3/3/2013
1
Slide 1
An Overview of Geotechnical Earthquake Engineering
Sudhir K Jain
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 2
Outline
Introduction to Seismic Design Principle
Dynamic Soil Properties
Site Effects
Soil Structure Interaction
Issues for Foundation Design
Liquefaction
Embankment Analysis
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
2
Slide 3
Some Remarks on
Seismic Design Principles
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 4
Seismic Design Principle
Large earthquakes are infrequent as compared to smaller earthquakes
Should a structure meant for 50 years be designed to remain undamaged for an earthquake that may occur once in 500 years?
The criteria is:
Minor (and frequent) earthquakes should not cause damage
Moderate earthquakes should not cause significant structural damage (but could have some non-structural damage)
Major (and infrequent) earthquakes should not cause collapse
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
3
Slide 5
Seismic Design Principle …
A well designed structure can withstand a horizontal force several times the design force due to:
Energy dissipation in a variety of ways, e.g.,
ductility
Overstrength
Redundancy
In many cases, limited deformation may be acceptable, e.g., slopes, retaining walls.
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 6
Response Reduction Factor
Hence, structure is designed for seismic force much less than what is expected under strong shaking if the structure were to remain linear elastic
Earlier codes just provided the required design force
It gave no direct indication that the real force may be much larger
Now, the codes provide for realistic force for elastic structure and then divides that force by some factor.
This gives the designer a more realistic picture of the design philosophy.
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
4
Slide 7
Increase in Permissible Stresses
Applicable for Working Stress Design
Permits the designer to increase allowable stresses in materials
For instance, 33% - 50% for load cases including seismic loads.
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 8
Site Specific Design Criteria
Seismic design codes meant for ordinary projects
For important projects, such as nuclear power plants, dams and major bridges site-specific seismic design criteria are developed
These take into account geology, seismicity, geotechnical conditions and nature of project
Site specific criteria are developed by experts and usually reviewed by independent peers
A good reference to read on this:
Housner and Jennings, “Seismic Design Criteria”, Earthquake Engineering Research Institute, USA, 1982.
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
5
Slide 9
Shaking is not the only issue!
Ground shaking can affect the safety of structure in a number of ways:
Shaking induces inertia force
Soil may liquefy
Sliding failure of founding strata may take place
Fire or flood may be caused as secondary effect
of the earthquake.
Fault rupture may pass through the structure
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 10
Direction of Ground Motion
During earthquake shaking, ground shakes in all possible directions.
Direction of resultant shaking changes from
instant to instant.
Structure must withstand maximum ground motion occurring in any direction.
Peak ground acceleration may not occur at the same instant in two perpendicular directions.
Hence for design, maximum seismic force is not applied in the two horizontal directions simultaneously.
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
6
Slide 11
Direction of Ground Motion …
On average, peak vertical acceleration is one-half to two-thirds of the peak horizontal acceleration.
Structures experience vertical acceleration equal to gravity (g) at all times.
Vertical acceleration is a concern for:
Stability issues (e.g., slopes)
Large span structures
Cantilever members
Prestressed horizontal members
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 12
Load Combination 0.9DL 1.5EL
Horizontal loads are reversible in direction.
In many situations, design is governed by effect of horizontal load minus effect of gravity loads.
In such situations, a load factor higher than 1.0
on gravity loads will be unconservative.
Hence, a load factor of 0.9 specified on gravity
loads.
