Enhanced hyperbolic Drucker-Prager criterion-based phase-field model for the brittle-ductile transition in rock under varying confining pressures

Abstract

The investigation of the brittle-ductile transition in rocks is crucial in rock engineering. In this study, we propose an enhanced elastoplastic phase-field model to replicate the mechanical behavior and failure modes of rock under increasing confining pressure. To effectively simulate tensile, tensile-shear, and compressive-shear failures during deformation, we employ the hyperbolic modified Drucker-Prager (D-P) criterion. This criterion approximates the D-P surface with a hyperbolic surface, thus addressing the limitations of the traditional D-P criterion, particularly under tensile-shear stress conditions. Introducing a modified variable damage-driving energy coefficient into the plastic free energy function ensures that a portion of the plastic work propels fracture propagation while the remaining energy dissipates. This modification enhances the physical realism of the phase-field model (PFM). To validate the efficacy of the model in replicating the mechanical behavior and failure modes observed in laboratory experiments, numerical simulations of rock samples containing a single pre-existing crack deformed under uniaxial compression are compared with data from published laboratory experiments that use Digital Image Correlation (DIC) technology. By incorporating confining pressure into the model and analyzing samples containing two pre-existing cracks with varying inclination angles, we find that the model accurately captures the mechanical behavior of rock as confining pressure is increased and as the rock approaches the brittle to ductile transition. We conclude that the presented model shows significant promise for simulating damage, fracturing, and failure in rock engineering projects.