An Integral Equation Model for a Pile in a Layered Transversely Isotropic Saturated Soil

In this paper, an integral equation model is established to predict the time-dependent response of a vertically loaded pile embedded in a layered Transversely Isotropic Saturated Soil (TISS).

Based on the fictitious pile method, the pile-soil system is decomposed into an extended saturated half-space and a fictitious pile. The extended half-space is treated as a layered TISS, while the fictitious pile is considered as a 1D bar. The pile-soil compatibility is accomplished by requiring that the axial strain of the fictitious pile be equal to the vertical strain of the extended layered TISS along the axis of the pile. The second kind Fredholm integral equation of the pile is then derived by using the aforementioned compatibility condition and the fundamental solution of the layered TISS, which is equivalent to the solution of the layered TISS subjected to a uniformly-distributed load acting vertically over a circular area with the radius equal to that of the pile. The fundamental solution of the layered TISS is obtained via the Reflection-Transmission Matrix (RTM) method for the layered TISS. Applying the Laplace transform to the Fredholm integral equation, and solving the resulting integral equation, the transformed solution is obtained. The time domain solution of the pile-soil system is retrieved via the inverse Laplace transform.

Numerical results of this paper agree with existing solutions very well, validating the proposed pile-soil interaction model. A parametric study is carried out to examine the influence of some parameters on the response of the pile-soil system.