Many designs of footings, columns, and positive steel in beams at the ends in frame structures are governed by this load combination
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
7
Slide 13
Dynamic Soil Properties
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 14
Dynamic Soil Properties
Behaviour of soil complex under static loads. Even more complex under dynamic loads
Need for simple methods to characterize complex behaviour
Analysis techniques:
Equivalent linear models
Cyclic non-linear models
Advanced constitutive models
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
8
Slide 15
Shear Modulus
Soil stiffness depends on strain amplitude, void ratio, mean principal effective stress, plasticity index, over consolidation ratio, and number of loading cycles
Shear Modulus
Tangent modulus
Secant modulus
Shear modulus varies with strain level. It is high at low strains
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 16
Shear Modulus …
Figure: Hysteretic stress-strain response of soil subjected to cyclic loading
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
9
Slide 17
Dynamic Properties
Shear modulus decreases with strain increase
Damping increases with strain increase
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 18
Maximum Shear Modulus (Gmax)
Can be obtained in a number of ways: shear wave velocity, laboratory tests, and empirical relationships
Shear wave velocity obtained from geophysical tests at strains lower than about 3x10-4%
Gmax = ρvs2
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
10
Slide 19
Soil Properties
Exploration data converted to shear modulus:
Gmax = 65N [Seed, and Idris 1983]
Gmax = 1000[35(N60)0.34] (σ’)0.4 [Seed,Wong,and Idris, 1986]
Gmax = 1000[20(N1,60)0.33] (σ’)0.5 [Seed,Wong,and Idris, 1986]
Gmax = 325(N60)0.68 [Imai, and Tonouchi, 1982]
Gmax = K (N60)0.66 [PWRI, 1998]
Where,
N60 = SPT value, uncorrected for over-burden pressure
N1,60 = SPT value, corrected for over-burden pressure
σ’ = Effective soil pressure Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 20
0
50
100
150
200
250
300
0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 5.E+05 6.E+05 7.E+05 8.E+05
Small-strain Shear Modulus(G max) (kN/m2)
Dep
th (
m)
G max (Eqn 2) G max (Eqn 3) G max (Eqn 5)
Gmax (Eqn 1) G max (Eqn 4)
Eqn (5)
Eqn (4)
Eqn (1)
Eqn (2)
Eqn (3)
Soil Properties …
Small strain Shear Modulus (Gmax)
Tends to vary
significantly,
depending on
which relationship
is used
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
11
Slide 21
Ground Motion Along Depth
Peak amplitude of underground motion is smaller than that at the surface
Variation of amplitude depends on
Earthquake characteristics
Frequency content
Type of soil and its distribution along depth
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 22
Ground Motions Along Depth …
Vertical distribution PGD
Vertical distribution PGV
Vertical distribution PGA
Figure: Distribution of peak amplitude of ground motion along depth, (Kanade, 2000)
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
12
Slide 23
Known Spectrum
Artificially generated time history [SIMQKE -1]
Back calculated time history [SHAKE 2000]
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.01 0.1 1 10Time perios (s)
Sp
ectr
al A
ccele
rati
on
(g
)
Functional - Target response spectrum Functional - Generated response spectrum
Safety - Target response spectrum Safety - Generated response spectrum
Ground Motions Along Depth …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 24
Artificially generated time history [SIMQKE-1]
Response time history [SHAKE 2000]
Response time history [SHAKE 2000]
Response time history [SHAKE 2000]
Assumed earthquake
Corresponding response
spectrum [SMSIM]
Figure: Schematic representation of procedure used for artificially generated time histories for earthquake motion
Ground Motions Along Depth …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
13
Slide 25
Underground Structures
When seismic waves hit the ground surface, these are reflected back into ground
The reflection mechanics is such that the amplitude of vibration at the free surface is much higher (almost double) than that under the ground
Codes allow the design spectrum to be one-half if the structure is at depth of 30m or below.
Linear interpolation for structures and
foundations if depth is less than 30m.
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 26
Site Effects
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
14
Slide 27
Site Effects
Motion at the base rock different from that at the top of soil.
Local amplification of the earthquake motion due to the soil profile at the site.
Site Effect.
