A Thermo-Mechanical Coupled Gradient Damage Model for Heterogeneous Rocks Based on the Weibull Distribution

This study develops a thermo-mechanical damage (TMD) model for predicting damage evolution in heterogeneous rock materials after heat treatment. The TMD model employs a Weibull distribution to characterize the spatial heterogeneity of the mechanical properties of rock materials and develops a framework that incorporates thermal effects into a nonlocal gradient damage model, thereby overcoming the mesh dependency issue inherent in homogeneous local damage models. The model is validated by numerical simulations of a notched cruciform specimen subjected to combined mechanical and thermal loading, confirming its capability in thermo-mechanical coupled scenarios. Sensitivity analysis shows increased material heterogeneity promotes localized, X-shaped shear-dominated failure patterns, while lower heterogeneity produces more diffuse, network-like damage distributions. Furthermore, the results demonstrate that thermal loading induces micro-damage that progressively spreads throughout the specimen, resulting in a significant reduction in both overall stiffness and critical strength; this effect becomes increasingly pronounced at higher heating temperatures. These findings demonstrate the model’s ability to predict the mechanical behavior of heterogeneous rock materials under thermal loading, offering valuable insights for safety assessments in high-temperature geotechnical engineering applications.