, >100mm). The hydraulic gradient should be based on the seepage gradient on the core-foundation contact (refer to Section 9.6.2 for guidance) PIC
For each defect size, calculate the probability of initiation by scour;
PI-scour = Ppath x PIC
Scour Erosion due to Coarse Grained Soil
Same as for Backward Erosion (Step 1 of Table D2)
Ppath
Estimate the probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and by representing the coarse grained soil as an equivalent crack width. The equivalent crack width can be assumed to be equal to the D15/4 value of the coarse grained soil. The hydraulic gradient should be based on the seepage gradient on the core-foundation contact PIC
Same as above
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version D-6
Table D4. Probability of Initiation of Erosion in a Crack or Hydraulic Fracture Across the Cut-Off Trench
Failure Path/Location (1) Assess the Probability of a
Continuous Pathway Ppath
(2) Estimate the probability of a hydraulic fracture occurring across the cut-off trench
(Phf)
(2) Estimate probability of erosion in the hydraulic fracture (PIC)
(3) Calculate the Probability of Initiation of Erosion (PI)
Erosion into Open Joints in Rock
Same as for Backward Erosion (Step 1 of Table D2)
Ppath
Estimate the probability of a hydraulic fracture occurring across the cut-off trench (Phf). Assess the weighting score from Table 9.3 and obtain the probability from Table 9.4.
Obtain probability of erosion from the most appropriate table from Tables 5.29 to 5.35 based on the core soil type and assuming the hydraulic fracture has a crack width of 5mm. The hydraulic gradient should be based on the estimated seepage gradient across the cut-off trench. PIC
For each defect size, calculate the probability of initiation across the cut-off trench
PI-crack = Ppath x Phf x PIC
Erosion into Coarse Grained Soil
Same as for Backward Erosion (Step 1 of Table D2)
Ppath
Same as above Same as above Same as above
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version D-7
Table D5. Probability of Continuation for Internal Erosion of the Embankment at or into the Foundation
Assess which Scenario is Applicable to the Failure Path under Consideration
Examples Probability of Continuation (PNE , PSE , PEE , PCE)
Scenario 1: Homogeneous zoning with no fully intercepting filter 1
HOMOGENEOUS EARTHFILL
1
HOMOGENEOUS EARTHFILL
No potential for filtering.
Probability for continuing erosion, PCE=1.0
PNE = PSE = PEE = 0
Scenario 2: Downstream shoulder of fine grained cohesive material which is capable of holding a crack/pipe.
See Section 10.1.3 for more details.
11A
ZONED EARTHFILL WITH COHESIVE SHELLS
1A11A
ZONED EARTHFILL WITH COHESIVE SHELLS
1A
Filtering does not occur if the crack/high permeability zone persists through the downstream shoulder zone.
Use Table 10.1 to determine the probability for continuing erosion, PCE.
Calculate PNE = 1.0 – PCE
PSE = PEE = 0
Scenario 3: Filter/transition zone is present downstream of the core or a downstream shoulder zone which is not capable of holding a crack/pipe.
1
21
EARTHFILL WITH CHIMNEY FILTER
3
2
13
ZONED EARTHFILL WITH CHIMNEY FILTER
313
ZONED EARTHFILL WITH GRANULAR SHELLS
1
21
EARTHFILL WITH CHIMNEY FILTER
1
21
EARTHFILL WITH CHIMNEY FILTER
3
2
13
ZONED EARTHFILL WITH CHIMNEY FILTER
3
2
13
ZONED EARTHFILL WITH CHIMNEY FILTER
313
ZONED EARTHFILL WITH GRANULAR SHELLS
313
ZONED EARTHFILL WITH GRANULAR SHELLS
Follow the procedure outlined in Section 10.1.4 to estimate the probabilities of No Erosion (PNE), Some Erosion (PSE), Excessive Erosion (PEE) and Continuing Erosion (PCE).
Figure A1 (Appendix A) shows a flow chart which summarizes the procedure.
Scenario 4: Piping into an open defect, joint or crack.
SOIL
CONDUIT
EROSION INTO OPEN JOINTS IN ROCK FOUNDATION
SOIL
OPEN JOINTED ROCK
EROSION INTO AN OPEN CRACK OR JOINT IN A CONDUIT OR WALL
SOIL
CONDUIT
EROSION INTO OPEN JOINTS IN ROCK FOUNDATION
SOIL
OPEN JOINTED ROCK
EROSION INTO AN OPEN CRACK OR JOINT IN A CONDUIT OR WALL
Step 1: Evaluate the opening size for No Erosion, Some Erosion, Excessive Erosion and Continuing Erosion using Table 10.10.
