piles in liquefaction–induced soil flow behind quay–wall...

1 INTRODUCTION

Pile foundations may sustain significant damage due to soil liquefaction, especially when soil flow occurs. The problem became intensely apparent during the 1995 Great Kobe Earthquake. Extensive soil flow was triggered along river and sea sides, causing seaward displacements to sheet pile quay-walls in the Kobe port area accompanied by considerable translation of the neighboring pile foundations (Ishihara, 1997, Tokimatsu et al., 1997, Yasuda et al., 1996), illus-trated in Figure 1.

soil flowsoil flow

Figure 1. Soil liquefaction along sea sides may cause significant seaward displacement to quay walls af-fecting the neighboring pile foundations.

Numerous numerical and experimental researches has been performed during the last decade

in order to figure out the mechanism of soil-pile interaction under soil flow conditions. The moving soil mass provides the driving force to the pile and displaces the pile a certain amount

Piles in Liquefaction–Induced Soil Flow behind Quay–Wall: A Simple Physical Method versus Centrifuge Experiments P. Tasiopoulou Research Ast., University of California, Davis, USA

N. Gerolymos Lecturer, National Technical University, Athens, Greece

T. Tazoh Director, Institute of Technology, Shimizu Corporation, Tokyo, Japan

G. Gazetas Professor, National Technical University, Athens, Greece

ABSTRACT: The paper presents a new physically simplified methodology for computing dis-placements and internal forces on piles under conditions of lateral spreading. The results com-pare well with results from centrifuge tests. To this end, 2D effective stress dynamic analysis of a cross-section of the wall-soil system without the presence of the piles is combined with an also 2D quasi-static analysis of a horizontal slice of the system with the group of piles.

depending on the relative stiffnesses between the pile and the liquefied soil (Boulanger et al., 2003), as depicted in Figure 2. Thus, the magnitude of the soil movement, the lateral load of the surficial non-liquefiable soil layer and the stiffness degradation in the liquefied zone are the key parameters that need to be taken into account when evaluating the pile response due to soil flow (Cubrinovsky et al., 2004).

Before liquefaction After liquefaction

flow

Before liquefaction After liquefaction

flowK

Figure 2. The moving soil mass provides the driving force to the pile and displaces the pile a certain amount depending on the relative stiffnesses between the pile, K, and the liquefied soil.

In engineering practice, several methods have been formulated based on these understand-

ings, either for designing purposes or prediction of field performance. In general, the methods can be classified into three categories: (a) the force methods, including the Japanese Road Asso-ciate Method (JRA, 1996), the limit equilibrium method (Dobry and Abdoun, 2000) and the vis-cous fluid method (Hamada 2002, Yasuda 2002), (b) the displacement methods, or else known as pseudo-static beam on nonlinear Winkler foundation method according to which the free field soil displacement is imposed to the pile through “p-y” springs (Boulanger et al., 2003), (c) the hybrid force–displacement methods, which are a combination of the first two (Cubrinovsky and Ishihara, 2004).

The aforementioned methods are mainly single pile analyses dependent on the soil profile and the geometry of the problem. Moreover, lots of assumptions are required regarding the stiffness degradation in the liquefied layer and soil-pile interaction issues, such as the direction of the load exerted on the pile by the upper non-liquefiable layer. Inevitably, considerable uncertainty is hidden behind all methods of post liquefaction analysis (Finn and Thavaraj, 2001).

In this study, we present a new physically simplified methodology, appropriate for every soil profile and type of pile configuration (single piles, pile groups). This methodology, described below, falls into the displacement–method category, but avoids the associated empirical selec-tion of stiffness–reduction factors and does not involve the use of p-y curves. Continuously, the method is applied to two different centrifuge experiments (Tazoh et al., 2005, Sato et al., 2001), reproducing the test results with satisfying accuracy for engineering purposes.

2 CENTRIFUGE EXPERIMENTS

Several series of dynamic centrifuge experiments were conducted at the Institute of Technol-ogy, Shimizu Corporation, in Japan, in order to evaluate the damage of pile–foundation systems triggered by liquefaction–induced soil flow after quay-wall collapse. One of these, Test Case CD, presented by Tazoh et al. (2005), explores the effect of the superstructure on the response

of a 2x2 pile group under soil flow conditions, portrayed in Figure 3. A partition was placed at the center of the laminar box behind the sheet pile quay-wall in order to separate the two pile–foundation models: the one with a superstructure (C side) and the other without a superstructure (D side), as depicted in Figure 3.

