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Seismic Design of SlopesEarth Dams and Embankments

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Amit Prashant

Indian Institute of Technology Gandhinagar

Short Course on

Geotechnical Aspects of Earthquake Engineering

04 – 08 March, 2013

Types of Slopes

Natural slopes w/o existing slip surfaces

Engineered slopes Highway and railway embankments

Earth dams

Levees and River bank protections

Cut slopes (with natural soil)

Slopes with retaining structures

Landfills (Solid waste)

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Slope Failures

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Embankment failure due to liquefaction in south of Lima Peru near the Pacific Ocean

A Dam Breach – Piping Failure

Location: Walla Walla County

Slope Failure!!

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Lower San Fernando Dam following the earthquake of 1971(Photos from National Information Service for EarthquakeEngineering, University of California, Berkeley)

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Cause of Failure

Major Cause Slope failure because of inertial loading

Increase in Shear Stress

Softening of materials strength or liquefaction.

Decrease in Shear Strength

Other Causes Crest settlement of dam caused by settlement or by

earthquake generated water waves in the reservoir.

Permanent deformation of foundation soils or dam body.

Fault displacement under the foundation.

Piping and erosion

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Cause of FailureIncrease in Shear Stress

Erosion / Excavation at the bottom of slope

Sudden drop in water level or drawdown of water bodies

Overloading at the top of slope

Water pressure from crack and fishers

Freezing of water creates even more pressure

Saturation of slopes due to rainfall

Transitory loading Earthquake loading

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Cause of FailureDecrease in Shear Strength

Weathering due to physicochemical activities

Decomposition of rocks / boulders due to wetting / drying process.

Structural degradation due to cyclic loading

Traffic, Earthquake loading, Hydrodynamic forces, etc.

Creep effects under sustained shear loading and seasonal variations on slopes

Cracking in cohesive soils

Change in void ratio in swelling clays

Decrease in effective stress due to pore pressure build-up Earthquake!!

Effect of vibrations on sensitive clays Earthquakes!!

Erosion of dispersive soils (cavity formations) during seepage

Progressive failure due to strain softening soil mass7

Failure Modes in Dams

Overtopping Erosion

Progressive failure to catastrophe

Piping Uncontrolled Seepage water

Structural Failure Failure of upstream/downstream slope

Cracking, deformation, and settlement

Overtopping / Piping

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Preventive Measures

1. Additional dam height

2. Measures to minimize erosion in the event of overtopping.

3. Filter sections as a defense against cracking.

4. Use of subrounded gravel/sand as filter material.

5. Near vertical chimney drain in the center portion

6. Zoning of the section to minimize saturation of materials.

7. Uniformly graded filter materials Self healing if cracking occurs.

8. Safe Rim slopes to avoid large slides into the reservoir.

9. Ground improvement to mitigate liquefaction potential

10. Suitable features to prevent piping.

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Investigations

Seismological Investigations Past earthquakes probability of future earthquakes

Need long seismic history

Geotechnical Investigations Topographic conditions.

Description of geology.

Foundation soils, bedrock and soils from borrow area.

Principal engineering properties: grain characteristics, plasticity, compaction, shear strength, dispersivity and hydraulic properties.

In-situ testing: piezocone penetration test, Standard Penetration Test or Field Vane Shear Test, seismic velocity profiling.

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Liquefaction

Foundation Soil Effective stress may not go to zero, but reduced shear

strength due to low effective stresses can cause large deformations

Sensitive clays of low to moderate plasticity are problem

Compaction of Embankment Compacted enough to make the material dilative

Compaction density

> 95% of MDD through standard proctor for embankments

> 98% of MDD through standard proctor for dams

Cohesive soils compacted at moisture content 2-4% higher than optimum

In cohesionless soils, 80% relative density is achieved

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Seismic Slope Stability

Static Slope Stability Analysis First!!

Seismic slope stability analysis Pseudo-static analysis

Assuming equivalent static force for seismic acceleration in unstable region

Factor of safety estimation

Permanent deformation analysis

Based on sliding block concept

Useful if Pseudo-static analysis does not satisfy required FOS.

Sophisticated dynamic analysis

Requires good estimates of material properties and input ground motion.

Useful if Permanent deformation analysis fails to satisfy requirements. Needed in big projects

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Static Slope Stability Analysis

Infinite Slopes Movement predominantly along planar or gently

undulating surfaces over a long stretch

Land Spreading!!