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 28
Mexico Earthquake of 1985
Earthquake occurred 400 km from Mexico City
Great variation in damages in Mexico City Some parts had very strong shaking
In some parts of city, motion was hardly felt
Ground motion records from two sites: UNAM site: Foothill Zone with 3-5m of basaltic
rock underlain by softer strata
SCT site: soft soils of the Lake Zone
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
15
Slide 29
Mexico Earthquake of 1985 …
PGA at SCT site about 5 times higher than that at UNAM site
Epicentral distance is same at both locations
Time (sec)
Figure from Kramer, 1996
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 30
Extremely soft soils in Lake Zone amplified weak long-period waves Natural period of soft clay layers happened to
be close to the dominant period of incident seismic waves
This lead to resonance-like conditions
Buildings between 7 and 18 storeys suffered extensive damage Natural period of such buildings close to the
period of seismic waves.
Mexico Earthquake of 1985 …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
16
Slide 31
Site Response Amplification
Depends on:
Soil properties (shear modulus, damping)
Soil depth
Contrast in soil properties
More amplification if greater contrast
Intensity of ground motion
Soil is elastic at low strains
Shear modulus decreases and damping
increases as soil strain increases
More amplification for weak motion
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 32
Site Response Amplification …
Figure: Relationship between maximum acceleration on rock and on soft sites (Idriss, 1990, 1991).
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
17
Slide 33
Site Response Amplification …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 34
Figure: Procedure for modifying ground motion parameters from a seismic hazard analysis to account for the effects of local site conditions
Site Response Amplification …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
18
Slide 35
Figure: Two hypothetical soil deposit overlying rigid bedrock: (a) site A; (b) site B. Soils are identical, except the s- wave velocity of the soil at site B is four times greater than that at site A.
Site Response Amplification …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 36
Figure: Amplification functions for sites A and B. Note that the softer soil at site A will amplify low-frequency input motions much more strongly than will the stiffer soils of site B. At higher frequencies, the opposite behaviour would be expected.
Site Response Amplification …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
19
Slide 37
Soil Effect
Recorded earthquake motions show that response spectrum shape differs for different type of soil profile at the site
Period (sec)
Fig. from Geotechnical Earthquake Engineering, by Kramer, 1996
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 38
This variation in ground motion characteristic for different sites is now accounted for through different shapes of response spectrum for three types of sites.
Spect
ral Acc
ele
ration C
oeff
icie
nt
(Sa/g
)
Period (s)
Fig. from IS:1893-2002
Soil Effect …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
20
Slide 39
Modern Codes (e.g., IBC) classify the soil type based on weighted average (in top 30m) of:
Soil Shear Wave Velocity, or
Standard Penetration Resistance, or
Soil Undrained Shear Strength
Soil Effect …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 40
Shape of Design Spectrum
The three curves in IS1893 have been drawn based on general trends of average response spectra shapes.
In recent years, the US codes (UBC, NEHRP and IBC) have provided more sophistication wherein the shape of design spectrum varies from area to area depending on the ground motion characteristics expected.
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
21
Slide 41
Soil Structure Interaction
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 42
Soil Structure Interaction
If there is no structure, motion of the ground surface is termed as Free Field Ground Motion
Normal practice is to apply the free field motion to the structure base assuming that the base is fixed.
This is valid for structures located on rock sites.
For soft soil sites, this may not always be a good
assumption.
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
22
Slide 43
Presence of structure modifies the free field motion since the soil and the structure interact. Hence, foundation of the structure experiences
a motion different from the free field ground motion.
The difference between the two motions is accounted for by Soil Structure Interaction (SSI)
SSI is not the same as Site Effects Site Effect refers to the fact that free field motion
at a site due to a given earthquake depends on the properties and geological features of the subsurface soils also.
Soil Structure Interaction …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 44
Consideration of SSI generally
Decreases lateral seismic forces on the structure
Increases lateral displacements
Increases secondary forces associated with P-
delta effect.
For ordinary structures, one usually ignores SSI.
