A Modified Micro-Macro Constitutive Model for Porous Rocks with Pressure-Sensitive Matrix by considering a New Hardening Law

Abstract

This paper aims mainly at providing an incremental elastoplastic constitutive model for heterogeneous porous rock-like materials in the frame of micromechanics. The studied material is considered to be made up of randomly distributed spherical pores embedded in a pressure-sensitive solid matrix obeying Drucker–Prager yield function. The effective elastic properties of porous rocks are obtained by the use of Mori and Tanaka homogenization scheme, which are on function of the bulk and shear moduli of the solid matrix and of the value of porosity. For the macroscopic nonlinear phase, a limit analysis-based macroscopic criterion is adopted to derive the basic constitutive rule by considering an associated plastic flow rule. In order to capture the typical hardening effects of rocks, an originally proposed hardening function of the solid matrix is also taken into consideration, which is related on the accumulated equivalent plastic strain. In order to verify its accuracy, the proposed micro-macro constitutive model is implemented by a numerical procedure including elastic predictions and plastic corrections and compared to experimental results of triaxial compression tests of sandstone with different confining pressures. It is observed that the numerical simulation is in accord with the experimental data, indicating that the obtained model is able to predict the main mechanical behaviours of rock-like materials.