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Paper No. PILTA

PILES IN LATERAL SPREADING: A SIMPLE METHOD VERSUS CENTRIFUGEEXPERIMENTS

Panagiota TASIOPOULOU 1, Nikos GEROLYMOS 2, George GAZETAS 3

ABSTRACT

The paper presents a new physically simplified methodology for computing displacements and structuralforces on piles under conditions of lateral spreading. The main method avoids the associated empiricalselection of stiffness reduction factors and does not involve the use of p -y curves. Instead, it introduces anelastic pseudo static numerical analysis of a horizontal slice from the liquef ied layer including the piles, inorder to estimate the soil-pile interaction under soil flow conditions in quantitative terms. This interactionis determined as a function of the relative stiffness between the pile and the liquefied soil. The pilestiffness is assumed to remain linear -elastic throughout the analysis. The predictions of the methodcompare well with results from centrifuge tests.

Keywords: Lateral spreading; pile; liquefaction; simplified method

INTRODUCTION

Numerous numerical and experi mental studies have been performed during the last decade in order tofigure out the mechanism of soil-pile interaction under soil flow triggered by extensive liquefaction. Themoving soil mass provides the driving force displacing the pile a certain amount, which depends on therelative stiffnesses between the pile and the liquefied soil (Boulanger et al., 2003). Thus, the magnitude ofthe soil movement, the lateral load of the surficial non-liquefiable soil layer and the stiffness degradationin the liquefied zone are the key parameters which need to be taken into account when evaluating the pileresponse due to soil flow (Cubrinovsky et al., 2004).

In engineering practice, several methods have been formulated. In general, they can be classified intothree categories: (a) the force methods, including the Japanese Road Associate Method (JRA, 1996), thelimit equilibrium method (Dobry and Abdoun, 2000), and the viscous fluid method (Hamada 2000,Yasuda et al., 2001); (b) the displacement methods, or else known as pseudo-static beam on nonlinearWinkler foundation methods according to which the free field soil displacement is imposed to the pilethrough empirical p -y s prings (Boulanger et al., 2003); (c) the hybrid force displacement methods,which are a combination of the first two (Cubrinovsky and Ishihara, 2004).

These methods are mainly single pile analyses dependent on soil profile and problem geometry.Moreover, many assumptions are made regarding the stiffness degradation in the liquefied layer and soil-

pile interaction issues, such as the appropriate direction of the force exerted on the pile by the upper non-liquefiable layer. Inevitably, considerable uncertainty is hidden behind all methods of post liquefactionanalysis (Finn and Thavaraj, 2001).

1 Ph. D. Candidate, School of Civil Engineering, National Technical University, Athens, Greece, [email protected] 2 Lecturer, School of Civil Engineering, National Technical University, Athens, Greece.3 Professor, School of Civil Engineering, National Technical University, Athens, Greece.
mailto:[email protected]:[email protected]:[email protected]

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5th International Conference on Earthquake Geotechnical EngineeringJanuary 2011, 10-13

Santiago, ChileIn this study, a new simple physical method is presented, appropriate for all kinds of soil profile and typesof pile configuration (single piles, pile groups). The method falls into the "displacement" inducedcategory, but avoids the associated empirical selection of stiffness reduction factors and does not involvethe use of p-y curves. It is applied to three different centrifuge experiments (Tazoh et al., 2005, Sato et al.,2001, Abdoun & Dobry, 1998), reproducing the test results with satisfying engineering accuracy(Tasiopoulou et al., 2009). However, herein, only the application to the centrifuge test by Tazoh et al.(2005) involving a 2x2 pile group will be demonstrated.

A NEW PHYSICALLY SIMPLIFIED METHOD

The analysis comprises three consecutive steps. In STEP 1 , the soil response without the piles isdetermined as in Fig. 1. To this end, a 2D effective stress numerical analysis is performed of a verticalsection of the problem and its soil profile. Ground inclination, topographic irregularities such as river

banks or existing structural boundaries such as quay-walls are included in the model, but not the piles.Thus, the "free field" soil response is obtained at the location to be occupied by the pile foundation, interms of:

the distribution of the horizontal soil displacement 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.

