Computational modelling of thermo-mechanical coupled brittle fracture for rocks using phase-field method

Thermally-induced rock deformation and fracture represent critical challenges in geotechnical engineering applications such as geothermal extraction and nuclear waste storage. This paper proposes a thermo-mechanical coupled phase-field model (PFM-TM) for simulating thermal cracking in brittle rocks. Based on the variational principle, the governing equations for multi-field coupling are derived, and a fourth-order degradation function is innovatively introduced to simultaneously govern the evolution of mechanical stiffness and thermal conductivity, accurately capturing rapid stiffness degradation and thermal resistance effects characteristic of brittle fracture. To address the challenges of multi-field coupled solving, a novel three-layer hierarchical subroutine architecture (HETVAL-USDFLD-UEL) is developed in ABAQUS, achieving efficient staggered solution through shared-node topology and Gauss-point data exchange. This framework can simultaneously handle transient heat conduction, thermal expansion, stress redistribution, and diffuse crack evolution, eliminating the need for mesh reconstruction and explicit crack tracking. The model accuracy is validated through thermal stress analysis of a thick-walled cylinder with analytical solutions and numerical simulation of thermal cracking in centrally heated borehole specimens, while the influence of various thermo-mechanical parameters is investigated. Application of the model to the Swedish APSE rock pillar stability experiment accurately reproduces the observed V-shaped conjugate fracture zones and failure depth. By integrating temperature, stress, and fracture analysis within a unified computational framework, this method provides an effective tool for predicting thermally-induced damage in high-temperature rock engineering applications.