Research Article LIQUEFACTION … II/JERS VOL II...Journal of Engineering Research and Studies...

Journal of Engineering Research and Studies E-ISSN0976-7916

JERS/Vol.II/ Issue II/April-June,2011/131-142

Research Article

LIQUEFACTION CHARACTERISTICS EVALUATION

THROUGH DIFFERENT STRESS-BASED MODELS: A

COMPARATIVE STUDY P. Raychowdhury

1* and P. K. Basudhar

2

Address for Correspondence

1*Department of Civil Engineering, Indian Institute of Technology, Kanpur 208016, India

2Department of Civil Engineering, Indian Institute of Technology, Kanpur 208016, India

E-mail: [email protected]

ABSTRACT The paper presents a comparative study of the predicted response of a liquefiable saturated sand deposit of Nigata city

under different seismic ground motion using three different stress based analytical models due to Finn et al. (1977),

Liou et al. (1977), and Katsikas and Wylie (1982). The results are also compared with simplified methods that are

adopted in the current design practice. It has been found that the models by Finn et al. (1977) and Katsikas and Wylie

(1982) result in close predictions, whereas the predictions by Liou et al. (1977) are significantly different, particularly

for predicting the rate of partial liquefaction for the chosen soil deposit and earthquake motions.

INTRODUCTION

Liquefaction is an earthquake-induced ground

failure phenomenon observed in saturated loose

sand deposits. Liquefaction involves generation

of excess pore pressure, loss of shear strength

and excessive volume contraction with

associated settlement. Although the simple

methods based on SPT and CPT results are most

commonly used in practice and also

recommended in the design provisions (FEMA-

356 and NEHRP, 2000), nonlinear site response

analysis and dynamic time history analyses are

recommended for design of high risk

infrastructures such as dams and nuclear power

plants. If the sand deposit is densely packed,

repeated shearing causes dilation instead of

contraction, helping the excess pore pressure to

be redistributed. The liquefaction potential of a

soil deposit depends on several factors, such as:

void ratio and relative density of soil, depth of

water table, effective confining stress, and

coefficient of lateral earth pressure, seismic and

geologic history of the site and intensity,

duration and other characteristics of ground

shaking. As such, a proper understanding of their

effects for evaluating the liquefaction

characteristics is essential. Seismic response of

saturated sand deposits and liquefaction

phenomenon has gained significant attention

after 1964 Niigata earthquake. Other significant

earthquakes, such as 1964 Alaska, 1989 Loma-

Prieta, 1995 Kobe and 2001 Bhuj earthquake,

have also demonstrated severe damaging

potential of soil liquefaction on buildings,

bridges, railways, ports and other infrastructures.

A qualitative understanding of the mechanism of

liquefaction of saturated sands subjected to

cyclic loading can be explained by critical void

ratio approach (Castro, 1975). Critical void ratio

is the void ratio of any sand, for which there will

be no volume change during drained shear. A

sand deposit having a void ratio above the

critical value tends to contract during shear, and

develops positive pore pressure under undrained

conditions, and has a potential to experience

liquefaction. Conversely, deposits having an

initial void ratio below critical value tend to

dilate during shear, producing a decrease in pore-

water pressure and a corresponding increase in

effective stress under undrained conditions. Till

date significant analytical, experimental,

numerical and post-earthquake field

investigations have been carried out to

understand the mechanism and predict the

potential of liquefaction and related

consequences.

Analytical models are developed to predict

liquefaction characteristics by Martin et al.

(1975), Liou et al. (1977), Finn et al. (1977),

Katsikas and Wylie (1982), Desai (2000),

Liyanapathirana and Poulos (2002), to name a

few. Some of the analytical models adopted

effective stress-based approach (e.g. Liou et al.

