## 1 Introduction  
The implementation of underground water reservoir technology in coal mines effectively addresses issues concerning safe and prosperous coal mining and the protection and utilization of groundwater resources in western mining areas [1, 2, 3]. In situations where the water content is high, prolonged exposure to groundwater has a weakening effect on the coal rock body and impairs its mechanical properties. Additionally, groundwater can cause the instability and collapse of the excavation area due to the presence of watertight coal pillars left in the reservoir, thus greatly threatening coal mine production and personnel safety. There are three main forms of water damage to underground coal pillar dams: (1) the instability of coal pillars caused by water pressure and erosion; (2) water surges caused by dam damage; and (3) the instability of coal pillar dams. Consequently, research on the mechanical properties and rupture mechanisms of waterlogged coal rock has become a significant trend in recent years [4; 5; 6]. Numerous experts have conducted extensive research on the mechanical properties and damage evolution of coal rock following water immersion. [PERSON] et al. [7] utilized nondestructive water immersion methods to conduct water immersion tests on coal-bearing rock systems of different lithologies. They found that mechanical indices, such as the uniaxial compressive strength, regularly decreased following water immersion in coal-bearing rock systems. [PERSON] et al. [8] performed uniaxial compression tests on three types of coal rock assemblies with varying water immersion durations to identify degradation patterns and mechanisms associated with the assemblies' mechanical properties. [PERSON] et al. [9] discovered that the coal rock's structure changed and the permeability increased as the immersion duration increased. [PERSON] et al. [10] conducted loading and unloading tests on coal rock under various water content conditions. Their results show that the bearing strength of coal rock decreases as the water content increases. Additionally, they observed an evident hysteresis phenomenon in the evolution of damage and deformation of the coal rock during the loading and unloading process. [PERSON] et al. [11] conducted experiments on coal rock specimens with varying levels of water content and observed that, as the water content increased, the peak stress, elastic modulus, and strain softening modulus decreased, while the peak strain increased. These results were obtained through uniaxial compression testing. [PERSON] et al. [12] observed a tendency for the tensile strength of coal rock to increase and then decrease after undergoing water immersion, according to Brazilian splitting experiments with varying immersion lengths. Additionally, they discovered a negative correlation between the pore-like ratio and the tensile strength. [PERSON] et al. [13] determined that the mechanical properties of coal rock remained consistent across different water content levels via triaxial compression testing, and they developed a water-force coupling damage model for coal rock using elastic damage mechanics. [PERSON] et al. [14] examined the time-dependent impact of water on coal's mechanical and mesoscale features, utilizing immersion experiments with varying immersion durations. [PERSON] et al. [15] examined the mean strength of assemblages comprising coal rock, mudstone, and non-mudstone through a numerical simulation of the law of water saturation. They discovered that, as the water saturation increases, the strength of the coal column decreases. These findings are relevant to coal seams consisting of rock-bearing strata that are uniformly distributed. [PERSON] et al. [16; 17] conducted a compression test on coal rock at various loading rates while adjusting the water content levels. Their study yielded insights into the impacts of the loading rates and water content on the overall stress-strain curves of coal rock assemblages.