Step 2: Estimate the conditional probabilities for No Erosion (PNE), Some Erosion (PSE), Excessive Erosion (PEE) and Continuing Erosion (PCE) by estimating the proportion of soils falling within each erosion category and using Table 10.11.
Scenario 5: Erosion into a toe drain
1
INTERNAL EROSION THROUGH THE EMBANKMENT INTO A TOE DRAIN
1
INTERNAL EROSION THROUGH THE FOUNDATION INTO A TOE DRAIN
1
INTERNAL EROSION THROUGH THE EMBANKMENT INTO A TOE DRAIN
1
INTERNAL EROSION THROUGH THE FOUNDATION INTO A TOE DRAIN
Estimate the probability of continuing erosion for erosion into a toe drain using Table 10.12. The assessment of erosion into a toe drain considers the observed condition of the toe drain (from video or external inspections) and the design and construction details of the toe drain.
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version D-8
Table D6. Probability of Progression for Internal Erosion of the Embankment at or into the Foundation
Applicable Failure Path/Location Probability of Forming a Roof (PPR) Probability of Crack Filling Action Not Effective (PPC) Probability that Upstream Zone Fails to Limit Flows (PPL)
All IE Embankment into Foundation Failure Modes
Assess the probability of the core material to form a roof of a pipe using Table 11.1.
PPR
Assess the probability of crack filling action not stopping pipe enlargement using Table 11.2.
PPC
For the case where erosion is occurring at the core-foundation contact, assess the probability that the upstream zone or concrete elements fail to limit flows using Table 11.3.
For the case where erosion initiates within a deep cut-off trench into open joints in a rock foundation, limitation of flows is embedded in the breach assessment and a probability for no flow limitation of 1.0 should be used.
PPL
Table D7. Probability of Unsuccessful Detection and Intervention for Internal Erosion of the Embankment at or into the Foundation
Probability of Not Detecting Probability of Not Intervening
Applicable Failure Path/Location
(1) Assess the Rate of Internal Erosion and Piping
(2) Assess the probability of the concentrated leak not being observable Pnol
(3) Assess the probability that given the leak is observable, that it is not detected Pnd
(4) Calculate the probability of not detecting the internal erosion Pndi
(5) Assess the probability that intervention and repair is not successful Pui
(6) Probability of Not Detect and Not Intervene
Pudi
All Failure Modes Estimate the approximate time for progression of piping and development of a breach using Tables 13.1, 13.2 and 9.3.
Assess the weighted score (WS) from Table 13.5 and obtain probability from Table 13.6.
Pnol
Assess the probability of not detecting the leak using Table 13.7.
Pnd
Calculate the probability of not detecting the internal erosion using Pnol from Step (2) and Pnd from Step (3);
= Pnol + [(1-Pnol) x Pnd]
Assess the probability that intervention and repair is not successful using Table 13.8.
Pui
Calculate the probability of unsuccessful detection and intervention using Pnol from Step (2), Pnd from Step (3) and Pui from Step (5);
Pudi = Pnol + [(1-Pnol) x Pnd x Pui]
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping - Guidance Document July 2008 Delta Version D-9
Table D8. Probability of Breach for Internal Erosion of the Embankment at or into the Foundation
Applicable Failure Path/Location
Branch on Event Tree (1) Screening of breach
mechanisms
(2) Probability of Breach by Gross Enlargement Pge
(3) Probability of Breach by Slope Instability Psi
(4) Probability of Breach by Sloughing or Unravelling
Psu
(5) Probability of Breach by Sinkhole Psd
(6) Calculate the Probability of Breach
All Failure Modes
Evaluate the probabilities of breach for each branch of the event tree (i.e. No, Some, Excessive and Continuing Erosion branches)
Assess which breach mechanisms are relevant to the type of dam zoning and failure path being considered using Table 13.1.
Only consider the breach mechanisms that are included for estimating the probability of breach.
Excluded breach mechanisms are assigned a probability of breach = 0.
The probability of breach by gross enlargement Pge= 0 for the No, Some and Excessive Erosion branches.
