byGordon A. Fenton

Dalhousie University, Halifax, Canada

Load and Resistance Factor Geotechnical Design Code Development in Canada

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Overview

1. Past: Where we’ve been

• allowable stress design

• partial (strength) vs. total resistance

factors

2. Present: Where we are

• current implementation in NBCC and

CHBDC

3. Future: Where we are going

• incorporating site/model understanding

• allowing for failure consequence

• how to get the factors?

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Past: Where we’ve been

• geotechnical design based on working

(allowable) stress prior to 1979

• 1979 and 1983 bridge foundation design codes

adopt partial factor format from Danish practice

• partial factor format did not lead to design

consistency with allowable stress approach, so

not readily accepted by geotechnical engineers.

• total resistance factor format adopted in the

bridge foundation design code in 1991

WSD TO LRFD

DEVELOPMENT OF A GEOTECHNICAL DESIGN CODE

� Working (or Allowable) Stress Design (WSD) was the

basis of geotechnical design until 1979,

� Geotechnical design codes have since been migrating

towards a Load and Resistance Factor Design (LRFD)

approach embedded in a Limit States Design (LSD)

framework,

ˆ ˆs iR F L≥ ∑

ˆ ˆgu u i ui ui

i

R I Lϕ η γΨ ≥ ∑

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WORKING STRESS DESIGN

� Factors of safety (Fs ) based on experience and

observed performance

� All uncertainty lumped into a single factor

� Many years of empirical experience (extensive

database)

� Simple, deterministic

� Does not lend itself to the estimation of failure

probability

� thus difficult to get a sense for probability of

failure

� Fs is not quantitatively meaningful

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LOAD AND RESISTANCE FACTOR DESIGN

RATIONALE

�account for load and resistance uncertainties separately

� introduce reliability-based design benefitsinto geotechnical designs, e.g. increased construction economies for low failure consequence (low risk) problems, increased investigation effort, etc.

�harmonize with structural codes

Load and Resistance Factor Design

• replaces single factor-of-safety with a set of partial safety factors(load and resistance factors) acting on individual components of resistance and load (Taylor, 1948, Freudenthal, 1951, 1956, Hansen, 1953, 1956)

Load and resistance factorsare derived to account for;

• variability in load and material properties

• variability in construction

• model error(approximations in design relationships)

• failure consequences

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Load and Resistance Factor Design

• load factors, γi > 1, account for variability in loads

• resistance factor, ϕ < 1, accounts for variability in soil properties, variability in construction, and model error

• consequence factor, Ψ , accounts for failure consequences

ˆ ˆ (LRFD)i iR Lϕ γΨ ≥∑

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Load and Resistance Factor Design

Two commonresistance factor implementations:

1) total resistance factor: a single resistancefactor applied to the final computed soilresistance (as shown in previous slide)

2) partial resistance factors: multiple resistancefactors applied to components of soilstrength separately, e.g. to tan(φ’ ), c’ ,etc. Also known as factored strength.

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Partial Resistance Factor Approach

• only explicitly considers uncertainties associated with material strength parameters(e.g. not with model error)

• often implemented with myriad partial factorsin order to account for all sources of material uncertainty – sense of real behaviour often lost

• may not capture true mechanism of failurewhen failure mechanism sensitive to changes in material strengths

• non-linearity issues: resistance based on partial resistance factors is not the same as total factored resistance based on unfactored material parameters

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Total Resistance Factor Approach

• resistance computed as with the WSD approach – better representation of actual failure mechanism

• resistance is factored onceat the end

• very similar to traditional Fs approach, except specifically applied to the resistance

• allows for a smoother transitionfrom WSD to LRFD

• allows engineers to work with “real” numbersuntil the last step where the result is factored.

• consistent with structural codes, where each material has its own single resistance factor – soil is an engineering material

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Comparison of LRFD Codes

• The following table lists the load and resistance factors used in a variety of geotechnical design codesfrom around the world.

• Where the code suggests a range of values (dependent, for example, on investigation intensity), only the range is presented.

