An efficient finite element scheme for elastic porous media

Abstract

A semi-analytical finite element scheme for the analysis of diffusion process in linear elastic porous media is presented. Variational principle based on Biot's Theory serves to establish discretized equilibrium and flow equations in terms of nodal displacements and fluid pore pressures. Time dependency of the system is removed by the Laplace transformation.The Laplace transforms of nodal pore pressures can be obtained by solving a standard eigenvalue system after releasing all nodal displacements through condensation. In the case of step loads commonly found in consolidation problems, die Laplace transforms can be inverted analytically. For general loading however, a series of step loads is introduced as its approximation, and the final solution is obtained by superposiiton.Three types of quadrilateral plane-strain finite elements are tested for their performance in solving 2-D consolidation problems by the present scheme. The quadrilateral element with eight displacement and four pore pressure nodes shows the best overall performance. Results from numerical examples indicate that the present scheme is extremely efficient. Solution of both the pore pressure and the displacement fields at any specified time can be determined explicitly without intermediate solutions.