Mixed-mode dynamic crack propagation in rocks with contact-separation mode transitions

We propose an interfacial contact/damage model for simulating dynamic fracture in rocks. An interfacial damage parameter, D, models the evolution of damage on fracture interfaces, while relative contact and contact-stick fractions model contact-separation and stick-slip transitions. The damage rate is determined by an effective stress, written as a scalar function of the normal and tangential components of the Riemann traction solution for assumed bonded conditions. We propose alternative definitions of the effective stress that generate failure criteria that resemble the Tresca and Mohr-Coulomb criteria for compressive stress states, and we compare their compressive strengths and fracture angles under a compressive loading. We adopt a stochastic Weibull model for crack-nucleation in which cracks nucleate at points where the effective stress exceeds the probabilistic fracture strength. We implement the nucleation model with an h-adaptive asynchronous spacetime discontinuous Galerkin (aSDG) method that captures accurately the complex fracture patterns that arise under dynamic loading conditions. Numerical examples illustrate the effects on fracture response of varying the stochastic nucleation parameters and the alternative definitions of the effective stress.