Phase-field simulations of unloading failure behaviors in rock and rock-like materials

In this work, we present the phase-field formulations for simulating the loading-unloading mechanical responses and failure behavior of brittle rock and rock-like materials. To describing the initial high stress states of rocks in unloading tests, we propose a new stress-based energy density threshold bridging the gap between phase-field evolution and specific failure criteria in geomechanics. This threshold function leads to the novel constitutive failure driving force contributing to phase-field evolution of geomaterials under unloading conditions. We employ the specific Mohr-Coulomb failure driving force in our phase-field model for unloading failure analysis, which enables to demonstrate the pressure-and stress-path-dependency behaviors in rock and rock-like materials. Then, we show two benchmark problems for numerical validation by comparing numerical results with reported experimental data. Furthermore, several fissured rock samples are simulated to study the effects of confining pressures and fissure arrangements on the unloading failure characteristics. Our model provides an alternative computational tool for a better understanding of the unloading failure mechanism, which will be beneficial to study the excavation damage zones and other geohazards in rock engineering.