ACCURACY OF PREDICTION WITH EFFECTIVE STRESS
ANALYSIS FOR LIQUEFACTION-INDUCED EARTH PRESSURE
ON A PILE GROUP
Ryosuke UZUOKA1 , Misko CUBRINOVSKI2, Feng ZHANG3, Atsushi YASHIMA4
and Fusao OKA5
ABSTRACT
Numerous buildings with pile foundation adjacent to quay walls were seriously damaged during
the 1995 Kobe earthquake. The mechanism of the earth pressure on a pile group has not yet
been clarified, and the precise prediction of the earth pressure is also very difficult. In this
paper, we predicted the earth pressures on a pile group due to liquefaction-induced ground flow
by a 3-dimensional soil-water coupled dynamic analysis. We simulated the series of large
shaking table tests in order to validate the analysis. As a result, the predicted earth pressures on
the piles and displacement of footing showed a quantitative agreement with the measured ones.
INTRODUCTION
Numerous structures with pile foundation in reclaimed ground were seriously damaged during
the 1995 Hyogo-ken Nambu earthquake (Matsui and Oda, 1996; Tokimatsu et al., 1996).
Among the damaged structures, many of them tilted and/or settled, in spite of the fact that no
significant damage to the superstructure was observed. In particular, the structures adjacent to
quay walls were severely damaged. Field investigations and numerical analyses for some
damaged pile foundations in reclaimed ground were conducted to clarify the mechanism of the
damage process (Uzuoka et al, 2002). The failures of piles were observed mainly within
reclaimed soft layers. These facts suggested that a large lateral ground deformation due to
liquefaction of reclaimed soils caused the serious damage of the pile foundations.
A large lateral ground deformation over one meter, so called liquefaction-induced flow, was
often observed behind quay wall or at initially inclined ground (Hamada and O’Rourke, 1992).
The ground flow behind quay walls can occur only when the quay walls move toward sea and
the driving force due to gravity is released. Hence, it is important to consider not only the
ground behavior but the quay wall behavior, since the movement of the quay walls affects the
ground behavior behind quay walls. If some structures exist adjacent to quay walls, the problem
becomes more complicated. The interaction among quay walls, structures and ground must be
considered. Thus, we must treat the system of ground, quay walls and structures.
1
Associate Professor, Tohoku University, Sendai, Japan
Senior Lecturer, University of Canterbury, Christchurch, New Zealand
3
Professor, Nagoya Institute of Technology, Nagoya, Japan
4
Professor, Gifu University, Gifu, Japan
5
Professor, Kyoto University, Kyoto, Japan
2
Liquefaction analysis has been developed since 1980’s by many researchers. The field
equations of current liquefaction analyses are based on Biot’s porous media theory (1962).
Although several formulations, which use different unknown variables, for example, u-U, u-w
and u-p formulations, have been used, the affect of the difference is not significant in the
earthquake problem (Zienkiewicz and Shiomi, 1984). The performance of constitutive models,
on the other hand, affects analytical results significantly, because the applicability of current
constitutive models has not yet been confirmed sufficiently (Arulanandan and Scott, 1994). We
need a further development of constitutive models in liquefaction analysis through simulations
of laboratory tests, model experiments and case histories.
In this study, we simulated the series of the large shaking table tests in order to clarify the
accuracy of the analysis. The shaking table tests measured the earth pressures on a pile group
adjacent to a quay wall during shaking and after shaking. The shaking direction and the weight
of the superstructure were examined in the shaking table tests. We tried to predict the earth
pressures on a pile group due to liquefaction-induced ground flow by two different 3dimensional liquefaction analysis codes which are called with “LIQCA” and “DIANA-J” in this
paper. The soil-water coupled formulations in both codes are based on porous media theory and
the constitutive equations for sand are based on elasto-plastic theory. We mainly focus on the
result with “LIQCA” in this paper. The some results with “DIANA-J” were presented by
Cubrinovski et al. (2005). This simulation is so called Class B prediction in which was
performed during the experiments. We used only the material properties by laboratory tests, the
model configuration before the experiments and the measured input motion. We discuss the
accuracy of the liquefaction analysis and 3-dimensional effects of the earth pressures on a pile
group in the liquefied ground through the simulations.
