A coupled hydro-mechanical phase-field model for mixed-mode fracture and full-stage permeability evolution in transversely isotropic rock with kinked fissures

Understanding the coupled hydro-mechanical (HM) fracture behavior and permeability evolution in transversely isotropic rock containing kinked fissures is critical for the stability assessment and disaster prevention of deep underground engineering. Although existing phase-field models (PFMs) can effectively simulate mixed‑mode fracture and post-cracking permeability evolution, they generally neglect the energy dissipation caused by compressive stress and fail to account for the full‑stage permeability evolution, especially during the pre‑cracking stage. In this study, a coupled HM-PFM is proposed for transversely isotropic rock with kinked fissures. The model first introduces a volumetric-deviatoric strain energy decomposition framework to distinguish Mode-I tensile and Mode-II shear fracture driving forces, explicitly incorporating compressive-stress-induced energy dissipation. Second, it establishes a loading-dependent porosity evolution equation to characterize permeability variation in the entire loading process, including the pre-cracking compaction stage. The model is implemented within a transversely isotropic constitutive framework coupled with Biot’s poroelasticity and Darcy’s law. Real-time nuclear magnetic resonance (NMR) tests are performed on layered sandstone specimens with a single kinked fissure at different bedding inclinations under triaxial hydro-mechanical coupling conditions to validate the feasibility and effectiveness of the newly proposed PFM. The results show that elastic modulus increases with bedding inclination, while peak strength exhibits a decrease-increase trend with a minimum at 60°. Maximum principal stress concentrates at fissure kinks, and maximum shear stress localizes at fissure tips, inducing symmetric shear-band failure. Permeability decreases during compaction and linear elasticity, rebounds after yielding, and increases sharply post-failure. The proposed model accurately reproduces experimental stress–strain curves, failure modes, and full-stage permeability evolution, and comparative benchmarks against existing PFMs further confirm its capability in capturing mixed-mode fracture interactions. Numerical results reveal that seepage pressure redistributes near fissures, forming high-velocity zones at crack tips, and that increasing bedding inclination deflects the seepage field and elevates peak flow velocity. The model provides a reliable numerical tool for analyzing mixed-mode fracture and hydro-mechanical behavior in transversely isotropic rock masses.