A New Coupled Analysis for Nearly Incompressible and Impermeable Saturated Porous Media on Mixed Finite Element Method: I. Proposed Method

Abstract

In the general mixed finite element analysis for the porous media, a fluid is assumed to be nearly incompressible; however, the solid may undergo a range of deformations from relatively large to small. If both constituent are assumed to be nearly incompressible and impermeable, the finite element analysis is very complex because of element locking. In order to overcome this difficulty, stable procedures using equal order elements have been introduced with stability analyses. However, these methods have a drawback that critical time steps in the stability analysis have to be determined by modal analysis. In this paper, a new coupled analysis based on a stable algorithm is introduced to remedy the drawback. First, governing equations for saturated porous media in frame of Biot's theory are derived on macroscopic sense, and that are represented into approximation forms which is divided into solid and fluid phase for finite element procedure. Moreover, a new coupled analysis based on a stable algorithm is introduced. In this procedure, the multi time step, the remeshing step and the sub iteration step are proposed for a stable analysis. These steps make it possible to simply solve numerical instabilities such as convergence and compatibility problems.