SHAKING TABLE TESTS
The dynamic shaking table tests were performed by Tanimoto et al. (2003). Table 1 shows the
experimental cases of shaking table tests. The shaking direction and the weight of the
superstructure were examined in the shaking table tests. Two different effective stress analysis
codes called by “LIQCA” and “DIANA-J” were used for each experimental case as shown in
Table 1. Figure 1 shows the plan view and cross section of test models and the locations of
transducers in the case of “16-1”. The model ground in a rigid soil container consisted of two
materials, Toyoura sand and Iwaki sand. Toyoura sand was a uniform fine sand, a mean
diameter D50 of 0.16 mm and a uniformity coefficient Uc of 1.2. Iwaki sand was a uniform
Table 1 Experimental cases of shaking table tests
Case Number Parts of
Depth of Mass of
Shaking
Analysis
of piles sheet pile liquefiable footing
direction
layer. Dr
14-1
3×3
70cm, 50%
Transverse
LIQCA
14-2
33cm×3 90cm, 35% 21.6kg Longitudinal DIANA-J
14-3
21.6kg Transverse
LIQCA
15-1
89cm×1
Transverse
LIQCA
5cm×2
15-2
21.6kg Transverse
LIQCA
+Vertical
15-3
170kg Longitudinal DIANA-J
16-1
170kg Transverse
LIQCA
16-2
320kg Longitudinal LIQCA
DIANA-J
16-3
2×2
140kg Longitudinal DIANA-J
Figure 1 Configuration of shaking table test in the case of “16-1” (Tanimoto et al., 2003)
coarse sand, a mean diameter D50 of 1.7 mm. Before preparation of the model ground, the
models of pile foundation and quay wall were installed in the container. Two horizontal struts
supported the quay wall during the preparation of the ground. The pile foundation consisted of
9 stainless piles with a diameter of 50.8 mm and a thickness of 1.5 mm. The quay wall was
made of a steel plate with a thickness of 6 mm. The cases of “14-1” and “15-1” have no footing,
hence the top of the piles are free. The other cases have the footing with various weights as
shown in Table 1. The dense sandy layer (Toyoura sand, Dr=90%) behind the sheet pile was
made by compaction. The loose sandy layer (Toyoura sand, Dr=35%) was prepared by pouring
Toyoura sand in the water. The dry layer above the water table was made of Iwaki sand in order
to keep its dry condition. A horizontal shaking was conducted along the shorter or longer side
of the container as shown in Table 1. Sinusoidal waves with a frequency of 5 Hz, 20 cycles and
the maximum acceleration of about 5 m/s2 were applied after the struts were removed.
NUMERICAL METHOD
The numerical method of “LIQCA” is briefly described in this section. A soil-water coupled
problem was formulated based on a u-p formulation (Oka et al., 1994). The finite element
method (FEM) was used for the spatial discretization of the equilibrium equation, while the
finite difference method (FDM) was used for the spatial discretization of the pore water
pressure in the continuity equation. Oka et al. (1994) verified the accuracy of the proposed
numerical method through a comparison of numerical results and analytical solutions for
transient response of saturated porous solids. The governing equations are formulated by the
following assumptions; 1) the infinitesimal strain, 2) the smooth distribution of porosity in the
soil, 3) the small relative acceleration of the fluid phase to that of the solid phase compared
with the acceleration of the solid phase, 4) incompressible grain particles in the soil. The
equilibrium equation for the mixture is derived as follows:
(1)
uS  divσ  b  0
S
where  is the overall density, u is the acceleration vector of the solid, σ is the total stress
tensor and b is the body force vector. The continuity equation is derived as follows:
k

n
(2)
div 
 grad p   F b   F u S    vS  F p  0
K
 w

where k is the coefficient of permeability,  w is the unit weight of the fluid,  F is the density
of the fluid,  vS is the volumetric strain rate of the solid, p is the pore water pressure, n is
porosity and K F is the bulk modulus of the fluid. Newmark implicit method was used for time
integration.


