A model for unsaturated porous media undergoing large inelastic strains

A formulation for a partially saturated porous medium undergoing large elastoplastic deformations is presented. 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, which is taken as reference pressure (passive air phase assumption). This pressure may either be the atmospheric pressure or the cavitation pressure (isothermal monospecies approach). The governing equations at macroscopic level are derived in a spatial and a material setting. Solid grains and water are assumed to be incompressible. The elasto-plastic behaviour of the solid skeleton is described by the multiplicative decomposition of the deformation gradient into an elastic and a plastic part. The Kirchhoff effective stress tensor and logarithmic principal strains are used in conjunction with an hyperelastic free energy function. 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 undrained dense sands under quasi static loading conditions conclude the paper.