Phase-field modeling of thermo-mechanical coupled brittle fracture for transversely isotropic rock

Thermally induced deformation and cracking in rocks with bedding structures are common issues in geotechnical engineering, such as in geothermal mining and nuclear waste storage. To address thermal cracking in rocks affected by weak material anisotropy, this study applies the law of energy conservation and the variational principle within the classical phase field framework. Transversely isotropic constitutive relations and second-order structural tensors are introduced to characterize material anisotropy. The fracture driving force is formulated based on the normal strain tension and compression decomposition, and various transversely isotropic structures are proposed. The thermal-mechanical coupled phase field model for brittle fracture in transversely isotropic rocks is validated by comparing analytical solutions and quenching test results with numerical simulations to ensure model reliability. Subsequently, the thermal shock fracture problem in transversely isotropic rocks with constant temperature differences on both sides is simulated where the proposed model reproduces the thermal fracture behavior of transversely isotropic rocks very well. Finally, quasi-static thermal fracture modeling of transversely isotropic heterogeneous rocks under variable temperature boundaries is conducted, along with a sensitivity analysis of anisotropic thermodynamic parameters. The results indicate that anisotropy in thermal parameters significantly affects crack expansion mechanisms. Cracks are suppressed parallel to the bedding direction due to increased stiffness but are more likely to propagate along directions with lower critical fracture energy. Larger particles can initially promote but later inhibit crack expansion, while an increased thermal expansion coefficient facilitates crack initiation. At the same anisotropy level, the thermal expansion coefficient has the greatest influence on crack propagation, followed by mechanical parameters, with thermal conductivity having the smallest effect.