The constitutive equation used for sand is a cyclic elasto-plastic model (Oka et al., 1999). The
constitutive equation is formulated by the following assumptions; 1) the infinitesimal strain, 2)
the elasto-plastic theory, 3) the non-associated flow rule, 4) the concept of the overconsolidated
boundary surface, 5) the non-linear kinematic hardening rule. Oka et al. (1999) discussed the
applicability of the constitutive model for cyclic undrained behavior of sand through a
comparison of numerical results and hollow cylindrical torsional shear tests. The model
succeeded in reproducing the experimental results well under various stress conditions, such as
isotropic and anisotropic consolidated conditions, with and without the initial shear stress
conditions, principal stress axis rotation, etc.
PERFORMANCE OF THE CONSTITUTIVE MODEL
Strain-controlled Shear Tests
Most of past researches discussed the cyclic undrained behavior of the constitutive model
through a comparison between the model and stress-controlled undrained shear tests with a
constant stress amplitudes. However, in the case of very loose sand such as Toyoura sand
(Dr=35%), the stress-controlled tests is not suitable for the understanding of deformation
characteristics, because the strain will easily exceed the measure range before the stress attains
the specific amplitude. In this study, we performed strain-controlled stage tests (Kazama et al.,
2000) in order to discuss the applicability of the constitutive model in a large strain range.
Table 2 Material parameters for the constitutive model
Name of soil profile
Density
Coefficient of permeability
Initial void ratio
Compression index
Swelling index
Quasi-overconsolidation ratio
Failure stress ratio
Phase transformation stress ratio
Initial shear modulus ratio
Dilatancy parameter
Hardening parameter
Reference strain parameter
 (t/m3)
k (cm/s)
e0


OCR*
M*f
M*m
G0/'m
D*0
n
B*0
B*1
P*r
E*r
Toyoura sand
Dr=30%
1.88
0.01
0.866
0.003
0.0006
1.0
1.158
0.909
853
1.0
2.0
2000
30
0.003
0.005
Toyoura sand
Dr=90%
2.00
0.01
0.642
0.0036
0.0002
1.5
1.406
0.909
3243
0.5
5.0
15000
100
0.01
0.03
Iwaki sand
1.36
1.1
1.019
0.0045
0.0009
1.0
1.229
1.087
753
0.2
2.0
1500
100
0.02
0.02
The specimen of the hollow cylindrical torsional shear test was 100 mm in outer diameter, 60
mm in inner diameter, and 100 mm in height. We used Toyoura sand as a testing material,
which is the same material as that used in the shaking table tests. Specimens were prepared by
the air pluviated procedure and the relative density at the end of the consolidation ranged
between 27% and 32%. The sample preparation method in the torsional shear tests was
different from that in the shaking table test. The effect of the different preparation method
assumed to be small on the liquefaction strength because the relative density was very small
(Tatsuoka et al., 1986). The test samples were isotropically consolidated, the initial effective
stress was 10 kPa with a backpressure of 100 kPa, and the B value was maintained at more than
0.97. The cyclic shear strain was applied under undrained condition in uniform triangular
cycles with a constant strain rate. The shear strain amplitude increased from 0.1% (5 cycles),
20% (2 cycles) to 30% (2 cycles) in 3 stages. The responses of shear stress and pore water
pressure were recorded. The recorded shear stress was corrected with a membrane tensile stress
because the tension of membrane cannot be ignored in a small shear stress range.
Determination of the Parameters
To discuss the performance of the constitutive model, the simulated results were compared with
the strain-controlled shear tests. Model parameters are summarized in the column of Toyoura
sand (Dr=35%) in Table 2. Detailed description about the parameters can be referred to
corresponding references (Oka et al., 1999). The following parameters, e0 ,  ,  , OCR* , M m* ,
M *f and G0 /  m were directly determined by physical property tests and undrained monotonic
shear tests (Fukushima and Tatsuoka, 1984).  can be determined by the slope of the
compression curve ( e  ln  m ) and  by the slope of swelling curve ( e  ln  m ), which were
(a) Histories of imposed shear strain
(b) Shear strain - shear stress relations
(c) Effective stress paths
(d) Histories of shear stress response
Figure 2 Simulation of undrained strain-controlled shear test
obtained at the consolidation process of the shear tests. The quasi-overconsolidation ratio
OCR* was set to be 1.0 based on the experimental condition. M m* and M *f were calculated by
using the mobilized angles at the monotonic shear tests. The initial shear modulus ratio G0 /  m
was a measured shear modulus at small strain condition divided by the initial consolidation
stress.