0 m

1.8 m

6.0 m

8.1 m

9 m

0.6 mDry Silica Sand No 8

Dr = 50%

Liquefiable Silica Sand No 8

Dr = 50 %

Toyoura SandDr = 90 %

Silica sand No 3

Sheet‐pileQuay‐wall

24 m

3.6 m

6 m3 mSuperstructure

Side – Dwith superstructure

Side – Cno superstructure

Partition FloatingQuay‐wall

0 m

1.8 m

6.0 m

8.1 m

9 m

0.6 mDry Silica Sand No 8

Dr = 50%

Liquefiable Silica Sand No 8

Dr = 50 %

Toyoura SandDr = 90 %

Silica sand No 3


24 m

3.6 m

6 m3 mSuperstructure

Side – Dwith superstructure

Side – Cno superstructure

Partition FloatingQuay‐wall

Figure 3. Geometry and soil properties of the centrifuge model of test Case CD, side D into the laminar box, in prototype scale (Tazoh et al., 2005). A partition behind the quay-wall separates the two pile-foundation models: the one with a superstructure (C side) and the other without a superstructure (D side).

The input motion at the base of the laminar box is shown in Figure 4 along with the recorded time histories of excess pore water pressure in the liquefied layer at the almost “free field”. Liq-uefaction starts at around 4 sec and 5 sec at the depths of z = 3 m and z = 5 m, respectively. Fig-ure 5 depicts the horizontal displacements of the footings and the quay-wall of the Case CD. Evidently, the horizontal displacement of the C-side footing (with no superstructure) is larger than that of the D-side footing, (with a superstructure), but the difference is not significant. The effect of the inertial force of the superstructure can be identified during the excitation period; however it can not be recognized during the liquefaction-induced soil flow some time after the end of excitation. Figure 6 illustrates the distribution of the maximum bending strains along the pile at the end of the shaking with and without the influence of the superstructure. It is evident that the effect of the inertial force of the superstructure on the final pile strains is not significant. Thus, the main load on the pile is the kinematic one coming from the soil-flow.

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

A:g

A:g

time (sec)

Tazoh et al. (2005)

Sato et al. (2001)

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

A:g

A:g

time (sec)

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

A:g

A:g

time (sec)

Tazoh et al. (2005)

Sato et al. (2001)

40

20

0

‐ 40

z = 3 m

Ϭνο

0 5 4001510 800 1200‐ 20

0

40

60

20

Ϭνο

t (sec)

z = 5 m

Excess Pore Pressure (kP

a)

(a) (b)

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

A:g

A:g

time (sec)

Tazoh et al. (2005)

Sato et al. (2001)

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

A:g

A:g

time (sec)

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

A:g

A:g

time (sec)

Tazoh et al. (2005)

Sato et al. (2001)

40

20

0

‐ 40

z = 3 m

Ϭνο

0 5 4001510 800 1200‐ 20

0

40

60

20

Ϭνο

t (sec)

z = 5 m


a)

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

A:g

A:g

time (sec)

Tazoh et al. (2005)

Sato et al. (2001)

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

A:g

A:g

time (sec)

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

0.6

0.4

0.2

0

‐ 0.2

‐ 0.4

‐ 0.60 5 10 15

A:g

A:g

time (sec)

Tazoh et al. (2005)

Sato et al. (2001)

40

20

0

‐ 40

z = 3 m

Ϭνο

0 5 4001510 800 1200‐ 20

0

40

60

20

Ϭνο

t (sec)

z = 5 m


a)

(a) (b)

Figure 4. (a) Input accelerograms recorded at the base of the centrifuge models of the two experiments (Tazoh et al., 2005 and Sato et al., 2001) in prototype scale, and (b) Indicative time histories of excess pore water pressures recorded in the “free field” (away from the pile foundation) at the depths 3 m and 5 m below the ground surface

0 5 10 15 400 800

0.8 m

0.1 m

0.15 m

Quay‐wall

With superstructure

No supersructure

t (sec)

Displacement

Figure 5. Time histories of displacements of the quay wall and the footing with and without the super-structure (Tazoh et al., 2005).