Breach by gross enlargement is negligible in cases where the downstream shell is unable to support a roof of a pipe. Evaluate whether this is applicable using Table 13.2.
If this breach mechanism is applicable, estimate the probability of breach by gross enlargement using Table 13.3.
Pge
(a) Estimate the probability of slope instability occurring due to the increased seepage flows. Assess the weighted score from Table 13.4 and obtain the probability from Table 13.5. This is done for each branch of the event tree [Some Erosion (Psi-i SE), Excessive Erosion (Psi-i EE) and Continuing Erosion (Psi-i CE)].
(b) Estimate the probability of loss of freeboard due to instability (Psi-lf). Assess the weighted score from Table 13.10 and obtain the probability from Table 13.11.
(c) Calculate the probability of breach by slope instability for each branch of the tree;
(a) Probability seepage will emerge into the downstream shell PS = 1.0.
(b) For dams with a downstream zone of earthfill, assess the weighted score from Table 13.12 and obtain the probability for each branch of the tree from Table 13.13; Some Erosion (Psu-SE), Excessive Erosion (Psu-EE) and Continuing Erosion (Psu-CE).
(c) For dams with a downstream zone of rockfill, assess the weighted score from Table 13.15 and obtain the probability for each branch of the tree from Table 13.16; Some Erosion (Psu-SE), Excessive Erosion (Psu-EE) and Continuing Erosion (Psu-CE).
(a) Estimate the probability of a sinkhole developing as a result of the internal erosion (Ps-f) from Table 13.18.
(b) Estimate the probability that the sinkhole causes loss of freeboard. Assess the weighted score from Table 13.19 and obtain the probability for each branch of the event tree from Table 13.20. Some Erosion (Ps-lf SE), Excessive Erosion (Ps-lf EE) and Continuing Erosion (Ps-lf CE).
(c) Calculate the probability of breach by sinkhole development;
Calculate the probability of breach for each branch of the event tree (i.e. Some Erosion, Excessive Erosion and Continuing Erosion branches) by summing the probabilities using de Morgan’s rule as follows;
No Erosion Branch (NE) Pbreach = 0 for NE Pbreach-NE = 0
0 Some Erosion Branch (SE)
Pge-SE = 0 (Psi-SE) = (Psi-i SE) x (Psi-lf). (Psu-SE) (Psd-SE) = (Ps-f) x (Ps-lf SE) Pbreach-SE= 1 – [(1 - Pge-SE) x (1 - Psi-SE) x (1 - Psu-SE) x (1 - Psd-SE)].
Excessive Erosion Branch (EE)
Pge-EE = 0 (Psi-EE) = (Psi-i EE) x (Psi-lf). (Psu-EE) (Psd-EE) = (Ps-f) x (Ps-lf EE) Pbreach-EE= 1 – [(1 - Pge-EE) x (1 - Psi-EE) x (1 - Psu-EE) x (1 - Psd-EE)].
Continuing Erosion Branch (CE)
Pge-CE from Table 13.3 (Psi-CE) = (Psi-i CE) x (Psi-lf). (Psu-CE) (Psd-CE) = (Ps-f) x (Ps-lf CE) Pbreach-CE = 1 – [(1 - Pge-CE) x (1 - Psi-CE) x (1 - Psu-CE) x (1 - Psd-CE)].
Appendix E Guidance for Failure Paths Not Covered by
the Unified Method
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
Appendix E Guidance for Failure Paths Not Covered by
the Unified Method
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
E1 Introduction
In some cases, it may not be possible to match a potential internal erosion failure path to the generic event tree framework described in Section 3.1. This may be due to an unusual type or configuration of the embankment dam or its foundations. In these circumstances, the risk analyst or risk analysis team will need to develop their own event tree structure to portray the postulated sequence of events.
This section provides additional guidance for those cases which are not adequately covered by the initiating mechanisms or failure path locations described in Section 3 of the Guidance Document. The following guidance for developing event trees and estimating structural probabilities has been extracted directly from Reclamation’s “Dam Safety Risk Analysis Methodology”, Version 3.3.1, May 2003.