(1977), Finn et al. (1977), Katsikas and Wylie



(1982), Liyanapathirana and Poulos (2002)),

while few of them adopted energy-based

approach (e.g. Desai, 2000). Experimental

studies including cyclic triaxial tests, shaking

table tests and centrifuge tests have been

conducted for the last four decades (e.g. Seed

and Lee (1966) Elgamal et al. 1996, Ashford et

al. 2000) to validate the theories and better

understand the mechanism. Simplified methods

to evaluate liquefaction characteristics from SPT

and CPT test results are developed by Seed and

Idriss (1982), Tokimatsu and Seed (1987),

Robertson and Wride (1998), Youd et al. (2001)

and Idriss and Boulanger (2008). Although

simplified total stress-based methods are used in

general practice for the ease of computation to

evaluate the liquefaction potential and associate

settlement, these methods are unable to account

for the progressive stiffness degradation of soil

due to repeated shearing and pore-pressure rise

during an earthquake event. As a result,

nonlinear site response analysis and dynamic

time history analyses are recommended for

design of high risk infrastructures such as dams,

bridges and nuclear power plants (Idriss and

Boulanger, 2008). In this study, three different

analytical models by Finn et al. (1977), Liou et

al. (1977), and Katsikas and Wylie (1982) are

studied to compare the response of saturated

sand deposit under earthquake motions. The

reason behind choosing these models for

comparison study are as follows: (a) these

models are pioneering and fundamental for

theoretical assessment of liquefaction

phenomenon, (b) they can account for nonlinear

stress-strain behavior of soil, (c) progressive rise

in excess pore pressure and associated

degradation of soil strength with time are well

captured in these models, and (d) these models

are widely used in the current design practice.

Moreover, a number of new numerical

liquefaction models have been derived based on

these models. For example, the model developed

by Finn et al. (1977), alternatively known as

DESRA model, has been widely used for

nonlinear site response analysis and liquefaction

characterization. Later on, this model is modified

and implemented in widely used software FLAC

(Itasca, 2005) and has been validated against

other software such as SHAKE (Schnabel et al.,

1972). In this study, for the purpose of

comparison, a liquefiable saturated sand deposit

of Niigata city is considered. A nonlinear shear

stress-strain relationship and a gradual

degradation of the shear modulus are considered

for all three models. Cyclic stress ratio, excess

pore pressure generation, effective stress

reduction and development of shear strain are

considered as four most important parameters

characterizing liquefaction potential. Dynamic

time history analysis is carried out to obtain the

time history of the above-mentioned liquefaction

parameters for earthquake motions from the

1964 Niigata and 1995 Kobe earthquakes.

Finally, the responses from these models are

compared with recent simplified methods

summarized in Youd et al. (2001).

Adopted Numerical Models

For the sake of completeness and proper

appreciation a brief description of the considered

models is provided in this section.

Model#1: Finn, Lee and Martin (1977)

This model includes formulation of constitutive

relations incorporating nonlinear methods to

predict the important features of the dynamic

response of saturated sand deposits that generally

occur when the pore-water pressure rises in the

sand deposit during earthquake shaking. The

model takes into account the important factors

that affect the dynamic response of a sand layer,

such as transient pore pressure rise, soil

damping, hardening, variation of shear modulus

with shear strain and changes in effective mean

normal stress.

The stress-strain behavior of sand in this model

is formulated using hyperbolic relationship

adopted by Hardin and Drnebvich (1972) as

shown in Equations 1 through 3.

γτ

γτ

0

0

0

1m

m

m

G

G

+

= (1)



(2)

(3)

where, Gm0 and τm0 are initial maximum shear

modulus and maximum shear stress,

respectively; K0 is coefficient of earth pressure at

rest, e is the void ratio, σv' is vertical effective

stress in pound/sq. ft.; and ε' is the effective

angle of shearing resistance. The maximum shear

modulus and shear stress (Gmn and τmn) at the nth

loading cycle are determined from the initial

peak values using the following expressions:

(4)

(5)

where, σv' is the effective vertical stress at the

beginning of nth loading cycle, σv0

' is the initial

effective vertical stress, ε vd is the accumulated

volumetric strain; and H1, H2, H3, and H4 are

constants, that were determined using

calibrations against experiments carried out in

simple shear apparatus. The volumetric strain,

ε vd is again related to the rate of change in pore

pressure (generation or dissipation) in the

following manner:

(6)

where, u is the pore pressure and Er is the one-

dimensional rebound modulus of sand at an

effective stress of σv'. The steps are repeated for

each cycle of an earthquake event using

numerical techniques, and responses including

pore pressure generation, shear stress, and shear

strain are obtained for any layer of a sand

deposit. A flowchart indicating the procedure

adopted by the model is provided in Figure 1 (a).