Similar centrifuge results with the same soil profile were described by Sato et al. (2001) indi-cating the seismic performance of a 2x8 pile group, situated 3 m behind the floating sheet pile quay-wall. Two different centrifuge models were designed: one with (Case 2) and one without the pile group (Case 1). Figure 4 shows the input wave recorded at the base of the model of Case 1, which caused excessive pore water pressure generation in the loose saturated sand layer and maximum seaward displacement of the quay-wall of 0.8 m during the shaking. In Case 2, the existence of the pile group limited the quay-wall movement to 0.45 m approximately. The footing of the pile foundation sustained even smaller displacement, about 6 cm. Long after the end of shaking, when considerable dissipation of pore water pressure has occurred the quay-wall reached a displacement of 1.15 m, while the footing displacement increased by a mere 2 cm. The trend of the time-dependent results is practically identical with that of the results of Test Case CD.

3 A NEW PHYSICALLY SIMPLIFIED METHODOLOGY

To begin with, the soil response without the piles needs to be identified. On these grounds, a 2D effective stress numerical analysis of the soil profile including the quay-wall – hereafter

called “free field” – is performed using the code FLAC, as depicted in Figure 7. Thus, the free field soil response behind the quay-wall is obtained in terms of:

the distribution of the horizontal soil movement with depth, the depth and the thickness of the liquefied zone, the strength degradation in the liquefied layer and the shear strain distribution with depth.

0

1

2

3

4

5

6

7

8

9

‐0.7 ‐0.5 ‐0.3 ‐0.1 0.1 0.3 0.5

bending strains

(10‐3)depth (m)

C ‐ side (NO superstructure)

D ‐ side (WITH superstructure)

Figure 6. Distributions of the maximum bending strains along the piles at the end of shaking with and without a superstructure. The influence of the superstructure in terms of bending distress of the piles is not as significant.

Although the dynamic numerical analysis provides the required results as a function of time,

we are primarily interested in the final values after the end of the shaking, which are also the maximum ones due to the accumulative nature of the liquefaction–induced soil flow. Obviously our methodology is not restricted to this code.

In the next step, a horizontal slice in the middle of the liquefied zone is isolated, including the piles and the quay-wall, as demonstrated in Figure 8. Our purpose is to perform an elastic plane strain analysis of this horizontal slice by imposing pseudo-statically a unit uniform displacement at the quay-wall boundary, illustrated in Figure 9, so as to estimate the ratio of the pile dis-placement to the soil displacement in the free-field (away enough of the piles), named ratio “α” and depicted in the same figure. This ratio of displacements represents the soil-pile interaction due to soil flow, in quantitative terms.

The numerical model of the horizontal slice consists of the liquefied soil with uniform prop-erties (shear modulus, Gl) surrounding the pile sections, as shown in Figure 9. So far, the pile sections are simulated as rigid bodies into the liquefied soil, Gl. In order to provide the required horizontal resistance to the pile sections against the moving soil mass, an out of plane horizontal spring, K, is connected to each pile section.


A:g



A:g


Figure 7. 2D Finite-difference mesh of a numerical model of the free field without the piles, in FLAC, before and after shaking.

Gl

GlHorizontal Slice

Large displacement and rotation of quay‐wall

Gl

GlHorizontal Slice

Large displacement and rotation of quay‐wall

Figure 8. A horizontal slice in the middle of the liquefied zone, Gl , is isolated, including the pile and the quay-wall sections.

In retrospect, a realistic numerical simulation of the horizontal slice at the middle of the liq-uefied zone requires the appropriate calibration of the horizontal stiffness of each pile section, K, and of the shear modulus of the liquefied soil, Gl.

Horizontal stiffness of each pile section, K Every single pile of the pile group is simulated as a vertical beam element with suitable

boundary conditions. The rotation at the top depends on the pile cap (Mokwa and Duncan,

2003), the number of piles of the foundation and the stiffness of the surrounding surficial non-liquefiable soil. All these features tend to restrain the rotation at the pile-head.