E2 Developing Event Trees
E2.1 Principles
Event trees are used to represent sequences or progressions of events that could result in adverse consequences when a dam or associated structure responds to various loading conditions. By providing a graphical representation of the logic structure for the progression of each failure mode, an event tree becomes the template for subsequent assignment of event probabilities and calculation of risk. The event tree is also a tool for evaluating changes in risk given certain actions and assumptions. In addition, it is a means for identifying where the greatest potential risks are. And perhaps most importantly, it fosters common knowledge and understanding of failure modes, and synergetic discussion of various issues associated with failure modes. The risk associated with one sequence in the event tree is the product of the load probability, the structural response (failure) probability given that the load has occurred, the adverse consequence given that the load and failure have both occurred, and the magnitude of that consequence. The total risk for the load category is the sum of the products for all event tree paths.
An event tree consists of a series of linked nodes and branches. Each node represents an uncertain event or condition. Each branch represents one possible outcome of the event or one possible state that a condition may assume. Together, all of the branches emanating from a node should represent the mutually exclusive and collectively exhaustive set of possible outcomes or states (this is typically not done in the load range branches). The branches are mutually exclusive if each branch unambiguously describes one and only one possible outcome (i.e. there is no “overlap” among them), and they are collectively exhaustive if together they describe all possible outcomes (i.e. probabilities add up to 1.0).
The event tree is constructed from left to right, starting with some initiator event and proceeding through events describing the response of the dam to each level of the initiator. These event sequences are developed all the way to breach of the dam, and finally to consequences that result.
Each event node is predicated on the occurrence of all directly-linked branches that precede it in the tree.
Appendix E Guidance for Failure Paths Not Covered by
the Unified Method
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
The best way to start creating an event tree is to establish failure modes through a failure mode screening process. Once a failure mode has been identified, the event tree should be formulated to show the sequence of events and/or conditions which would have to take place or exist in order for the dam to respond in an adverse manner. Often it is useful to begin with “logic diagrams” that generally list the various sequential steps needed to take place during a given failure mode. These diagrams are less complex than the formally constructed event trees. The event tree should also identify possible interventions which could terminate the development of the adverse consequence. An example of this might be consideration of construction of an alternative(s) that would prevent the continued development of adverse consequences. For instance - have an “intervention” node in an event tree for a seepage related failure mode where the probability of successfully constructing say filters, or drains, or a berm, etc., is considered. Successful intervention would terminate one path of the event tree.
Case histories can provide additional insight for identifying failure modes and for breaking down the modes into sequences of events, a process sometimes called “failure mode decomposition”.
Failure and incident information provided in case history reports describe the progression and sequence of the events that have occurred for other dams. This information provides the means for conceptualizing and specifying the occurrences, conditions, and interventions that could be pertinent to the dam under consideration. For many dam types and applicable failure modes, there are often one or more especially well-documented failure(s) or incident(s) that chart the progression of events in some detail. Incidents that have progressed nearly to failure but have stopped for some reason provide information that is as valuable as information regarding complete failures.
The potential failure modes should be identified and each event in the progression should be explicitly and unambiguously documented (such that all team members have a common understanding of the potential failure modes) for later use in the structural response probability estimation phase. Considerable effort should be devoted to determining atypical failure modes that might be unique to the dam in question. The potential for adverse consequences associated with improper operation of the facilities should be considered as one of these unique failure modes.
E2.2 Complexity
The size and complexity of the event tree depend on what is known about the dam and its expected behavior under different loading conditions, on the complexity of the failure modes considered, on the number of load ranges needed, and to some degree on the purpose of the risk analysis. The event tree must balance needs for comprehensiveness and detail against needs for consistency, clarity, and communication. Too little detail can reduce the ability to target specific risk contributors and can create problems in making reasonable structural response probability estimates. Too much detail, and the event tree becomes unmanageable or incomprehensible to a degree that important insights are lost. Techniques for achieving an appropriate level of detail in the event trees include the following:
Appendix E Guidance for Failure Paths Not Covered by
the Unified Method
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
• Truncate non-failure branch pathways as early as possible - There is no need to propagate event sequences once it becomes apparent that they cannot lead to an uncontrolled release of the reservoir. The reasons why an event sequence branch is truncated are an important part of the risk analysis documentation.
• Construct separate event trees for each load type, and sometimes, for each load increment - These trees will often be similar or identical, but constructing them separately and sequentially better organizes the process.
• Use a staged approach - As with any other engineering analysis, it is unreasonable to expect that everything can be fully captured in an event tree on the first pass through the problem. A comparatively simple initial effort can identify the key elements in the tree that need to be expanded and less important parts that can be pruned in subsequent iterations.