Discretization of soil

medium

Calculation of initial G0, τm, shear wave

velocity Vs, initial pressure wave velocity, VP1

and VP2, time step for shear wave model and

time step for pressure wave model

Calculation of shear

strain and shear stress

from shear wave sub-

model

Earthquake

input motion

Calculation t

C c

∂

∂ from

t

G s

∂

∂

Calculation of S , , , σww

from pressure wave sub-

model

Calculation of S , , , σww from

pressure wave sub-model

Calculation of new G and Vs

from effective stress

Figure 1(a): Flow charts showing steps

adopted in Model #1

Model#2: Liou, Streeter, and Richart (1977)

The model by Liou et al. (1977) considered the

soil deposit as one dimensional, two-phase

medium composed of water and soil skeleton.

The model is constituted by coupling two sub-

models, namely, shear wave sub-model and

pressure wave sub-model. The component of

ground motion parallel to ground surface is

treated as shear wave sub-model, whereas the

component perpendicular to the ground surface

is treated as pressure wave sub-model. The rate

of change of in the constrained compressibility is

computed from modulus reduction. The shearing

strain causes the increase of constrained

compressibility, and the soil tends to settle. In

undrained condition, this leads to rise of pore

water pressure and reduction in effective stress.

The dependence of the constrained modulus of

the skeleton upon the dynamic shear modulus

and the dependence of the shearing properties on

the transient effective stress provide the coupling

between the two parts of the model. A brief



discussion on each sub-model and their coupling

is provided herein.

Shear Wave Submodel

The shear wave sub-model is used to calculate

shearing stress, shearing strain, and modulus

reduction caused by the motion bedrock. The

propagation of the shear waves in one-

dimensional unsaturated soil deposits is modeled

by Ramberg-Osgood relationship (Ramberg and

Osgood, 1943) (shown in Equations 7 and 8).

For initial loading:

(7)

For reloading and unloading:

(8)

Where, τi, and γi represent the coordinates of the

strain reversal point on the τ-γ plane. α, R, and

C1 are constants describing a given soil. Gm0 and

τm0 are determined after Hardin and Drnebvich

(1972) as shown in Equations 1 through 3.

The dynamic equation of motion for the shear

wave propagating through the solid matrix of the

soil column in x-direction can be written as:

(9)

And

(10)

where, ρ = mass density of saturated soil, g =

acceleration of gravity, θ = surface slope of the

constant thickness of soil layer, ux = horizontal

particle displacement in x-direction, U = velocity

of the soil skeleton in x-direction.

Pressure Wave Submodel

By assuming the solid grains to be

incompressible and by neglecting small terms,

the relationship can be obtained.

(11)

where, Cw= compressibility of water, P* =

excess pore pressure, n = porosity of soil, w and

w* are displacements defined in such a way, that

volume of solid and volume of water that pass

through a unit area fixed in space are, (1-n)w and

nw*. The quantity –nP

* represents the excess

tensile force acting on the portion of a unit area

of soil occupied by water, is denoted by S*.

(12)

If S0 is initial hydrostatic value of tensile force

and S is the current value of the same quantity,

then,

(13)

Stress-strain relation for the soil skeleton is:

(14)

In the theory of linear poro-elasticity, Cc is

related to G0 and the compressibility of the

skeleton, Cb, by,

(15)

Where, Gs is the secant shear modulus of the soil

skeleton. Finally, propagation of the plane shear

waves in saturated deposits is represented as:

(16)

Coupling Between Two Sub-models

The numerical model for liquefaction is

constituted by coupled shear wave and pressure

wave motions. In the model, the deposit below

water table is divided into a number of equal

distance intervals and both sub-models are

applied to them. Since in saturated soils

volumetric disturbances travel at a speed much

greater than the shear wave speed, N time steps

are needed in the pressure wave sub-model for

every time step in shear wave sub-model.



(17)

The shear wave sub-model is first used to

calculate shearing stress, shearing strain, and

reductions in Gs caused by the motion of the

bedrock. The rate of change of in the constrained

compressibility, ∂Cc/∂t is then computed from

∂Gs/∂t. The pressure wave motions generated by

changes in Cc are then calculated from the

pressure wave sub-model. The shearing strain

causes the increase of Cc, and the soil tends to

settle. In undrained condition, this leads to rise of

pore water pressure and reduction in effective

stress. The steps are summarized in Figure 1 (b).