Although the dynamic numerical analysis provides the required results at all times, the residual valuesafter the end of the shaking are of greater importance, due to the accumulative nature of the liquefaction induced soil flow.

Figure 1. Problem definition.

In STEP 2 , a horizontal section through the middle of the liquefied layer including the piles is analysed in2-D, subjected to the "free-field" unit displacement at the boundary. The ratio of the pile displacementover the soil displacement in the free-field (adequately away from the piles) is estimated, hereafter termed

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Santiago, Chileratio as depicted in Fig. 2 in a plan view. This ratio of displacements reflects the soil-pile interaction dueto soil flow, in quantitative terms. An elastic pseudo-static plane strain analysis of the horizontal section isconducted (Fig. 3). The pile group configuration is well represented, as is the liquefied soil layer withuniform shear modulus, G L, surrounding the piles. The pile sections are simulated as rigid inclusions intothe liquefied soil, G L. In order to attribute the appropriate horizontal resistance to the pile sections againstthe moving soil mass, an out of plane horizontal spring, K , is connected to each pile section.

It is evident that the effectiveness of the numerical analysis of the horizontal slice at the mid-depth, zs depends on the appropriate calibration of the following "key" parameters:

the horizontal stiffness of each pile section, K , and the shear modulus of the liquefied soil, G L.

Horizontal stiffness, K of each pile sectionEvery single pile of the pile group can be simulated as a vertical beam element, a column, withappropriate kinematic constraints at the boundaries (boundary conditions). The rotation at the top dependson the rigidity of the pile cap, the number of piles and their axial and lateral stiffness. Increasing any ofthese parameters tends to restrain the rotation at the pile head.

Figure 2. Definition of the ratio a as the ratio of the residual free-field soil displacement over theresidual pile group displacement due to liquefaction induced soil flow (plan view).

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Figure 3. Numerical model of the horizontal slice. The pile sections sustain the same horizontaldisplacement due to the pile cap constraint.

The active length of the pile depends on the depth to fixity, below the liquefied layer. The depth to fixityis defined in literature as the length of an equivalent column of the same stiffness with the pile stiffness to

produce the same displacements under lateral load. Depth-to-fixity values can be estimated from availablecharts in dimensionless form based on subgrade reaction modulus, pile diameter and rigidity, provided byseveral researchers (Priestley et al. 1996, Budek et al. 2000, Caltrans 1990). In general, the depth to fixityis measured from the ground surface. However, in the current case of liquefaction induced soil-flow,where the liquefied soil cannot provide significant support to the piles (while flowing around them), thedepth to fixity can be measured from the end of the liquefied zone. Therefore, the active length of the pile-column can be estimated by adding the depth to fixity to the portion of the pile embedded in the liquefiedzone and its overlying layers.

In retrospect, every single pile is equivalent to a column of a certain length fixed at the bottom with a

certain degree of rotational freedom at the top. The pile slice in the numerical model is just a section of themid-depth of the liquefied layer. Thus, the horizontal stiffness, K , of each pile section, is defined as the

point load that must be exerted on the pile-column at that depth, to cause a unit displacement at the samedepth.

Shear modulus, G L of the liquefied soilIn the framework of an elastic analysis of the horizontal slice, an equivalent linear shear modulus of theliquefied soil can be estimated by the following equation:

(1)

where, H L is the thickness of the liquefied zone, is the residual shear stress and is the accumulatedshear strain after the end of shaking, obtained from the numerical analysis of the free field (STEP 1) . Thisis how the stiffness degradation of the soil due to liquefaction is taken into account.

Herein, the elastic pseudo-static analysis of the horizontal slice has been conducted for three different pileconfigurations:

single pile 2x2 pile group (Tazoh et al., 2005) and

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Santiago, Chile 2x8 pile group (Sato et al., 2003).

The ratio , is obtained as function of the relative stiffness between the pile and the liquefied soil, K/G L,shown in Fig. 4 for the abovementioned different pile configurations.

When the relative stiffness tends to zero ( K/G L 0), the ratio tends to unity, which means that the pilesections move just like the soil, as a rigid inclusion. On the contrary, when the relative stiffness tends toinfinity ( K/G L ), the ratio tends to zero. This is due to the fact that the soil has practically zeroshear strength ( G L 0) and flows around the piles without exer ting any significant load on them.Moreover, Fig. 4 indicates that increasing the number of piles, the resistance of the foundation to themoving soil mass becomes stronger. It is worth mentioning that the numerical modeling of the pile-groupsection into the liquefied soil is based on the assumption that due to the pile-cap constraint the pilessustain the same horizontal displacement over all their depth.

