## 4 Simulation Analysis of Key Roof-Cutting Parameters for GSER  
### Simulation Scheme and Model Construction  
Taking the 9306 working face of Anshun Coal Mine as the research object, a three-dimensional numerical model of FLAC 3D is constructed based on the topographical characteristics of the karst mountainous area. Combining with the previous research, reasonable roof-cutting parameters at different burial depths were selected to determine the numerical simulation scheme, as shown in Table 2. The deformation and stress distribution characteristics of the roof in GSER under different burial depths and different roof-cutting parameters were analyzed. Using FLAC(3D) 5.0 software, a 3D numerical model with a length of 1400 m, a width of 750 m, and a height of 408-560 m was constructed. The grid size ranged from 0.2 to 20 m, and the total number of grid cells in the model was 548,682. The model calculations adopted the Mohr-Coulomb criterion with displacement boundary constraints applied to the bottom and sides and an overall gravitational acceleration of 9.8 m/s\({}^{2}\). A 100 m boundary coal pillar was left around the model. An example of the 3D model and the simulation scheme are shown in Figure 7. The model excavated the 9302 working face, the 9304 working face, the roadway of the 9306 working face, roof cutting of the 9306 working face, and \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Coal Seam Burial Depth/m**} & \multicolumn{2}{c}{**Fix the Cutting Height as an Integer**} & \multicolumn{2}{c}{**Fix the Cutting Angle as an Integer**} \\ \cline{2-5}  & **Cutting Height/m** & **Cutting Angle/\({}^{\circ}\)** & **Cutting Angle/\({}^{\circ}\)** & **Cutting Height/m** \\ \hline \multirow{5}{*}{450} & 5.5 & 0.9 & 0 & 5.4 \\  & 6 & 6.8 & 5 & 5.8 \\  & 6.5 & 11.6 & 10 & 6.3 \\  & 7 & 15.8 & 15 & 6.9 \\  & 7.5 & 19.4 & 20 & 7.6 \\  & 8 & 22.7 & 25 & 8.4 \\  & / & / & 30 & 9.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Critical values of key cutting parameters based on the critical tensile strength of the main roof (taking an average coal seam burial depth of 450 m as an example). Figure 6: Reasonable range of critical cutting parameters under different burial depths based on the critical tensile strength of the main roof: (**a**) fix the cutting height as an integer; (**b**) fix the cutting angle as an integer. the 9306 working face, sequentially. Among them, the roadway of the 9306 working face was 6 m wide and 2.2 m high, with a roof-cutting seam width of 0.05 m. Excavation was gradually carried out until the operation reached equilibrium. Field drilling and coring were conducted on the surrounding rock of the intake roadway at the 9306 working face of Anshun Coal Mine, and rock samples were prepared according to standardized requirements. In the laboratory, standardized rock samples underwent a series of tests including uniaxial compression, triaxial compression, Brazilian splitting, shearing, and bulk density measurements. These tests were conducted to obtain the physical and mechanical parameters of the coal and rock mass in the study area, such as bulk modulus, shear modulus, tensile strength, cohesion, internal friction angle, and density, as shown in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Numerical Simulation Scheme** & **Coal Seam Burial Depth/m** & **Cutting Height/m** & **Cutting Angle/\({}^{\circ}\)** & **Tensile Stress in the Uncut Part/MPa** \\ \hline Scheme 1 & 350–400 & 5 & 0 & 8.6–7.2 \\ Scheme 2 & 350–400 & 6 & 10 & 9.2–7.5 \\ Scheme 3 & 400–450 & 6 & 5 & 9.2–7.7 \\ Scheme 4 & 400–450 & 7 & 15 & 9.4–7.5 \\ Scheme 5 & 400–450 & 8 & 20 & 12.3–7.3 \\ Scheme 6 & 450–500 & 7 & 5 & 13.1–11.0 \\ Scheme 7 & 450–500 & 7 & 10 & 10.1–8.4 \\ Scheme 8 & 500–550 & 8 & 5 & 23.2–19.5 \\ Scheme 9 & 500–550 & 8 & 10 & 16.8–13.8 \\ Scheme 10 & 500–550 & 8 & 15 & 11.5–9.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical simulation scheme.