Lateral response of pile foundations in liquefiable soils

(1)

Full length article

Lateral response of pile foundations in lique

ﬁable soils

Asskar Janalizadeh, Ali Zahmatkesh

*

Babol University of Technology, Babol, Iran

a r t i c l e i n f o

Article history:

Received 6 March 2015 Received in revised form 5 May 2015

Accepted 6 May 2015 Available online 11 June 2015 Keywords: Pile foundations Lateral spreading Liquefaction Pseudo-static method

a b s t r a c t

Liquefaction has been a main cause of damage to civil engineering structures in seismically active areas. The effects of damage of liquefaction on deep foundations are very destructive. Seismic behavior of pile foundations is widely discussed by many researchers for safer and more economic design purposes. This paper presents a pseudo-static method for analysis of piles in liquefiable soil under seismic loads. A free-field site response analysis using three-dimensional (3D) numerical modeling was performed to deter-mine kinematic loads from lateral ground displacements and inertial loads from vibration of the su-perstructure. The effects of various parameters, such as soil layering, kinematic and inertial forces, boundary condition of pile head and ground slope, on pile response were studied. By comparing the numerical results with the centrifuge test results, it can be concluded that the use of the p-y curves with various degradation factors in liquefiable sand gives reasonable results.

1. Introduction

The liquefaction is one of the challenging issues in geotechnical engineering and it damages structures and facilities during earth-quakes. This phenomenon was reported as the main cause of damage to pile foundations during the major earthquakes (Kramer, 1996). In many earthquakes around the world, extensive damage to piles of bridges and other structures due to liquefaction and lateral spreading has been observed (Boulanger et al., 2003). Failures were observed in both sloping and level grounds and were often accompanied with settlement and tilting of the superstructure (Adhikari and Bhattacharya, 2008). The loss of soil strength and stiffness due to excess pore pressure in liquefiable soil may develop large bending moments and shear forces in the piles. If the residual strength of the liquefiable soil is less than the static shear stresses caused by a sloping site or a free surface such as a river bank, sig-nificant lateral spreading or downslope displacements may occur. The moving soil can exert damaging pressures against the piles, leading to failure (Finn and Fujita, 2002). The performance of structures above piles depends widely on the behavior of pile foundations under earthquake loading. During past earthquakes, because of inadequacy of the pile to sustain large shear forces and bending moments, the extensive damage in liquefiable soil has

been caused due to both lateral ground movement and inertial loads transmitted to piles. Under earthquake loading, the perfor-mance of piles in liqueﬁed ground is a complex problem due to the effects of progressive buildup of pore water pressures and decrease of stiffness in the saturated soil (Liyanapathirana and Poulos, 2005). These effects involve inertial interaction between structure and pile foundation, signiﬁcant changes in stiffness and strength of soils due to increase of pore water pressures, large lateral loads on piles, kinematic interaction between piles and soils, nonlinear response of soils to strong earthquake motions, kinematic loads from lateral ground displacements, and inertial loads from vibration of the su-perstructure (Bradley et al., 2009; Gao et al., 2011).

Various approaches including shaking table and centrifuge tests and also various numerical methods have been developed for the dynamic response analysis of single pile and pile group. The soile pileestructure interaction has been investigated using the centri-fuge test (e.g.Finn and Gohl, 1987; Chang and Kutter, 1989; Liu and Dobry, 1995; Hushmand et al., 1998; Wilson, 1998; Abdoun and Dobry, 2002; Su and Li, 2006) and shaking table test (e.g.Mizuno and Liba, 1982; Yao et al., 2004; Tamura and Tokimatsu, 2005; Han et al., 2007; Gao et al., 2011; Haeri et al., 2012). The obvious advantage of shaking table and centrifuge tests is the ability to obtain detailed measurements of response in a series of tests designed to physically evaluate the importance of varying earth-quake characteristics (e.g. level of shaking, frequency content), soil proﬁle characteristics, and/or pileesuperstructure characteristics (Wilson, 1998). However, some limitations exist in centrifuge tests, for example, sand grains in centrifuge tests correspond to bigger gravel particles in prototype (Towhata, 2008).

To simulate the piles in liqueﬁable soil layers,Finn and Fujita (2002), Klar et al. (2004), Oka et al. (2004), Uzuoka et al. (2007), * Corresponding author. Tel.: þ98 9158342367.

E-mail address:A.zahmatkesh@stu.nit.ac.ir(A. Zahmatkesh).

