###### Abstract  
The water-flowing fractured zone development height (WFZDH) is of great importance for water prevention and control in coal mines. The purpose of this research is to obtain a WFZDH prediction method of the first mining face based on thin plate theory, considering the rock stratum as a thin plate. By analyzing the thin plate, we expect to derive formulas for deflection, thus further analyzing the deformation of the rock formation. Existing methods tend to analyze the rock stratum as if they were beams, and their results are errors from reality. The proposed method is more realistic in analyzing the rock stratum as a plate. The theoretical discrimination method for the WFZDH based on thin-plate theory was investigated using theoretical analysis, numerical simulation, and field measurements. A mechanical model of the key stratum (a hard and thick rock stratum that controls the activity of all rock formations overlying a mining site, either locally or up to the surface) as a thin plate was established. The formulae for the deflection of the key stratum and the critical span for fracture were obtained from this model. The failure of the key stratum must meet two conditions: the key stratum's suspended span exceeds the critical span at which key strata first fracture, and the free space height below the key stratum is greater than its maximum deflection. Based on the above demarcation basis and key stratum failure conditions, the method of discriminating the WFZDH and its applicable conditions are proposed. In accordance with Yeping Coal Mine's geological background, the method was applied to discriminate the WFZDH, and the WFZDH was calculated to be 54 m. The results of the numerical simulation show that WFZDH is 55 m, and the measured results using the double-end water plugging device observation method and the Borehole TV method are 55.3 m-58.9 m. By comparing and analyzing the results obtained via various methods, the results show that the WFZDH analyzed using thin-plate theory is similar to those measured in the field and obtained through numerical simulation, verifying the appropriateness and practicability of the WFZDH discrimination method based on thin-plate theory. This research obtained the WFZDH of Yeping Coal Mine, which ensured its safe mining and provided guidance for the estimation of WFZDH in other mines with similar conditions. thin plate theory; water-flowing fractured zone development height; key stratum; mining covered rock; maximum deflection 20212166241  
China, there are more aquifers, and the problem of large water surges in mines can occur at any time. Also, due to the thicker coal seams in the western mine, the fissures and bed separations above them are more fully developed, which is more likely to lead to sudden water accidents [8; 9; 10]. The roof bed separations act as possible water storage spaces and water conduits, with a high probability of triggering water damage in mines [11; 12]. The water-flowing fractured zone development height (WFZDH) is closely related to coal mine water control work. It is of great significance to understand the WFZDH under various geological environments in order to achieve safe, economical, and environmentally sustainable mine development [13; 14]. In light of the findings on the deformation and failure of rock formation above the working face, Chinese scholars have conducted extensive research in this field. In 1981, [PERSON] made a creative proposal for the \"masonry beam\" mechanical model for the overlying strata [15]. Since then, [PERSON] has enriched and developed this theory and proposed the \"key stratum\" theory [16; 17]. This theory posits that the position of the main key stratum exerts a significant influence on the WFZDH. Once this critical height is reached, the main key stratum will begin to fracture. These fractures will then propagate, or spread and extend, through the entire thickness of the main key stratum.