## 1 Introduction  
With the rapid development of global transportation, the geological challenges faced in tunnel construction are becoming increasingly severe. In high geothermal and water-richenvironments, the surrounding rock of tunnels is frequently exposed to the combined effects of high temperature and water, resulting in significant rock corrosion and fatigue deterioration. This results in deformation, instability, and potential collapse, causing engineering disasters. Consequently, it is essential to investigate the damage evolution and failure mechanisms of rock under the combined effects of high temperature and water is particularly important for the safety and stability of tunnel construction. Currently, numerous scholars have conducted extensive research on the damage mechanisms and failure characteristics of rocks under the effects of temperature, water, or their combined effect. [PERSON] et al. [1] conducted uniaxial compression tests on sandstone at temperatures ranging from 200 \({}^{\circ}\)C to 1000 \({}^{\circ}\)C and found that the expansion of mineral grains and anisotropy lead to changes in the physical and mechanical properties of the sandstone. [PERSON] et al. [2] studied the mechanical and mineralogical changes in granite with different grain sizes under the effect of temperature, revealing that grain expansion was the cause of the mechanical property changes, with coarse-grained granite being more significantly affected. [PERSON] et al. [3] examined the effects of different cooling media on the mechanical properties of granite and limestone at temperatures ranging from 25 \({}^{\circ}\)C to 800 \({}^{\circ}\)C, discovering that air cooling had a minimal impact on the mechanical properties, while all cooling media caused a degradation in the compressive strength of the rocks. [PERSON] et al. [4] performed Brazilian splitting tests on high-temperature granite (150-600 \({}^{\circ}\)C) under two cooling methods, natural cooling and liquid nitrogen cooling, and they found that liquid nitrogen cooling effectively promoted the development of internal cracks in high-temperature granite and reduced its mechanical properties. [PERSON] et al. [5] analyzed the damage evolution of granite under thermal cycling at 400 \({}^{\circ}\)C, observing that as the number of heating-cooling cycles increased, the weight loss rate and volume expansion rate of the granite increased exponentially, while the evolution of internal micro-cracks was described using acoustic emission parameters. These studies show that various high-temperature conditions and cooling methods significantly influence the mechanical properties of rocks, leading to a reduction in strength, crack propagation, and degradation of internal structures. In studies on the effects of water on rocks, [PERSON] et al. [6] investigated the impact of different water contents on the damage characteristics of red sandstone, finding that higher water content led to greater damage, and derived a damage constitutive model for sandstone at different water contents using [PERSON]'s model. [PERSON] et al. [7], using sandstone from the Lanzhou water supply project crossing highly claye sandstone, conducted uniaxial compression tests under different soaking times and combined XRD and SEM techniques, concluding that water absorption and softening were the reasons for the reduced durability of the sandstone. [PERSON] et al. [8] used ARAMIS to study the damage evolution of sandstone under dry and saturated conditions, discovering that the quartz content significantly influenced the water-weakening effect, and higher clay content resulted in more significant damage. [PERSON] et al. [9] conducted uniaxial and triaxial compression tests on sandstone from Wyoming, USA, and developed a predictive model for compressive strength based on water content and grain size, finding that as water content and grain size increased, the compressive strength of the sandstone decreased. [PERSON] et al.