Finite Slopes Planer Wedge Method

Circular Slip surface

Swedish circle, Friction circle

Method of slices: OMS, Simplified Bishop’s, Bishop’s Rigorous method

Non-circular Slip surface

Log spiral

Method of slices: Simplified Janbu’s, Janbu’s rigorous method, Generalized Limit Equilibrium method

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Non-circular Slip Surface

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Conditions for Stability Analysis

Various Phases of Construction

Short-term stability after construction

Long-term stability after construction

Rapid drawdown: dams and Levees

AND THEN…..

Natural disturbance Flooding

Heavy precipitations

Accumulation of material from up stream

Earthquakes

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Total-Stress / Effective-Stress Analysis

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Total Stress Analysis Effective Stress Analysis

fu = 0, saturated clay

fu ≥ 0Partially saturated clay

uc

tanc f f

f

c

Parameters obtained from:UC testUU testCU test (without pore pressure)

Applicable to Undrained conditions Clays

Parameters obtained from:Direct ShearCU test (with pore pressure)CD test

Applicable to Drained/Undrained conditions Clays and Sands

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Factor of safety

Along critical slip surface

It does not account for uncertainties involved in determination of soil properties and geometric properties of the slope More uncertainty Larger FOS

Higher FOS is taken if slope failure may cause: Expensive repair/reconstruction

Secondary failures to other structures

Damage to structures of high importance

Usual range of FOS for Static analysis = 1.25 – 1.5

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Resisting force

Driving forceFOS

Back to- Seismic Slope Stability

Pseudo-static analysis: Basics

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Sliding

Slope

ah(t)

av(t)

Wkg

WaF h

hh Wk

g

WaF v

vv

g

ak h

h g

ak v

v Seismic Coefficient:

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Factor of Safety and Seismic Coefficient

Complex ground shaking replaced by a single constant unidirectional pseudo-static acceleration

Can we consider peak seismic acceleration with FOS=1? (No deformation…) Too conservative

We can allow some deformation, what should be the seismic coefficient.

For sure, some deformation is acceptable…. A value lower than peak seismic acceleration can be used to

compute seismic coefficient

FOS can be taken in the range of 1.0 - 1.1

Is there any other factor to consider?

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Waves travelling through Slope

Long wavelengths (Low frequency) cause the unstable zone to move in-phase along the full height.

Fort short wavelengths (higher frequency) the soil at two different locations in unstable zone may move in opposite directions

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Kramer, 1996

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Concept of Average Acceleration

We can compute the stresses at different points throughout the slope for a given seismic input.

Integrate horizontal components of the stresses in the area above slip surface total horizontal force in that region.

Average acceleration = Total horizontal force divided by mass of the zone.

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Kramer, 1996

Example of Average acceleration

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Seismic coefficient

Seismic coefficient can be slightly lower than peak average acceleration (aavg)max

From example

amax = 0.60g

(aavg)max = 0.22g

kh = 0.11g to 0.18g

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g

ak

avg

hmax8.05.0

Seismic coefficient (contd….)

Terzaghi (1950)

0.1g for severe earthquake (RF Intensity IX)

0.2g for violent, destructive earthquake (RF X)

0.50g for catastrophic earthquake

Mercuson (1981)

Seismic coefficient should be one-third to one-half of the PGA the embankment is subjected to

What do you Think?

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Hynes and Franklin (1984) Embankment with yield acceleration (FOS=1.0) of

one-half the PGA will experience permanent deformation of less than about 0.1m.

Deformation limited to 1.0m if yield acceleration is greater than one-sixth of Peak Average Acceleration

Based on upper bound graph

See figure for the concept of peak average acceleration

Seismic coefficient (contd….)

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Permanent Seismic Deformation (Hynes and Franklin, 1984)

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Seismic coefficients suggested in 1966 for use inpseudostaticanalysis (after Seed 1966)

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IITK-GSDMA Guidelines forSeismic Coefficient

In the absence of site-specific estimates of design peak ground, the design seismic inertia forces for equivalent-static slope stability assessment shall be taken as:

Where FH is the horizontal inertial force, Z is the Zone Factor given in IS:1893 - Part 1 (2002), I is the importance factor as per Table 1, S is an empirical coefficient to account for the amplification of ground motion between bedrock and the elevation of the toe of the dam or embankment (Table 2), and W is the weight of the sliding mass.

If the estimate of design peak ground horizontal acceleration (PHGA) at the elevation of the toe of the dam is available, the design seismic inertia forces for equivalent-static slope stability assessment shall be taken as:

where amax is the design PHGA at the elevation of the toe of the dam.

The vertical inertial force during an earthquake may be neglected in the design.

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IITK-GSDMA Guidelines forSeismic Coefficient (contd…)

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IS:1893

IITK-GSDMA

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IITK-GSDMA

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Thank You