Soil Structure Interaction …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
23
Slide 45
Radiation Damping
Structure
Artificial Boundary
Analytical Region
Scattering Wave
Transmitted Wave Reflected Wave
Infinite Soil Medium
Ground Surface
Radiation of energy to infinity
Also called geometric damping or geometric
attenuation
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 46
Issues for Foundation Design
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
24
Slide 47
Foundations
Lessons from Past Earthquakes:
Seismic damage, particularly to low height bridges, often caused by foundation failures.
Foundation failures could be due to:
Excessive ground deformation
Loss of stability
Bearing capacity problem
Large foundation displacements may cause:
Relative shifting of and damage to the superstructures,
Damage to the bearings
Backfills cause large forces on abutments. Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 48
Wing walls may break loose from the abutments due to excessive backfill forces.
Poor soils (soft soil and a high water table) contributed to a lot of damage to bridges in the past earthquakes.
Examples:
Nigata earthquake of 1964
Alaska earthquake of 1964.
Foundations …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
25
Slide 49
Modes of Foundations Failure
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 50
Modes of Failure for Spread Footings
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
26
Slide 51
Modes of Failure for Pile Footings
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 52
Shallow Foundations in Clay
Cyclic loading during earthquake
Generally, clay does not loose much strength during cyclic undrained loading
There may be some settlement, lateral movement or rotation, depending on
Factor of safety under static condition
Generally, good seismic performance due to adequate factor of safety in static loading
Concern: site effects
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
27
Slide 53
Shallow Foundations in Dry Sand
Under cyclic shear, dry sand reduces in volume
Settlement of ground (and hence the foundation) during earthquake motion
Settlement more significant for loose sand than for dense sand
Structure: part on shallow footing and part on end bearing piles:
Part on footing may undergo settlement relative
to the other part
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 54
Shallow Foundation in Saturated Sand
Liquefaction is a major concern
Liquefaction
Geologically young sand
Saturated sand
Loose sand
Right particle size distribution
Liquefaction can occur at the same site in subsequent earthquakes
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
28
Slide 55
Shallow Foundations … (Contd…)
Lateral flow (lateral spreading) of liquefied sand can occur
Liquefaction leads to surface settlement after the water pressure dissipates
Liquefaction occurs first adjacent to the spread footing and then under it
Liquefaction may occur after the earthquake motion has stopped
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 56
Deep Foundations in Clay
Gapping may occur near the ground surface
Pile foundation failures in buildings in the Mexico 1985 earthquake
Due to low factors of
safety
Development of a gap adjacent to a pile subject to cyclic lateral load in clay (after Swane and Poulos, 1984).
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
29
Slide 57
Deep Foundations in Sand
Bridge performance in Alaska (1964) earthquake (Ross et al 1969) shows:
Large foundation displacements for
foundations in saturated sands
Foundations in gravel and gravelly sands
have much less damage
Foundations on rock not damaged
Foundations by piling through sands to
bedrock have minor damage
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 58
Foundations on Raked Piles
Particularly vulnerable to severe damage during earthquakes
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
30
Slide 59
Liquefaction
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 60
Liquefaction
In case of loose or medium dense saturated soils, liquefaction may take place.
Sites vulnerable to liquefaction require
Liquefaction potential analysis.
Remedial measures to prevent liquefaction.
Else, deep piles are designed assuming that soil
layers liable to liquefy will not provide lateral
support to the pile during ground shaking.