• Limit the number of load increments for initiator events - Bounds for load increments should be chosen specifically to bracket load ranges where it is expected that the structural response (or the consequences of dam failure) will be fundamentally different from the structure’s response (or the dam failure consequences) in other load ranges. Sometimes load ranges are selected to represent information available from related analyses. Dividing the full range of possible loading values into a few increments is usually sufficient for most problems. While any number of increments can be used, there must be sufficient reason to suspect that considering different load increments will lead to different structural responses or to some fundamental change in the adverse consequences.
E3 Estimating Structural Response Probabilities
Summarized below is a process for making structural response probability estimates that has been found to work well for various risk analyses. All steps described below are performed jointly by all the participants of the risk analysis team.
E3.1 Step 1.
The first step is to be sure each team member has a clear understanding of each node of the event tree. (An event tree node represents a choice at which the preceding event must be considered to have happened and two or more subsequent events could take place.) This is best done by having the facilitator(s) write out the description of the node at the top of a flip chart (or some other visual means that is readily accessible at any time). An open discussion usually takes place during this step where team members freely discuss their understandings of the event node and the wording being proposed. The facilitator should then capture the thoughts of the group into the description of the node. For instance, a node description for “unfiltered exit” might be:
Appendix E Guidance for Failure Paths Not Covered by
the Unified Method
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
“the soil particles that are being carried by seepage flow must exit from the dam at a location where there is no filter present to trap the soil. A filter is defined as a soil that reasonably meets Reclamation’s design standard for filters.”
It is perfectly acceptable to further decompose the node in the word description. For instance, a node description as above might also add:
“The zone 2 of the embankment must reasonably meet filter criteria for the zone 1. The zone 3 outer shell must reasonably meet filter criteria for the zone 2".
E3.2 Step 2.
The group then ‘brainstorms’ any and all information that is pertinent to the event node being discussed. Each piece of information is listed on the flip chart in either a ‘factors leading to a higher probability’ or ‘factors leading to a lower probability’ column depending on whether the information is can be used as evidence to support or oppose belief in the event. The listing is usually done on the same chart immediately below the node description. The terms ‘factors leading to a higher probability’ and ‘factors leading to a lower probability’ are used in terms of the event node, as described, actually happening. The team should agree that the information is being placed in the correct column. Disagreements are usually solved by using clear wording that describes the information or by adding an opposing view in the opposite column. The purpose of this step in the process is to display all the information that will be used in making the estimate for all team members to see and discuss. As described below in step 3, the team members can judge for themselves the importance of the information being listed as they make their estimates.
Nearly any type of information is permissible to be listed if it helps the team members make their estimates. For instance, “gradation limits in construction specification meet filter criteria for the zone 1" might be listed in the ‘factors leading to a lower probability ’ column for the ‘unfiltered exit’ description discussed above in step 1. Others might be “93 out of 95 gradation tests of as-constructed earthfill showed acceptable limits were achieved” [factors leading to a lower probability]; “2 out of 95 gradation tests of as-constructed earthfill failed the limits and were left in place” [factors leading to a higher probability]; “the specified gradation is likely to segregate during placement” [factors leading to a higher probability].
Also to be listed are any similarities/dissimilarities with the case histories being used as a comparison. For instance, “the zone 2 for ‘Dam X’ (the case history dam) was much less compatible for the zone 1 than is the dam under study” [factors leading to a lower probability].
Even information of a general nature or member biases can be listed. For instance, one team member might want to list his/her concerns as to the appropriateness of the filter criteria used in the listing of the above information and include this in the ‘factors leading to a higher probability ’ column. An example showing a record of steps 1 and 2 is shown below. Considerable report writing time can be saved if this chart can be created on a computer as the discussion takes place.
Appendix E Guidance for Failure Paths Not Covered by
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A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
E3.3 Step 3.
Once a clear understanding of what the node of the event tree represents has been established (step 1), and all relevant issues by team members related to that node have been aired and summarized (step 2), then a probability estimate may be made for the node of interest.
The team should obtain “reasonable high” and “reasonable low” probability estimates. Elicit a “reasonable low” probability estimate by selecting a trial value and asking “Is it unlikely that the actual probability value is less than this value?” Elicit a “reasonable high” estimate by selecting a trial value and asking “Is it likely that the actual probability is less than this value.
