This article presents an overview of the application of analytical methods in the theories of elasticity, poroelasticity, flow, and transport in porous media and plasticity to the solution of boundary value problems and initial boundary value problems of interest to geomechanics. The paper demonstrates the role of the analytical method in geomechanics in providing useful results that have practical importance, pedagogic value, and serve as benchmarking tools for calibrating computational methodologies that are ultimately used for solving more complex practical problems in geomechanics. There are 315 references cited in this article.

In this paper, we examine the coupled thermo-poromechanical behaviour of a fluid-saturated porous medium of infinite extent bounded internally by a fluid-filled cavity. The mechanical behaviour of the porous skeleton can either be Hookean elastic or elasto-plastic, with a constitutive response corresponding to a modified Cam Clay plasticity model. The fluid within the cavity can be subjected simultaneously to a temperature rise and a pressure pulse. The paper presents analytical results for the spherically symmetric thermo-poroelasticity problem and these are used to validate the thermo-poroelasticity module of a computational code. We proceed to examine the thermo-poroelasto-plasticity problem. Results presented in the paper illustrate the interaction between thermal and mechanical phenomena and their influence on the cavity fluid pressure and the skeletal stresses at the cavity boundary. The paper presents solutions that will be of value in benchmarking exercises.

This paper presents a technique for determining the near surface permeability of geomaterials and involves the application of a uniform flow rate to an open central region of a sealed annular patch on an otherwise unsealed flat surface. Darcy’s flow is established during attainment of a steady pressure at a constant flow rate. This paper describes the experimental configuration and its theoretical analysis via mathematical and computational techniques. The methods are applied to investigate the surface permeability characteristics of a cuboidal block of Indiana limestone measuring 508 mm. An inverse analysis procedure is used to estimate the permeability characteristics at the interior of the Indiana limestone block. The resulting spatial distribution of permeability is used to estimate the effective permeability of the tested block.