Modeling of Hydro-mechanical Coupled Fracture Propagation in Quasi-brittle Rocks Using a Variational Phase-Field Method

This paper presents a new variational phase-field model aimed at investigating the fully coupled hydro-mechanical-damage processes in saturated quasi-brittle rocks. Biot’s poroelasticity theory is incorporated with a damage-dependent permeability to describe both Darcy-type seepage in the solid matrix and Poiseuille-type flows in the cracked domain. The fluid pressure is introduced into a unified phase-field framework modified with a mixed-mode crack driving force. This framework can predict and reproduce complex crack initiation and propagation while explicitly determining the apparent crack width. First, the formulations of the proposed model are given. Then the fully coupled system is implemented using the finite element method and an alternate minimization Newton–Raphson iterative solver, facilitated by user subroutines provided by the software ABAQUS. The proposed model is validated by three benchmark problems. Subsequently, fracture propagation, pressure diffusion, and mechanical behavior are simulated and discussed in homogenous and heterogeneous quasi-brittle rock samples with pre-existing flaws under uniaxial compression, respectively. Finally, the proposed model is applied to simulate the damage evolution and investigate the fluid pressure distribution in jointed rock structures. The practicality and computational efficiency of the proposed model in accurately simulating realistic crack propagation and fluid pressure distribution in rock engineering problems are demonstrated.