Determine if the group feels that any given value within the established range should be more likely than any other. Stated another way, does the group feel that all values within the range are equally likely? If there is no single “most reasonable” or “popular value”, then a uniform distribution should be used. If there are reasons to suspect one value is more likely, these reasons should be stated for the record and a triangular distribution should be used with the peak of the triangle placed at the value which would be expected to occur most often. Related discussions on establishing estimate distributions are provided in Section V.B of the Dam Safety Risk Analysis Methodology (Reclamation, 2003).
The team should be told how the distributions will be used in the Monte Carlo analysis. The expected value for the both the uniform distribution and the triangular distribution will be the mean value of all the random selections for each variable during the simulation. For the uniform distribution this should not be a problem. However, if the group believes that an erroneous mean value is to be used about which the random simulation should pick values equally distributed, then the group might reconsider if a triangular distribution should be used.
The mean of the triangular distribution is often not the same as the mode. During the simulation, values will be equally distributed about the mean. The mode will be the value randomly selected more often than any other during the simulation, but the 50th percentile will often be some other value. If many of the distributions for events in the event tree are skewed like this, it may result in the “most popular” estimate calculated for annualized life loss being off-center within the range estimated from the Monte Carlo simulation. This is not a technical problem, but it may be difficult to communicate the reasons to those not well versed in probability and statistics.
Verbal descriptors can be used for assigning response probabilities when there is not a basis (i.e. appropriate statistical information) for use of what can be termed the “known” failure frequency rate method. For example, under these circumstances the team members can use the subjective information that was generated during step 2 (“factors leading to a higher probability ” versus “factors leading to a lower probability ” exercise) to judge if the event tree node designated “unfiltered exits” is more likely or unlikely relative to the scale of verbal descriptors as shown in Table E1. An alternative subjective probability mapping scheme developed by Barneich et al (1996) is presented in Table E2.
Appendix E Guidance for Failure Paths Not Covered by
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Table E1 – Probability Mapping Scheme (Bureau of Reclamation, 2003)
Verbal Descriptors Descriptor Probability Virtually Certain 0.999
Very Likely 0.99
Likely 0.9
Neutral 0.5
Unlikely 0.1
Very Unlikely 0.01
Virtually Impossible 0.001
Table E2 – Mapping scheme linking description of likelihood to quantitative probability (adapted from Barneich et al 1996)
Description of Condition or Event
Order of Magnitude of Probability Assigned
Occurrence is virtually certain 1 Occurrence of the condition or event are observed in the available database 10-1
The occurrence of the condition or event is not observed, or is observed in one isolated instance, in the available database; several potential failure scenarios can be identified.
10-2
The occurrence of the condition or event is not observed in the available database. It is difficult to think about any plausible failure scenario; however, a single scenario could be identified after considerable effort.
10-3
The condition or event has not been observed, and no plausible scenario could be identified, even after considerable effort. 10-4
In the example being used, the team members might assign a verbal descriptor of “very unlikely” (probability of 0.01) to the node described as “unfiltered exit” in step 1 above based on the available information:
“93 of 95 gradation tests of as-constructed zone 3 earthfill materials generally met Reclamation filter criteria for the zone 2 earthfill material where seepage might exit”
“Zone 3 earthfill materials are such that they are not likely to separate and segregate during placement”
Appendix E Guidance for Failure Paths Not Covered by
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A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
“As-built drawings indicate that zone 2 and zone 3 earthfill materials were placed to the lines and grades specified”
Estimates of response probabilities can sometimes be made on a more quantitative basis by comparing known historical or statistical databases that are relevant to the node for which a response probability is being estimated. An example of this method for estimating a response probability for a node described as “unfiltered exit” might be:
“Reclamation has about 150 dams that have clay tile drains”
“22 of these clay tile drain systems have been shown to have defects or crushed zones that compromise the integrity of the drain”
“While none of these 22 compromised clay tile drain systems have lead to failure of a Reclamation structure, there have been 6 incidences where material was piped through the compromised portions of the clay tile drain system, i.e., Clark Canyon Dam”
Based on the outlined information, one could assign an estimated response probability of 0.04 (6/150) for an “unfiltered exit” related to Reclamation dams with clay tile drain systems. The statistical information presented here for drains and piping incidents is only hypothetical, but this type of information could be gathered in many cases to help make probability estimates. Any available statistical information of this nature should be presented in establishing the likely ranges for the probability estimate.