Peer review under responsibility of Institute of Rock and Soil Mechanics, Chi-nese Academy of Sciences.

http://dx.doi.org/10.1016/j.jrmge.2015.05.001

Contents lists available atScienceDirect

Journal of Rock Mechanics and

Geotechnical Engineering

(2)

Cheng and Jeremic (2009), Comodromos et al. (2009), andRahmani and Pak (2012) used three-dimensional (3D) ﬁnite element method. The complexity and time-consuming nature of 3D nonlinearﬁnite element method for dynamic analysis makes it useful only for very large practical projects or research and not feasible for engineering practice. However, it is possible to obtain reasonable solutions for nonlinear response of pile foundations with fewer computations by relaxing some of the boundary con-ditions in full 3D analysis (Finn and Fujita, 2002).

The simple approach for modeling and simulation of the piles in liquefied grounds is based on scaling of p-y springs, where p and y are the soil resistance per unit length of the pile and pile lateral displacement, respectively. Because of complexity and time-consuming of two-dimensional (2D) and 3D numerical modeling, most of the designers and researchers prefer to use one-dimensional (1D) Winkler method based on finite element or finite difference method for the seismic analysis of pile foundations. In pseudo-static method, a static analysis is carried out to obtain the maximum response (deflection, shear force and bending moment) developed in the pile due to seismic loading. In Winkler models, p-y curves are used to define the behavior of the nonlinear spring at any depth. These p-y curves can be obtained from the results of model tests or field (Liyanapathirana and Poulos, 2005). The Winkler assumption is that the soilepile interaction resistance at any depth is related to the pile shaft displacement at that depth only, inde-pendent of the interaction resistances above and below (Wilson, 1998).

This pseudo-static method has been suggested early byMiura et al. (1989), Miura and O’Rourke (1991), Liu and Dobry (1995), JRA (1996), AIJ (1998)and recently byLiyanapathirana and Poulos (2005)andElahi et al. (2010). This method for pile seismic anal-ysis sometimes underestimates, and sometimes overestimates shears, moments and deﬂection of the piles. However, in many practical conditions, the results of pseudo-static method are reasonable (Tabesh, 1997).

In this paper, a pseudo-static method has been applied for esti-mation of the response of pile during dynamic loading. First, de ﬁ-nition of the geometry and the soil modeling parameters are presented. Next, the numerical model is vertiﬁed by means of the centrifuge test. And then the effects of various parameters, including soil layering, kinematic and inertial forces, boundary condition of pile head and ground slope, on the behaviors of piles are studied. 2. Numerical analysis

All simulations were conducted using the open-source compu-tational platform OpenSees (McKenna and Fenves, 2007). This platform allows for developing applications to simulate the per-formance of structural and geotechnical systems subjected to static and seismic loadings. In this paper, the steps for calculation of pile response are summarized as follows:

(1) A free-ﬁeld site response analysis was performed during the dynamic loading using 3D numerical modeling. From this analysis, time history of ground surface acceleration and the maximum ground displacement along the length of the pile can be calculated.

(2) The dynamic analysis was performed using the time history of ground surface acceleration calculated in Step 1 for pile length above ground and superstructure with aﬁxed base. From this analysis, the maximum acceleration of superstructure can be calculated.

(3) In 1D Winkler analysis, the maximum soil displacement proﬁle calculated in Step 1 and the maximum acceleration of super-structure in Step 2 were applied to the pile as shown inFig. 1.

First, the time history of the ground surface acceleration and the maximum ground displacement at each depth were obtained from the free-field site response analysis.Taboada and Dobry (1993)and Gonzalez et al. (2002)showed that the pore pressure time histories recorded at the same elevation are identical, indicating the 1D behavior of the model. In free-field analysis, the model consists of a single column of 3D brick elements. The soil layers were modeled using cubic 8-noded elements with u-p formulation in which each node has four degrees of freedom: three for soil skeleton dis-placements and one for pore water pressure. To consider the effect of the laminar box in the numerical simulation, nodes at the same depths were constrained to have equal displacements in the hori-zontal and vertical directions. The pore water pressures were allowed to freely develop for all nodes except those at the surface and above the water table. The bottom boundary was assumed fixed in all directions.

The material model plays a key role in the numerical simulation of the dynamic behavior of liquefiable soils. The model inDafalias and Manzari (2004), a critical state two-surface plasticity model, was used in this paper. This model requires fifteen material pa-rameters and two state papa-rameters to describe the behavior of sands and has been amply tested for simulating the behavior of granular soils subjected to monotonic and cyclic loadings (Jeremic et al., 2008; Taiebat et al., 2010; Rahmani and Pak, 2012). The key advan-tages of the model are that (1) it is relatively simple and (2) it has a unique calibration of input parameters. Thus, a single set of pa-rameters independent of void ratio and effective consolidation stress level was used for the Dafalias and Manzari’s material model. Table 1 presents the material parameters for Nevada sand. The additional parameters used for free-field analysis are presented in Table 2. It can be noted that at the onset of liquefaction, change of soil particles creates additional pathways for water. This leads to a sig-nificant increase in permeability coefficient (Rahmani et al., 2012). In this study, the permeability coefficient value was increased 10 times the initial value (suggested byRahmani et al. (2012)).

