A new phase field model for mixed-mode brittle fractures in rocks modified from triple shear energy criterion

Fracture initiation, propagation, merging and branching in rocks are considerably complicated and commonly exhibit a great variety of patterns. How to characterize and capture the complicated fracturing process is still a challenging task for recent studies. In this study, a new double phase field model (DPFM) for mixed-mode fractures in rocks modified from triple shear energy criterion is proposed. We introduce two independent phase field variables to describe the tensile fractures and shear fractures individually. In the proposed DPFM, a new fracture driving force based on triple shear energy criterion is proposed and a hybrid formulation is adopted for constructing the new fracture governing equations. Differently from the existing phase field models, our new model can comprehensively consider the influence of cohesion, internal friction angles and intermediate principal stress. Uniaxial compression tests on rock specimens with an inclined flaw and double flaws are performed to validate our DPFM. We also test the fracture patterns of rocks with intermittent fissures in 3D compressive-shear tests. It is observed that the proposed new DPFM can capture the complicated fracturing processes and fracture coalescence types, which are in good agreement with the existing experimental and numerical results.