liquefaction iit roorkee dec 26 2012
TRANSCRIPT
Soil Liquefaction: Experimental and Field Investigations
Prof. T. G. SitharamDepartment of Civil Engineering and Chairman, CiSTUP
Indian Institute of Science, Bangalore-560 012.
IIT Roorkee, 26th Dec 2012
Jan 26 2001
Soil Liquefaction Introduced by Casagrande in 1936 The effective strength of saturated
cohesion less soil is reduced drastically due to sudden loading.
wu
w' uσσstressEffective
φtanuστ
φtanστstrengthShear
w
'
Liquefaction occurs when solid material transforms into liquid state due to the increased pore pressure
Issue of liquefaction and ground failure
Northridge, 1994
fjfg
Satellite image of Liquefaction at Bhuj
Jan 15, 2001
Jan 31, 2001
http://earthobservatory.nasa.gov
More than 10,000 sq km area was liquefied during Bhuj earthquake
Liquefaction during Bhuj Earthquake 2001
Field investigations have found abundant evidence of mud volcanos, sand boils, and fissures from which salty ground water erupted over an area exceeding 10,000 square kilometers. Evidence of the expelled water can also be seen on the MISR images.
Pre -January 15 Post January 31, 2001
Liss III FCC images
"false-color“ (MISR) Images
9
Million Dollar Bridge after 1964 Alaska earthquake
Showa Bridge after 1964 Niigata earthquake
Building in Kobe after 1995 earthquake
1964
1995 1999 2001
Bridge in Taiwan after 1999 Chi-Chi earthquake
Kandla port building after 2001 Bhuj earthquake
Damages due to local site effects and liquefaction in earthquakes
Earthquake Damage in Mexico City, Mexico, September 19, 1985 - resonance
1985
The effect of the subsoils on the earthshaking and building damage is emphasized.
10
Guerro EQ 1985 – Mexico city, Mexico Spitak EQ 1988 – Leninakan, Armenia (Soviet U) Loma Prieta EQ 1989 – San Francisco bay area, US Kobe EQ 1995 – coastal areas of city, Japan Kocaeli EQ 1999 – Adapazari, Turkey Erzincan 1992 – Turkey, resonance Bhuj EQ 2001 – Bhuj, India-Liquefaction Christchurch , New Zealand Earthquake 2010
Ground Failure Resulting from Liquefaction
Bearing capacity failure of foundations Sand Boils Flow failure of slopes Lateral spreads Rising of buried structures to the
surface Retaining wall failure Landslides and floods
Liquefaction – Susceptibility and Potential
Liquefaction Susceptibility Evaluation is done by considering the soil
properties alone
Earthquake loading is not taken into account
Liquefaction Potential Both soil properties and earthquake
loading are considered
Liquefaction Susceptibility Based on Soil Properties
Age of the soil
Index properties of soil
Shape of particles
Relative density of soil
Permeability of soil
Liquefaction Susceptibility Index Properties – Chinese Criteria
w = 0.87LL
Saturated moisture content, w (%)
NON-LIQUEFIABLE SOIL: w < 0.87LL or LL > 33.5 or Clay fraction > 20% or Plasticity Index > 13
LL = 33.5
POTENTIALLY LIQUEFIABLE SOIL IF: Clay fraction (0.005 mm) is less than 20% Plasticity Index is less than or equal to 13.