For free-ﬁeld analysis, the simulations were carried out in two loading stages. At theﬁrst stage, the soil skeleton and pore water weight were applied to soil elements. The values of stress and strain in this stage were used as initial values for the next stage of loading. At the second stage, dynamic analysis was performed by applica-tion of an input moapplica-tion to the model base.

F=Msxamax

s

p-y materials

Pile

Fig. 1. A beam on the nonlinear Winkler foundation (BNWF) model for pseudo-static analysis.

(3)

In the second step, after free-ﬁeld analysis, pile length above ground and superstructure were modeled. The pile was modeled as beam column elements with elastic section properties. The structure was modeled at the pile head. Generally, the super-structures above the pile foundations are multi-degree of freedom systems, but in the design of pile foundations, the superstructure was modeled as a single mass at the pile head to simplify the analysis. In this step, the base model was alsoﬁxed.

The model considered for the third step (pseudo-static analysis) is shown inFig. 1. There are two versions of the pseudo-static BNWF method. These two methods are different in the way in which the lateral load on pile due to ground movement (kinematic load) is considered. Thefirst BNWF requires free-field soil movements as an input. The free-field soil displacements are imposed on the free ends of the p-y springs due to lateral dilatation layers. In the second BNWF, the limit pressures over the depth of the lateral spreading soil were applied and the p-y springs were removed in this interval. In case of limit pressure, interaction of the soil and pile was not modeled, because the analysis is simple and can be done by hand calculation. Inertia forces from superstructure are represented as static forces applied simultaneously with lateral spreading de-mands. When limit pressures are applied directly to the pile nodes, bending moments and cap displacements depend on acceleration records and are greatly overpredicted for small to medium motions. This can be explained by the fact that the lateral spreading dis-placements were not large enough to mobilize limit pressures and actual pressures are smaller than limit pressures. However, for large motions, the pile cap displacements were considerably under-predicted (Brandenberg et al., 2007). In this paper, the free-field soil movement was used as an input. The cap mass, multiplied by the maximum acceleration of the superstructure obtained from Step 2 as a lateral force (F), was applied at the pile head. The material properties of p-y curves for non-liquefied sand were computed based onAPI (1987). These curves are defined by the following equation: P ¼ Putanh Kz Puy (1) where Puis the ultimate bearing capacity at depth z, K is the initial modulus of subgrade reaction, and y is the lateral deflection. The initial tangent stiffness (Kin), based on Eq. (1), is obtained as Kin¼ Kz. The p-y curves were modeled as zero-length elements with PySimple1 materials. Under dynamic loading, the piles are influenced by kinematic loads from lateral ground displacements and inertial loads from vibration of the superstructure.Fig. 1shows an idealized schematic of the BNWF model for kinematic (F) and inertial (

D

s) loads. The loss of bearing capacity for piles in loose

sandy soils (particularly vulnerable to liquefaction and lateral spreading during dynamic loading) also occurred. Therefore, the excessive forces imposed on the foundation due to ground displacement led to shearing of the piles and subsequent structural collapse of the superstructure. There are three methods for considering the influence of liquefaction on p-y curves in sand. In thefirst case, the lateral resistance of liquefiable sand is assumed to be zero. This method can lead to large design responses and high construction costs which may be very conservative (Rollins et al., 2005). Another approach is to treat liquefiable sand as undrained soft clay and use the p-y curves for soft clay. The undrained shear strength used in this case is obtained as a ratio of undrained shear strength to initial effective overburden stress usingfield data, and it is a function of overburden stress and relative density (Rollins et al., 2005; Varun, 2010). The third method for the simulation of pile response in liquefiable soils is the use of reduction factors, called p-multipliers. The p-y curves in liquefiable sand are multiplied by a factor usually between 0.01 and 0.3 to decrease the strength of sand due to liquefaction (Rollins et al., 2005; Brandenberg et al., 2007; Varun, 2010). In this paper, the third method (p-multipliers) was used. The free-_{field soil displacement and lateral force in head pile} were imposed incrementally using a static load control integrator. 3. Validation of the proposed method

The performance and ability of the proposed approach to simulate pile behavior in liqueﬁable soil have been demonstrated by comparison between the numerical simulations and centrifuge tests performed byWilson (1998). In these tests, the soil pro_ﬁle consisted of two horizontal layers of saturated uniformly graded Nevada sand (seeFig. 2). On prototype scale, the lower layer was 11.4 m thick with relative density of 80% (dense) and the upper was 9.1 m thick with relative density of 35% (loose). The single pile was a Table 1

Material parameters for Nevada sand (Rahmani and Pak, 2012).

