A micro-mechanics-based elastic-plastic model for porous rocks: applications to sandstone and chalk

A micro-mechanics-based elastic-plastic model is proposed to describe mechanical behaviors of porous rock-like materials. The porous rock is considered as a composite material composed of a solid matrix and spherical pores. The effective elastic properties are determined from the classical Mori-Tanaka linear homogenization scheme. The solid matrix verifies a pressure-dependent Mises-Schleicher-type yield criterion. Based on the analytical macroscopic yield criterion previously determined with a nonlinear homogenization procedure (Shen et al. in Eur J Mech A/Solids 49:531-538, 2015), a complete elastic-plastic model is formulated with the determination of a specific plastic hardening law and plastic potential. The micro-mechanics-based elastic-plastic model is then implemented for a material point in view of simulations of homogeneous laboratory tests. The proposed model is applied to describe mechanical behaviors of two representative porous rocks, sandstone and chalk. Comparisons between numerical results and experimental data are presented for triaxial compression tests with different confining pressures, and they show that the micro-mechanical model is able to capture main features of mechanical behaviors of porous rock-like rocks.