• To assess the relative conservatismof the various codes, the required area of a spread footing designed against bearing failure (ULS) using , , c´ = 100, φ´ = 30° is computed in the rightmost column. The codes are ranked from the most conservative (top) to theleast conservative (bottom).

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ˆ 3700DL = ˆ 1000LL =

Values of Load and Resistance Factors

Code Dead Load

Live Load

tan(φ’ ) c’ Bearing Sliding Area

CFEM – 1992 1.25 1.5 0.8 0.5-0.65 5.22

NCHRP 343 – 1991 1.3 2.17 0.35-0.6 0.8-0.9 4.88

NCHRP12-55 - 2004 1.25 1.75 0.45 0.8 4.70

Denmark – 1965 1.0 1.5 0.8 0.57 4.47

AASHTO – 2007 1.25 1.75 0.45-0.55 0.8-0.9 4.23

B. Hansen – 1956 1.0 1.5 0.83 0.59 4.15

AS 5100 – 2004 1.2 1.8 0.35-0.65 0.35-0.65 4.14

CHBDC – 2006 1.2 1.7 0.5 0.8 4.07

AS 4678 – 2002 1.25 1.5 0.75-0.95 0.5-0.9 3.89

Eurocode7 Model 1 1.0 1.3 0.8 0.8 3.06

Eurocode7 Model 2 1.35 1.5 0.71 0.91 3.04

ANSI A58 – 1980 1.2-1.4 1.6 0.67-0.83 2.84

(shallow foundations)

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Present: Where we are

1. National Building Code of Canada (2010)

specifies Limit States Design, but resistance

factors do not appear in the code – they

appear in the User’s Guide. Importance

factors applied to (site specific) snow, wind,

and seismic loads.

2. Canadian Highway Bridge Design Code

(2006) specifies both Limit States Design and

the required resistance factors. Importance

factors applied to snow, wind, and seismic

loads.

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National Building Code of Canada User’s Guide

2010

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Canadian Highway Bridge Design Code 2006

Reliability-Based Design Goals:

• Account for uncertaintyrationally and consistently

• Make use of PDFs of loads and resistances(at least mean and variance)

• Quantify probability of failure

• Achieve societally acceptable levels of riskfor our engineered systems (where risk = failure consequence times failure probability)

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Future: Where we’re going

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RELIABILITY-BASED CODE OBJECTIVES

“You pay for a site investigation whether you have one or

not” (Institution of Civil Engineers, Inadequate Site

Investigation, 1991)

There is a desire in the Canadian geotechnical community

to:

� provide a means to adjust design/construction economies based

on level of site understanding

� take site investigation/modeling intensity into account in the design

process

� provide rationale for increased investigation/modeling effort

� provide a means to adjust geotechnical system reliability based

on potential failure consequences

� higher reliability for more important structures/systems regardless of

loading type

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RATIONALE FOR RELIABILITY-BASED

FOUNDATION DESIGN

Reliability-based design concepts

� allow quantification of reliability,

� allow designs to target a specified reliability level,

� reward better site investigation by permitting a higher

factor to be used in design, thus permitting a more

economical design while ensuring acceptable reliability,

� lead to harmonization with other structural codes by

establishing a common conceptual framework to address

reliability issues.

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CONCEPTUAL OVERVIEW FOR RELIABILITY-

BASED DESIGN

� the probability and consequence of failure are considered in

determining resistance and consequence factors

� reliability-based resistance factors are applied to the resistance,

� at both ultimate and serviceability limit states

� and, eventually, under both static and seismic loading conditions

� cost-effective resistance and consequence factors depend on

� the degree of understanding of the site conditions and accuracy of the design

model (resistance factors)

� the consequence of not providing adequate geotechnical resistance to imposed

loads (consequence factor)

� the overall goal is to save money, for specified tolerable risk and

required performance, by considering the trade-off between initial

design and construction costs and long-term costs, including cost of

failure.

