Strength prediction of dry and saturated brittle rocks by unilateral damage-friction coupling analyses

Crack growth and frictional sliding are two essential dissipative mechanisms that govern nonlinear mechanical behaviors of brittle rocks. Usually, unilateral contact as well as damage-friction coupling at cracks render great difficulties to analytical prediction of rock failure. This paper aims at deriving a new strength criterion through homogenization-based unilateral damage-friction coupling analyses. For closed frictional cracks, failure functions of the Mohr–Coulomb type and the Drucker–Prager type are obtained from a generalized friction criterion with back-stress hardening/softening. For open cracks, an elliptical failure function is achieved from a strain energy-release rate based damage criterion. Thus, the resulting strength criterion consists of two parts, whose continuity and smoothness at any crack opening-closure transition is guaranteed theoretically, independently on material properties. The basic results are then extended to take into account pore pressure effect and a simple relation between the strength envelopes for the dry and saturated cases is found. In addition, original discussions are delivered on basic features required by the damage resistance in order to capture strain hardening/softening of cracked rocks. By predicting brittle failure from constitutive equations, this work favors the development of a theoretically unified and thermodynamically consistent micro–macro model.