A bounding surface viscoplastic damage model for time-dependent rock deformation

A novel bounding surface viscoplastic damage (BS-VPD) framework is proposed in this study for capturing the time-dependent rock deformation driven by subcritical cracking. Our constitutive creep model has been estab-lished via imposing effective control over stress-state evolution with respect to the characteristic surfaces while enforcing strictly the thermodynamic constraint. In particular, a new viscoplastic flow rule is first developed by upscaling the microscopic subcritical cracking towards macroscopic creep characterization based on the bounding surface concept. A continuum damage criterion has then been deduced from the maximum dissipation principle for capturing realistically the strain hardening and damage softening during sustained creep loading. By further completing the model with a novel strategy for regulating the interactive surface evolution, we have thus reproduced successfully the progressive transition from stable subcritical cracking characteristic of decelerating creep into unstable propagation during accelerating rupture. In addition, a hierarchical procedure has also been formulated in this study to facilitate straightforward calibration via conventional laboratory testing, and the applicability of our BS-VPD model is then verified against constant strain-rate and creep tests of brittle rocks representing distinct lithologies (i.e., granite, sandstone, and gneiss). The close agreement between model simulation and experimental measurement suggests that the proposed BS-VPD framework is able to capture faithfully the trimodal creep behaviour of brittle rocks across primary, secondary, and tertiary regimes.