Micromechanics-Based Models for Induced Damage in Rock-Like Materials

Abstract

Rocks are typical cohesive-frictional heterogeneous geomaterials. The existence and growth of cracks plays a predominant role in their nonlinear mechanical behavior. When rocks are subjected to external loads or suffer unloading process from their initial stress state, there may involve two main dissipation processes: material damage induced by crack growth as well as inelastic deformation caused by frictional sliding along closed cracks. The main difficulty in constitutive modelling is to consider the inherent coupling between these two competing processes. This chapter presents in a unified homogenization-thermodynamics framework some micromechanical formulations for modelling induced damage in rock-like materials. Rocks weakened by microcracks are viewed as a matrix-cracks heterogeneous system where microcracks are considered as inclusions embedded in the matrix phase. The linear homogenization method and problem decomposition technique are applied to derive the effective properties and the system free energy particularly with the Mori-Tanaka scheme. Under the isotropic simplifications for both damage and plastic strains, the damage-friction coupling analyses are performed and the analytical solution to the constitutive equations are achieved under the conventional triaxial compression loading conditions. As an illustration, the analytical stress–strain relations are applied to simulate a typical quasi-brittle rock. In addition, further extension of the present formulation to take into account induced anisotropies and unilateral effects is finally addressed.