Liq
uid
Lim
it, L
L
60
50
40
30
20
10
0 0 20 40 60 80
Chinese Criteria Adapted to ASTM Definitions of Soil Properties (Perlea et al., 1999)
Evaluation of Liquefaction Potential
Peak acceleration
Magnitude
= 0.65 rdPGA
g ’vo
vo 1MSF
Demand
Capacity
Loading
Resistance
CSR
CRRFS
SPT
CPT
Vs
Most research
Issues with Existing Methods of Characterizing the Earthquake Loading
Considers single ground motion hazard level
Single earthquake magnitude – 7.5 and MSF takes care of EQ magnitudes
max0.65 vo d
vo
rCSR
g
a
MSF
(after Youd et al. 2001)
Liquefiable
Non-Liquefiable
Depth Reduction Factor - rd
The Shear stress at a depth “h” is calculated by assuming that the soil column is rigid.
rd is introduced to account for the flexibility of soils
maxrigid body
ah
g
ddeformable soil rigid bodyr
Seed and Idriss, 1971
rd – Cetin and Seed (2004)
Evaluates rd as a function of Depth Earthquake magnitude Ground acceleration Soil Stiffness
*,12
*,12
*max ,12
0.341( 0.0785 7.586)*
max ,12 *max ,12
0.341(0.0785 7.586)
23.013 2.949 0.999 0.05251
16.258 0.201( , , , )
23.013 2.949 0.999 0.05251
16.258 0.201
s
r
s
w sd V
sdw s
V
a M V
er d Mw a V
a M V
e
d
Magnitude Reduction Factor
Earthquake Magnitude, MW
Mag
nitu
de S
calin
g Fa
ctor
, MS
F
Youd and Noble, 1997
2.24
2.56
10
W
MSFM
Youd et al., 2001
Assessment of Liquefaction Potential Based on SPT Data (Deterministic Method)
Liquefiable
Non-Liquefiable
Seed and Idriss, 1985
& Youd et al., 2001
Probabilistic Seismic Hazard Analysis
24
• DSHA assumes a single scenario with a DSHA assumes a single scenario with a single magnitude and a single distance.single magnitude and a single distance.
• We don’t know when EQs will occur, where We don’t know when EQs will occur, where they will occur and how big they will be.they will occur and how big they will be.
• PSHA assumes many scenarios considering PSHA assumes many scenarios considering all magnitudes, all distances and all effects.all magnitudes, all distances and all effects.
• PSHA characterizes uncertainty in location, PSHA characterizes uncertainty in location, size and frequency, of earthquakes & size and frequency, of earthquakes & combines all of them to compute the hazard.combines all of them to compute the hazard.
Steps Taken to Evaluate the Liquefaction Potential
Peak horizontal acceleration (PHA) values at bed rock level was evaluated using Probabilistic seismic hazard analysis.
Since site characterization data was not available, the surface level peak ground acceleration (PGA) were evaluated for four NEHRP site classes (Site class A to D).
Deaggregated the seismic hazard with respect to magnitude
Evaluation of liquefaction return period – based on PGA values.
Probabilistic Correlations Based on SPT Data
Cetin et al. (2004)
1 60 1 2
53 4 0 6L
( ) (1 ) ln
ln (ln( / )P
eq
av
N FC CSR
Mw P FC
0.65 i voeq d
vo
aCSR r
g
Where PL – Probability of liquefaction (as a fraction);
Φ – standard normal cumulative distribution function;
(N1)60 – corrected N value; FC – fineness content in percentage; CSReq – cyclic stress ratio without MSF; Mw – moment magnitude of earthquake; ' σ v0 - effective vertical pressure at the given
depth; Pa – atmospheric pressure (in the same unit as σ
‘v0 );
- regression coefficients and
σ z- model uncertainty.
CPT Based Correlation – Probabilistic Method (Moss et al., 2006)
1.0451 1
0
(0.110 ) 0.001 (1 0.850 )
7.177ln( ) 0.848ln 0.002(ln( ) 20.923PL
1.632
c c f f f
v
q q R R c R
CSR Mw
qc1 - normalized tip resistance
Rf - friction ratio (in percentage)
c - normalization exponent Where PL - probability of liquefaction; qc1 - normalized tip resistance; Rf – friction ratio (in percentage); c - normalization exponent; CSR - cyclic stress ratio; Mw -moment magnitude of earthquake; σ ′ v 0 - effective overburden pressure.