Another useful way to incorporate performance based probability assessments is to consider certain repeated events or multiple examples of an identical condition as repeated Bernoulli trials.
If a random event has a probability of occurrence of p, the probability that this event will occur in n independent trials, pn, is given by the following equation:
pn = 1 - (1 - p)n
An example would be a pair of fair dice thrown 10 times. The probability of getting two sixes each time the dice are thrown is 1/36. The probability of getting the two sixes at least once in 10 throws is 1 - (1 - 1/36)10, or about 25 percent.
It is appropriate to consider this equation in two situations where structural response probabilities are being estimated. One situation is where a potential initiating event takes place many times over the life of a dam, and each time the event occurs there is the same probability that this event will trigger some other event. In this situation, p is the probability that the initiating event will trigger some other event, and n is the number of times the initiating event has occurred. Another situation is where many dams have the same component, and if this
Appendix E Guidance for Failure Paths Not Covered by
the Unified Method
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
component is present, there is a certain probability it will cause some other event or condition to happen. In this situation, n is the number of dams and p is the probability the condition will cause the other event to happen.
One way this can be used is to check the reasonableness of a probability estimate. Assume a given reservoir has reached elevation 5340 fifteen times in the last forty years, and that no soil materials have appeared in seepage collection weirs during that time period. Assume that when the team is considering piping, the team members estimate the probability is .3 that material movement would begin should the reservoir reach elevation 5340 in any given year. The above equation says it is nearly certain (a 99.53 percent chance) that material movement should begin if the reservoir rises above 5340 fifteen times. Since the reservoir has been above that elevation
fifteen times and no material has been observed, the .3 probability estimate would seem unreasonable (unless other factors could be placed in the “factors leading to a higher probability” evidence column).
E3.4 Step 4.
The risk analysis participants then identify the factors from step 2 that had the greatest effect on the probability estimate generated in step 3. Returning to the flip chart containing the factors pertinent to the event, the team should identify those items on the flip chart which were most important in arriving at the probability estimates. In addition, the team should indicate why it believes the most significant factors should receive more weight than others. This can include a discussion of what adverse situations actually exist versus what adverse situations only have the potential to occur. While this process may result in debate among the participants, this discussion can bring out additional information which was not previously available or readily understood. This information and discussion should be documented by the recorder.
E3.5 Step 5.
The facilitator(s) should ensure the risk analysis participants have reached consensus on the probability and uncertainty estimates. This does not mean that the facilitator(s) must force all members to accept a single estimate. Rather, the facilitator(s) must sense the group’s feeling as discussion takes place, suggest a reasonable starting place as a best estimate, and canvass the group’s willingness to accept the estimate. The facilitator(s) may use words like “I’m sensing the group feels fairly neutral about this estimate, how about 0.5?” Or, “I sense there are more reasons to believe we are on the likely rather than the unlikely side of being neutral.” If the discussion indicates the event is not very probable, the facilitator(s) could use the verbal descriptors by suggesting: “I sense the group feels this event is not very likely, should this be very unlikely or virtually impossible?”
If the group cannot agree on an estimate, the divergent opinions must be accounted for in the analysis. At this point, the facilitator(s) should focus more on getting agreement on the possible range and characteristic probability distribution for the estimate (see Section V). The facilitator(s) should lead the discussion between the protagonists of the opposing views and identify the underlying premises or key evidence supporting each argument. This is a very fruitful area to obtain ideas that would suggest further exploration or analysis to resolve
Appendix E Guidance for Failure Paths Not Covered by
the Unified Method
A Unified Method for Estimating Probabilities of Failure of Embankment Dams by Internal Erosion and Piping Guidance Document Delta Version July 2008
the differences. The use of the software “Precision Tree” and “@Risk” makes it very easy to carry a range or different distributions through the risk analysis calculations, and to examine “what if” scenarios to determine how a given piece of information might affect the outcome.
If the group cannot agree that a range or distribution will adequately characterize their judgement, then the analysis can be conducted using each representative estimate in separate calculations.
The separate calculations for risk would then be reported along with the descriptions of the conflicting ways the group members saw the problem.
E3.6 Step 6.
Once consensus is reached on the specific response probability estimate and uncertainty, the process continues by repeating steps 1 through 5 for each remaining node of the event tree.
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