Axially Loaded End-Bearing Pile Foundations: Analytical Formulation Incorporating Soil Nonhomogeneity

Abstract

This paper demonstrates a new analytical formulation for axially loaded end-bearing pile foundations embedded in a nonhomogeneous soil deposit. The nonhomogeneity in the analysis is introduced through an analytical expression that describes parabolic, linear, and hyperbolic variations of the shear modulus with depth. Soil deformation is modeled using separable functions, and the governing equations for pile–soil interaction are derived based on the extended Hamilton’s principle. Bessel functions are employed to obtain the solution of the differential equation governing soil motion. Because of nonconstant coefficients in the pile differential equation, a closed-form analytical solution to the differential equation is not feasible. To solve for the pile, the approximate analytical Ritz procedure is employed in which a trial function for the pile displacement satisfying the geometric boundary condition a priori is assumed. The degree of accuracy of the developed analytical formulation (for both static and dynamic response) is ensured with existing analytical and finite-element formulations available in the literature. Furthermore, a parametric study is performed to investigate the effect of nonhomogeneity on the pile response, and it is found that nonhomogeneity is particularly important for soft soil deposits.