Elasticity Critical state Yield surface parameter, m Plastic modulus Dilatancy Dilatancy-fabric

G0 n M c lc e0 x h0 ch nb A0 nd zmax cz

150 0.05 1.14 0.78 0.027 0.83 0.45 0.02 9.7 1.02 2.56 0.81 1.05 5 800

Table 2

Additional parameters for pseudo-static and free-ﬁeld analysis (Wilson, 1998; Rahmani and Pak, 2012).

Dr(%) Permeability (m s1)

Saturated unit weight (kN m3)

Dry unit weight (kN m3) Friction angle () Void ratio, e 35 7.05 105 _19.11 _14.9 ₃₀ _0.743 80 3.7 105 _19.91 _16.2 _39.5 _0.594

(4)

steel pipe of 0.67 m in diameter, 18.8 m in length, and 19 mm in wall thickness. The pile tip was about 3.8 m above the container base. The superstructure mass (Ms) was 49.1 Mg. Properties of Nevada sand with Dr¼ 35% and 80% are presented inTable 2. The Kobe acceleration record (Fig. 3) was used as an input to shake model.

It is important to specify stiffness and lateral resistance of the p-y curves in liquefiable soil as explained in Section2. Three cases were considered to evaluate the effects of variations in stiffness and lateral resistance of the p-y curves on the testing results. These cases include: (1) use of the p-y curves without the influence of liquefaction; (2) use of the p-y curves with a constant degradation factor in liquefied sand; and (3) use of the p-y curves with various degradation factors in liquefiable sand. In case (2), different degradation factors can be considered between 0.05 and 0.5 to reduce the strength of liquefiable soil. In this case, because of the small strength of liquefiable soil, especially that of surface ground, a degradation factor of 0.1 was considered. In case (3), variation in degradation factor with depth was taken from a small value (top of liquefiable layer) to 1.0 (bottom of liquefiable layer). An exponential decay function from bottom to top of liquefied layer is proposed as R¼ R0e

z

HlnðR0Þ ₍₂₎

where R is a degradation factor, as a function of distance from the top of the layer (z); H is the liqueﬁable layer thickness; and R0is the degradation factor at the top of the layer. Both the ultimate resis-tance and initial stiffness of the p-y curves in the liqueﬁable layer were taken to be R% of their unreduced magnitudes.

In free-ﬁeld analysis under the Kobe acceleration record scaled to 0.04g, 0.12g and 0.22g, because of the ground level, lateral displacement (

D

s) was less than about 5 cm and the effects of ki-nematic loads on seismic response are small. Therefore, in these tests, it is reasonable to only consider the inertial loads for calcu-lation of the pile response. The superstructure displacement was calculated using acceleration of the superstructure obtained from the tests carried out byWilson (1998). The comparison between the observed and simulated results of superstructure displacement is shown inFig. 4. In cases (2) and (3), by considering the centrifuge test results, the best predictions were obtained with degradation factor of 0.1. These results clearly illustrate that the performance and accuracy of BNWF mainly depend on the accuracy in selection of the correct curves. As seen inFig. 4, the deﬂections observed during the centrifuge test are much larger than those simulated without the inﬂuence of liquefaction. This is due to the loss of bearing capacity for the piles in loose and medium sandy soils during dynamic loading. It can be noted that use of constant degradation factors at various depths gives unreasonable results. The pile head displacements have a good agreement with the available experimental data in case (3).

Fig. 5compares the maximum bending moment recorded from the centrifuge tests with that obtained from present analysis. In this ﬁgure, variation of R is similar to case (3) andFig. 5shows that the results obtained from the numerical analysis agree with the values recorded during the centrifuge test. It can be said that increasing the value of R from a small value at the top of the layer to 1.0 at the bottom of the layer produces a reasonable response for the piles. Therefore, this method was used for subsequent analysis.

4. Results and discussion

In this section, the behavior of pile for various conditions is discussed. The soil profile is the same as the one used in the centrifuge test performed by Wilson (1998). The profile has two layers: the upper layer is liquefiable (relative density of 35%) while

Fig. 3. Acceleration record of Kobe earthquake scaled to 0.22g used in the centrifuge test byWilson (1998). 0.1 0.15 0.2 0.25 0.3 0.35 0 5 10 15 20 25 Case (1) Case (2) Case (3) Centrifuge test Superstructure acceleration (g) S u pe rs tr uc tu re di sp la ce m ent (cm )

Fig. 4. Comparison of superstructure displacement in various cases with the centrifuge tests byWilson (1998). Bending moment (kN m) 0 500 1000 1500 0 5 10 15 20 Simulation Centrifuge test Dep th (m )

Fig. 5. Comparison of bending moment proﬁles with the centrifuge tests byWilson (1998).