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
31
Slide 61
Difficult to obtain undisturbed samples
Approach based on in-situ tests preferred
SPT and CPT based procedures are popular
Simplified procedure of Seed and Idriss used with SPT values
Liquefaction Analysis
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 62
North Bank: Rail and Road : At Center of Embankment : Water Level 1.0 m below GL
amax/g 0.60 h w 1.00 g w 0.98 h emb 21.00 g emb 1.85 g sub 0.85 M 7.00
D Rng Depth %Fine g sat s v u 0 s v ' Avg.N C N C 60 (N l ) 60 r d K m K a K s CSR eq CSR 7.5 CSR L FS liq CSR eql % e D V
0.0-1.5 0.75 8.20 1.85 40.24 0.00 40.24 6.22 2.00 1.00 12.44 0.67 1.09 1.00 0.66 0.26 0.15 0.11 0.42 0.37 1.95 0.03
1.5-3.0 2.25 8.00 1.85 43.01 1.23 41.79 8.80 2.00 1.00 17.60 0.65 1.09 1.00 0.64 0.26 0.24 0.17 0.64 0.38 1.95 0.03
3.0-4.5 3.75 8.30 1.85 45.79 2.70 43.09 12.08 1.50 1.00 18.16 0.63 1.09 1.00 0.63 0.26 0.21 0.15 0.56 0.38 1.93 0.03
4.5-6.0 5.25 8.50 1.85 48.56 4.17 44.40 16.30 1.31 1.00 21.43 0.61 1.09 1.00 0.62 0.26 0.26 0.18 0.68 0.38 1.50 0.02
6.0-7.5 6.75 6.15 1.85 51.34 5.64 45.70 20.68 1.18 1.00 24.45 0.58 1.09 1.00 0.62 0.26 0.31 0.21 0.81 0.38 1.18 0.02
7.5-9.0 8.25 8.00 1.85 54.11 7.11 47.01 24.47 1.08 1.00 26.53 0.56 1.09 1.00 0.60 0.25 0.35 0.23 0.92 0.39 1.00 0.02
9.0-10.5 9.75 6.40 1.85 56.89 8.58 48.31 27.72 1.01 1.00 27.90 0.54 1.09 1.00 0.59 0.25 0.41 0.27 1.07 0.38 0.88 0.01
10.5-12.0 11.25 6.40 1.85 59.66 10.05 49.62 24.75 0.94 1.00 23.35 0.52 1.09 1.00 0.58 0.24 0.30 0.19 0.78 0.38 1.36 0.02
12.0-13.5 12.75 6.40 1.85 62.44 11.52 50.92 26.00 0.89 1.00 23.17 0.49 1.09 1.00 0.58 0.24 0.30 0.19 0.81 0.37 1.34 0.02
13.5-15.0 14.25 6.40 1.85 65.21 12.99 52.23 30.63 0.85 1.00 25.92 0.47 1.09 1.00 0.57 0.23 0.31 0.19 0.84 0.37 1.05 0.02
15.0-16.5 15.75 6.40 1.85 67.99 14.46 53.53 33.25 0.81 1.00 26.86 0.45 1.09 1.00 0.57 0.22 0.35 0.22 0.97 0.36 1.00 0.02
16.5-18.0 17.25 7.33 1.85 70.76 15.93 54.84 36.13 0.77 1.00 27.97 0.43 1.09 1.00 0.56 0.21 0.36 0.22 1.02 0.35 0.50 0.01
18.-19.5 18.75 7.00 1.85 73.54 17.40 56.14 39.00 0.74 1.00 29.03 0.40 1.09 1.00 0.55 0.21 0.45 0.27 1.31 - - -
19.5-21 20.25 7.00 1.85 76.31 18.87 57.45 44.63 0.72 1.00 32.04 0.38 1.09 1.00 0.55 0.20 (N l ) 60 Greater than 30 hence
soil is Non - Liquefiable
TOTAL D 0.23
rd is calculated at the center of depth range below top of embankment Units : Tons & Meters
Liquefaction Analysis (Example)
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
32
Slide 63
S.No. Details Depth of Liquefaction
Soil Settlement
Functional Evaluation Motion (0.1g)
1. North Embankment (Rail & Road) - -
2. South Rail Embankment - -
3. South Road Embankment - -
Safety Evaluation Motion (0.6g)
4. North Embankment (Rail & Road) 18.75 0.26
5. South Rail Embankment 14.25 0.19
6. South Road Embankment 14.25 0.18
Liquefaction Analysis (Example) …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 64
Embankment Analysis
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
33
Slide 65
Slope failure due to
Inertial loading, and/or
Softening of material strength or liquefaction
Fault displacement under the foundation
Not being addressed here
Issues for Embankments
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 66
Pseudo-static slope stability analysis
Factor of safety concept
Permanent deformation analysis as per Newmark’s sliding block approach
Two Methods
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
34
Slide 67
Complex ground shaking replaced by a single constant unidirectional pseudo-static acceleration
Ensure adequate factor of safety against sliding
How to choose seismic coefficient and factor of
safety?
