A thermodynamically consistent phase-field model for frictional fracture in rocks

Frictional fracture phenomena in geological media are often closely related to fault instability in earthquakes and slip surface formation in geohazards. In this work, we propose a new phase-field model for capturing frictional fractures in pressure-sensitive geomaterials. Our model has three novel features: (i) a thermodynamically consistent energetic interface for contact and friction conditions; (ii) incorporation of a level set function to couple phase-field evolution and frictional-contact slips; and (iii) a transition from stored energy to yielding for describing different plastic-like frictional stick–slip fractures. Based on the energy conservation law and a variational inequality of virtual work, we formulate the governing equations for frictional fractures, including the dynamic equilibrium equation, phase-field evolution law, and most importantly, frictional interface plastic-like driving forces. We also present a robust numerical technique to handle the spatiotemporal formation and evolution of frictional fractures in rocks. We validate the model by simulating several benchmark examples. Our model is shown to reproduce both frictional stick and slip phenomena in rocks. We also apply this model to study the effect of confining pressure on frictional crack initiation and propagation in rocks, which helps us better understand the deep mechanisms of frictional fracture.