## 3 Results
#### 3.1.3 Quantification of Excavation-Induced Fracture Zone  
The excavation-induced fracture zone (\(y_{j}\), \(z_{j}\)) is composed of loosened fracture zone \(j_{1}\), secondary fracture zone \(j_{2}\), and crack initiation zone \(j_{3}\). The excavation failure range is  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Soak Period** & \(\mathbf{y_{s}}\) & \(\mathbf{z_{s}}\) & **Soak Period** & \(\mathbf{y_{s}}\) & \(\mathbf{z_{s}}\) \\
**(d)** & **(m)** & **(m)** & **(d)** & **(m)** & **(m)** \\ \hline
15 & 0.110 & 0 & 360 & 2.203 & 1.483 \\
30 & 0.458 & 0.062 & 480 & 2.437 & 1.732 \\
60 & 0.883 & 0.115 & 960 & 3.024 & 2.375 \\
120 & 1.364 & 0.607 & 1440 & 3.389 & 2.788 \\
180 & 1.664 & 0.918 & 1920 & 3.661 & 3.105 \\
240 & 1.884 & 1.147 & 2560 & 3.945 & 3.444 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Influence of soaking time on the range of the fissure zone in water.  
Figure 13: Curve of influence of soaking time on the range of the fissure zone in water.  
obtained through the mechanical analysis of the circular standardization of a non-circular roadway, and the following formula is obtained [25; 26]:  
\[a=\min\left\{k_{x}\left(\frac{S}{\pi}\right)^{1/2},{({r_{c}}^{2}+{h_{c}}^{2})}^{1 /2}\right\} \tag{47}\]  
In the formula,  
\(a\) represents the theoretical radius of the roadway, \(S\) represents the actual cross-sectional area of the roadway, \(h_{c}\) represents the height of the straight wall section, \(r_{c}\) represents the radius of the arch section (half of the width of the rectangular roadway), and \(k_{x}\) represents the correction coefficient of the roadway section, which is 1.1-1.3.  
The surrounding rock is mainly subjected to shear failure, and the radius of loosened fracture zone \(j_{1}\) and secondary fracture zone \(j_{2}\) is as follows:  
\[R_{a}=a\left[\frac{(P+C\cot\varphi)(1-\sin\varphi)}{C\cot\varphi}\right]^{ \frac{1-\sin\varphi}{2\sin\varphi}} \tag{48}\]  
In the formula, \(P\) represents the stress of the original rock, \(C\) represents the cohesion of the roof surrounding rock, and \(\varphi\) represents the internal friction angle of the roof surrounding rock.  
In the evolution analysis model of the water conduction channel on the roof of the roadway excavation, the starting point of the fracture zone in the roadway excavation is at the geometric center of the head of the roadway excavation, and the geometric expression is as follows:  
\[\left\{\begin{aligned} y_{j}=R_{a}\\ z_{j}=R_{a}+r_{c}\end{aligned}\right. \tag{49}\]  
In the formula, \(R_{a}\) is the radius of the loosened fracture zone and the secondary fracture zone determined by Formula (48), and \(r_{c}\) represents the radius of the arch section (half of the roadway width for a rectangular roadway).  
It is noted that when the section form of the roadway is a rectangular section with a high span ratio less than 1, which is common in coal roadways, the range expression of the excavation fracture zone can be obtained:  
\[\left\{\begin{aligned} y_{j}=k_{x}\left(\frac{d_{x}b_{x}}{\pi} \right)^{1/2}\cdot\left[\frac{(P+C\cot\varphi)(1-\sin\varphi)}{C\cot\varphi} \right]^{\frac{1-\sin\varphi}{2\sin\varphi}}\\ z_{j}=k_{x}\left(\frac{d_{x}b_{x}}{\pi}\right)^{1/2}\cdot\left[\frac {(P+C\cot\varphi)(1-\sin\varphi)}{C\cot\varphi}\right]^{\frac{1-\sin\varphi}{2 \sin\varphi}}+\frac{d_{c}}{2}\end{aligned}\right. \tag{50}\]  
In the formula, \(d_{c}\) represents the roadway width.  
The section form of roadway No.9103 is a common rectangular section in a coal roadway, with a high span ratio of 0.8. The comprehensive mechanized excavation method was adopted, and there was no instantaneous violent energy dynamic impact. The final calculation results of the excavation-induced fracture area are \(y_{j}=1.496\) m and \(z_{j}=3.496\) m.