Although, in principle, remaining parameters could be determined by physical property tests
and undrained monotonic and cyclic shear tests, the data adjusting method is more practical to
determine the soil parameters. The values of material parameters are selected in order to
provide a good description of the stress-strain relations and effective stress paths under cyclic
loading conditions. The data adjusting method was used for determining the dilatancy
parameters; D0 and n , the hardening parameters, B0* and B1* and the reference strain
parameters,  rP* and  rE * . These parameters basically influence effective stress paths, stressstrain curves and liquefaction strength curves from undrained tests. The dilatancy parameters,
D0 and n control the decrease in the mean effective stress before the cyclic mobility condition
and adjust the slope of the liquefaction strength curve. The hardening parameters and the
reference strain parameters, on the other hand, mainly control the behavior under cyclic
mobility. They affect effective stress path and stress-strain relations in a lower mean effective
stress range and larger strain range. Hence, by using the results of the strain-controlled tests, we
could determine these parameters rationally and easily.
Comparison between the Constitutive Model and Laboratory Tests
Figure 2 shows the test results (“Test”) and simulated results (“Model”) for Toyoura sand. (a)
histories of imposed shear strain, (b) shear strain - shear stress relations, (c) effective stress
paths and (d) histories of shear stress response are depicted. During the first stage with the
shear strain amplitude of 0.1%, the model and specimen completely liquefied. In the first cycle
of the second stage with the shear strain amplitude of 20%, a large shear stress was mobilized.
In the consequence cycles, the response of shear stress became small again. The simulated
results are in good agreement with the test results, although the simulated results slightly
overestimate the experimental shear stress at the second cycle of the second stage. According to
the results, the applicability of the constitutive model for deformation characteristics in a shear
strain range of 30% and under an undrained condition was confirmed.
NUMERICAL DATA FOR THE ANALYSIS
FEM Model
Figure 3 shows the 3-dimensional finite element model of the experimental case “16-1”. The
soils were modeled with 8-node isoparametric solid elements. We used the cyclic elasto-plastic
model for all soil layers. The parameters for each soil layer are shown in Table 2 mentioned
above. The parameters for the loose sandy layer were the same as that used in the previous
section. The parameters for the dense sandy layer were determined based on conventional
laboratory tests (Tatsuoka et al., 1982). The parameters for the dry layer were determined based
on drained strain-controlled shear tests. The elements above the water table were treated as dry
elements without DOF (Degree Of Freedom) of pore water pressure. The piles, footing and
quay wall were modeled by linear elastic beam elements, linear elastic solid and linear elastic
plate elements respectively. In order to represent the volume of piles, we used hybrid beam
elements for each pile (Zhang et al., 2000). The hybrid elements consist of conventional beam
elements at the center of a pile and elastic solid elements around the beam elements as shown in
Figure 4. No slip in the horizontal directions between the structures and soil was assumed, and
only vertical slip was considered.
Figure 4 FE mesh around piles
Figure 3 FE mesh of whole model
Figure 5 Time history of input acceleration
Boundary Conditions
As to the deformation boundary condition, the bottom of the model was set to be rigid, and all
lateral boundaries were set to be fixed only in the normal direction for the container wall. The
input acceleration as shown in Figure 5 was set at the rigid bottom boundary. As to the drainage
boundary condition, the lateral and bottom boundaries were supposed to be impermeable while
the water table was permeable.
Initial Conditions
The initial stress state was computed by the static two-stage analysis considering the making
procedure of the experimental model. At the first stage, the gravity force was loaded to the
whole model under the condition that the quay wall was horizontally fixed by the struts. At the
second stage, the horizontal DOF of the struts on the quay wall were gradually released.
Following the second stage, we conducted the dynamic analysis with keeping internal variables.
