## 5 Quantitative Relationship between Microseismic Event Energy and Water-Conducting Fractures  
The distribution law of microseismic events was obtained by microseismic monitoring and numerical simulation. In order to obtain the quantitative analysis of the water-conducting fracture zone, according to reference [40], the stress intensity factor \(K_{1}\) was obtained as follows:  
\[K_{1}=\sigma_{y}\sqrt{\pi a} \tag{1}\]  
In the formula, \(\sigma_{y}\) is the stress component perpendicular to the crack direction at the crack front end, according to the numerical simulation; \(a\) is half the length of the crack.  
Numerical simulation calculations show that the strength of \(\sigma_{y}\) was 19.8 MPa when the fracture occurred; by measuring the crack length, we know that the length of \(a\) is 20 mm. Therefore, the stress intensity factor \(K_{1}\) can be obtained as:  
\[K_{1}=156.915\big{(}MPa\cdot\sqrt{\mathrm{mm}}\big{)} \tag{2}\]  
The relationship between stress intensity factor and energy release rate is:  
\[G_{1}=\frac{{K_{1}}^{2}}{\mathrm{E}} \tag{3}\]  
In the formula, \(E\) is the elastic modulus of the rock formation when cracks occur. The previous sections of this paper determined the range of the water-conducting fracture zone. When the height ranges from the coal seam were 40-70 cm (rock layer 16-rock layer 20), the average value of the elastic modulus was 9.06 GPa.  
The energy release rate is calculated as:  
\[G_{1}=2.7177(\mathrm{N/mm}) \tag{4}\]  
Finally, the energy \(E_{1}\) generated by the crack tip (that is, the crack in the rock layer) was obtained as:  
\[E_{1}=108.708J \tag{5}\]  
It can be concluded that when the energy of microseismic events is greater than 108.708 J in similar simulation experiments, cracks will be produced, that is, \(E_{1}=108.708\) J, and cracks will continue to develop into water-conducting fracture zones.  
Figure 10: The development trends of the water-conducting fracture zone in the mining process.  
To better study the location of the cracks and judge the development height of the water-conducting fracture zones, Table 2 shows the specific locations of the cracks and the magnitudes of microseismic energy. It can be seen from Table 2 that the propulsion degree is between 51.8 cm and 249.8 cm, and all the microseismic events meet the conditions for cracking, of which 50% are big events [41]. From the location of microseismic events the development height of water-conducting fracture zone was determined to be between 51 cm and 61 cm.  
To study the specific location of cracks in overlying rock structures, the microseismic events of cracks in the physical model are summarized. The microseismic energy envelope is drawn as shown in Figure 11. The microseismic events in the figure are connected to form the semi-arch shown in the figure, and the cracks are generated and continuously penetrate to form the water-conducting channel, that is, the formation of the water-conducting fissure zone. Compared with the energy concentrated source line, the development position and height of the water-conducting fissure zone were better verified.  
According to the real-time monitoring of microseismic monitoring equipment, the total energy and frequency of microseismic events when cracks are generated in each working face excavation are summarized. There were 19 cycles of weighting at the end of mining in the working face, as shown in Figure 12. These were measured when the excavation was 51.8, 73.4, 87.8, 102.2, 120.2, 138.2, 149, 249.8, 203, 228.2, 235.4, and 138.2 cm.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Advancing** & **Distance from Coal** & **Distance from** & **Microseismic** \\
**Degree/cm** & **Seam Height/cm** & **Open Cut/cm** & **Energy/J** \\ \hline
51.8 & 3.41 & 2.45 & 131.036 \\ \hline  & 163.64 & 45.38 & 176.599 \\
73.4 & 125.69 & 60.24 & 171.957 \\  & 48.09 & 58.55 & 159.414 \\ \hline
87.