Gl

Unit displacement

Pile‐cap constraint

pile section

Quay‐w

all

liquefied soil

Gl

Unit displacement


pile section

Quay‐w

all

liquefied soil

Free‐field displacement

Disp. 1

Pile‐group displacement

Disp. 2

liquefied soil

Ratio “α” =Disp. 2

Disp. 1

Gl

Unit displacement


pile section

Quay‐w

all

liquefied soil

Gl

Unit displacement


pile section

Quay‐w

all

liquefied soil


Disp. 1


Disp. 2

liquefied soil


Disp. 1Ratio “α” =

Disp. 2


Disp. 2

Disp. 1

Gl

Unit displacement


pile section

Quay‐w

all

liquefied soil

Gl

Unit displacement


pile section

Quay‐w

all

liquefied soil


Disp. 1


Disp. 2

liquefied soil


Disp. 1

Gl

Unit displacement


pile section

Quay‐w

all

liquefied soil

Gl

Unit displacement


pile section

Quay‐w

all

liquefied soil


Disp. 1


Disp. 2

liquefied soil



Disp. 2


Disp. 2

Disp. 1

Figure 9. (Top) Numerical model of the horizontal slice. The pile sections sustain the same horizontal displacement due to the pile–cap constraint. (Bottom) Definition of the ratio “α”.

The “active” length of the beam element depends on the depth to fixity, below the liquefied layer. Therefore, every single pile is simulated as a vertical beam fixed at the bottom with a cer-tain degree of rotational freedom at the top depending on the aforementioned kinematic con-straints.

Based on this simulation, the pile section of the numerical model is just a section of the beam element at a characteristic depth at the middle of the liquefied zone. Thus, the horizontal stiff-ness, K, of each pile section, is defined as the point load exerted on the beam, in order to cause a unit displacement of the beam at the characteristic depth, as depicted in Figure 10.

0.0

0.2

0.4

0.6

0.8

1.0

0.001 0.01 0.1 1 10 100 1000

K/EI

z/L

0.0

0.2

0.4

0.6

0.8

1.0

0.001 0.01 0.1 1 10 100 1000

K/EI

z/L

0.0

0.2

0.4

0.6

0.8

1.0

0.001 0.01 0.1 1 10 100 1000

K/EI

z/L

0.0

0.2

0.4

0.6

0.8

1.0

0.001 0.01 0.1 1 10 100 1000

K/EI

z/L

Figure 10. Dimensionless horizontal stiffness along the pile for free to fixed boundary conditions at the pile head.

0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

K / Gl

ratio "α"

1

0.8

0.6

0.4

0.2

00.1 1 10 100

single pile

2x2 pile group

2x8 pile group0.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100

K / Gl

ratio "α"

1

0.8

0.6

0.4

0.2

00.1 1 10 100

single pile

2x2 pile group

2x8 pile group

Figure 11. The ratio “α” as a function of the relative stiffnesses between the pile and the liquefied soil for three different pile configurations: single pile, 2x2 and 2x8 pile group, obtained from several parametric numerical analyses of the horizontal slice.

Shear modulus of the liquefied soil, Gl

In the framework of an elastic analysis of the horizontal slice, an equivalent linear shear

modulus of the liquefied soil can be determined as:

0

1 liqHres

l liqres

G dzH

(1)

Hliq is the thickness of the liquefied zone, τ is the residual shear stress and γ is the maximum shear strain after the end of shaking, obtained from the numerical analysis of the free field. That is how the stiffness degradation of the liquefied soil is taking into account.

The elastic pseudo-static analysis of the horizontal is conducted for two different pile con-figurations: (a) a 2x2 pile group (Tazoh et al., 2005) and (b) a 2x8 pile group (Sato et al., 2003).

0

0.2

0.4

0.6

0.8

1

0 0.5 1

w / ( p L EI wmax )

z/L

uniform load

inverted triangle load

inverted trapezoid load

0

0.2

0.4

0.6

0.8

1

0 0.5 1

w / ( p L EI wmax )

z/L

uniform load

inverted triangle load

inverted trapezoid load

Figure 12. Deformation shape of a pile with no rotation at the top and the bottom, determined for three different load distributions: uniform, inverted triangle shaped and inverted trapezoid one.

