Bounds on the complete stress–strain relation for a crack-weakened rock mass under compressive loads

Abstract

The interactions among multiple parallel sliding cracks in rock materials are examined asymptotically in an explicit and quantitative manner in order to reveal fully their so-called shielding and magnification effects on the complete stress–strain relation. Based on the micromechanical framework and the asymptotic analysis, analytical upper and lower bounds are proposed for the complete stress–strain relation for rock masses containing multiple rows of echelon cracks. The present model studies further influence of both the interaction among crack rows and mutual collinear interaction on the constitutive relation and strength for a crack-weakened rock mass. The closed-form explicit expression for the complete stress–strain relation of rock masses containing echelon cracks subjected to compressive loads is obtained. The complete stress–strain relation includes the stages of linear elasticity, nonlinear hardening, strain softening. The results show that the complete stress–strain relation and the strength of a crack-weakened rock mass depend on the crack interface friction coefficient, the sliding crack spacing, the fracture toughness of rock materials, orientation of cracks, the crack half-length and the crack density parameter.