## 5 Application in Predicting Water Inrush  
In the previous work of predicting water inrush in deep coal mines, the rock properties were generally homogeneous. In this section, based on the actual engineering background of coal seam 15 in the Huatai coal mine of China, applying the above results, the influence of rock heterogeneity on water inrush is studied. As shown in Figure 13, the depth of coal seam 15 is 1180 m, the length of the working face is 140 m, and the distance between the aquifer and the coal seam is about 85 m. The angle of the coal seam is 15\({}^{\circ}\). The fractured area is induced by the coal mining. Groundwater can flow into the coal seam through the fractured area. Based on the statistical analysis of long-term experimental and engineering measured data, the researchers and engineers found that the thickness of the fractured area can be calculated by some functions of the length of the working face, the depth of the coal seam, and the angle of the coal seam, and therefore obtained the empirical equations. The empirical formulas are [33]:  
\[h_{1}=0.7007+0.1079L \tag{28}\]  
\[h_{1}=0.303L^{0.8} \tag{29}\]  
\[h_{1}=0.00851H+0.1665\alpha+0.1079L-4.3579 \tag{30}\]  
where \(L\) is the length of the working face, m; \(H\) is the depth of the coal seam, m; and \(\alpha\) is the angle of the coal seam. The thickness of the disturbed area is 15.8 m, 15.8 m, and 23.3 m calculated by the above empirical formulas, and the largest one, 23.3 m, is the thickness of the disturbed area. Figure 12: The rock damage change with time at different pH values and temperature (\(k_{av}=2\)): (a) T = 75 \({}^{\circ}\)C; (b) pH = 6.6; (c) pH = 6. Figure 13: The geometric model. The conception of the water inrush coefficient is proposed based on the statistical analysis of long-term water inrush data and defined in the Regulation for Coal Mine Water Prevention and Control [34],  
\[K=\frac{P}{M} \tag{31}\]  
where \(K\) is the water inrush coefficient, MPa/m; \(P\) is the water pressure, MPa; \(M\) is the thickness of the aquifuge, m. If the water inrush coefficient is over 0.1 MPa/m, the water inrush will occur. In the 1970s, considering the thickness of the disturbed area and the height of water intrusion into the aquifuge, the water inrush coefficient was revised as  
\[K=\frac{P}{M_{eff}} \tag{32}\]  
\[M_{eff}=M-h_{1}-h_{2} \tag{33}\]  
where \(M_{eff}\) is the thickness of the effective aquifuge, m; \(h_{2}\) is the height of water intrusion into aquifuge, m. The height of water intrusion into the aquifuge is 0 m in this case. The water pressure is 6.17 MPa calculated by Equations (32) and (33). The bottom boundary of the aquifer is applied 6.17 MPa, and no flow is applied to the left, right, and top boundaries of the geometric model. From the results of previous analysis in Section 3, when the scale parameter is constant, setting different shape parameters can simulate the rocks that have the same average porosity but different heterogeneity, and the larger the shape parameter is, the more homogeneous the rock. Therefore, the scale parameter is set as 0.12, the shape parameters are set as 2 and 8, respectively, to simulate the different initial rock heterogeneity. The shape parameter should be as large as possible to simulate homogeneity rock, which is set as 50. The model parameters are listed in Table 3. These parameters are from the rock compression test. The rock specimens are from the roof and floor rock strata of coal seam 15. The testing machine is MTS815.03. In addition, the effective thermal conductivity and the effective volumetric heat capacity are calculated by Equations (21) and (20), and the permeability is calculated by Equation (25), and these three parameters are governed by the porosity generated by the Weibull distribution random numbers.