A nonlinear strength criterion for rock-like materials based on fracture mechanics

A nonlinear strength criterion for rock-like materials is developed in this paper. Taking α as an angle of micro-failure orientation in rock-like materials, a formulation between α and load is derived from a mixed-mode fracture criterion based on linear elastic fracture mechanics. According to micro-failure experimental phenomena of rock-like materials, a failure characteristic parameter under triaxial compression condition is chosen, which is relevant to confining pressure and is an invariant. A theoretical nonlinear strength criterion is also derived, which is exactly in the same mathematical form as the original Hoek–Brown empirical strength criterion. In addition, it is also found that the coefficient m in the Hoek–Brown criterion has physical meaning which is related to the ratio between the uniaxial compressive strength and the uniaxial tensile strength.