## 3 Results
#### 3.1.2 Quantification of Water-Induced Fracture Zone  
In the \"geometry injury\" dual-control water inrush prediction model, the water-induced fracture zone (\(y_{s}\), \(z_{s}\)) is composed of implicit waterbody zone \(s_{1}\), softened fracture zone \(s_{2}\), and hydraulically fractured zone \(s_{3}\). The water pressure gradient is \(\Delta p\). According to [PERSON]'s law [10; 13], the expression form of the water pressure gradient can be obtained:  
\[\Delta p=\frac{Q\cdot L}{A\cdot K} \tag{38}\]  
In the formula, \(Q\) represents the minimum volume flow of fracture conductivity, \(L\) represents the length of fracture, \(A\) represents the area of the fracture opening cross-section, and \(K\) represents the permeability coefficient of coal-rock mass. If the equivalent hydraulic opening of a coal-rock mass fracture is equal to the equivalent radius of the fracture opening cross-section, \(b\), it is substituted into the calculation of the fracture opening-cross section area:  
\[\Delta p=\frac{Q\cdot L}{\pi b^{2}\cdot K} \tag{39}\]  
If the inclination angle of the coal-bearing stratum to the horizontal plane is \(\beta_{1}\) and the inclination angle of the main joint to the coal-bearing stratum is \(\beta_{2}\), the range of hydraulically fractured zone \(s_{3}\) can be obtained:  
\[\left\{ \begin{array}{ll}s_{3_{2}}=\max\Bigl{\{}\cos\beta_{1}\cos\beta_{2} \cdot L_{z},&\sin\beta_{1}\sin\beta_{2}\cdot L_{y}\Bigr{\}}\\ s_{3_{y}}=\max\Bigl{\{}sin\beta_{1}\sin\beta_{2}\cdot L_{z},&cos\beta_{1}\cos \beta_{2}\cdot L_{y}\Bigr{\}}\end{array} \right. \tag{40}\]  
It is assumed that after the water chemical damage, the cohesion and internal friction angle of the coal mass decrease to a certain proportion compared with that before the damage, respectively:  
\[C^{\prime}=C(1-S_{c}/100) \tag{41}\]  
\[\varphi^{\prime}=\varphi(1-S_{\varphi}/100) \tag{42}\]  
In the formula, \(C^{\prime}\) represents the cohesion after hydrochemical damage, \(S_{C}\) represents the percentage coefficient of cohesion reduction, \(\varphi^{\prime}\) represents the internal friction angle after hydrochemical damage, and \(S_{\varphi}\) represents the percentage coefficient of internal friction angle reduction. To determine the values of \(S_{C}\) and \(S_{\varphi}\), coal-rock samples (sandstone) from roadway No.9103's working face were immersed in a solution with a pH value of 5. Peak shear strength tests were conducted at different soaking times (\(t\) = 7 d, 30 d, 60 d, 90 d, 120 d). Regression analysis was performed on the measured cohesion and internal friction angle to obtain a goodness of fit > 0.95. The expressions for the changes in \(S_{C}\) and \(S_{\varphi}\) over time are as follows:  
\[S_{c}=6.45\ln(t+11.59)-12.56 \tag{43}\]  
\[S_{\varphi}=0.0912t^{0.76}+1.15 \tag{44}\]Since the water chemical damage occurs mainly on the contact surface, the range of softened fracture zone \(s_{2}\) can be obtained:  
\[\left\{ \begin{aligned} s_{2z}&=K\pi b^{2}\cdot(p-C^{ \prime}-\sigma_{z}\cdot\tan\varphi^{\prime})/Q\\ s_{2y}&=K\pi b^{2}\cdot(p-C^{\prime}-\lambda\sigma_{z} \cdot\tan\varphi^{\prime})/Q\end{aligned} \right. \tag{45}\]  
Then, the geometric expression of the water-induced fracture zone can be expressed as follows:  
\[\left\{ \begin{aligned} y_{s}&=s_{2y}+s_{3y}\\ z_{s}&=s_{2z}+s_{3z}\end{aligned} \right. \tag{46}\]  
The soaking time of water in the working face of roadway No.9103 was gradually adjusted from 0 d to 2560 d, and the range of the water-induced fracture area under different soaking times was calculated, as shown in Table 2. It was drawn into an influence curve, as shown in Figure 13.  
The development of water-induced fracture zones in the working face is primarily influenced by the hydrochemical effects of accumulated water, leading to a decline in the physical and mechanical properties of the surrounding rock, with the soaking-softened fracture zone being predominant. As shown in Figure 13 and Table 2, the extent of the softened fracture zone increases with the duration of soaking.