The ratio “α”, is obtained as function of the relative stiffness between the pile and the lique-

fied soil, K/Gl, shown in Figure 11. When the relative stiffness tends to zero (K/Gl → 0), the ratio “α” tends to unity, which

means that the pile sections move just like the soil, as a rigid body. On the contrary, when the relative stiffness tends to infinity (K/Gl → ), the ratio “α” tends to zero. This is due to the fact that the soil has practically zero shear strength (Gl → 0) and flows around the pile without exert-ing any significant load on them. Moreover, Figure 11 indicates that increasing the number of piles, the resistance of the foundation to the moving soil mass becomes stronger. It is worth mentioned at this point that the numerical modeling of the pile-group section into the liquefied soil is based on the assumption that the piles sustain the same horizontal displacement due to the pile-cap constraint.

In conclusion, as long as the relative stiffness, K/Gl, is determined, the ratio “α” can be esti-mated. Eventually, multiplying the ratio “α” with the free-field soil displacement in the middle of the liquefied zone, at the position where the piles would be present behind the quay-wall, we can calculate the pile displacement at the same characteristic depth.

In the last step of the methodology, the whole pile deformation and mainly the pile displace-ment at the top, remains to be evaluated. The deformation shape of each pile, simulated as a beam element, is defined primarily by its boundary conditions and secondarily by the load dis-tribution along it, as depicted in Figure 12. A potential load distribution, is imposed on the pile, so as to obtain its deformation shape as a function of the unknown load value, “p”.

Until now, we have just estimated the pile displacement in the middle of the liquefied zone. Using this known displacement, we can calibrate the shape function of the pile with depth and finally, estimate the unknown load value, “p”. Continuously, the distribution of the pile dis-placements with depth, as long as the bending moments along the pile, can be determined by imposing the already fully known load distribution on the beam-pile.

0

1

2

3

4

5

6

7

8

9

‐15 ‐10 ‐5 0 5 10 15 20

shear stress (kPa)

depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16

shear strain (10‐2)

depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

‐15 ‐10 ‐5 0 5 10 15 20

shear stress (kPa)

depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16


depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

free‐field displacement (m)

depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

‐15 ‐10 ‐5 0 5 10 15 20

shear stress (kPa)

depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16


depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

‐15 ‐10 ‐5 0 5 10 15 20

shear stress (kPa)

depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16


depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

(i)(ii)

0

1

2

3

4

5

6

7

8

9

‐15 ‐10 ‐5 0 5 10 15 20

shear stress (kPa)

depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16


depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

‐15 ‐10 ‐5 0 5 10 15 20

shear stress (kPa)

depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16


depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

‐15 ‐10 ‐5 0 5 10 15 20

shear stress (kPa)

depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16


depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

‐15 ‐10 ‐5 0 5 10 15 20

shear stress (kPa)

depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16


depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

0

1

2

3

4

5

6

7

8

9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


depth (m)

Tazoh et al. (2005)

Sato et al. (2001)

(i)(ii)

Figure 13. Distributions of horizontal soil displacements, shear strains and stresses, obtained from the numerical analysis of the two models: (i) Tazoh et al., 2005 (Case CD) and (ii) Sato et al. (2001) without the piles.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10 12

time (sec)

Quay‐w

all diplacement at top (m)

Tazoh et al. (2005)

Sato et al. (2005)

(i)

(ii)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 2 4 6 8 10 12

time (sec)

Quay‐w

all diplacement at top (m)

Tazoh et al. (2005)

Sato et al. (2005)

(i)

(ii)

Figure 14. Horizontal quay wall displacements, obtained from the numerical analysis of the two models: Tazoh et al., 2005 (Case CD) and Sato et al. (2001) without the piles.

4 COMPARISON WITH RESULTS FROM CENTRIFUGE TESTS

The results obtained from the numerical analysis of the free field including the quay-wall in the first step for the two centrifuge experiments (Tazoh et al., 2005 and Sato et al., 2001) are il-lustrated in Figures 13 to 16. The only differences between the two models, both the centrifuge and the numerical ones are the input wave motions, shown in Figure 4 and the distance of the quay wall from the boundaries parallel to it, depicted in Figure 3. According to the excess pore pressure time histories, demonstrated in Figures 15 and 16, the liquefaction seems more exten-sive in case of Tazoh et al. model. This is one of the reasons why the quay-wall displacement of this model is larger than the one of the Sato et al. model, as portrayed in Figure 14.