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FLOATING RESISTANCE FACTOR TABLE

(CONCEPTUAL)

HIGH Consequence

1.0 0.8 0.6

1.2 1.0DEFAULT VALUE

0.8

1.4 1.2 1.0

LOW Consequence

LOW Uncertainty HIGH Uncertainty

RELIABILITY-BASED DESIGN CODE DEVELOPMENT

Basic idea is to split traditional into

1. Load factors – from load section of code,

2. Resistance factors, : capture “resistance” uncertainty� Depend on level of site and prediction model understanding

� Propose three degrees of site understanding: high, typical, and low

� Consider SLS and ULS resistance factors separately (different target maximum acceptable failure probability)

3. Consequence factor, : captures system importance (failure consequence)� Propose three consequence levels: high, typical, and low

� High: β = 3.7 (pf

= 1/10,000) at ULS, β = 3.1 (pf

= 1/1000) at SLS

� Typical: β = 3.5 (pf

= 1/5,000) at ULS, β = 2.9 (pf

= 1/500) at SLS

� Low: β = 3.1 (pf

= 1/1,000) at ULS, β = 2.3 (pf

= 1/100) at SLS

and gu gsϕ ϕ

Ψ

sF

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LOAD AND RESISTANCE FACTOR DESIGN

� Ultimate Limit State (ULS)

Factored ultimate geotechnical resistance ≥ effect of factored ULS loads

where

= consequence factor,

= ultimate geotechnical resistance factor,

= ultimate characteristic geotechnical resistance,

= i’th ULS load factor,

= i’th load effect for a given ULS.

ˆ ˆgu u ui ui

i

R Lϕ γΨ ≥∑

Ψ

guϕˆ

uR

uiγˆ

uiL23

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LOAD AND RESISTANCE FACTOR DESIGN

� Serviceability Limit State (SLS)

Factored serviceability geotechnical resistance ≥ effect of factored SLS loads

where

= consequence factor,

= serviceability geotechnical resistance factor,

= serviceability characteristic geotechnical resistance,

= i’th SLS load factor, and

= i’th load effect for a given SLS.

ˆ ˆgs s si si

i

R Lϕ γΨ ≥∑

Ψgsϕ

ˆsR

siγˆ

siL

DEGREE OF SITE AND PREDICTION MODEL

UNDERSTANDING

Site and prediction model understanding includes;

� understanding of the ground and the geotechnical

properties throughout the site,

� the type and degree of confidence about the

numerical prediction models to be used to estimate

serviceability and ultimate geotechnical resistances,

and

� observational (monitoring) methods for

confirmation.

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DEGREE OF SITE AND PREDICTION MODEL

UNDERSTANDING

Motivation:

� Differentiating between levels of site understanding

allows for design economies – the greater the level of

understanding, the lower the risk of failure and the

greater the economy of the final design should be.

� Allows the designer to show “proof” (thus justifying

higher design phase costs) that increased understanding

(e.g. increased site investigation) leads to construction

savings and lower total project costs.

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DEGREE OF SITE AND PREDICTION MODEL

UNDERSTANDING

Three levels of site understanding are proposed in the next CHBDC:

� High understanding: Extensive project-specific investigation procedures and/or knowledge is combined with prediction models of demonstrated (or proven) quality to achieve a high level of confidence with performance predictions.

� Typical understanding: Usual project-specific investigation procedures and/or knowledge is combined with conventional prediction models to achieve a typical level of confidence with performance predictions.

� Low understanding: Understanding of the ground properties and behaviour are based on limited representative information (e.g. previous experience, extrapolation from nearby and/or similar sites, etc.) combined with conventional prediction models to achieve a lower level of confidence with the performance predictions.

