A unified micromechanics-based damage model for instantaneous and time-dependent behaviors of brittle rocks

• A micromechanics-based damage model only containing 7 parameters is developed for instantaneous and time-dependent inelastic behaviors of brittle rocks.
• An original creep damage evolution law in terms of microstructure evolution by subcritical cracking is introduced.
• A fast explicit integral algorithm is explored to solve the strain history-dependent integration.
• The constitutive formulations are achieved in a unified and consistent damage-friction coupling analyses.

This paper presents a unified micromechanics-based damage model for instantaneous and time-dependent inelastic behaviors of brittle rocks subjected to compressive stresses. The constitutive model is formulated in a combined homogenization/thermodynamics framework. The inelastic deformation is induced by frictional sliding along closed cracks, and strongly coupled with damage evolution by crack growth. Material degradation is described by a scalar-valued internal damage variable that is decomposed into two parts: an instantaneous part induced by applied stresses and a time-dependent part by subcritical cracking due to stress corrosion. Based on the system free energy determined with the Mori–Tanaka homogenization scheme, we propose a Coulomb-type friction criterion, which serves simultaneously as the yielding function and plastic potential, implying the use of an associated flow rule. An instantaneous damage criterion based on the conjugated force associated with the damage variable and a time-dependent damage criterion in terms of progressive evolution of microstructure are introduced. For the latter, an efficient computational algorithm is explored to solve numerically the strain history-dependent integration. As the first phase of validation, the proposed model is finally applied to simulate two typical brittle rocks, Dagangshan diabase and Xiangjiaba sandstone.