A Probabilistic Seismic Hazard Curve
1.00E-11
1.00E-10
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000PGA(g) at ground level
Me
an
An
nu
al
Ra
te o
f E
xc
ee
da
nc
e
Total hazard
5.4
5.2
5.0
4.8
4.6
4.4
5.6
4.2
5.8
4.0
Performance-Based EarthquakePerformance-Based EarthquakeEngineeringEngineering
Uncertainty in earthquake loading.
Consider the entire range of earthquake
magnitude and acceleration.
Evaluation of liquefaction return period is
possible.
Performance-Based EarthquakePerformance-Based EarthquakeEngineeringEngineering
Uncertainty in earthquake loading.Consider the entire range of earthquake magnitude and acceleration.Evaluation of liquefaction return period is possible.
DV IMG DV DM dG DM EDP dG EDP IM d
Intensity measure
Engineering demand parameter
Damage measure
Decision variable
Repair cost
Crack width
FSL PGA
( ) ( / ) ( / ) ( / ) ( )DV P DV dv DM dm P DM IM P EDP IM IM
Deaggregation of Seismic Hazard for Probabilistic Liquefaction Evaluation
Seismic hazard is sub divided into
number of acceleration and magnitude
increments
Incremental mean annual rate of
exceedance for these acceleration-
magnitude combinations are determined
MSF is not considered in evaluating the
CSR value.
Probabilistic Performance Based Evaluation of Factor of Safety Against Liquefaction
0.65 i voeq d
vo
aCSR r
g
max
*iL L
1 1
[FS FS a , ] ,aM
iL
NN
j a jFSj i
P m m
i
*1 60 1 2 , 3 4 0 5 6
L L
( ) (1 ) ln( ) ln( ) (ln( / )P[FS FS a , ] eq i L j v a
j
N FC CSR FS m P FCm
,ia jm
Kramer and Mayfield, 2007
Incremental MARE for ai and mj
Where - annual rate at which factor of safety will be less than
NM number of magnitude increments; Na number of peak acceleration increments;
incremental annual frequency of exceedance for
acceleration ai and magnitude mj
*LFS
,ia jm
Probabilistic Evaluation of Corrected N-Value Required to
Prevent Liquefaction
max
*ireq req
1 1
[N N a , ] ,aM
ireq
NN
j a jNj i
P m m
i
req 1 2 , 3 4 0 5 6req req
N (1 ) ln( ) ln( ) (ln( / )P[N N a , ] eq i j v a
j
FC CSR m P FCm
Kramer and Mayfield, 2007
A Typical Seismic Hazard Curve
1.00E-11
1.00E-10
1.00E-09
1.00E-08
1.00E-07
1.00E-06
1.00E-05
1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000PGA(g) at ground level
Me
an
An
nu
al
Ra
te o
f E
xc
ee
da
nc
e
Total hazard
5.4
5.2
5.0
4.8
4.6
4.4
5.6
4.2
5.8
4.0
Liquefaction Hazard Curves
1.E-08
1.E-06
1.E-04
1.E-02
0 5 10 15 20 25 30 35 40
Corrected N Value
An
nu
al
rae
of
Ex
ce
ed
an
ce
Bhuj
Jamnagar
Rajkot
Ahmadabad
Surat
Vadodara
Effect of fines on Liquefaction
0
0.05
0.1
0.15
0.2
0.25
1 10 100 1000Cycles to Initial Liquefaction (N L )
Cyc
lic
Str
ess
Rat
io (
CSR
)
Clean Sand (CRR=0.184)
Clean Sand+5%Silt (CRR=0.2025)
Clean Sand+10%Silt (CRR=0.15)
Clean Sand+15%Silt (CRR=0.15)
Clean Sand+20%Silt (CRR=0.138)
Clean Sand+25%Silt (CRR=0.114)
Clean Sand+30%Silt (CRR=0.081)
Clean Sand+35%Silt (CRR=0.106)
Clean Sand+40%Silt (CRR=0.0995)
Clean Sand+45%Silt (CRR=0.10008)