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ULS GEOTECHNICAL RESISTANCE FACTORS

(STATIC LOADING)

Limit State Degree of UnderstandingLow Typical High

Shallow FoundationsBearing resistance 0.45 0.5 0.6Passive resistance 0.4 0.5 0.6Horizontal resistance (sliding) 0.75 0.8 0.85

Ground AnchorsStatic analysis – tension 0.3 0.4 0.5

Static test – tension 0.55 0.6 0.65

Deep Foundations – PilesStatic analysis

Compression 0.35 0.4 0.5Tension 0.35 0.4 0.45

Static testCompression 0.5 0.6 0.7Tension 0.3 0.4 0.5

Dynamic analysis – compression 0.3 0.4 0.5

Dynamic test – compression (field measurement and analysis)

0.4 0.5 0.6

Horizontal passive resistance 0.4 0.5 0.6

guϕ

(for illustration only – factors are not finalized) 28

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SLS GEOTECHNICAL RESISTANCE FACTORS

(STATIC LOADING)

Limit StateDegree of UnderstandingLow Medium High

Shallow FoundationsSettlement 0.7 0.9 1.0

EmbankmentsSettlement 0.7 0.8 0.9Lateral displacements 0.6 0.7 0.8

Deep Foundations – PilesSettlement 0.8 0.9 1.0Lateral displacements 0.7 0.8 0.9

Retaining SystemsSettlement 0.35 0.4 0.45Horizontal Deformation 0.4 0.45 0.5

AnchorsDisplacement 0.5 0.6 0.7

gsϕ

(for illustration only – factors are not finalized)

CONSEQUENCE FACTOR

Motivation:

� Different structures will have different consequences of failure.

For example, the failure of an expressway bridge has far higher

consequences (life threat, economic, etc.) than does the failure

of a low volume rural bridge.

� The target maximum acceptable failure probability of a

structure with high failure consequence should be significantly

lower than that for a structure with low failure consequence.

� Rational assessment on the basis of failure probability and

consequence of failure will allow for more realistic allocation of

infrastructure budgets.

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CONSEQUENCE FACTOR

Geotechnical systems can be assigned consequence levels

associated with exceeding various limit states;

�High consequence – structure is designed to be essential

to post-disaster recovery (e.g. hospital or bridge lifeline),

and/or has large societal and/or economic impacts,

�Typical consequence – structure is designed for typical

failure consequences, e.g. the usual office building, bridge,

etc. This is the default consequence level.

�Low consequence – failure of the structure poses little

threat to human safety, e.g. storage utilities, very low

traffic volume bridges, temporary structures.

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CONSEQUENCE FACTOR TABLE

Consequence

Level

Reliability Index, β(SLS in parentheses)

ExampleConsequence Factor, Ψ

High 3.7 (3.1)Lifelines, Emergency

0.9

Typical 3.5 (2.8)Highway bridges

1.0

Low 3.1 (2.3)Secondary bridges

1.1

(for illustration only – factors are not finalized)

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SUMMARY OF PHILOSOPHICAL CHANGES

� introduced three levels of site understanding – high,

typical (default), and low – through the resistance factor

� resistance factors vary with site understanding – higher for better

understanding

� this approach allows for greater economies in the tradeoff between

design/investigation effort and overall construction costs

� introduced three levels of failure consequence – high,

typical (default), and low – through the consequence

factor

� consequence factor, which modifies the factored resistance, varies

with consequence level – lower for higher consequences

� this also allows for greater economies in the tradeoff between

target reliability and construction costs

The Random Finite Element Method involves a combination of

Random Field Theory (e.g. Fenton and Vanmarcke 1990)

with the

Finite Element Method (e.g. Smith and Griffiths 2004)

The method takes into account the mean, standard deviation

and spatial correlation length of the input ground

parameters as well as for random loading.

The method takes full account of the statistical nature of local

averaging of ground properties over the finite elements.

The method is applied in a Monte-Carlo framework.

Determination of Resistance Factors

Level III: Fully Probabilistic Analysis

The Random Finite Element Method (RFEM)

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RFEM

The Random Finite Element Method (RFEM) offers many advantages over

conventional probabilistic analysis tool—especially for nonlinear analyses.

-reduced model error: no a priori judgment relating to the shape or

location of the failure surface. The FE analysis “seeks out” the critical

mechanism.

