Geometrical and material non linear analysis of fully and partially saturated porous media

A formulation for a partially saturated porous medium undergoing large elastic or elastoplastic deformations is presented. The porous material is treated as a multiphase continuum with the pores of the solid skeleton filled by water and air, this last one at constant pressure. This pressure may either be the atmospheric pressure or the cavitation pressure. The governing equations at macroscopic level are derived in a spatial and a material setting. Solid grains and water are assumed to be incompressible at the microscopic level. The elastoplastic behaviour of the solid skeleton is described by the multiplicative decomposition of the deformation gradient into an elastic and a plastic part. The effective stress state is limited by the Drucker-Prager yield surface. The water is assumed to obey Darcy's law. Numerical examples of the Liakopoulos' test and of strain localisation of dense and loose sand conclude the paper.