Clean Sand+50%Silt (CRR=0.113)
Clean Sand+60%Silt (CRR=0.123)
Clean Sand+75%Silt (CRR=0.1148)
Silt (CRR=0.1108)σ'3c = 100kPa, f = 0.1Hz, RD c = 53%
N = 20
CRR = 0.0772e0.0178(RD )
CRR = 0.0311e0.0263(RD )
CRR = 0.0081e0.0387(RD )
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 20 40 60 80 100 120
Relative Density, RD (%)
Cyc
lic
Res
ista
nce
Rat
io (
CR
R)
Clean Sand
Clean Sand + 5%Silt
Clean Sand + 10%SIlt
Clean Sand + 15%Silt
Clean Sand + 20%Silt
Clean Sand + 25%Silt
Clean Sand + 30%Silt
Clean Sand + 35%Silt
Clean Sand + 40%Silt
Clean Sand + 45%Silt
Clean Sand + 50%Silt
Clean Sand + 60%Silt
Clean Sand + 75%Silt
Silt
Upper Bound Curve
Mean Curve
Lower Bound Curve
σ'3c = 100kPa, f = 0.1Hz
Limitations of cyclic triaxial laboratory experiments
•Non uniformity of strains and stress fields
•End restraint effects
•Membrane penetration effects
•Difficulties in preparing identical loose specimens at low confining pressures
•Repeatability (with in lab) and reproducibly (lab to lab) of test results
Experimental investigations:(Vaid et al. 1990; Hyodo et al., 1994; Zlatovic and
Ishihara, 1995; Baziar and Dobry, 1995; Toyota et al.,
1995; Talaganov, 1996; Vaid and Thomas, 1997; Lade
and Yamamuro,1997; Amini et al, 2000; Naeini, 2001;
Naeini and Baziar, 2004; Govida Raju, 2005)
Cyclic behaviour of granular materials using DEM: Hakuno et al, (1988); Kishino (1990); Tan (1990); Sitharam (1991); Ng (1993); Nakase, Takeda and Oda (1999) Ravichandran and Meguro (2001); Sitharam (2003); Dinesh (2003); Ashmawy et al (2003); Roberto (2004); Mourad Zeghal and Usama El Shamy (2005).
6
Calculation Cycle
t
f
f
kft
k
n
ft
n
c,
n
t
f
f
kft
k
n
ft
n
c,
n
kft
k
n
ft
n
c,
n
ftk
n
ft
n
c,
n
tk
n
ft
n
c, c,
n
Imposed boundary condition
Forces
Gravity Forces Law Of motion Integrate Acceleration
Displacements
Contact law
Imposed Boundary conditions
Modified program Trubal•Based on Cundall(1979, 1984)•Implemented the concept of micromechanics – Waterloo Version•Subroutines incorporated to extract micromechanical parameters such as average coordination number, anisotropic coefficients etc.
• A subprogram to calculate- overlap vol, bfr, void ratio• Periodic space boundary condition• A subroutine subassembly - to look at phase transformation• Plot files were developed using java
Discrete Element Method
Undrained tests – Constant Volume simulations - Ng (1993); Ng and Dobry (1994); Nimbkar (1996); Dubujet and Dedecker (1998); Nagaraja Rao (1998); Sitharam (2003); and Dinesh (2003).
12
Parameters involved in Micromechanics
N
M
M= Total number of contact pointsN= Total number of particles
• Average Coordination number
rij
rij
rd aaa
2
3 n
ijn
ijn
d aaa2
3 t
ijt
ijt
d aaa2
3
Micro structural features are quantified by introducing anisotropy coefficients:
rija n
ija tija are the symmetric second order deviatoric tensors representing
coefficient of fabric, normal contact force and tangential contact force anisotropy.