Other Numerical Conditions
A time integration step of 0.00125 second was adopted to ensure the numerical stability. The
hysteresis damping by the constitutive model was basically used, and Rayleigh damping
proportional to initial stiffness was used in order to describe the damping especially in the high
frequency domain. The factor of Rayleigh damping, which was determined by assuming that
the damping factor is 3% and the first natural period of the ground was 0.09 second, was set to
be 0.0009.  and  in Newmark method were set to be 0.3025 and 0.6 to ensure the numerical
stability.
TYPICAL RESULTS OF THE PREDICTION AND EXPERIMENT
The typical results of the prediction and experiment in the case of “16-1” are depicted. The
behavior of ground and structure are discussed.
Behavior of the Ground
Figure 6 shows the distribution of the excess pore pressure ratio and deformed configuration of
the whole model after the shaking. The excess pore pressure ratio represents the ratio of excess
pore water pressure to the initial effective overburden pressure in this study. The deformation
scale is the same as the configuration scale. The loose sand layer completely liquefied where
the excess pore pressure ratio became one. The liquefaction caused the large movement of the
quay wall and the back soil toward the waterside. The simulated deformed configuration
showed a qualitative agreement with the experimental one, although the simulated horizontal
displacement in the loose sandy layer was smaller than the experimental one.
Figure 7 shows the time histories of the excess pore water pressure in the ground in the case of
“16-1”. The excess pore water pressure was the increment of pore water pressure from the
initial pore water pressure. All output points are located in the loose sandy layer as shown in
Figure 3. At the points P1 and P4, the simulated and experimental results show that the loose
sandy layer completely liquefied, although the experimental ones fluctuated larger than the
simulated ones. At the point P3, the simulated pressure also fluctuated as the experimental
pressure. This is due to the fluctuation of total stress by the shaking, because the P3 was closed
to the container rigid wall. At the point P2, the pressure was significantly affected by the
deformation of the quay wall. The simulated one was different from the experimental one, since
the simulated horizontal displacement of the quay wall was different from the experimental
one.
Behavior of the Structures
Figure 8 shows the time histories of the horizontal displacement of the quay wall and the
footing. Both points are located at the top of the structure as shown in Figure 3. The predicted
displacement of the footing agreed with the experiment one. The displacement of the footing
decreased after it passed the peak value because of the recovery force of the elastic pile.
However, the prediction underestimated the measured displacement of the quay wall. The
discrepancy in the displacement of the quay wall was large in early period from about 0.5
second to 1.5 second. One of the reasons for the discrepancy was that the accuracy of the
prediction for the initial condition was not good, since the error was generated from the start of
the dynamic analysis. We need further investigation for the quantitative prediction of the
structure deformation.
Figure 6 Distribution of excess pore pressure ratio and deformed configuration after shaking
(a) P1, in left side of quay wall
(b) P2, behind quay wall
(c) P3, between piles and container wall
(d) P4, in right side of quay wall
Figure 7 Time histories of excess pore water pressure in the loose sandy layer
(a) D1, at top of quay wall
(b) D2, at top of footing
Figure 8 Time histories of the horizontal displacement of the structures
Earth Pressures on the Piles
Figure 9 shows the distributions of peak bending moment for piles. The locations of the output
piles are shown in Figure 4. The peak times for the experiment and the simulation are different
each other because the peak times of the horizontal displacement of piles are different as shown
in Figure 8 (b). The peak earth pressures, namely interaction pressures affected by peak
deformation and stiffness of ground and piles, caused the peak bending moments. The predicted
bending moments agree with the measured bending moments very well. This good agreement
corresponds with the well-predicted horizontal displacement of the footing.
The distributions of the peak bending moment are different for the different locations in the pile
group. We can understand the following tendencies from the simulated and experimental
results. 1) The larger curvatures in the distribution curves were observed at the closer piles to
the quay wall. 2) The peak moments at the piles No.4, 5 and 6 on the centerline of the pile
group were slightly smaller than that at the piles No.1, 2 and 3 on the outside of the pile group.
With respect to these points, the simulation qualitatively reproduced the measured distributions.
The 3-dimensional distribution of the liquefaction-induced ground flow as shown in Figure 6
caused the earth pressures which varied with the locations of the piles in the pile group.