(5)

the lower layer (relative density of 80%) is not. Three different ground slopes of 1%, 2%, and 4% were considered. The water table was supposed to be 1 m, 2 m, 3 m, and 4 m below the ground. This means that the thicknesses of non-liquefiable surface crust are 1 m, 2 m, 3 m, and 4 m. The input motion for the model was a 20-cycles sinusoidal wave with a frequency of 2 Hz and the peak acceleration of 0.5g. It should be noted that the intensity, frequency content (e.g. predominant period) and the duration of strong shaking are important characteristics of an earthquake (Rathje et al., 1998). These characteristics affected the response of piles. The pile re-sponses largely depend on the shaking amplitude. Increase in the shaking amplitude (because of more reduction of restraint on liq-uefied soil) resulted in a decrease in the restraint against bending under the lateral load, and the maximum bending moment in piles significantly increased (Gao et al., 2011). The frequency also had a significant effect on pile response.

The free-field analysis showed that displacement of level ground is significantly less than that of the sloping ground.Fig. 6 compares the displacement of sloping ground when the thickness of the non-liquefiable surface layer is 1 m and 2 m with ground slope of 2%. Thisfigure highlights the importance of non-liquefiable surface layer as a key parameter on ground displacement. When liquefaction occurs in sloping ground, because of displacements developing up to several meters, large lateral forces may act on the pile. This phenomenon is commonly called lateral spreading (Klar et al., 2004). In lateral spreading, the driving forces only exceed the resisting forces during those portions of the earthquake that impose net inertial forces in the downslope direction. Each cycle of net inertial forces in the downslope direction causes the driving forces to exceed the resisting forces along the slip surface, resulting in progressively and incrementally lateral movement (Day, 2002). Based on the results of free-field analysis, the displacement profile can be matched with constant displacement across the upper soil layer, a linear variation across the liquefiable and non-liquefiable layers.

The variations in bending moment along piles in different ground slopes for various conditions are presented inFigs. 7e10. The results show that in sloping grounds, when a non-liquefiable soil layer overlies a liquefiable soil layer and piles are embedded in the non-lique_{fiable soil layer, the lateral spreading has more} influences on the damage of piles. An increase in bending moment

occurred as the ground slope increased. After liquefaction, if the static shear stress caused by sloping ground is more than the shear strength of liquefiable soil, the non-liquefiable surface crust over-lying a liquefied soil layer can slide with a considerable amount of displacement. In this condition (lateral spreading), the non-liquefiable surface layer was carried along with the underlying fully liquefiable soil and a large lateral force was imposed on the embedded piles (Ashour and Ardalan, 2011). This force due to the lateral movement of the non-liquefiable layer has the potential to induce large bending moments in the piles leading to failure.

The boundary condition of the pile head has an important effect on the pile responses (moments, shear and deflections). In layered soil deposits, a liquefiable soil layer is overlain by a non-liquefiable layer; when the pile head is free, the maximum bending moment

Displacement (m) D ep th (m ) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 1 m 2 m

Fig. 6. Displacement proﬁle at two different thicknesses of non-liqueﬁable surface layer when the ground slope is 2%.

Bending moment (kN m) -500 0 500 1000 1500 2000 -14 -12 -10 -8 -6 -4 -2 0 1% 2% 4% D epth (m )

Fig. 7. Variations in bending moment along the pile in different sloping grounds (free head, without superstructure).

Bending moment (kN m) -2000 -1000 0 1000 2000 -14 -12 -10 -8 -6 -4 -2 0 1% 2% 4% D epth ( m )

Fig. 8. Variations in bending moment along the pile in different sloping grounds (ﬁxed head, without superstructure).

(6)

develops at a depth corresponding to the interface of liquefiable and non-liquefiable layers (seeFigs. 7 and 9). When the pile head is fixed, the maximum bending moment develops at two locations: (1) at the pile head and (2) at the interface of the two layers (see Figs. 8 and 10).

The dynamic effects during earthquake on deep foundations are critically important. These effects include the kinematic forces applied by the soil to the pile foundation and the inertial forces of the superstructure due to earthquake. The combination of cyclic horizontal kinematic loads due to ground displacements and in-ertial loads from the superstructure determines the critical load for piles during the shaking phase (Cubrinovski et al., 2009). The ki-nematic loads depend on the magnitude of ground deformations and the stiffness of the soil during a given loading cycle. Due to the

in_{fluence of liquefaction on free-field soil response and soilepilee} structure interaction, the magnitudes of inertial and kinematic loads change (Han et al., 2007). When the acceleration of ground surface or superstructure mass is large or lateral dynamic stiffness of pile group due to pile and/or soil stiffness is small, the inertial effects may become important (Elahi et al., 2010). Figs. 7 and 8 illustrate that in the absence of a superstructure, the maximum bending moment near the pile head decreases significantly, and a major difference is observed at that location between piles with and without superstructure, but the values are approximately un-changed at large depths (Figs. 9 and 10). In other words, the same kinematic forces were developed in the piles with and without superstructure. At greater depths, where the inertial effects from the superstructure are less significant, pile damage can occur due to the lateral loads arising from lateral spreading (the excessive ground movement). Both inertial and kinematic loads can cause damages at the pile head.

