A microcrack model for the deformation and failure of brittle rock

Abstract

A continuum model derived from the mechanics of tensile microcracks is presented which describes the deformation of brittle rock. The model employs the assumption that stress and time‐dependent microcrack growth is responsible for the inelastic deformation. Microcrack growth is assumed to occur by two mechanisms: stress‐induced crack growth (time independent) and stress corrosion (stress and time dependent). From the analysis of individual cracks a criterion for the initiation of damage (crack growth) is derived. This results in the specification of initial and subsequent damage surfaces in stress space which are similar to yield surfaces in the theory of plasticity. When the stress state is below the damage surface, no stress‐induced crack growth can take place. For stress states on the damage surface, crack growth accompanies any increase in loading, thus expanding the damage surface. By generalizing the results obtained from the analysis of single cracks, a continuum description of the behavior of an ensemble of cracks in an otherwise elastic body is derived. The resulting constitutive equation is essentially elastic but accounts for material behavior due to microcrack growth through the inclusion of an internal state variable which is a measure of the crack state. The form of the evolutionary equation for the crack state parameter is determined from the fracture mechanics analysis of single cracks and experimental results on time‐dependent crack growth in rock. Model simulations of quasi‐static uniaxial and triaxial compression tests are presented, and the results are compared to the results of a similar laboratory test on Westerly granite.