Stress-force-fabric relationship is developed from these parameters. Contribution of each component can be understood explicitly and offer micromechanical explanations associated with shear deformation. (Rothenburg and Bathurst, 1989; Chanthawarangul, 1993 and Sitharam et al., 2002).
13
Tangential contact forceAverage normal contact forceContact orientation
Cyclic triaxial numerical simulations using DEM
Test series:
Initial state of assembly
Stress path
during shearing
Boundary control
Void ratio of compacted assembly,
(ec)
Confining pressure
(kPa)
Amplitude of axial
strain, (%)
1 Isotropically compressed
Undrained Strain
controlled
0.59 0.58 0.54
25 50
100
0.14 to 0.6
0.3 to 1.2 0.6 to 1.67
2 Isotropically compressed
Undrained Strain
controlled 0.56 50
0.24 to 0.73
Numerical simulation program
• Shear modulus = 70 GPa• Poisson’s ratio = 0.3 • Density = 2650 kg/m3 • Coefficient of contact friction = 0.3 • Particle size = 0.4 – 2 mm
Particle properties
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10
Paricle size (mm)
% F
iner
Assembly of spheres
14
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Number of cycles
Axi
al s
trai
n,
(%
)
1 2 3
3 = 50 kPa; ec = 0.58
= 0.6 %; f= 1.42 Hz
-20
-15
-10
-5
0
5
10
15
20
Number of cycles
Dev
iato
ric
stre
ss, q
(kP
a)
1 2 3
3 = 50 kPa; ec = 0.58
= 0.6 %; f= 1.42 Hz
Strain controlled cyclic triaxial simulations
Axial strain Vs number of cycles
Deviator stress Vs number of cycles
-8
-6
-4
-2
0
2
4
6
8
0 5 10 15 20 25 30
Mean p (kPa)
Dev
iato
r st
ress
, q (
kPa)
3 = 25 kPa; ec = 0.59
f = 1.42 Hz
-8
-6
-4
-2
0
2
4
6
8
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8Deviatoric strain (%)
Dev
iato
r str
ess,
q (k
Pa)
3 = 25 kPa; ec = 0.59
f = 1.42 Hz
Variation of deviator stress with deviatoric strain
Variation of deviator stress with mean p
Liquefaction
15
0
0.5
1
1.5
2
2.5
3
3.5
4
0 1 2 3 4 5 6 7
Number of cycles
Ave
rage
coo
rdin
atio
n nu
mbe
r
0
0.2
0.4
0.6
0.8
1
1.2
Pore
pre
ssur
e ra
tio, U
3 = 25 kPa; ec = 0.59
f = 1.42 Hz
Average coordination number
Pore pressure ratio
Plot of average coordination number and pore pressure ratio with number of cycles
0
0.5
1
1.5
2
2.5
3
3.5
4
-5 0 5 10 15 20 25
Mean p (kPa)
Ave
rage
coo
rdin
atio
n nu
mbe
r
3 = 25 kPa; ec = 0.59
f = 1.42 Hz
-40
-30
-20
-10
0
10
20
30
0 1 2 3 4 5 6 7
Number of cycles
Cha
nge
in n
umbe
r of c
onta
cts Vertical contacts
(80 -90
Horizontal contacts (0 -10
Average coordination Vs mean p
Change in the number of vertical and horizontal contacts Vs number of cycles
16
0
0.5
1
1.5
2
2.5
3
1 10 100 1000 10000
Number of cycles for initial liquefaction
Shea
r stra
in (%
)
= 50 kPa, = 0.56 - 0.58
25 - 100 kPa, = 0.59 -0.54
Experimental results
Talaganov (1996)
3 =
ec
Present study
3
ec
Relationship between shear strain and number of cycles for initial liquefaction
17
0
0.2
0.4
0.6
0.8
1
1.2
0.001 0.01 0.1 1 10
Shear strain, (%)
Pore
pre
ssur
e ra
tio, U
= 25 - 100 kPa
= 50 kPa; = 0.56
3
3
Dobry (1985) N = 10
Upper bound Lower bound
ec
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1 Cycle ratio (N/NL)
Pore
pre
ssur
e ra
tio (
U)
= 100 kPa; = 0.6 - 1.1 %
= 0.6 %; = 25 - 100 kPa
= 50 kPa; = 0.56 - 0.58
3
3
3
ec
Talaganov (1996) Upper bound Lower bound
Pore water pressure generation during cyclic loading
The pore water pressure computed based on the mean pressure between the undrained (effective) and drained (total) stress path during strain controlled cyclic triaxial tests.
