BFree Finite Element Approach for Saturated Porous Media: Consolidation

M M Stickle,M Pastor,A Yague

doi:10.1155/2016/4256079

Abstract

TheBfree finite element approach is applied to the governing equations describing the consolidation process in saturated poroelastic medium with intrinsically incompressible solid and fluid phases. Under this approach, where Voigt notation is avoided, the finite element equilibrium equations and the linearization of the coupled governing equations are fully derived using tensor algebra. In order to assess theBfree approach for the consolidation equations, direct comparison with analytical solution of the response of a homogeneous and isotropic water-saturated poroelastic finite column under harmonic load is presented. The results illustrate the capability of this finite element approach of reproducing accurately the response of quasistatic phenomena in a saturated porous medium.

Highlights

The range of interesting problems involving porous media has increased dramatically in recent years
It is worth recalling that the motion of fluid within a porous medium is usually expressed in terms of an Eulerian coordinate system with respect to the current configuration of the solid skeleton [6]
The B free finite element approach is applied to the governing equations describing the consolidation process in saturated poroelastic medium

Summary

Introduction

The range of interesting problems involving porous media has increased dramatically in recent years. In order to obtain accurate, robust, and efficient solutions of the coupled partial differential equations that come up from TPM, numerical techniques are usually required In this context, the finite element method is one that has achieved significant results [5,6,7,8,9,10,11]. Zienkiewicz and coworkers presented the tensorial form for the sake of completeness of the referred text, but it seems that this approach was avoided in the finite element implementation. It is worth mentioning [16]. In order to assess the accuracy of the B free approach, a direct comparison with an analytical solution is presented

Consolidation Equations for Saturated Soils

Variational Formulation of the Consolidation Equations

B Free Finite Element Approach

Numerical Application

Conclusions