## 4 Construction of the Dynamic and Static Abutment Pressure Calculation Model
### Case Checking  
For a heavy topsoil slope, the rock strata above the rupture range of the roof can be simplified into one rock group. Considering the large thickness of the bedrock, the displacement angle \(\alpha\) is around 82\({}^{\circ}\). The mining depth is 860 m and the inclined length of the working face is 100 m. Other calculation conditions are as follows: coal seam thickness  
Figure 10: Dynamic abutment pressure calculation model [45].  
\(M=7.0\) m, working face depth \(H=860\) m, working face width \(I=100\) m, overburden average bulk density \(\gamma=0.025\) MN/m\({}^{3}\), fracture angle \(\theta=82^{\circ}\), layer friction coefficient \(f=0.2\), internal friction angle \(\varphi=28.5^{\circ}\), and side pressure coefficient \(\gamma=0.5\). The stress concentration coefficient \(k=2\). The vertical supporting force of coal wall \(N_{0}\) is calculated by the static abutment pressure calculation formula. The calculating interval of the independent variable in the final calculated segment function is:  
\[[0\;7],[7\;63],[63\;126],[126\;130],[130\;\infty], \tag{8}\]  
The calculation process is simplified, and the rock above the fracture range is taken as a rock group, so its thickness M1 is around 800 m. By plugging working face parameters into Equations (5)-(7), and taking rock bulk density \(\gamma\) as 2.5 t/m\({}^{3}\), the specific lateral abutment pressure calculation formula can be obtained as follows:  
\[\sigma=\begin{cases}1.25+0.57x&(0,\;7)\\ 0.75x&(7,\;63)\\ 71.6-0.39x&(63,\;126),\\ 0.18x&(126,\;130)\\ 21.5&(130,\;\infty)\end{cases} \tag{9}\]  
Through calculation, the lateral abutment pressure distribution of the coal body on one side of the 1300 goat is obtained, as shown in Figure 11. It can be seen from the figure that the peak position of lateral abutment pressure of the coal body outside the goat is about 63 m away from the goat, and the peak value of abutment pressure is about 47 MPa. The low stress area is 0-28 m away from the goat. The abutment pressure affected area is 28 m-130 m away from the goat. The original rock stress area is 130 m away from the goat. This monitoring result is consistent with the mining influence range revealed by the microseismic monitoring results.  
The distance between the outer section of the belt transport down chute in the 1301 working face and the 1300 goat is 80 m, which is just within the influence range of abutment pressure on the side of the 1300 goat. The vertical stress here is about 40 MPa, much higher than the uniaxial compressive strength of the coal seam, 15 MPa. Therefore, rockburst can easily occur during the driving of the outer section of the belt transport down chute in the 1301 working face.  
Based on the above calculation results, the influence areas of the goat in the 1300 working face are divided, and the final goat influence danger zone is shown in Figure 12. It can be seen that the duct of the 1301 belt transport down chute is completely under the influence range of the goat of the 1300 working face, which further confirms the root cause of the previous multiple rockburst events.  
Figure 11: Lateral abutment pressure curve of the 1300 goat.