## 3 Analysis of Pressure Relief Effect of Cutting Top Parameters
### Pressure Relief Effect of Different Top Cutting Parameters
#### 3.2.1 Pressure Relief Effect of Roof-Cutting Height  
Figure 5 shows the distribution curves of the maximum and minimum principal stresses at a roof-cutting height of 9 m in the reserved roadway along the working face direction when the working face was mined for 100 m. Point 0 on the horizontal axis indicates the position of the working face. According to Figure 5a, it can be seen that in the advanced working face, different cutting depths have a relatively small impact on the change in maximum principal stress of the roadway roof, indicating that the pressure relief effect of the roadway roof at different cutting depths in the advanced working face is relatively small. During the period of GERRC, as the distance between the lagging working face increased, the distribution of the maximum principal stress on the roof of the retention roadway varied with different roof-cutting heights. When the lagging working face was between 20 m and 60 m, the difference in the maximum principal stress of the retention roadway roof at different roof-cutting heights increased. This is demonstrated by the fact that the maximum principal stress was the smallest at a roof-cutting height of 9 m, at 3.3 Mpa. This was 0.8 MPa and 0.5 MPa lower than the 4.1 MPa and 3.8 MPa observed at a roof-cutting height of 7 m and 11 m, respectively. Therefore, when the roof-cutting height is 9 m, the pressure relief effect of the retained roadway roof is the best. According to Figure 5b, it can be seen that in the advanced working face, different cutting heights have a relatively small impact on the minimum principal stress of the roadway roof, indicating that different cutting angles have a relatively small impact on the concentration of mining stress in the roadway of the advanced working face. The minimum principal stress was the smallest when the lagging working face was 0-20 m and the cutting height was 7 m. As the distance between the lagging working face increased, the distribution difference of the minimum principal stress was obvious. When the lagging working face was 20-60 m and the cutting height was 9 m, the minimum principal stress \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Rock** & **Formation** & **Unit Weight** & **Bulk** & **Shear** & **Internal** & **Cohesive** & **Tensile** \\
**Formation** & **Thickness** & **kN/m\({}^{3}\)** & **Modulus** & **Modulus** & **Friction** & **Force MPa** & **Strength** \\  & **m** & **GPa** & **GPa** & **Angle (\({}^{\circ}\))** & **MPa** & **MPa** \\ \hline Mudstone & 7.00 & 24.00 & 2.88 & 1.53 & 26.00 & 1.17 & 1.30 \\ Fine sandstone & 14.00 & 26.00 & 10.35 & 7.74 & 36.00 & 3.15 & 4.20 \\ Mudstone & 5.00 & 24.00 & 2.88 & 1.53 & 26.00 & 1.17 & 1.30 \\ Sandy mudstone & 11.00 & 25.00 & 3.60 & 1.89 & 29.00 & 1.35 & 2.10 \\ Fine sandstone & 6.20 & 26.00 & 10.35 & 7.74 & 36.00 & 3.15 & 4.20 \\ Sandy mudstone & 3.00 & 25.00 & 3.60 & 1.89 & 29.00 & 1.35 & 2.10 \\ Coal & 3.30 & 14.00 & 1.35 & 0.63 & 23.00 & 0.72 & 0.14 \\ Mudstone & 2.00 & 24.00 & 2.88 & 1.53 & 26.00 & 1.17 & 1.30 \\ Middle sandstone & 20.00 & 26.00 & 9.38 & 6.54 & 34.00 & 3.13 & 3.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Thickness of each rock formation in the numerical model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Structure** & **Shear Stiffness** & **Normal Stiffness** & **Poisson** & **Internal Friction** \\  & **N/m** & **N/m** & **Ratio** & **Angle (\({}^{\circ}\))** \\ \hline Surface & 1e8 & 2e6 & 0.25 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical and mechanical index of the structural plane element. was 2.3 MPa and 0.9 MPa smaller than the cutting height of 7 m and 11 m, respectively. Therefore, when the cutting height is 9 m, the concentration of mining stress on the roof of the reserved roadway is the smallest.