Steady-State Solutions of Multilayered and Cross-Anisotropic Poroelastic Half-Space due to a Point Sink

Abstract

This paper presents analytical solutions for the steady-state response of displacements and stresses in a half-space subjected to a point sink. The half-space is modeled as a multilayered poroelastic medium with both the permeability and the poroelasticity being cross anisotropic. The basic governing equations are presented in dimensionless style, and the state vector method together with the Hankel transform technique is adopted to solve them and obtain a transfer matrix in a clearly arranged way. Forward and backward transfer matrix techniques are utilized in the analytical formulation of solutions for a multilayered half space. Numerical results are presented to conduct some parametric studies and illustrate the influence of layering and material inhomogeneity on the settlement of the soils. The numerical evaluations of the solutions in the multilayered porous media can be easily achieved with high efficiency and accuracy.