The inertia effects of the superstructure before development of the pore water pressures and liquefaction are important and the kinematic effects can often be neglected.Ishihara (1997)stated that inertial forces are the cause of development of the maximum bending moment near the pile head. These forces are predominant before liquefaction and are confirmed by the results ofFigs. 7e10. If the shaking continues after liquefaction, the inertial forces are combined with kinematic forces on the pile foundation arising from large cyclic ground deformations. It can be said that the kinematic loading in the areas of lateral spreading with relatively strong non-liquefiable surface layers is important. Then, the pile failure near the bottom of the liquefiable layer is likely influenced by kinematic loads from the liquefiable layer, while failure near the pile head is likely influenced by inertial loads from the superstructure and ki-nematic loads from the non-liquefiable layer. It should be noted that the bending moments are underpredicted when the structural inertia forces are neglected.

The pile response is sensitive to the thickness of the non-liquefiable surface layer (H) and thickness of the liquefiable layer (L).Fig. 11shows variations in pile head displacement when the ratio of thickness (H/L) for different sloping grounds is increased. The pile head displacement increases to a peak value and then decreases with subsequent increase in thickness ratio. As the thickness of the non-liquefiable surface layer increases, horizontal kinematic loads due to ground displacements also increase and

-500 0 500 1000 1500 2000 -14 -12 -10 -8 -6 -4 -2 0 1% 2% 4% Bending moment (kN m) D epth (m )

Fig. 9. Variations in bending moment along the pile in different sloping grounds (free head, with superstructure).

Fig. 10. Variations in bending moment along the pile in different sloping grounds (ﬁxed head, with superstructure).

H/L P) mc ( t ne me ca l psi d da e h eli 0 0.1 0.2 0.3 0.4 0.5 0.6 0 10 20 30 40 50 60 1% 2% 4%

(7)

result in higher pile head displacement. However, when the non-liquefiable surface layer is thick, because of increasing effective stress on the liquefiable layer, ground displacements are decreased, resulting in smaller values of pile head displacement. In addition, when the non-liquefiable surface layer is thick, due to increase of static shear stress in ground with great slopes, ground displace-ment and pile head displacedisplace-ment also increase.

5. Conclusions

This paper presents a method for analysis of piles in liquefiable soil under seismic loads. Three steps for calculation of pile response were: (1) free-field response analysis using 3D numerical modeling for calculation of ground surface acceleration and the maximum ground displacement along the length of the pile, (2) the dynamic analysis of pile length above ground and superstructure for calcu-lation of the maximum acceleration of superstructure, and (3) 1D Winkler analysis for calculation of pile response. All simulations in three steps were conducted using the open-source computational platform OpenSees. After verification of the numerical model using a centrifuge test, analyses were carried out for various conditions. By comparing the numerical results with the centrifuge test, it can be concluded that using the p-y curves with various degrada-tion factors in liquefiable sand produces reasonable results. In addition, the non-liquefiable surface layer especially in sloping ground plays a key role in ground displacement. When the pile head is free, the maximum bending moment develops at a depth corresponding to the interface of liquefiable and non-liquefiable layers. When the pile head is fixed, there are two locations for developing the maximum bending moment: (1) at the pile head and (2) at the interface of the two layers. Moreover, at greater depths, where inertial effects from the superstructure are less significant, pile damage may occur due to lateral loads arising from lateral spreading. Both inertial and kinematic loads can cause damages at the pile head.

Conﬂict of interest

The author confirms that there are no known conflicts of interest associated with this publication and there has been no signi_{ficant financial support for this work that could have} influ-enced its outcome.

References

Abdoun T, Dobry R. Evaluation of pile foundation response to lateral spreading. Soil Dynamics and Earthquake Engineering 2002;22(9e12):1051e8.

Adhikari S, Bhattacharya S. Dynamic instability of pile-supported structures in liqueﬁable soils during earthquakes. Shock and Vibration 2008;15(6):665e85.

American Petroleum Institute (API). Recommended practice for planning, designing and constructingﬁxed offshore platforms (RP 2A-WSD). Washington, DC, USA: API; 1987.

Architectural Institutive of Japan (AIJ). Recommendation for design of building foundations. 1998.

Ashour M, Ardalan H. Piles in fully liqueﬁed soils with lateral spread. Computers and Geotechnics 2011;38(6):821e33.

