Micro-Thermomechanical Modeling of Rocks With Temperature-Dependent Friction and Damage Laws

Temperature serves as a critical yet elusive factor impacting the mechanical properties of deep rocks. In this work, we shall develop a new micro-thermomechanical model for rocks based on the Mori-Tanaka homogenization scheme. Free energy and thermodynamic forces are deduced within the framework of irreversible thermodynamics, including the local stress applied on the mesocracks, damage driving force, macroscopic stress, and entropy. The salient innovation of this study lies in formulating subtle physically based temperature-dependent friction and damage laws, considering the influence of ambient temperature on the mesocracking in rocks. Through a coupled friction-damage analysis, a temperature-dependent quasi-static strength criterion and analytical stress-strain-damage relations are then derived. Physical implications and calibration methods of each parameter in the proposed model are meticulously presented. Furthermore, a semi-implicit plasticity damage decoupled procedure (SIPDDC) integration algorithm is employed for the numerical implementation of the proposed model. Subsequently, numerical simulations are conducted to obtain the mechanical response of Jinping marble, Beibei sandstone, and Gongjue granite under various real-time temperature-confining pressure coupling conventional triaxial compression tests (TP-CTC). The congruence of stress-strain curves between model predictions and experimental data validates the robust performance and potential applicability of the proposed model. High ground temperatures have a crucial influence on the stability of deep rocks. Establishing a robust calculation model is paramount for the feasibility and reliability analysis of deep rock engineering. However, incorporating mesocracking mechanisms into such models remains challenging. This paper presents an advanced micro-thermomechanical model based on homogenization theory, aiming to investigate the macro- and micromechanical behaviors of rocks under different ambient temperature conditions. The model innovatively considers the temperature-dependent characteristics of mesocracking. The model demonstrates satisfactory numerical performance and can effectively capture temperature-dependent mechanical behaviors of three typical rocks, that is, marble, sandstone, and granite. This work provides a new perspective from a micromechanical standpoint for the theoretical and engineering analysis of deep rock mechanics under high-temperature and high-pressure conditions. A homogenization-based micro-thermomechanical constitutive model is established considering temperature-dependent friction and damage laws A temperature-dependent strength criterion and analytical damage-stress-strain relations are derived through cross-scaling analysis The model possesses robust numerical performance and shows a promising application prospect in deep rock engineering analysis