Hydro-mechanical-damage modelling of hydraulic fracturing processes in granite with single and double pre-existing flaws

Pre-existing discontinuities and intrinsic heterogeneity in granite critically influence hydraulic fracture initiation, propagation and coalescence, yet their fully coupled hydro-mechanical evolution is still not insufficiently understood. Here, a fully coupled hydro-mechanical-damage (HMD) framework is developed within a finite-element COMSOL-MATLAB platform, integrating poroelastic deformation, Darcy flow, damage-governed stiffness degradation, and permeability evolution, while explicitly accounting for stress concentration at flaw tips and bridges. The model is validated against laboratory hydraulic fracturing tests on granite specimens containing single flaws, reproducing the observed fracture initiation locations and propagation patterns. Parametric simulations are then conducted to quantify the roles of vertical stress, flaw dip angle and bridging angle. Results show that injection pressure exhibits a characteristic three-stage evolution and can develop a suction-type pressure drop near the advancing fracture front due to fluid lag. Upon the application of a 5 MPa vertical stress, the breakdown pressure increased relative to the unstressed condition, the pore pressure distribution region expanded by approximately 100%, and fracture reorientation toward the maximum principal stress direction was induced, leading to systematic alterations in seepage patterns and stress redistribution. As the flaw dip angle was varied from perpendicular to parallel with respect to the maximum principal stress direction, the breakdown pressure decreased by over 20%. In double-flaw configurations, fracture propagation was predominantly governed by interaction mechanisms such as competitive growth and stress shadowing, resulting in geometry and vertical stress dependent coalescence behavior. Furthermore, tensile stress superposition within the rock bridge contributed to an approximate 20% reduction in breakdown pressure compared to single-flaw scenarios.