Relationship between pore pressure ratio and cycle ratio for sand samples for different parameters
Pore pressure ratio Vs shear strain at ten cycles
18
0
0.5
1
1.5
2
2.5
3
3.5
4
0 2 4 6 8 10 12Axial strain, (%)
Dev
iato
ric
anis
otro
pic
coef
fici
ent(
adn /a
dr /adt )
0
50
100
150
200
250
300
350
400
450
Dev
iato
r st
ress
, q (
kPa)
adn
adr
adt
3 = 100 kPa; ec = 0.54
= 0.6%
q
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 2 4 6 8 10 12Axial strain, (%)
Ave
rage
coo
rdin
atio
n nu
mbe
r
= 0.3 % 0.5 % 0.6 %
3 = 100 kPaec = 0.54
0
50
100
150
200
250
300
350
400
0 2 4 6 8 10 12Axial strain, (%)
Dev
iato
r st
ress
, q (
kPa)
= 0.3%
0.6 %
0.5%
3 = 100 kPa ec = 0.54
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500Mean p (kPa)
Dev
iato
r st
ress
, q (
kPa)
3 = 100 kPaec =0.54
Post liquefaction behaviour of granular materials
Deviator stress Vs
mean p
Deviator anisotropic coefficients and deviator stress Vs axial strain
Deviator stress Vs
axial strain
Average coordinaion number Vs
axial strain
19
Dynamic properties of granular materials
Details of numerical test program
Sl No Initial state of the
assemblyStress path Frequency
(Hz)
Void ratio of initially
compacted assembly (ec)
Confining pressure, s3
(kPa)
Amplitude of axial strain,
(%)
1
Isotropically compressed
Undrained1.42
0.510.480.45
50100200
7.0x10-5
to 26.85 x10-5 to 27.2 x10-5
to 2
0.480.510.54
1006.85 x10-5 to 7.1 x10-1
1.42 – 0.14 0.48 100 6.85 x10-5 to 2
2 Constant p 1.42 0.48 100 6.85 x10-5 to 2
3 Drained 1.42 0.48 100 6.85 x10-5 to 2
4 Anisotropicallycompressed
Undrained 1.42 0.48 100 6.85 x10-5 to 2
20
AxialStrain
DeviatorStress
(d)
AT
AL E
max
Axial
max
Deviator
max
max
E
)1(
)1(2
EG
T
L
A
AD
4
Where = Poisson’s ratio and may be estimated as 0.5 for saturated undrained specimens.