Figure 4. The ratio as a function of the relative stiffness between the pile and the liquefied soil forthree different pile configurations: single pile, 2x2 and 2x8 pile group, obtained from several

parametric numerical analyses of the horizontal slice.

In retrospect, as long as the relative stiffness, K/G L, is determined, the ratio can be estimated.Eventually, multiplying the ratio with the free-field soil displacement at the mid-depth of the liquefiedzone, at the position which the piles occupy behind the quay-wall, as obtained from the free field analysis(STEP 1) , the pile displacement can be calculated at the mid-depth of the liquefied zone.

In STEP 3 , the total pile deformation at all depths and mainly the pile displacement at the top, isevaluated. The deformation shape of each pile, simulated as a beam element, is defined primarily by its

boundary conditions and only marginally by the load distribution along it. In other words, it has beenfound that the shape of the load distribution (uniform, p ; triangular, 0 p; trapezoidal, 0.5 p 1.5 p) alongthe pile only slightly affects the response of the pile in terms of displacements. This observation simplifiesthe analysis of pile response: a potential load distribution (e.g. trapezoidal) is chosen to be imposed on the

pile. We, thus, obtain its deformation shape as a function of the unknown p .

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Santiago, ChileUsing the known pile displacement at the mid-depth of the liquefied zone (from STEP 2 ), the shapefunction of the pile with depth is calibrated and thus, the unknown load intensity, p is estimated. Finally,the distribution of the pile displacements with depth, as well as the bending moments along the pile, aredetermined by imposing the already fully known load distribution on the pile-column. The parameters ofthe method are summarized in Table 1.

Table 1. The parameters of the proposed simple method.Soil

G L shear modulus of liquefied soilHL thickness of liquefied zone

z s mid-depth of liquefied zone measured from the

ground surface

u ff free-field horizontal soil displacement at the

characteristic depth and at the location potentiallyoccupied by the pile foundation

Pile

zp mid-depth of liquefied zone measured from the top ofthe pilel active length of the pile

Khorizontal stiffness of the pile-column at the

characteristic depth

Soil-Pile Interaction

K /G L relative stiffness between the pile and the liquefied

zone at the characteristic depth

ra t i o the ratio of horizontal pile displacement over thehorizontal soil displacement at the characteristic

depth

pload intensity describing the potential load distribution

along the pile

COMPARISON WITH CENTRIFUGE RESULTS

Several series of dynamic centrifuge experiments were conducted at Shimizu's Institute of Technology, inJapan (Tazoh et al., 2005), to evaluate the response of pile-foundation systems triggered by liquefactioninduced soil flow after quay-wall collapse. The test, chosen to be analysed with the proposed simplemethod, is illustrated in Fig. 5 in prototype scale. It includes a 2x2 pile group fixed at the bottom and

placed 3m away from the floating quay-wall. The soil profile contains a liquefiable layer of relativelyloose sand ( H L = 3.6 m), underlying a surficial unsaturated non-liquefiable crust. The input baseaccelerogram is also shown at the base of the model in Fig. 5 in prototype scale.

The first step of the method involves the centrifuge model, as depicted in Fig. 5, without the pile group; itis simulated and analysed numerically using the finite difference code FLAC . The numerical simulationinvolves the constitutive law by Byrne (1991) for pore pressure generation which is incorporated in thestandard Mohr-Coulomb plasticity model. The deformed grid after the end of shaking is shown in Fig. 6,indicating a relative horizontal displacement of the top of the quay-wall equal to 1.35m. It is worthmentioning that the displacement of the quay-wall recorded during the centrifuge test was less than 0.8 m

but with the pile group.

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Figure 5. Geometry and soil properties of the centrifuge model of test Case CD, side D into thelaminar box, in prototype scale (Tazoh et al., 2005). The input motion is illustrated at the base of the

model in prototype scale.

