## 3 Prediction of Water-Storable Separation Layer Location
### Prediction of Water-Conducting Fracture Zone Height Based on Multivariate Nonlinear Regression  
By comprehensively considering the quantitative factors of mining thickness, working face oblique length, and coal seam burial depth on the height of the water-conducting fracture zone, a multi-factor nonlinear regression prediction model is constructed under the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Number** & **Name of Stratum** & **Stratigraphic Age** & **Thickness** & **Density** & **Modulus of** & **Poisson’s** \\  & & & **(m)** & **(kg/m\({}^{3}\))** & **Elasticity (10\({}^{3}\) MPa)** & **Ratio** \\ \hline
11 & Loess & Quaternary System & 91 & 1470 & 0.21 & 0.37 \\
10 & Red earth & Neogene & 109 & 2020 & 1.04 & 0.35 \\
9 & Gravel rock & Luohe Formation and Yijun Formation & 198 & 2600 & 16.72 & 0.30 \\
8 & Sandy mudstone & Anding Formation & 29 & 2510 & 0.81 & 0.36 \\
7 & Mudstone & Anding Formation & 87 & 2590 & 1.57 & 0.38 \\
6 & Sandy mudstone & Anding Formation & 46 & 2510 & 0.81 & 0.36 \\
5 & Coarse sandstone & Anding Formation & 15 & 2490 & 10.01 & 0.28 \\
4 & Medium grained sandstone & Zhihuo Formation & 24 & 2420 & 12.30 & 0.28 \\
3 & Silstone & Zhihuo Formation & 16 & 2480 & 1.87 & 0.33 \\
2 & Coarse sandstone & Yan’an Formation & 18 & 2490 & 10.01 & 0.28 \\
1 & Carbonaceous mudstone & Yan’an Formation & 13 & 2480 & 1.87 & 0.33 \\
12 & No. 3 coal & Yan’an Formation & 11 & 1380 & 1.42 & 0.45 \\
13 & Medium grained sandstone & Fuxian Formation & 13 & 2420 & 12.30 & 0.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main physical and mechanical parameters of the overlying strata of the No. 3 coal seam. condition of comprehensive mining with weak overlying strata [21]. This model provides a certain basis for predicting the development height of water-conducting fractures in the 1304 working face of Guojiahe Mine. Research analysis reveals that there is a nearly linear relationship between the height of developed water-conducting fractures and the mining thickness, a logarithmic relationship with the inclined length of the working face, and an exponential relationship with the burial depth of the coal. Based on the above functional relationships, the development height of water-conducting fractures in soft overlying strata with respect to each factor was established, fitted, and the following regression prediction model was derived:  
When considering only the mining thickness, the following regression model was derived:  
\[H_{li}=\frac{100\Sigma M}{-0.05\Sigma M+8.34}+53.49\pm 33.19 \tag{4}\]  
where \(H_{li}\) represents the height of the water-conducting fracture zone, measured in meters (m), and \(\Sigma M\) represents the mining thickness, measured in meters (m). Based on the comprehensive consideration of mining thickness and working face length, a corresponding regression model is derived, as follows:  
\[H_{li}=\frac{100\Sigma M}{0.21\Sigma M+3.73}+80.38\ln L-397.51\pm 24.59 \tag{5}\]  
where \(L\) represents the inclined length of the working face, measured in meters (m). Taking into account the three factors of mining thickness, working face inclination length, and coal seam burial depth, a corresponding regression model is derived, as follows:  
\[H_{li}=\frac{100\Sigma M}{0.17\Sigma M+0.76}+58.30\ln L+4.71\sqrt{S}-630.8\pm 2 0.53 \tag{6}\]  
where \(S\) represents the burial depth of the coal seam, measured in meters (m). Using the measured data of the four mines in Table 2, we substitute them into Formulas (4)-(6) to determine which formula has the highest prediction accuracy. We then use the formula with the highest accuracy to calculate the height of the water-conducting fracture zone in the 1304 working face of Guojiahe coal mine. Through analysis, it is concluded that, by comprehensively considering multiple influencing factors, the prediction accuracy and rationality can be improved. Therefore, according to Formula (6), we calculate the height of the water-conducting fracture zone for the 1304 working face of Guojiahe coal mine.