Calculation of initial G0, τm, shear

wave velocity Vs and time step for

shear wave sub-model

Calculation of shear

strain and shear stress

from shear wave sub-

model

Calculation soil densification

from shear wave sub-model

Calculation of effective stress

from pore water pressure and

total stress

Calculation pore water pressure

and seepage velocity from pressure

wave sub-model

Calculation of new G and Vs

from effective stress

Discretization of soil

medium

Earthquake

input motion

Figure 1(b): Flow charts showing steps

adopted in Model #2

Model#3: Katsikas, and Wylie (1982)

This model is also an effective stress-based

numerical model that provides the interaction

between shearing deformation and transient

pore-water pressure development. One-

dimensional propagation of shear waves through

the solid matrix of the soil and pressure waves

through the pore water is the principal part of the

model. The volumetric soil deformation provides

the means of coupling the shear and pressure

waves during motion.

Specific features of this one-dimensional model

are the preservation of the inelastic soil character

during shearing, coupling between shear wave

propagation and pore-water pressure

development and seepage, and the association of

excess pore-water pressure development with the

inelastic volumetric deformation of the solid

matrix and reasonable validation of the model

against shaking table tests. The modeling

approach is discussed briefly here.

Under cyclic straining the structure change of the

soil is given by,

(18)

where, ∆εv = net solid matrix deformation, ∆εvs

= volume reduction (densification) due to

particle rearrangement, ∆εvr = volume

expansion(rebound) due to relaxation of soil

matrix. Based on a number of experimental

studies, elastic rebound of the soil can be

described as:

(19)

where, εvr is corresponding soil rebound, σ0 is

mean effective stress, and A and σ are constants.

From experimental results an empirical

expression is developed by Katsikas (1979) for

the soil rebound:

(20)

σ0 is mean effective stress in pounds/sq. ft. Then

the soil densification increment, ∆εvs,

corresponding to a time increment ∆t, during

straining may be given as:

(21)

where Nc= Number of cycles from the beginning

of straining, γ(%)= instantaneous shear strain at

the end of a time increment ∆t, ∆γ(%) = change

in shear strain over time ∆t, and A1, A3 =

parameters that depend on soil properties. The

following expressions were derived by the first



writer, Christos A. Katsikas, based on the

experimental results:

(22)

(23)

where,Dr= relative density of the soil and D50=

grain diameter in mm corresponding to 50%

finer. The in elastic volumetric deformation of

the solid matrix is associated with the generation

of excess pore water pressure through the

coupling between the shear wave propagation

through soil skeleton and the pressure wave

propagation through pore water. The numerical

analysis is done by method of characteristics.

The steps are shown through a flowchart in

Figure 1(c).

Input Earthquake Motions Considered in the

Study

In this study, two ground motion time histories

from 1964 Niigata Earthquake and 1995 Kobe

earthquake have been used. The detail

information of the ground motions are given in

Table 1. The acceleration, velocity and

displacement time histories along with Fourier

amplitude spectra are shown in Figure 4 and 5.

These acceleration time histories are applied at

the bottom of the deposit as input excitation.

Calculation of initial mass,

stiffness and damping matrices

Discretization soil medium in

form of a MDOF shear building

Calculation of initial G0, τm and

then soil spring stiffness.

Calculation acceleration, velocity,

displacement for each DOF and then

shear strain and shear stress for each

layer: shear wave sub-model

Generation of pore pressure

from volumetric compaction

Calculation of effective

stress from pore water

pressure and total stress

Dissipation of pore pressure

and thus calculation of

resultant pore pressure

Calculation of new G and

therefore stiffness matrix from

effective stress

Earthquake

input motion

Figure 1(c): Flow charts showing steps

adopted in Model #3

Table 1 Details of ground motion time history used

Earthquake Magnitude Station Component PGA (g) PGV cm/sec) PGD (cm)

1964 NIIGATA 7.5 701 B1F SMAC-A EW 0.21 70.26 31.06

1995 Kobe

6.9 JMA EW 0.82 81.26 17.68

0 10 20 30 40 50 60 70 80 90 100 110 120-0.2

-0.1

0.0

0.1

0.2

0.3

Acceleration (g)