Damping ratio, D is a measure of energy dissipated to the maximum elastic strain energy
Where AL= area enclosed by the hysteresis loop AT= area enclosed by the shaded triangle
1st cycle – Hysteresis loop
21
Hysteresis loop for different cyclic strain amplitude
Variation of shear modulus with shear strain
Variation of damping ratio with shear strain
22
0
0.05
0.1
0.15
0.2
0.25
0.3
0.0001 0.001 0.01 0.1 1 10
Shear strain, (%)
Dam
ping
ratio
, (D
)
= 50 kPa; = 0.51
= 100 kPa; = 0.48
= 200 kPa = 0.45
3
3
3
ec
ec
ec
f = 1.42 Hz
Seed and Idriss (1970) Upper bound Lower bound
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
Mod
ulus
ratio
(G/G
0)
= 0.48
= 0.51
= 0.54
Seed and Idriss, (1970) Upper bound Lower bound
3 = 100 kPaf = 1.42 Hz
ec
ec
ec
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
Mod
ulus
rat
io (
G/G
0)
= 50 kPa; = 0.51
= 100 kPa; = 0.48
= 200 kPa; = 0.45
Seed and Idriss (1970) Upper bound Lower bound
3
f = 1.42 Hz
3
3
ec
ec
ec
0
0.05
0.1
0.15
0.2
0.25
0.3
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
Dam
ping
ratio
(D)
= 0.48 = 0.51 = 0.54
Seed and Idriss (1970) Upper bound Lower bound
3 = 100 kPaf = 1.42 Hz
ec
ecec
Effect of confining pressure Effect of void ratio
Modulus ratio vs shear strain
Modulus ratio Vs shear strain
Damping ratio Vs shear strain
Damping ratio Vs shear strain
23
0
10
20
30
40
50
60
70
80
90
100
0.1 1 10Particle size (mm)
% f
iner
Grad 1; Cu = 1.36
Grad 2 Cu = 1.18
0
0.05
0.1
0.15
0.2
0.25
0.3
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
Dam
ping
ratio
(D
)
Cu = 1.35
Cu = 1.18
Seed and Idriss(1970) Upper bound Lower bound
ec = 0.48 f = 1.42Hz
Particle size gradation curve
0
10
20
30
40
50
60
70
80
0.0001 0.001 0.01 0.1 1 10
Shear strain, (%)
She
ar M
odul
us, G
(M
Pa)
Cu = 1.18
Cu = 1.35
ec = 0.48
3 = 100 kPaf = 1.42 Hz
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
Mod
ulus
ratio
, G/G
0
Cu = 1.18
Cu = 1.35
Seed and Idriss (1970) Upper bound Lower bound
ec = 0.48
3 = 100 kPaf = 1.42 Hz
Effect of gradation
Shear Modulus vs shear strain
Damping ratio vs shear strain
Modulus ratio vs shear strain
24
0 5 10 15 20 25 30
-0.10
-0.05
0.00
0.05
0.10 0.0 0.5 1.0 1.5 2.0 2.5 3.0
-0.10
-0.05
0.00
0.05
0.10
Axia
l st
rain
, (%
)
time, sec
frequency, f = 0.14 Hz
A
xia
l st
rain
, (%
)
frequency, f = 1.42 Hz
Effect of frequency
0
10
20
30
40
50
60
70
80
90
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
Sh
ear
mo
du
lus,
G (
MP
a)
f = 1.42 Hz
f = 0.14 Hz
3 = 100 kPaec = 0.48
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0001 0.001 0.01 0.1 1 10
Shear strain, (%)
Mod
ulus
ratio
, G/G
0
f = 1.42 Hz
f = 0.14 Hz
3 = 100 kPaec = 0.48
Seed and Idriss (1970)Upper boundLower bound
0
0.05
0.1
0.15
0.2
0.25
0.3
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
Dam
ping
rat
io,
D
f = 1.42 Hz
f = 0.14 Hz
Seed and Idriss(1970) Upper bound Lower bound
ec = 0.48
3 = 100 kPa
Shear modulus Vs shear strain
Axial strain Vs time
Modulus ratio Vs shear strain Damping ratio
Vs shear strain
25
0
20
40
60
80
100
120
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
She
ar m
odul
us, G
(M
Pa)
q/p = 0
q/p = 0.6
3 = 100 kPaec = 0.48
f =1.42 Hz
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
Mod
ulus
rat