Figure 6. Initial finite difference mesh (above) and deformed grid (below) of the numerical modelwithout the piles. The residual horizontal displacement at the top of the quay-wall is estimated 1.35

m after the end of shaking.

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Santiago, ChileLiquefaction takes place within the loose sand layer, according to the excess pore pressure ratio timehistories (Fig. 7), obtained numerically. Liquefaction has indeed been observed during the centrifugeexperiment. It should be made clear, that direct rigorous comparison between the centrifuge and thenumerical results cannot be performed at this stage due to the presence of piles in the centrifuge test andtheir absence in the numerical model. However, a relatively similar response of the soil is expected awayenough from the piles. In this framework, a comparison of the acceleration time histories within theliquefied layer (3m below the ground surface) between experimental and numerical results has beenattempted in Fig. 8. There are significant similarities between the two accelerograms, such as cut-off ofthe acceleration, due to the occurrence of liquefaction, increasing the validity of the numerical analysis ofthe free -field response. Admittedly, differences also exist, especially in the shape of the individualacceleration cycles.

Figure 7. Computed time histories of excess pore pressure ratio at depths of 4, 3.5, 5.5 and 6 mbelow the ground surface, in the free-field (without the presence of piles).

Figure 8. Above: acceleration time history recorded during the centrifuge experiment 3m below theground surface away from the piles. Below: acceleration time history in the free field obtained

numerically.

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Santiago, ChileThe distributions of the residual shear stresses and strains as well as of the horizontal soil displacementsare obtained at a distance of 3m behind the quay-wall (at the location to be occupied by the pile group).These distributions are useful while proceeding to the second step where important parameters of the

problem such as G L , u ff and K/G L , ratio a and u p are determined. The values of these parameters areshown in Table 2. Each pile of the pile group is considered to be equivalent to a beam element fixed at the

bottom with no rotation at top.

Table 2. The values assigned to the parameters of the methodology during its application to thecentrifuge experiment by Tazoh et al. (2005).

Tazoh et al. (2005)

So i l

G L (kPa) 125

HL (m) 3.6

z s (m) 3.9

u ff (m) 0.505

Pi le

z p (m) 3.3

l (m) 8.1

K (kN/m) 585

Soi l -Pi le

In t e ra c t i o n

K /G L (m) 4.6

ra t i o 0.146

u p (m) 0.074

p uniform (kN/m) 3.8

p triangular (kN/m) 4.2

p trapezoidal (kN/m) 4

At the end of second step, the pile horizontal displacement at that depth has been estimated. To obtainestimates of the distributions of horizontal displacements and bending strains three different loaddistributions (uniform, triangular and trapezoidal), of yet unknown intensity p , are imposed on the pile-

beam element. The deformation line of the pile is thus obtained as a function of p , which can bedetermined from one known point of the pile displacement at the mid-depth of the liquefied zone ( zp,u p).Then, the bending strains along the pile are obtained through double differentiation of the displacements.The displacements and bending strains along the pile are depicted in Fig. 9, and they are compared withthe experimental recordings showing satisfying agreement. In particular, the trapezoidal distribution seemsto give the most accurate prediction of both displacements and bending strains.

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Figure 9. Estimated range of the horizontal displacement and bending strains along the piles, asobtained from the simplified methodology, in comparison with the centrifuge results by Tazoh et al.

(2005).

CONCLUDING REMARKS

In this paper, a simple physically-motivated methodology is highlighted for the evaluation of pile responsedue to liquefaction induced soil flow. The main characteristics of this methodology are: It avoids the associated empirical selection of stiffness reduction factors and does not involve the

use of p-y curves. It combines the results of analysis of a vertical 2D section of the geometry without the presence

of piles, and of the pseudo static analysis of a horizontal 2D slice containing the piles. Interaction between soil and piles is determined as a function of the relative stiffness between pile andliquefied soil.

The effectiveness of the new methodology in combination with suitable engineering judgment andreasonable assumptions can provide sufficient accuracy for designing pile groups against liquefaction-induced large soil displacements.

AKNOWLEDGEMENTS

The work of this paper was conducted for the project DARE, financed by a European Research Council(ERC) Advanced G rant under the Ideas Program in Support of Frontier Research [Grant Agreement228254].

Analysis

Analysis

Analysis

(10 -6)

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