Numerical implementation of fundamental solution for solving 2D transient poroelastodynamic problems

Abstract

This paper presents the numerical implementation of boundary element formulation for solving two-dimensional poroelastodynamic problems in time domain. The derivation of the time-dependent integral equations is based on the Biot’s theory and the reciprocal theorem. The analytical form of a 2D fundamental solution in time domain for porous media with incompressible components (solid particles and fluid) is derived and validated. After the analytical time integration of the fundamental solution kernels, a time-marching procedure is established. The comparison of different time interpolation functions shows that the mixed interpolation gives more stable response. In addition, the linear θ method is used in order to improve the numerical stability of the proposed approach. Finally, two examples are presented to investigate the stability and the accuracy of this approach for wave propagation analyses.