Seismic Design of Slopes I - Indian Institute of Technology ...

Seismic Design of Slopes
Earth Dams and Embankments
I
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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Embankment failure due to liquefaction in
south of Lima Peru near the Pacific Ocean
Slope Failures
A Dam Breach – Piping Failure
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Location: Walla Walla County
Slope Failure!!
Lower San Fernando Dam following the earthquake of 1971
(Photos from National Information Service for Earthquake
Engineering, University of California, Berkeley)
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2

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 Failure
Increase 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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3

Cause of Failure
Decrease 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 mass
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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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4

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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5

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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7

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
Total Stress Analysis
Effective Stress Analysis
f u = 0, saturated clay
c u
f u ≥ 0
Partially saturated clay
c
tanf
c f
Parameters obtained from:
UC test
UU test
CU test (without pore pressure)
f
Parameters obtained from:
Direct Shear
CU test (with pore pressure)
CD test
Applicable to
• Undrained conditions
• Clays
Applicable to
• Drained/Undrained conditions
• Clays and Sands
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8

Factor of safety
• Along critical slip surface
Resisting force
FOS Driving force
• 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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Back to- Seismic Slope Stability
Pseudo-static analysis: Basics
a h (t)
Sliding
Slope
a v (t)
F
h
ahW
g
k W
h
F
v
avW
g
k W
v
Seismic Coefficient:
k
h
ah
g
k
v
av
g
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9

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
Kramer, 1996
• 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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Concept of Average Acceleration
Kramer, 1996
• 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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Example of Average acceleration
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Seismic coefficient
• Seismic coefficient can be slightly lower than peak
average acceleration (a avg ) max
a avg
0.5
0.8
• From example
a max = 0.60g
(a avg ) max = 0.22g
k h = 0.11g to 0.18g
k
h
g
max
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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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Seismic coefficient (contd….)
• 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
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Permanent Seismic Deformation (Hynes and Franklin, 1984)
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13

Seismic
coefficients
suggested in
1966 for use in
pseudostatic
analysis
(after Seed 1966)
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IITK-GSDMA Guidelines for
Seismic 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 F H 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 a max 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 for
Seismic Coefficient (contd…)
IS:1893
IITK-GSDMA
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IITK-GSDMA
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Thank You
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