Boulanger RW, Kutter BL, Brandenberg SJ, Singh P, Chang D. Pile foundations in liqueﬁed and laterally spreading ground during earthquakes: centrifuge ex-periments and analyses. Davis, USA: Center for Geotechnical Modeling, Uni-versity of California; 2003. Report No. UCD/CGM-03/01.

Bradley BA, Cubrinovski M, Dhakal RP, MacRae GA. Intensity measures for the seismic response of pile foundations. Soil Dynamics and Earthquake Engi-neering 2009;29(6):1046e58.

Brandenberg J, Boulanger RW, Kutter BL, Chang D. Static pushover analyses of pile groups in liqueﬁed and laterally spreading ground in centrifuge tests. Journal of Geotechnical and Geoenvironmental Engineering 2007;133(9):1055e66.

Chang GS, Kutter BL. Centrifugal modeling of soil-pile-structure interaction. In: Engineering Geology and Geotechnical Engineering: Proceedings of the 25th Symposium, Reno, Nevada. Rotterdam, the Netherlands: A.A. Balkema; 1989. p. 327e36.

Cheng Z, Jeremic B. Numerical modeling and simulation of pile in liqueﬁable soil. Soil Dynamics and Earthquake Engineering 2009;29(11e12):1405e16.

Comodromos EM, Papadopoulou MC, Rentzepris IK. Pile foundation analysis and design using experimental data and 3-D numerical analysis. Computers and Geotechnics 2009;36(5):819e36.

Cubrinovski M, Ishihara K, Poulos H. Pseudo-static analysis of piles subjected to lateral spreading. Bulletin of the New Zealand Society for Earthquake Engi-neering 2009;42(1):28e38.

Dafalias YF, Manzari MT. Simple plasticity sand model accounting for fabric change effects. Journal of Engineering Mechanics 2004;130(6):622e34.

Day RW. Geotechnical earthquake engineering handbook. New York, USA: McGraw-Hill; 2002.

Elahi H, Moradi M, Poulos HG, Ghalandarzadeh A. Pseudostatic approach for seismic analysis of pile group. Computers and Geotechnics 2010;37(1e2):25e39.

Finn WDL, Fujita N. Piles in liqueﬁable soils: seismic analysis and design issues. Soil Dynamics and Earthquake Engineering 2002;22(9e12):731e42.

Finn WDL, Gohl WB. Centrifuge model studies of piles under simulated earthquake loading from dynamic response of pile foundationsdexperiment, analysis and observation. Geotechnical Special Publication American Society of Civil Engi-neering (ASCE) 1987;11:21e38.

Gao X, Ling XZ, Tang L, Xu P. soilepileebridge structure interaction in liquefying ground using shake table testing. Soil Dynamics and Earthquake Engineering 2011;31(7):1009e17.

Gonzalez L, Abdoun T, Sharp MK. Modelling of seismically induced liquefaction under high conﬁning stress. International Journal of Physical Modelling in Geotechnics 2002;2(3):1e15.

Haeri SM, Kavand A, Rahmani I, Torabi H. Response of a group of piles to liquefaction-induced lateral spreading by large scale shake table testing. Soil Dynamics and Earthquake Engineering 2012;38:25e45.

Han JT, Kim SR, Hwang JI, Kim MM. Evaluation of the dynamic characteristics of soilepile system in liqueﬁable ground by shaking table tests. In: The 4th In-ternational Conference on Earthquake Geotechnical Engineering. Thessaloniki, Greece; 2007. Paper No. 1340.

Hushmand B, Scott RF, Crouse CB. Centrifuge liquefaction tests in a laminar box. Geotechnique 1998;38(2):253e62.

Ishihara K. Terzaghi oration: geotechnical aspects of the 1995 Kobe earthquake. In: Proceedings of the 14th International Conference on Soil Mechanics and Foun-dation Engineering. Rotterdam, the Netherlands: A.A. Balkema; 1997. p. 2047e73.

Japanese Road Association (JRA). Speciﬁcation for highway bridges, part V: seismic design. Tokyo, Japan: JRA; 1996.

Jeremic B, Cheng Z, Taiebat M, Dafalias Y. Numerical simulation of fully saturated porous material. International Journal for Numerical and Analytical Methods in Geomechanics 2008;32(13):1636e60.

Klar A, Baker R, Frydman S. Seismic soilepile interaction in liqueﬁable soil. Soil Dynamics and Earthquake Engineering 2004;24(8):551e64.

Kramer SL. Geotechnical earthquake engineering. Upper Saddle River, USA: Pren-tice-Hall Inc.; 1996.

Liu L, Dobry R. Effect of liquefaction on lateral response of piles by centrifuge model tests. NCEER Bulletin 1995;9(1):7e11.

Liyanapathirana DS, Poulos HG. Seismic lateral response of piles in liquefying soil. Journal of Geotechnical and Geoenvironmental Engineering 2005;131(12): 1466e79.