Pseudo-Static Analysis
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 68
Newmark’s Sliding Block Model
Developed originally for evaluation of seismic slope stability
Motivated by concerns about realistic ground motions that are much higher than the traditional design based on pseudo-static stability analysis
If FOSslid < 1.0
What will happen? Will the structure collapse?
Not, if the permanent deformation is within an
acceptable limit
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
35
Slide 69
Time (s)
Figure: Development of permanent displacement for actual earthquake ground motion
W
T N
θ
Newmark’s Sliding Block Model …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 70
Deformations accumulate when the rigid body acceleration exceeds the yield acceleration.
Newmark’s Sliding Block Model …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
36
Slide 71
Embankment Analysis (Example)
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 72
Assuming No Liquefaction
Static load (only self weight): FOS=1.99
Pseudo-static: Yield coeff (FOS=1.0) is 0.275g
FOS Approach by:
Terzaghi (1950): Yield coeff. should be >0.20g
Mercuson (1981): Yield coeff. > 0.2g-0.3g
Hynes and Franklin (1984): Yield coeff of 0.1g
will give permanent deformation less than 1m.
Embankment Analysis (Example) …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
37
Slide 73
Permanent Deformation by Newmark’s Sliding Block Concept
Makdisi and Seed (1978) approach: 5 -15 mm
Ambraseys and Menu (1988): 39 mm
Yegian et al. (1991): 30mm
Permanent deformation of about 40mm quite acceptable.
Embankment Analysis (Example) …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 74
Liquefied soil layers may not transmit significant amount of shear waves.
Will the embankment be stable under its own weight?
Liquefied soil layers will loose considerable amount of strength.
Liquefaction of Sub-Soil
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
38
Slide 75
Residual strength of liquefiable soil strata considered as per Seed and Harder (1990)
FOS against self weight:
1.39 for North Embankment
1.18 for South Rail Embankment
1.31 for South Road Embankment
Embankment will be stable due to its own weight after foundation soils have liquefied
Embankment Analysis (Example) …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 76
Figure: Relationship between Corrected ‘Clean Sand’ Blow Count (N1)60
and Undrained Residual Strength (Sr) (Seed and Harder, 1990)
Liquefaction of Sub-Soil …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
3/3/2013
39
Slide 77
Conservative Assumptions:
Liquefaction occurs early during shaking
Base of embankment still sustains PGA of
0.60g
Deformations computed for 0.60g but with residual strength of liquefiable soils
Embankment Analysis (Example) …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 78
Details North Bank
Embankment
South Bank Embankment
Rail Road
FOS for Static Case (No earthquake)
1.39 1.18 1.31
Yield Acceleration (for FOS = 1.0)
0.1g 0.048g 0.08g
Permanent Displacement Considering PGA = 0.6g (in mm)
Ambraseys and Menu (1998) 353 1310 497
Yegian et al. (1991) 317 1190 502
Makdisi and Seed (1978) 50-400 200-1000 80-700
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Analysis Using Residual Strength
Embankment Analysis (Example) …
3/3/2013
40
Slide 79
Deformation of 500mm: acceptable.
Deformation of 1300mm: on the higher side; but can be handled as an emergency measure in a relatively short time
These deformations are for maximum embankment height and with conservative assumptions
Remedial measures not recommended.
Embankment Analysis (Example) …
Sudhir K. Jain Course on Geotech Earthq Engg / March 2013
Slide 80 Sudhir K. Jain Course on Geotech Earthq Engg / March 2013