Continuum model of inelastically deformed brittle rock based on the mechanics of microcracks

For typical stress levels encountered in engineering and in much of geophysics, rock is a highly nonelastic brittle material, in which stress induced microcracks are principally responsible for the nonelastic behavior. When loading occurs beyond the previous peak differential stress (sigma1-sigma3), brittle rock behaves like an elastic-plastic material. At lower stress levels, brittle rock is more appropriately described as a para-elastic material. In the para-elastic regime, cyclic loading produces large hysteresis in strain and rock typically exhibits discrete memory. In this paper, a continuum model derived from the mechanics of microcracks is presented which describes the deformation of brittle rock under constant (creep) and cyclicly varying loads. The model employs the assumption that time and stress dependent microcrack growth is responsible for the plastic deformation. Because the rock matrix is essentially elastic, a quasi-elastic formalism is adopted in which the crack behavior is included as an internal state variable. Evolution of the crack density function is specified by generalizing the experimentally determined behavior of single cracks to that of a random ensemble of microcracks. Stress corrosion is assumed to be the dominant mechanism of time-dependent crack growth. In the para-elastic regime, the crack density is unchanging, however, the cracks open and close in response to varying stress levels producing hysteresis in strain and a memory of stress reversal points. By formulating the microcrack models into a continuum framework, a constitutive law is produced which describes both the elastic-plastic and para-elastic deformation regimes