(a) Pile No.4
(b) Pile No.5
(c) Pile No.6
(d) Pile No.1
(e) Pile No.2
(f) Pile No.3
Figure 9 Distributions of peak bending moment for piles
Soil Behavior around the Pile group
Figure 10 shows the distributions of deviatoric strain and excess pore water pressure around the
pile group in the case of “15-1”. The upper figures (a) and (b) show the distributions in the
gravel layer at the height of 1.6m. No excess pore water pressure was generated in the gravel
layer because the gravel layer kept dry state during the shaking. The localized large deviatoric
strain is observed in the waterside (left side) at the closest piles to the quay wall. The maximum
deviatoric strain is about 90%, which exceed the specific shear strain range discussed in the
section 4.3. We need further discussion about the performance of the constitutive model for the
gravel in larger strain region. The lower figures (c) and (d) the distributions in the liquefied
loose sand layer at the height of 1.2m. In contrast to the gravel layer, the excess pore pressure
ratio of the loose sand becomes almost 1.0. However, the excess pore water pressure in the
waterside at the closest piles to the quay wall is slightly smaller than that in the other parts. The
decrease in the excess pore water pressure ratio is related to the dilatancy under the large
deviatoric strain region as shown in Figure 10 (c).
(a) Deviatoric strain at height of 1.6m
(b) Excess pore water pressure at height of 1.6m
(c) Deviatoric strain at height of 1.2m
(d) Excess pore water pressure at height of 1.2m
Figure 10 Distributions of deviatoric strain and excess pore water pressure around the piles
ACCURACY OF PREDICTION WITH EFFECTIVE STRESS ANALYSES
Figure 11 summarizes the measured and predicted results of the residual horizontal
displacement of sheet pile and the peak horizontal displacement of footing for experimental
cases. This figure includes not only results with “LIQCA” but those with “DIANA-J”. The
predicted peak horizontal displacement of footing coincided with the experimental results. The
predicted residual horizontal displacement of quay wall, however, underestimated the
experimental results. The horizontal displacement of the quay wall is very large in the
experiment because the loose sand at both sides of the quay wall liquefied. The large
displacement of the quay wall is related to the initial stress state, the interaction between the
quay wall and the background, the effect of geometrical nonlinearity, etc. We need further
investigation on the quantitative prediction of deformation of the structures, in particular the
quay wall.
CONCLUSIONS
We tried to predict the earth pressures on a pile group due to liquefaction-induced ground flow
by a 3-dimensional liquefaction analysis. The targets of the simulation were the experimental
results of the large shaking table tests. A soil-water coupled problem was formulated based on a
u-p formulation and the constitutive equation used for sand was an elasto-plastic kinematic
hardening model. This simulation is so called Class B prediction using achieved input motion
and model configuration.
We performed strain-controlled tests with different constant strain amplitudes in order to assess
the capability of the constitutive model in a large strain range. The determination of the
Figure 11 Summary of the measured and predicted results for the residual horizontal
displacement of sheet pile and the maximum horizontal displacement of footing
parameters by using the results of the strain-controlled tests was easier than the conventional
method. In addition, the capability of the constitutive model for deformation behavior in a shear
strain range of 30% and under undrained condition was confirmed.
The loose sandy layer (Toyoura sand, Dr=35%) completely liquefied in both predicted and
experimental results. The liquefaction caused the large movement of the quay wall and the back
soil toward the waterside. The predicted deformed configuration qualitatively agreed with the
experimental one. Moreover, the predicted horizontal displacement of the footing agreed with
the experimental one although the prediction underestimated the horizontal displacement of the
quay wall in the experiments. The 3-dimensional distribution of the liquefaction-induced
ground flow caused the earth pressures which varied with the locations of the piles in the pile
group. The larger curvatures in the distribution were observed and reproduced at the closer
piles to the quay wall.
ACKNOWLEDGEMENTS
The support of Special Project for Earthquake Disaster Mitigation in Urban Areas by Ministry
of Education, Culture, Sports, Science and Technology is gratefully acknowledged. The authors
wish to thank the research group chaired by Professor Koji Tokimatsu, Tokyo Institute of
Technology, for their providing the experimental data and suggestions. The authors thank
Minako Shibasaki and Takashi Asano, formerly graduate student of Tohoku University for their
cooperation in the analyses and laboratory tests.
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