Modelling three-dimensional stress-dependent failure of hard rocks

Abstract

Hard rocks exhibit three-dimensional (3D) stress-dependent failure under true triaxial compression. The deformability and strength of hard rocks under true triaxial compression differ from those under traditional loading schemes of conventional triaxial compression tests. For the purpose of characterizing these distinctive features, including 3D stress-dependent brittleness and the failure process and 3D stress-induced anisotropy, a new model suited for hard rocks was proposed in this paper. In the new model, the 3D stress-dependent brittleness under true triaxial compression tests was reflected by a determination method of the internal variable considering the influences of both $${\sigma }_{2}$$ and $${\sigma }_{3}$$ . For the failure process, different evolutions in cohesion and the friction angle were applied to realize different failure processes under different 3D stresses, and their 3D stress dependency was identified by the 3D brittleness index defined in this paper. The 3D stress-induced anisotropy involved in the deformation and failure of hard rocks under true triaxial compression was described via the deformation modulus evolution. The formulation for the stress-induced stiffness matrix and the model framework is fully thermodynamically consistent. The model was implemented in the 3D elasto-plastic cellular automaton system, and good agreement was achieved between the numerical simulation and experimental results, indicating that the new model can be applied to describe the failure behaviours of hard rocks under 3D stress.