## 1 Introduction  
Mine water inrush has become a major disaster facing mines in China. The damage to overlying rock caused by high-intensity mining is becoming increasingly severe, and the complex geological environment makes the mechanism of water inrush more complex and difficult to predict [1]. During the mining process, differences in lithology and the physical-mechanical properties of various rock strata cause adjacent layers to deform and settle at different rates, resulting in separation between the layers. Under the continuous infiltration of surrounding rock water into the separation space, a water-storable separation layer is formed. As the mining area continues to advance, the combined effects of the subsidence of the upper rock layers, increased internal water pressure, and the tendency of the lower rock layers to develop fractures cause vertical fractures to connect with the water-storable separation layer, resulting in water inrush hazards. Separation layer water accumulation is a special manifestation of roof water. During mining activities, overlying rock strata separation occurs, and the accumulated water in the separation layer can break under the influence of water pressure, stress, or mining disturbances, leading to a rapid dispersal of water to the underground, causing disasters. Before the infiltration of accumulated water in the separation layer, there are no warning signs. During a water inrush, the water volume is immense and instantaneous, with strong destructive power, making prevention difficult and causing significant losses to many mines [2]. It can be seen that analyzing the dynamic evolution characteristics of overlying rock strata, studying the development height of water-conducting fractures, and predicting the water inrush volume are key to preventing separation layer water hazards [3,4]. This is also one of the main research hotspots in the field of mine water hazard prevention and control in China. [PERSON], [PERSON], and others [5] have conducted a large number of experiments and theoretical analyses on the position, thickness, and influencing factors of the roof strata separation layer. They found that the key stratum mainly controls the migration and failure of the roof strata, and that the separation layer is most likely to occur at the interface between the key stratum and the roof strata, with its maximum development height controlled by the key stratum. [PERSON], [PERSON], et al. [6] theoretically studied the mechanical structure and stress conditions of the formation of overlying rock strata from the mechanical properties and structural state of rocks. They analyzed the occurrence sites of overlying rock strata and provided a maximum delamination prediction method for those overlying rock strata. [PERSON] [7] studied the fracture laws of the upper rock strata and lower impermeable water-bearing strata of the Cuimu and Zhaoxian mines in the Yonglong mining area and analyzed the conditions for the occurrence of sudden water in layered spaces. They constructed a structural mechanics model of the \"sudden water layer zone\" in the mining rock mass and proposed a prediction method for water inrush from layers. [PERSON], [PERSON] [8] conducted strength tests on sandstone and claystone samples that were heated to temperatures as high as 1200 \({}^{\circ}\)C and then exposed to water, determining the range of rock failure zones. The study indicates that claystone layers exhibit significant crack propagation when exposed to water and after being subjected to high temperatures, leading to an increased degree of rock structure damage. Additionally, the mechanical properties of the rocks, such as compressive strength, tensile strength, and Young's modulus, were significantly reduced. Through a series of experiments and numerical simulations, it was concluded that the presence of water significantly affects the mechanical properties of the rocks, thereby having an important impact on the range of rock failure zones.