Abstract

This paper aims at enriching a homogenization-based anisotropic damage model for hard rocks under complex loading. A new damage criterion is proposed to capture material strain softening. Within the framework of irreversible thermodynamics, we are particularly concerned with two strongly coupled dissipative mechanisms: frictional sliding and damage by microcracking, which usually take place at cracks within cohesive geomaterials under compression. Focusing on the representative elementary volume containing multiple crack families, the free enthalpy of the matrix-cracks system is obtained. Importantly, a back-stress term is involved in the local stress applied to microcracks. This back stress plays the hardening/softening role in the friction criterion which is formulated at local scale. Strain hardening owns to the accumulation of frictional shearing and dilatancy while strain softening is caused by crack growth. The multiscale damage model is used to simulate laboratory tests on the Westerly granite under true triaxial compressions.

Introduction

When subjected to compressive loads, hard rocks present nonlinear mechanical behaviors and induced material anisotropies. In that process, two main dissipative mechanisms have been largely identified: damage by crack growth and frictional sliding along closed crack faces, which are usually strongly coupled to each other on crack scale. Theoretical investigations have shown that the damage friction coupling analyses allow explaining a large number of experimental phenomena involved in brittle or quasi-brittle materials. Concerning constitutive modeling, the standard Eshelby's solution-based homogenization procedure for heterogeneous materials was recently applied successfully to describing the mechanical and poromechanical behaviors of cracked frictional solids.

This paper presents a homogenization-based anisotropic damage model for hard rocks under complex loading. Within the thermodynamic framework, we are particularly concerned with two strongly coupled dissipative mechanisms: frictional sliding and damage by microcracking, which usually take place at cracks in cohesive geomaterials under compression. Focusing on the representative elementary volume containing multiple crack families, the free enthalpy of the matrix-cracks system is obtained. Importantly, a back-stress term is involved in the local stress applied to microcracks. This back stress plays the hardening/softening role in the friction criterion which is formulated at local scale. Strain hardening owns to the cumulation of frictional shearing and dilatancy while strain softening is caused by crack growth. A new damage criterion is proposed to capture strain softening of the material. Finally, the multiscale damage model is used to simulate laboratory tests on the Westerly granite under true triaxial compressions.

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