# Experimental Study on Damage Constitutive Model of Rock under Thermo-Confining Pressure Coupling
## 1 Introduction  
In geological environments, confining stress and temperature are two primary factors. Deep underground engineering often operates under high confining stress and elevated temperatures. The mechanisms of disaster formation in underground engineering are highly complex and differ significantly from the basic properties of rock under normal conditions. On the one hand, high temperatures typically cause damage to microstructures and expansion of fractures within the rock, which reduces the rock's stiffness, leading to a decrease in compressive strength and elastic modulus [1]. On the other hand, confining pressure alters the pore structure of the rock, induces new cracks, and significantly changes the properties of the rock. Several scholars have studied the effects of temperature on the physical and mechanical properties of various rocks, summarizing and analyzing the changes in these properties with temperature variation [2; 3; 4]. Some researchers have used X-ray computed tomography (CT) technology to study the effects of temperature on the heterogeneity and anisotropy of granite. They observed that the porosity of granite increases with temperature after high-temperature treatment, and its heterogeneity and anisotropy also increase with temperature, with initial cracks below 200 \({}^{\circ}\)C having the most significant impact [5]. Moreover, as thetemperature rises, the mineral particles in rock samples fracture and decompose, causing significant changes in the elastic modulus [1; 6; 7]. Under low-temperature conditions, the elastic modulus of rocks increases linearly with decreasing temperature, while Poisson's ratio remains unchanged [8]. Compared to high temperatures, high confining pressures can inhibit crack propagation and damage evolution, causing the failure characteristics of rocks to gradually transition from brittle to ductile failure [9; 10]. Triaxial compression tests reveal that different confining pressure conditions significantly affect the mechanical and deformation characteristics of rocks [11]. Compressive strength and elastic modulus increase with confining pressure [12], primarily because increased confining pressure suppresses rock expansion, alters crack propagation paths [13], and thereby affects mechanical parameters, microcrack distribution, and energy evolution laws [14]. Based on these foundations, researchers have used analytical methods to calculate the equivalent elastic modulus of fractured rocks with random discrete fractures and regular fractures under confining pressure, providing a better evaluation of the deformation behavior of fractured rock masses [15]. Considering the combined effects of temperature and confining pressure, triaxial compression tests under different confining pressures and temperatures explore the impacts of these factors on the mechanical and deformation characteristics of rocks [16]. Increased confining pressure significantly enhances the compressive strength and elastic modulus of rocks [17], while the elastic modulus exhibits nonlinear changes with temperature [18]. The effects of temperature and confining pressure on rocks are coupled [19], causing significant changes in the microstructure of rocks [20]. Microcracks develop differently in various rock types [21; 22], leading to significant differences in rock properties. Based on the principles and results of field tests, the relationship between rock elastic modulus and other geotechnical parameters (such as joint distribution, continuity, deformation mode, and stiffness [23]) can be analyzed. By combining the strain energy theory of continuum mechanics and fracture mechanics [24], relevant parametric models can be established to describe changes in the elastic modulus [25], thereby determining the typical range of rock elastic deformation capacity [26].