0 10 20 30 40 50 60 70 80 90 100 110 120-40

0

40

80

Velocity (cm/s)

(a)

0 10 20 30 40 50 60 70 80 90 100 110 120

Time (sec)

-40

-20

0

20

40

Displacement (cm)

(b)

(c)

0.01 0.1 1 10 100

Frequency (Hz)

0

5000

10000

15000

20000

25000

Fourier Amplitude (cm/sec) (d)

Figure 4: (a) Acceleration time history, (b) velocity time history, (c) displacement time history and

(d) Fourier amplitude spectrum for E-W component of 16th June 1964 Niigata Earthquake



0 10 20 30 40 50-1.2

-0.8

-0.4

0.0

0.4

0.8Acceleration (g)

0 10 20 30 40 50

-80

-40

0

40

80

120

Velocity (cm/s)

(a)

0 10 20 30 40 50

Time (sec)

-20

-10

0

10

20

Displacement (cm)

(b)

(c)

0.01 0.1 1 10 100

Frequency (Hz)

0

10000

20000

30000

Fourier Amplitude (cm/sec) (d)

Figure 5: (a) Acceleration time history, (b) velocity time history (c) displacement time history, and (d)

Fourier amplitude spectrum for E-W component of 16th January 1995 Kobe Earthquake, station

JMA

Soil Profile Considered in the Study

For this study, a liquefiable soil profile, zone B

of Niigata city (Seed and Idriss, 1982) has been

considered. The subsoil at Niigata city consists

of mainly thick alluvial sand deposits, which

have been overlaid along the coast by deposits of

dune sand. The sand deposits are relatively loose

at ground surface and become denser with

increasing depth. The depth of alluvial sand

exceeds 100 meters. Niigata sand is fine sand

consisting of grains that are subangular to

subrounded. The specific gravity is Gs =2.67, the

maximum void ratio is emax = 0.99, the minimum

void ratio is emin = 0.55 the mean diameters are

D50 = 0.23mm and D10 = 0.13mm, and

coefficient of uniformity Uc = 2.34. The grain

size distribution curve reported by Ishihara and

Koga (1981) is an average curve of the Niigata

sand. The water table was approximately at 0.9

m below the ground surface (Seed and Idriss,

1982). The unit weight of the sand above water

table and the submerged unit weight below water

table were estimated as 17.5 kPa, and 8.0 kPa,

respectively. Poisson’s ratio for Niigata Zone B

sand is approximated as 0.4 and the coefficient

of horizontal earth pressure is estimated as 0.46

(from Seed and Idriss, 1982). A nonlinear

relationship is adopted for shear stress-strain

relationship after Ramberg and Osgood (1943)

(Equations 6-7). The values of Gm0 and τm0 at

different depths in the soil deposit are given in a

tabular form (Table 2). Figure 2 (a) shows the

standard penetration blow counts for the chosen

site (Seed and Idriss, 1987). Before performing

the dynamic analyses, simplified method as

summarized in Youd et al. (2001) is used to

calculate the liquefaction potential of the deposit.

The methods summarized in Youd et al. (2001)

are widely used by the design practice and are

recommended by most of the current design

codes such as Federal Emergency Management

Agency (FEMA, 1996) and National Earthquake

Hazard Reduction Program (NEHRP, 2000).

According to Youd et al. (2001), a deposit is

considered to be potentially liquefiable when the

cyclic stress ratio (CSR) induced by an

earthquake is greater that the cyclic resistance

ratio (CRR) of that deposit. Equation (3) to (5) is

used to derive CSR and CRR for a deposit and a

potential earthquake in that region.

Table 2 Initial G0 and Am0 estimated for zone B of Niigata sand

Layer Number 1 2 3 4 5 6 7

Gm0 (MPa) 22 28.3 33.5 38 42.1 45.7 49.1

τm0 (Pa) 5.5 9.1 1.5 21 28.3 36.1 43.2



0 20 40 60

Blows/ft

80

60

40

20

0

Depth (ft)

20

10

0

Depth (m)

0 0.5 1 1.5 2 2.5

CRR/CSR

80

60

40

20

0

Depth (ft)

20

10

0

Depth (m)

Niigata (M=7.5, pga=0.21g)

Kobe (M=6.9, pga=0.82g)

Liq Non-liq

(a) (b)

