A finite element model for variably saturated geomaterials. A space and time discretisation for a multiphase porous material model at large elasto-plastic strain

A finite element formulation for an isothermal saturated and partially saturated porous medium undergoing large elastic or inelastic deformations is presented. This model is derived from the general thermo-hydro-mechanical model for porous materials developed in the previous contribution from the authors to this volume. The porous medium is treated as a multiphase continuum with the pores of the solid skeleton filled by water and air, this last one at constant pressure. The governing equations at macroscopic level are derived in a spatial setting. Solid grains and water are assumed to be incompressible at the microscopic level for simplicity. The consistent linearisation of the fully non linear coupled system of equations is derived. A spatial finite element formulation of the governing equations conclude this chapter.