The soil-structure interaction in general has been a concern; therefore, more research is needed to further understand and better model this interaction (Abdel-Mohti and Pekcan
2013a,
b), Khodair and Hassiotis (
2013). The primary purpose of using piles is to transfer the loads from the superstructure and the abutment to a reliable soil, in cases where the soil near the ground surface can not support the applied loads. Piles can transfer both axial and lateral forces. As the pile is subjected to lateral loads, the soil mass surrounding the pile plays a key-role in providing lateral support for the pile. The nature of pile–soil interaction is three dimensional and to complicate the problem further, soil is a nonlinear and anisotropic medium. Therefore, finding a closed form solution to such problem is extremely difficult. Several methods have been used to predict the response of the composite pile–soil system. The persistent obstacle in such processes is to find a valid approximation for soil representation. The subgrade reaction approach provides the simplest solution for the pile–soil interaction problem. In this approach, the pile is treated as an elastic laterally loaded beam. The soil is idealized as a series of independent springs with constant stiffness, where the lateral stiffness at one point does not affect the lateral stiffness at other points along the depth of the pile. The spring stiffness, or modulus of subgrade reaction, is defined as the ratio of the soil reaction per unit length of the pile as described in Eq. (
1):
where
p is the soil resistance per unit length of the pile,
K
h
is the modulus of subgrade reaction, and
y is the lateral deflection of the pile.
The behavior of the pile is assumed to follow the differential equation of a beam:
(2)
where
x is length along pile, and
E
p
I
p
is the flexural stiffness of pile. The solution for the differential equation are readily available and can be found in Hetenyi (
1946). The subgrade reaction has been widely accepted in the analysis of soil-structure interaction problems (Reese and Matlock
1956; Broms
1964). However, a drawback of the method is its inability to account for the continuity of soil. Additionally, the linear representation of the subgrade reaction for the soil elements along the depth of the pile fails to account for the non-linear nature of the soil. The p-y approach is another method for handling pile–soil interaction. The only difference between the p-y method and the subgrade reaction method is that the former is based on defining a nonlinear relationship between the soil reaction and the lateral deflection at each point along the depth of the pile. Therefore, a p-y relationship is defined at each distinctive point along the depth of the pile. The solution to Eq. (
2) can be obtained using the finite difference method and computers. Appropriate boundary conditions must be imposed at the pile head to insure that the equations of equilibrium and compatibility are satisfied at the interface between the pile and the superstructure. The concept of a p-y curve was first introduced by McCelland and Focht (
1958). The development of a set of p-y curves can introduce a solution to the differential equation in Eq. (
2), and provide a solution for the pile deflection, pile rotation, bending moment, shear, and soil reaction for any load capable of being sustained by the pile. Several methods to obtain p-y curves have been presented in the literature (Georgiadis and Butterfield
1982; O’Neill and Gazioglu
1984; Dunnavant and O’Neill
1989). These methods rely on the results of several empirical measurements. Some researchers such as Ruesta and Townsend (
1997) and Gabr et al. (
1994) have attempted to enhance p-y curve evaluation based on in situ tests such as cone penetration, pressuremeter and dilatometer. However, such attempts have focused on the soil part of soil pile interaction behaviors. Robertson et al. (
1985) developed a method that used the results of a pushed in pressuremeter to evaluate p-y curves of a driven displacement pile. Attempts towards deriving p-y curves using three dimensional finite element model has been provided by Brown Dan and Shie (
1990,
1991). A simple elastic–plastic material model is used for the soil to model undrained static loading in clay soils. p-y curves are developed from the bending stresses in the pile, where nodal stresses along the pile are used to obtain bending. The finite element method (FEM) is considered the most powerful tool in modeling soil-structure interaction. The FEM has several advantages over the other methods, some of which are the: (1) versatility of the method allows for modeling different pile and soil geometries, (2) capability of using different boundary and combined loading conditions, (3) discretization of the model into small entities allows for finding solutions at each element and node in the mesh, (4) feasibility for modeling different types of soil models and various material behavior for piles, and (5) ability to account for the continuity of the soil behavior. Several researchers have used the FEM to model pile–soil interaction. Desai and Appel (