Figure 2: (a) Standard penetration resistance of zone B, Niigata City and (b) Liquefaction potential

calculated after Youd et al. (2001)

where, τav = average cyclic stress, 'vo = total

vertical stress before shaking, 'vo = effective

vertical stress before shaking, amax = peak ground

acceleration, rd = reduction factor due to depth,

(N1)60 = corrected blow count, CRR7.5 = cyclic

resistance ratio for an earthquake with magnitude

7.5, MSF = magnitude scaling factor. In this

study, for the Niigata soil profile zone B, CSR

and CRR are calculated for both Niigata and

Kobe motion. Figure 2(b) shows the profile of

the ratio of CRR to CSR, in which the

liquefaction zone (when CRR<CSR) and non-

liquefaction zone (when CRR>CSR) are

identified. It can be observed that for the Niigata

motion, the site is liquefiable up to a depth of 35

ft (11.5m), whereas for the Kobe motion, the

entire deposit is potentially liquefiable according

to the methods after Youd et al. (2001).

Results and Discussion

Considering the representative soil profile of

Niigata city zone, B and using the earthquake

excitation mentioned above, the comparison of

responses from three models are studied. Figures

3 through 6 show the results of the time history

analyses in terms of cyclic stress ratio, excess

pore pressure, normalized effective stress, and

shear strain, respectively. The above mentioned

response parameters are most important to

evaluate the liquefaction potential of a deposit.

The results shown here correspond to the

response of soil layer at a depth of 10 m. It is

important to note that based on simplified

analysis after Youd et al. (2001), for both the

earthquake motions the soil is liquefiable at

depth 10m. Figures 4a and 4b show the cyclic

stress ratio time history for Niigata EW motion

and Kobe JMA motion, respectively, calculated

using all the three models considered herein.

Cyclic resistance ratio calculated after Youd et

al. (2001) is also noted here. It can be observed

from Figure 3a that prediction of model 1 and

model 3 indicates that the deposit liquefies at

about 8.5 sec for Niigata motion. The

liquefaction triggering is defined as the condition

when cyclic stress ratio (i.e. the demand) exceeds

the cyclic resistance ratio (i.e. the capacity).

Figure 4b, similarly shows that model 1 and 3

indicates liquefaction occurrence at 7.2 sec for

the Kobe motion. Model 2 prediction does not

indicate any liquefaction in both the cases. It

should be noted that ~7-10sec in Niigata motion

and 7-12 sec in Kobe motion is approximately

the duration of the strong motions.



0 4 8 12

Time (sec)

-0.2

0.0

0.2

0.4

0.6

0.8 Model #1

Model #2

Model #3

0 2 4 6 8 10

Time (sec)

-0.2

-0.1

0.0

0.1

0.2

0.3

Cyclic Stress Ratio

CRR (Youd et al., 2001) (a) (b)

CRR (Youd et al., 2001)

Figure 3: Cyclic stress ratio: (a) Niigata motion and (b) Kobe motion

Another important feature of the liquefaction is

the generation of excess pore water pressure and

consequent reduction in effective stress. Figure

4a and 4b show the time histories for excess pore

water pressure normalized by total static vertical

stress predicted through the different models as

adopted. It is observed that for Niigata motion,

all three models predict liquefaction at about 10

sec, considering that liquefaction is defined when

excess pore pressure is 100% of the total stress.

However, it can be seen that the rise of excess

pore pressure with time varies significantly from

model to model. Especially model 2 indicates a

very steep curve compared to other two models.

This variation leads to significant difference in

prediction of partial liquefaction characteristics.

For example, at time = 6sec, excess pore

pressure ratio is 22%, 90% and 30% using model

1, 2 and 3, respectively. For Kobe motion,

similar responses are observed. Note that

simplified methods summarized by Youd et al.

(2001) based on SPT and CPT data are unable to

predict the pore-water pressure built up. The

effective stress responses also show the similar

result (Figure 5a and 5b).

Shear strain induced by liquefaction is one of the

most critical consequences of liquefaction.

Liquefaction is often defined as a situation when

shear strain is increased to ±5% (Seed and Idriss,

1987). Figure 6a and 6b show the comparative

predictions of liquefaction induced shear strain

for Niigata and Kobe motions, respectively.