In the second step, every single pile of the pile groups is simulated as a beam fixed both at the top and the bottom, following the assumption that the pile cap does not allow any rotation at the pile heads. The horizontal stiffnesses, K, are calculated at the characteristic depths depicted in Figure 17 which coincide with the middle of the liquefied layer. The values required to esti-

mate the pile displacement at the characteristic depth are given in table 1. Once the relative stiffness is estimated for each model, the ratio “α” is determined, choosing the 2x2 pile-group curve in case of the Tazoh et al. model and the 2x8 pile-group curve for the Sato et al. model.

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12

time (sec)

Excess pore pressure ratio

z = 4 m

z = 3.5 m

z = 5.5 m

z = 6 m

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12

time (sec)


z = 4 m

z = 3.5 m

z = 5.5 m

z = 6 m

Figure 15. Time histories of excess pore pressure ratio at depths of 4, 3.5, 5.5, 6 m below the ground sur-face, obtained from the numerical analysis of the Sato et al. model (2001) without the piles.

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14

time (sec)


z = 4 m

z = 3.5 m

z = 5.5 m

z = 6 m

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14

time (sec)


z = 4 m

z = 3.5 m

z = 5.5 m

z = 6 m

Figure 16. Time histories of excess pore pressure ratio at depths of 4, 3.5, 5.5, 6 m below the ground sur-face, obtained from the numerical analysis of the Tazoh et al. model (2005) without the piles.

In the last step, five different potential load distributions are imposed on the “pile-beam”. A

range of estimated values regarding the displacements and the bending moments along each pile of the pile group are illustrated in Figure 18 for the two models. The range of pile displacements is not very sensitive to the shape of the load distribution whereas the bending moments vary significantly, especially on the top. However, the maximum bending moment for both of the two models was recorded at the pile tip, during the centrifuge experiments.

5 CONCLUDING REMARKS

In this paper, a new simple physically-motivated methodology is proposed for the evaluation of pile response due to liquefaction–induced soil flow. The main characteristics of this method-ology verified above are:

It avoids the associated empirical selection of stiffness–reduction factors and does not in-volve the use of p-y curves.

