Deformations and Stresses in Finite Porous Medium

Abstract

Deformations and stresses in a fluid saturated porous medium of finite width are analyzed. The porous medium is assumed to be a binary mixture consisting of a linear elastic fluid and a linear elastic solid. The equilibrium equations for the solid constituent and all constitutive equations are expressed in terms of the solid displacements in a two-dimensional space. In addition to these equations the boundary conditions for a surface line load are obtained by separating the problem into symmetric and antisymmetric parts. Governing equilibrium equations are solved using standard and extended finite sine and cosine transformations for symmetric and antisymmetric parts, respectively. The final expressions are obtained by superposing the symmetric and antisymmetric solutions resulting from inverse standard and extended finite sine and cosine transformations. The stresses for the solid and fluid constituents and diffusion forces are obtained in terms of solid displacements by means of constitutive equations. The problem is of practical importance especially in the case of elevated roads which are supported by retaining walls from both sides.