-a “worst case” spatial correlation has been clearly identified for most

geotechnical problems which leads to the highest probability of

failure. We don’t need to know the correlation length.

-allows for the investigation of the affect of site understanding on

design

and code development.

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Degree of Site Understanding

Shallow Foundation Bearing Capacity

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Shallow Foundation Bearing Capacity

RESISTANCE FACTORS FOR BEARING CAPACITY

Resistance factors can be estimated theoretically;

o for various failure consequence levels (e.g. low, pm=

0.01, or high, pm = 0.0001)

o for various levels of site understanding.

Note the worst case correlation length.

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Earth Pressure Analysis

Active Pressure

Consider a frictional soil where we map tanφ’ onto the mesh (c’=0)

Typical realizations of the Monte-Carlo simulations.

Light zones are low strength and dark zones are high strength 39

H

Single soil sample at a depth of H/2 and H/2 away from the wall

2

H

2H

Now sample the soil and predict force

on the wall using traditional methods.

Design the factored wall resistance

against sliding to be ˆgu u s aR F Pϕ =

Earth Pressure Analysis

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Estimated probability that the actual active force on wall exceeds the

factored design resistance for a) friction angle and unit weight

independent, and b) friction angle and unit weight strongly

correlated

Earth Pressure Analysis

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Shallow Foundation Settlement

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Shallow Foundation Settlement

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Shallow Foundation Settlement

Various sampling schemes to predict foundation settlement

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Shallow Foundation Settlement

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Deep Foundations

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Deep Foundations

Failure probability as a function of

1. site understanding, r

2. residual variability, cv

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Deep Foundation Resistance Factors

D = averaging domain under the footing

Q = sampling region

H = depth to bedrock

Parameters Values Considered

Coefficient of variation,

Vc

0.1, 0.2, 0.3, 0.5

Correlation length, θ (m) 0.1, 1.0, 2.0, 3.0, 6.0, 10.0, 50.0

Sampling distance, r (m) 0.0, 4.5, 9.0

Resistance factor, ϕgu 0.4, 0.5, 0.65

Consequence factor, ψu

0.80, 0.85, 0.90, 0.95, 1.00,

1.05, 1.10, 1.15, 1.20

September 21, 2009

Fig. 1 Sampling layout Table 1 Parameters considered

Soil cohesion, c, is assumed to be lognormally distributed

with mean µc=100 kN/m2 , friction angle with mean µc =20o

Consequence Factors for Bearing Capacity

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Target pf

0.93 1.13

September 21, 2009

Fig. 2 Failure probability plot Fig. 3 Failure probability-consequence factor plot

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Consequence Factors for Bearing Capacity

φgu=0.5

Fig. 5 High failure consequence plot

ψu=0.95

Fig. 6 Low failure consequence plot

ψu=1.15

Fig. 4 Resistance factor plot

September 21, 200951

Consequence Factors for Bearing Capacity

September 21, 2009

Source Consequence Level

Low Medium High

Recommended 1.15 1.0 0.90

AASHTO (2007) 1.25 1.0 0.91

AS 5100.3 (2004) - 1.0 0.83

Eurocode I (Gulvanessian et al., 2002) 1.11 1.0 0.91

NBCC (2005, snow and wind loads) 1.25 1.0 0.87

NBCC (2005, earthquake loads) 1.25 1.0 0.77

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Consequence Factors for Bearing Capacity

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How to Use Theoretical Results

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SUMMARY

o Geotechnical design codes are migrating towards LRFD/LSD to

allow;

• harmonization with structural codes

• quantification of reliability

o Soil and rock are typically site specific and highly (spatially)

variable. The development of LRFD in geotechnical engineering is a

significant challenge.

o Reliability-based design codes are currently largely developed

through calibration with WSD.

o Design codes should allow for varying degrees of site understanding

and take failure consequence into account.

o Sophisticated probabilistic tools exist to assess risk and develop

required resistance and consequence factors (e.g. RFEM).

o Much work is still required, but efforts are ongoing world-wide.