1.3 m

L = 7.5 m9m

Liquefied layer

2 m

6 m

3 m

P

1.3 m

L = 7.5 mL = 7.5 m9m

Liquefied layer

2 m

6 m

3 m

P

EI = 17000 kNm2

0.6 m

L = 8.0 m9m

Liquefied layer

2 m

6 m

3.5 m

P

0.6 m

L = 8.0 mL = 8.0 m9m

Liquefied layer

2 m

6 m

3.5 m

P

EI = 6480 kNm2

1.3 m

L = 7.5 m9m

Liquefied layer

2 m

6 m

3 m

P

1.3 m

L = 7.5 mL = 7.5 m9m

Liquefied layer

2 m

6 m

3 m

P

EI = 17000 kNm2

0.6 m

L = 8.0 m9m

Liquefied layer

2 m

6 m

3.5 m

P

0.6 m

L = 8.0 mL = 8.0 m9m

Liquefied layer

2 m

6 m

3.5 m

P

EI = 6480 kNm2

1.3 m

L = 7.5 m9m

Liquefied layer

2 m

6 m

3 m

P

1.3 m

L = 7.5 mL = 7.5 m9m

Liquefied layer

2 m

6 m

3 m

P

EI = 17000 kNm2

0.6 m

L = 8.0 m9m

Liquefied layer

2 m

6 m

3.5 m

P

0.6 m

L = 8.0 mL = 8.0 m9m

Liquefied layer

2 m

6 m

3.5 m

P

EI = 6480 kNm2

1.3 m

L = 7.5 m9m

Liquefied layer

2 m

6 m

3 m

P

1.3 m

L = 7.5 mL = 7.5 m9m

Liquefied layer

2 m

6 m

3 m

P

EI = 17000 kNm2

0.6 m

L = 8.0 m9m

Liquefied layer

2 m

6 m

3.5 m

P

0.6 m

L = 8.0 mL = 8.0 m9m

Liquefied layer

2 m

6 m

3.5 m

P

EI = 6480 kNm2

Figure 17. Each pile of the 2x8 pile group of the Sato et al. (2001)model (Top) and of the 2x2 pile group of the Tazoh et al. (2005) model (Case CD -- Bottom), is simulated as a vertical beam element with no ro-tation at the top and the bottom. The horizontal stiffness, of the pile is estimated at a characteristic depth of 3 m (3.5 m for the Tazoh et al model) from its top, which coincides with the middle of the liquefied layer. Table 1. Table of the values needed to determine the ratio “α” and the pile displacements at the middle of the liquefied layer for the two models:

depth (m)

Gl (kPa)

K (kN/m)

K /Glff‐disp (m)

ratio

"α" pile disp.

(m)

3.50 90 370 4.1 0.5 0.152 0.076

depth (m)

Gl (kPa)

K (kN/m)

K /Glff‐disp (m)

ratio

"α" pile disp.

(m)

3.00 200 1020 5.1 0.42 0.105 0.044

Tazoh et al.

(2005)

Sato et al.

(2001)

It introduces an elastic pseudo static numerical analysis of a horizontal slice into the lique-fied layer including the piles, in order to estimate the soil-pile interaction under soil flow conditions in quantitative terms. This interaction is determined as a function of the relative stiffness between the pile and the liquefied soil. The pile stiffness is assumed to remain lin-ear-elastic throughout the analysis.

It can be applied to any type of soil profile and pile configuration (single pile or pile group).

The effectiveness of the new methodology in combination with suitable engineering judg-ment and reasonable assumptions can provide sufficient accuracy for designing and evalu-ating purposes.

0

1

2

3

4

5

6

7

0 0.02 0.04 0.06 0.08

pile diplacement (m)

depth (m)

Centrifuge experiment

Range of predicted values

0

1

2

3

4

5

6

7

0 0.02 0.04 0.06 0.08


depth (m)

0

1

2

3

4

5

6

7

0 0.02 0.04 0.06 0.08


depth (m)





0

1

2

3

4

5

6

7

‐600 ‐400 ‐200 0 200 400 600

bending strains (μ)

depth (m)



0

1

2

3

4

5

6

7

‐600 ‐400 ‐200 0 200 400 600


depth (m)





0

1

2

3

4

5

6

7

8

0 0.05 0.1 0.15


depth (m)



0

1

2

3

4

5

6

7

8

0 0.05 0.1 0.15


depth (m)

0

1

2

3

4

5

6

7

8

0 0.05 0.1 0.15


depth (m)





0

1

2

3

4

5

6

7

8

‐1500 ‐1000 ‐500 0 500 1000 1500


depth (m)





0

1

2

3

4

5

6

7

0 0.02 0.04 0.06 0.08


depth (m)



0

1

2

3

4

5

6

7

0 0.02 0.04 0.06 0.08


depth (m)

0

1

2

3

4

5

6

7

0 0.02 0.04 0.06 0.08


depth (m)





0

1

2

3

4

5

6

7

‐600 ‐400 ‐200 0 200 400 600


depth (m)



0

1

2

3

4

5

6

7

‐600 ‐400 ‐200 0 200 400 600


depth (m)





0

1

2

3

4

5

6

7

8

0 0.05 0.1 0.15


depth (m)



0

1

2

3

4

5

6

7

8

0 0.05 0.1 0.15


depth (m)

0

1

2

3

4

5

6

7

8

0 0.05 0.1 0.15


depth (m)





0

1

2

3

4

5

6

7

8

‐1500 ‐1000 ‐500 0 500 1000 1500


depth (m)





Figure 18. Calculated range of distributions of (a) the horizontal displacement, and (b) the bending strain, in comparison with the centrifuge test results by Sato et al., 2001 (Top), and Tazoh et al., 2005 (Bottom).

ACKNOWLEDGMENTS

This work forms part of an EU 7th Framework research project funded through the European Research Council (ERC) Programme “Ideas”, Support for Frontier Research – Advanced Grant, under Contract number ERC-2008-AdG 228254-DARE.