1976) presented a finite element procedure that can allow for nonlinear behavior of soils, nonlinear interaction effects, and simultaneous application of axial and lateral loads. The pile was modeled as a one-dimensional beam element and the interaction between the pile and the soil was simulated by a series of independent springs. The variations of the generalized displacements and internal forces were described by means of energy functionals incorporating the adjoint structure concept. Thompson (
1977) developed a two-dimensional finite element model to produce p-y curves for laterally loaded piles. The soil was modeled as an elastic-hyperbolic material. Desai and Kuppusamy (
1980) introduced a one dimensional finite element model, in which the soil was simulated as nonlinear springs and a beam column element for the pile. The Ramberg–Osgood model was used to define the soil behavior. Faruque and Desai (
1982) implemented both numerical and geometric non-linearities in their three-dimensional finite element model. The Drucker-Prager plasticity theory was adopted to model the non-linear behavior of the soil. The researchers declared that the effect of geometric non-linearity can be crucial in the analysis of pile–soil interaction. Kumar (
1992) investigated the behavior of laterally loaded single piles and piles group using a three-dimensional non-linear finite element modeling. Greimann et al. (
1986) conducted a three dimensional finite element analysis to study pile stresses and pile–soil interaction in integral abutment bridges. The model accounted for both geometric and material nonlinearities. Nonlinear springs were used to represent the soil, and a modified Ramberg–Osgood cyclic model was used to obtain the tangential stiffness of the nonlinear spring elements. Kooijman (
1989) presented a quasi three-dimensional finite element model. The rationale behind his model was that for laterally loaded piles, the effect of the vertical displacements was assumed to be negligible. Therefore, it was plausible to divide the soil into a number of interacting horizontal layers. For these layers an elastoplastic finite element discretization was used. The contact algorithm in this model was based on defining an interface element, which characterized the tangential and normal behavior of pile and soil contact. This simulated slip, debonding, and rebonding of the pile and the soil. Bijnagte et al. (
1991) developed a three-dimensional finite element analysis of the soil-structure interaction. The model utilized an elastic-perfectly plastic theory implementing the Tresca and the Mohr–Coulomb failure criteria. That paper introduced recommendations for the design of piles and design values for thermal expansion coefficients. Arsoy et al. (
1999) developed a plane strain finite element model with symmetry around the centerline of the bridge. The abutment was modeled using linear stress–strain criteria. The approach fill and the foundation soil were modeled using hyperbolic material properties. The loads applied on the model represent the loads reflected from the superstructure and the abutment. Ellis and Springman (
2001) developed a plane strain FE model for the analysis of piled bridge abutments. The study used an equivalent sheet pile wall having the same flexural stiffness per unit width as the piles and soil that it replaced. Faraji et al. (
2001) used a three dimensional FE model to study the effect of thermal loading on pile–soil-interaction. The authors relied on the p-y method to model the non-linear behavior of the soil. The soil pressure distribution on the abutment is typically nonlinear and varies with depth, amount, and mode of wall displacement. A small parametric study was conducted to study the effect of the level of soil compaction on the response of the composite pile–soil system. Rajashree and Sitharam (
2001) developed a nonlinear finite element model of batter piles under lateral loading. In their model, the nonlinear soil behavior was modeled using a hyperbolic relation for static load condition and modified hyperbolic relation, including degradation and gap for cyclic load condition.
The research described in this paper presents a numerical investigation to study the composite pile–soil system. The objectives of this research are to: (1) analyze pile–soil interaction using the finite difference software LPILE 2012 and the finite element software Abaqus/Cae and SAP2000, (2) compare the bending moments and lateral displacements induced along the depth of the pile using the finite difference method and the finite element models, and (3) conduct a parametric study to determine the effect of relevant design parameters which include the soil modulus of elasticity, increasing the amount of clay surrounding the piles, and varying the number of soil springs on the pile induced bending moment and lateral displacements along its depth.