Theoretical Discrimination Method of Water-Flowing Fractured Zone Development Height Based on Thin Plate Theory

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.