REFERENCES

Boulanger R. W., Kutter B. L., Brandenberg S. J., Singh P., and Chang P., (2003), Pile Foundations in Liquefied and Laterally Spreading Ground during Earthquakes: Centrifuge Experiments and Analyses, Report No. UCD/CGM-03/01, Department of Civil and Environmental Engineering, University of California at Davis.

Cubrinovsky M., and Ishihara K., (2004), “Simplified Method for Analysis of Piles undergoing Lateral Spreading of Liquefied Soils”, Soils and Foundations, Vol. 44, No. 5, pp. 119-133.

Cubrinovsky M., Kokusho T., and Ishihara K., (2004), “Interpretation from large-scale shake table tests on piles subjected to spreading of liquefied soils”, Proceedings of 11th Int. Conf. Soil Dynamics and Earthq. Engrg. / 3rd Int. Conf. Earthq. Geotech. Engrg., Berkeley, USA, Vol. 2, pp. 463-470.

Dobry R., and Abdoun T. H., (1998), “Post-Triggering Response of Liquefied Soil in The Free Field and Near Foundations,” State-of-the-art paper, Proc. ASCE 1998 Specialty Conference on Geotechnical Earthquake Engineering and Soil Dynamics (P. Dakoulas, M. Yegian and R. D. Holtz, eds.), Univer-sity of Washington, Seattle, Washington, August 3-6, Vol. 1, pp. 270-300.

Dobry R., and Abdoun T. H., (2000), “Recent studies on seismic centrifuge modeling of liquefaction and its effect on deep foundations”, Proceedings of the fourth International Conference on Recent Ad-vances in Geotechnical Earthquake Engineering and Soil Dynamics , San Diego.

Finn Liam W. D., and Thavaraj T., (2001), “Deep Foundations in liquefiable soils: Case Histories , cen-trifuge tests and methods of analysis” , Proceedings of the fourth International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, San Diego.

Ishihara K., (1997), “Geotechnical aspects of the 1995 Kobe Earthquake”, Proceedings of 14th Int. Conf. SMFE, Terzaghi Oration, Hamburg.

Mokwa R. L., Duncan J. M (2003), “Rotational restraint of pile caps during lateral loading”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 129(9), pp. 829-837.

Ramos R., Abdoun T. H., and Dobry, R., (2000), “Effect of Lateral Stiffness of Superstructure on Bend-ing Moments of Pile Foundation Due to Liquefaction-induced Lateral Spreading,” Proc. 12th World Conf. on Earthquake Engineering, Auckland, New Zealand, Jan. 30 - Feb. 4, 8 pages.

Sato M., Tazoh T. and Ogasawara M. (2001), “Reproduction of Lateral Ground Displacement and Lateral Flow –Earth Pressure Acting on Pile Foundations using Centrifuge Modeling”, Proceedings of the Fourth International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, San Diego.

Tazoh T., Gazetas G. (1996), “Pile Foundations Subjected to Large Ground Deformations: Lessons from Kobe and Research Needs”, Proceedings of the Eleventh World Conference on Earthquake Engineer-ing, Acapulco, Mexico, paper 2081.

Tazoh T., Sato M., and Gazetas G., (2005), “Centrifuge Tests on Pile−Foundation−Structure Systems Af-fected by Liquefaction−Induced Soil Flow after Quay Wall Failure”, Proceedings of the 1st Greece – Japan Workshop: Seismic Design, Observation, and Retrofit of Foundations, Athens, Oct. 11-12 pp. 79-106.

Tokimatsu K., Oh-oka H., Samoto Y., Nakazawa A., and Asaka Y., (1997), “Failure and Deformation Modes of Piles Caused by Liquefaction-Induced Lateral Spreading in 1995 Hyogo-ken Nambu Earth-quake”, Proceedings of the Third Kansai International Forum on Comparative Geotechnical Engi-neering, (KIG-Forum ’97), pp. 239-248.

Yasuda S., Ishihara K., Harada K., and Namura H., (1996), “Area of Ground Flow Occurred behind Quaywalls due to Liquefaction”, Proceedings of the Third Kansai International Forum on Compara-tive Geotechnical Engineering, (KIG-Forum ’97), pp. 85-93.

piles in liquefaction–induced soil flow behind quay–wall...

Documents