io, G
/G0
q/p = 0
q/p = 0.6
3 = 100 kPaec = 0.48
f = 1.42 Hz
Seed and Idriss (1970) Upper bound Lower bound
0
0.05
0.1
0.15
0.2
0.25
0.3
0.0001 0.001 0.01 0.1 1 10
Shear strain, (%)
Dam
ping
rat
io (
D)
q/p = 0
q/p = 0.6
3 = 100 kPaec = 0.48
f = 1.42 Hz
Seed and Idriss(1970) Upper bound Lower bound
Effect of Initial Anisotropy
Shear modulus Vs shear strain
Modulus ratio Vs shear strain
Damping ratio Vs shear strain
26
Constant p Drained test Undrained test
90 1 00 110
-100
0
1 00
q (
kPa)
8 0 100 12 0
M ean p (k P a )9 8 100 10 2
0
10
20
30
40
50
60
70
80
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
She
ar m
odul
us, G
(M
Pa)
Constant p cyclic triaxial test
Drained cyclic triaxial test
Undrained cyclic triaxial test
3 = 100 kPa; e = 0.48
f = 1.42 Hz
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0001 0.001 0.01 0.1 1 10
Shear strain, (%)
Mod
ulus
ratio
, G/G
0
Undrained cyclic test
Drained cyclic test
Constant p cyclic test
Seed and Idriss (1970) Upper bound
Lower bound
3 = 100 kPa; ec = 0.48
f = 1.42 Hz
0
0.05
0.1
0.15
0.2
0.25
0.3
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
Dam
ping
ratio
Undrained cyclic test
Drained cyclic test
Constant p cyclic test
Seed and Idriss (1970) Upper bound
Lower bound
3 = 100 kPa; ec = 0.48
f = 1.42 Hz
Effect of Stress Path
Shear modulus Vs shear strain
Modulus ratio Vs shear strain
Deviator stress Vs mean p
Damping ratio Vs shear strain
27
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0001 0.001 0.01 0.1 1 10
Shear strain, (%)
Mod
ulus
ratio
, G/G
0
= 50 - 100 kPa; = 0.51 -0.45
= 100 kPa; = 0.48 - 0.54
= 100 kPa; = 0.48; cu = 1.18 - 1.35
= 100 kPa; = 0.48; f = 0.42 - 1.42
= 100 kPa; = 0.48; q/p = 0 - 0.6
Constant p cyclic triaxial test 3 = 100 kPa; ec = 0.48; f = 1.42 Hz
Drained cyclic triaxial test
3 = 100 kPa; ec = 0.48; f = 1.42 Hz
Seed and Idriss (1970) Upper bound Lower bound
Undrained cyclic triaxial test
3
3
3
3
3
ec
ec
ec
ec
ec
Modulus ratio Vs shear strain
28
0
0.05
0.1
0.15
0.2
0.25
0.3
0.0001 0.001 0.01 0.1 1 10Shear strain, (%)
Dam
ping
rat
io, (
D)
= 50 - 100 kPa; = 0.51 - 0.45
= 100 kPa; = 0.48 -0.54
= 100 kPa; = 0.48; Cu = 1.18 -1.35
= 100 kPa; = 0.48; f = 0.42 - 1.42 Hz
= 100 kPa; = 0.48; q/p = 0 - 0.6
Constant p cyclic triaxial test 3 = 100 kPa; ec = 0.48; f = 1.42 Hz
Drained cyclic triaxial test 3 = 100 kPa; ec = 0.48; f = 1.42 Hz
3
3
3
3
ec
ec
ec
Seed and Idriss (1970) Upper bound Lower bound
3
ec
Undrained cyclic triaxial testec
Damping ratio Vs shear strain
29
Conclusions
• DEM simulates the features of liquefaction, pore water
pressure build up, post liquefaction behaviour and dynamic
properties of granular materials. • DEM results are comparable to experimental results
• Captured the effects of initial void ratio, confining pressure and
amplitude of axial strain. • Liquefaction potential and pore water pressure generation exhibit an
unique relationship irrespective of confining pressure, initial void
ratio and amplitude of cyclic strains. • Post liquefaction undrained (constant volume) monotonic strength
depends on the amplitude of axial strain. • Insignificant effect of amplitude of axial strain on stress path has
been observed very similar to experimental investigation.
30