0 4 8 12

Time (sec)

0

20

40

60

80

100 Model #1

Model #2

Model #3

0 4 8 12

Time (sec)

0

20

40

60

80

100

Excess Pore Pressure (%)

(a) (b)

Figure 4: Excess pore pressure ratio: (a) Niigata motion and (b) Kobe motion



0 4 8 12

Time (sec)

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10

Time (sec)

0.0

0.2

0.4

0.6

0.8

1.0

Normalized Effective Stress

Model #1

Model #2

Model #3

(a) (b)

Figure 5: Effective stress ratio: (a) Niigata motion and (b) Kobe motion

It can be seen that model 2 indicates liquefaction

occurrence (shear strain = 5%) at about 9 sec for

Niigata motion, whereas other two models

indicates shear strain well below 5% for this

motion. On the other hand, for Kobe motion,

according to model 2, liquefaction occurs (shear

strain = -5%) at 9.5 sec, whereas model 3

indicates liquefaction occurrence at 11 sec.

Model 1 shows that shear strain does not reach

5% for this case. Note that the simplified method

suggested by Tokimatsu and Seed (1987) which

is also adopted in the design practice such as

FEMA-356 (FEMA, 2000) and NEHRP

(NEHRP, 2000), indicates, indicate that the shear

strain of this layer does not reach 5% shear strain

under these earthquake motions. The overall

observation from the comparative study indicates

that model 1 and 3 predictions are similar and are

close to that by simplified methods summarized

in Youd et al. (2001), whereas model 2

prediction is significantly different from that by

the other two models. Since model 1 (Finn et al,

1977, alternatively known as DESRA model) is

widely accepted in the earthquake engineering

community and is well-validated against several

case studies and other dynamic response

evaluation software such as SHAKE (Schnabel

et al., 1972), it may be assumed that this model’s

prediction is somewhat accurate. Based on the

above assumption, it may be concluded that

model 2 is under-predicting the cyclic stress

ratio, but over-predicting the rate of excess pore

pressure generation and the rate of effective

stress reduction significantly. In addition, model

2 is also over-predicting the induced shear strain

in the soil deposit. This over-prediction is

significantly high after 7 sec for Niigata motion

and 9.5 sec for the Kobe motion.

0 4 8 12

Time (sec)

-8

-4

0

4

8

0 2 4 6 8 10

Time (sec)

-2

0

2

4

6

Shear Strain (%)

Model #1

Model #2

Model #3

5% shear strain

Figure 6: Shear strain: (a) Niigata motion and (b) Kobe motion



CONCLUSIONS

In this study, a comparative analysis involving

three effective stress-based analytical models,

Finn et al. (1977), Liou et al. (1977) and

Katsikas et al. (1982) is carried out for predicting

the response of a liquefiable saturated sand

deposit of Niigata city under different earthquake

ground motions. All three models assume

nonlinear shear stress-strain relationship, and a

gradual degradation of the shear modulus. The

strength degradation is coupled with pressure

wave propagation through the pore water and

consequent volume change. Comparison results

are shown in terms of four most important

parameters characterizing liquefaction potential:

cyclic stress ratio, excess pore pressure

generation, effective stress reduction and

development of shear strain. Dynamic time

history analysis is carried out to obtain the time

history of the above-mentioned parameters for

earthquake motions from the 1964 Niigata and

1995 Kobe earthquakes. The results are also

compared with simplified methods that are

adopted in current design provisions such as

FEMA (1996) and NEHRP (2000). It has been

found that the prediction by the models of Finn

et al. (1977) and Katsikas et al. (1982) matches

well, whereas the prediction by Liou et al. (1977)

is significantly different for the chosen soil

deposit and ground motions. This difference of

response involving Liou’s model is particularly

significant for the excess pore pressure

generation and consequent strength loss as

indicated by higher rate of partial liquefaction

(Figure 4a-b and 5a-b). This may be due to the

difference in considering the excess pore

pressure generation used in Liou’s model. In

general, however, the time indicating full

liquefaction (pore pressure =100%) is close for

all three models (~10-12 sec).

REFERENCES

• Ashford S. A., Rollins, K. M., and Lane, D.

(2004). “Blast-Induced Liquefaction for Full

Scale Foundation Testing,” Journal of

Geotechnical and Geoenvironmental

Engineering, ASCE, 130(8), 798-806.

