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.

The Analytical Method in Geomechanics

The time-harmonic response of a cylindrical elastic bar (pile) partially embedded in a homogeneous poroelastic medium and subjected to a vertical load is considered. The bar is modeled using 1D elastic theory valid for long bars in the low-frequency range, and the porous medium using Biot's 3D elastodynamic theory. The bar is bonded to the surrounding medium along the contact surface. The problem is formulated by decomposing the bar/porous medium system into a fictitious bar and an extended porous medium. A Fredholm's integral equation of the second kind governs the distribution of axial force in the fictitious bar. The integral equation involves kernels that are displacement and strain influence functions of a poroelastic half-space subjected to a buried, uniform vertical patch load. The governing integral equation is solved by applying numerical quadrature. The solutions for axial displacement and axial force of the bar, and the pore pressure are also derived. Selected numerical results for vertical imp...

V. Apirathvoraku

Papers

Quasi-static bending of a cylindrical elastic bar partially embedded in a saturated elastic half-space