McKenna F, Fenves GL. The OpenSees command language manual. Version 1.2. Berkeley, USA: Paciﬁc Earthquake Engineering Research Center, University of California; 2007.http://opensees.berkeley.edu.

Miura F, O’Rourke TD. Lateral spreading effects on pile foundations. In: Proceedings of the 3rd US-Japan Workshop on Earthquake Resistant Design of Lifeline Fa-cilities and Countermeasures for Soil Liquefaction. MCEER; 1991.

Miura F, Stewart HE, O’Rourke TD. Nonlinear analysis of piles subjected to lique-faction induced large ground deformation. In: Proceedings of the 2nd US-Japan Workshop on Liquefaction, Large Ground Deformations and Their Effect on Lifelines. MCEER; 1989.

Mizuno H, Liba M. Shaking table testing of seismic building-pile-soil interaction. In: Proceedings of the 5th Japan Earthquake Engineering Symposium, Tokyo, Japan; 1982. p. 1713e20.

Oka F, Lu CW, Uzuoka R, Zhang F. Numerical study of structure-soil-group pile foundations using an effective stress based liquefaction analysis method. In: Proceedings of the 13th World Conference on Earthquake Engineering, Van-couver, Canada; 2004. Paper No. 3338 (CD-ROM).

Rahmani A, Fare OG, Pak A. Investigation of the inﬂuence of permeability coefﬁcient on the numerical modeling of the liquefaction phenomenon. Scientia Iranica 2012;19(2):179e87.

Rahmani A, Pak A. Dynamic behavior of pile foundations under cyclic loading in liqueﬁable soils. Computers and Geotechnics 2012;40:114e26.

Rathje EM, Abrahamson NA, Bray JD. Simpliﬁed frequency content estimates of earthquake ground motion. Journal of Geotechnical and Geoenvironmental Engineering 1998;124(2):150e9.

Rollins K, Gerber T, Lane J, Ashford S. Lateral resistance of a full-scale pile group in liqueﬁed sand. Journal of Geotechnical and Geoenvironmental Engineering 2005;131(1):115e25.

Su D, Li XS. Effect of shaking intensity on seismic response of single-pile foundation in liqueﬁable soil. In: Ground modiﬁcation and seismic mitigation. ASCE; 2006. p. 379e86.

Tabesh A. Lateral seismic analysis of piles. PhD Thesis. Sydney, Australia: Depart-ment of Civil Engineering, University of Sydney; 1997.

(8)

Taboada VM, Dobry R. Experimental results of model No. 1 at RPI. In: Arulanandan K, Scott RF, editors. Veriﬁcation of numerical procedures for the analysis of soil liquefaction problems. Rotterdam, the Netherlands: A.A. Bal-kema; 1993. p. 3e18.

Taiebat M, Jeremic B, Dafalias YF, Kaynia AM, Cheng Z. Propagation of seismic waves through liqueﬁed soils. Soil Dynamics and Earthquake Engineering 2010;30(4): 236e57.

Tamura S, Tokimatsu K. Seismic earth pressure acting on embedded footing based on large-scale shaking table tests. In: Seismic performance and simulation of pile foundations in liqueﬁed and laterally spreading ground. Reston, USA: American Society of Civil Engineers; 2005. p. 83e96.

Towhata I. Geotechnical earthquake engineering. Berlin-Heidelberg, Germany: Springer-Verlag; 2008.

Uzuoka R, Sento N, Kazama M, Zhang F, Yashima A, Oka F. Three-dimensional nu-merical simulation of earthquake damage to group-piles in a liqueﬁed ground. Soil Dynamics and Earthquake Engineering 2007;27(5):395e413.

Varun V. A non-linear dynamic macroelement for soil structure interaction analyses of piles in liqueﬁable soils. PhD Thesis. Atlanta, USA: School of Civil and Envi-ronmental Engineering, Georgia Institute of Technology; 2010.

Wilson DW. Soil-pile-superstructure interaction in liquefying sand and soft clay. PhD Thesis. Davis, USA: University of California; 1998.

Yao S, Kobayashi K, Yoshida N, Matsuo H. Interactive behavior of soil-pile-superstructure system in transient state to liquefaction by means of large shake table tests. Soil Dynamics and Earthquake Engineering 2004;24(5):397e 409.

Ali Zahmatkesh was born in 1984 in Ferdows, Khorasan, Iran. He received his M.Sc. degree in Geotechnical Engi-neering from Mazandaran University, Iran in 2010. Since 2012, he is a Ph.D. student at Babol University of Tech-nology. His thesis topic is Analysis of Performance of Pile Foundations in Liqueﬁed Soils. His research interests cover soil improvement, soil liquefaction and numerical modeling.