A thermodynamically consistent SPH-PFM model for modelling crack propagation and coalescence in rocks

Abstract

In this study, we describe a smoothed particle hydrodynamics coupled phase field method model in thermodynamically consistent (SPH-PFM model) for simulating crack propagation and coalescence in rocks. The evolution process of parameters in the SPH-PFM model is realized by explicit time integration through the leap-frog method. The crack initiation, propagation and coalescence processes are driven by the volumetric strain and deviatoric strain split of elastic strain energy. According to Benzeggagh–Kenane criterion, the relationship of mode-I and II critical energy release rate is corrected to realize mixed-mode fracture. The continuity to discontinuity of rocks after fracture is achieved by introducing an interaction parameter. The SPH-PFM model is used to simulate the fracture of rock samples, including intact rock samples, rock samples containing an inclined fissure and two parallel fissures under uniaxial compression. All numerical simulation results agree well with previous experimental analysis and numerical results. Overall, the methods and results presented here provide a powerful computational tool for the study of rock fractures in rock mechanics.