• Castro, G. (1975). “Liquefaction and Cyclic

Mobility of Saturated Sand”, Journal of

Geotechnical Engineering Division, ASCE,

101 (6), 551-569.

• Desai, C. (2000). “Evaluation of liquefaction

using disturbed state and energy

Approaches”. Journal of Geotechnical

Engineering Division, ASCE, 126(7), 618–

31.

• Elgamal A. W, Zeghal M, Parra E. (1996)

“Liquefaction of reclaimed island in Kobe,

Japan.” Journal of Geotechnical

Engineering Division, ASCE, 122(1), 39–49.

• FEMA 356, Prestandard and Commentary

for the Seismic Rehabilitation of Buildings,

American Society of Engineers, Virginia.,

2000.

• Finn, W. D. L., Lee, K. W., Martin, G. R.

(1977) “An effective stress model for

liquefaction”. Journal of Geotechnical

Engineering Division, ASCE, 103(GT6),

517–33.

• Itasca (2005). “Fast Lagrangian Analysis of

Continua”. Itasca. FLAC manual, 2005.

• Idriss, I. M. and Boulanger, R. W. (2008).

“Soil Liquefaction during Earthquakes”,

Engineering Monograph, Earthquake

Engineering and Research Institute (EERI),

Oakland, California.

• Ishihara, K. and Koga, Y. (1981). "Case

Studies of Liquefaction in the 1964 Niigata

Earthquake," Soils and Foundations,

Japanese Society of Soil Mechanics and

Foundation Engineering, 21(3), Sept 1981,

35-52.

• Katsikas, C. A. and Wylie, E. B. (1982).

“Sand Liquefaction: Inelastic Effective

Stress Model”. Journal of the Geotechnical

Engineering Division, ASCE, 108(1), 63-81.

• Liou, C. P., Richart, F. E. and Streeter, V. L.

(1977). “Numerical Model for

Liquefaction”. Journal of the Geotechnical

Engineering Division, ASCE, 103 (6), 589-

606.

• Liyanapathirana, D. S. and Poulos, H. G.

(2002). “A numerical model for dynamic

soil liquefaction analysis”. Soil Dynamics

and Earthquake Engineering, 22 (2002),

1007–1015.

• Martin, G. R., Finn, W. D. L. and Seed, H.

B. (1975). “Fundamentals of Liquefaction

under Cyclic Loading”. Journal of the


101 (5), 423–438.

• NEHRP, Recommended Provisions for

Seismic Regulations for New Buildings,

Building Seismic Safety Council,

Washington, D.C., 2000.

• Ramberg, W. and Osgood, W. T. (1943).

“Description of Stress-strain Curves by

Three Parameters”, Technical Notes 902,

NASA, Washington D. C.



• Robertson, P. K., and Wride, C. E. (1998).

‘‘Evaluating cyclic liquefaction potential

using the cone penetration test.’’ Canadian

Geotechnical Journal, 35(3), 442–459.

• Schnabel, P. B., Lysmer, J. and Seed, H. B.

(1972). “SHAKE: A Computer Program for

Earthquake Response Analysis of

Horizontally Layered Sites’, Report No.

EERC 72-12, Earthquake Engineering

Research Center, University of California,

Berkeley.

• Seed, H. B. and Idriss, I. M. (1982). “Soil

Liquefaction during Earthquakes”,

Engineering Monograph, Earthquake

Engineering and Research Institute (EERI),

Oakland, California.

• Seed, H. B. and Lee, K. L. (1966).

“Liquefaction of Saturated Sands During

Cyclic Loading”, Journal of Geotechnical

Engineering Division, ASCE, 92 (SM6),

105-134.

• Tokimatsu, K. and Seed, H. B. (1987).

“Evaluation of Settlement in Sand due to

Earthquake Shaking”. Journal of the


113 (8), 861-878.

• Youd, T. L. et al. (2001). “Liquefaction

resistance of soils: Summary report from the

1996 NCEER and 1998 NCEER/NSF

Workshops on Evaluation of Liquefaction

Resistance of Soils.” Journal of

Geotechnical and Geoenvironmental

Engineering, ASCE, 127(10), 817–833.

Research Article LIQUEFACTION … II/JERS VOL II...Journal of Engineering Research and Studies...

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