## 1 Introduction  
Based on existing research, the higher temperature of fires can reach and exceed 1000 \({}^{\circ}\)C [1]. When a fire occurs, high temperatures may cause irreversible damage to rock, resulting in the reduction in macroscopic physical and mechanical properties [1, 2, 3]. For tunnel fires, high-temperature damage inevitably affects a tunnel's bearing capacity and stability [4]. Therefore, the corresponding damage constitutive model has been established to accurately depict the mechanics of rock behavior in these scenarios, holding immense importance for related engineering fires and post-disaster safety assessment. Regarding the impact of high-temperature damage on the physical mechanics of rocks, [PERSON] et al. showed that as the temperature rises, there is a decrease in tensile strength [5]. Similarly, in an investigation into the effects of high-temperature treatment on sandstone, [PERSON] et al. heated sandstone to different temperatures and then cooled it using natural cooling, water cooling, and liquid nitrogen (LN2); they discussed the evolution of thermal shock damage and its damage mechanism in high-temperature rock when subjected to different cooling methods [6]. The results indicate that heat and cooling treatment have a notable impact on the mechanical properties of rocks. As the processing temperature increases, the dynamic peak stress and strain decrease. [PERSON] et al. studied the physical and mechanical parameters of granite specimens processed at high temperatures and showed the following: with the increase in temperature, the volume of granite expands, the mass decreases, the density decreases, and the absolute value of the three rates of change increases with the rising temperatures [7]. [PERSON] et al., through various experiments, studied the physical and mechanical properties of sandstone after being subjected to high-temperature treatment and standing for different durations and obtained the effect of different temperatures on the properties of sandstone after high-temperature damage [8]. The above studies show that the detrimental impact of high-temperature damage on the mechanical properties of the rock mass should not be overlooked. In the study of the damage constitutive model, many scholars have used mathematical analysis methods [9], numerical methods [10], and experimental methods [11] to describe the mechanical behavior of rock damage from macro- and micro-perspectives and have established corresponding mathematical and physical models [12; 13; 14; 15; 16; 17; 18]. [PERSON] et al. classified the rock into three segments: intact material, impaired material, and micro-defects [19]. They redefined the damage variable from the standpoint of energy dissipation and introduced the influencing factor of the correlation between damaged materials and micro-defects. Using fitting logistics, the damage evolution equation obtained by the function was used to quantify the impact of energy dissipation on the spread of micro-defects. [PERSON] et al. applied the energy release rate to the traditional elastic stress-strain relationship and assumed that the microscopic strength of the rock satisfies the Weibull distribution [20]. Conventional triaxial tests have demonstrated the model's ability to accurately depict the evolution of damage in the surrounding rock, thereby providing a robust representation of its behavior. [PERSON] and [PERSON] proposed a constitutive model that accounts for the coupled behavior of plasticity and damage, while also considering the poroelastic effect through the incorporation of effective stress space coupling for the plastic mechanism and the damage mechanism of post-peak softening. The triaxial compression test showed that the shear process can predicted by the model. Characteristics of stress-strain behavior, effective stress paths, and pore pressure variations were apparent in medium shale specimens [21].