Time Domain Traction and Flux Fundamental Solutions for 3D Saturated Poroelastic Media with Incompressible Constituents

AbstractOne of the key factors in the time domain boundary element method (BEM) for dynamic poroelasticity is an applicable fundamental solution of the governing differential equations. With the completion of the fundamental solutions, this paper is dedicated to the simple time domain traction and fluid flux fundamental solutions for the three-dimensional (3D) u-p formulation of saturated porous media where fluid and soil particles are assumed incompressible in comparison with the compressibility of the soil structure. First, the explicit Laplace transform fundamental solutions are obtained from the governing differential equations which were written in terms of solid displacements and fluid pressure. Subsequently, the closed form time domain traction and fluid volumetric flux fundamental solutions are derived by analytical inversion of the Laplace transform solutions. Finally, a set of numerical results are presented which demonstrate the accuracy and some salient features of the derived analytical transient traction and fluid flux fundamental solutions.