Integral Equation for Dynamic Poroelasticity in Frequency Domain with BEM Solution

Abstract

This paper presents a singular integral equation technique for solving dynamic poroelasticity problems. The poroelastic governing equations are presented using total stress variables instead of the partial stress ones in Biot's formulation. It is then established that there exists an analogy between the dynamic thermoelasticity and the dynamic poroelasticity if they are formulated in the frequency domain. The integral equations are derived based on the reciprocity energy principle. The fundamental solutions of point force and source are obtained from thermoelasticity literature according to the analogy. A two‐dimensional boundary element program is developed for the numerical solution. To verify the computer code, several fundamental one‐dimensional problems involving poroelastic columns excited either from the top or at the bottom by stress, pressure, or displacement are examined using both the boundary element technique and the exact solutions. In two‐dimensional geometry, we investigate a soil stratum under strip loading. A preliminary Coulomb failure analysis is conducted.