## 3 Pressure Relief Mechanism of Roof Cutting
### Analysis of Roof Cutting Effect  
The numerical simulation is computed using the control variable method. First, the roof cutting angle is determined. The angle is used as a variable to analyze the stress evolution features associated with different roof cutting angles. A roof cutting height of 13.5 m can guarantee that the coal seams overlying the main roof strata are totally cut off in this section of the calculation, which is based on a thorough analysis that combines theoretical calculations and engineering practices. It also makes it possible to clearly observe how the roof cutting angle affects the strata's stress-evolution characteristics. Four types of roof cutting schemes, namely, no roof cutting and roof cutting angles of \(10^{\circ}\), \(15^{\circ}\), and \(20^{\circ}\), are implemented, and the stress changes in the surrounding rock of the roadway are compared and analyzed. Figure 4 displays the vertical stress distribution of the rock around the roadway at various roof cutting angles, while Figure 5a displays the vertical stress curve. Without a cut roof, concentration of vertical stress occurs on both sides of the roadway, resulting in floor heaving and roof sagging, putting the roadway in a high-stress situation. This situation can easily lead to deformation of the roadway's surrounding rock. The analysis of the vertical stress variation on the right-hand side of the roadway is the main emphasis of this work. The displacement and vertical stress curves show that vertical stress rises quickly with distance, reaching a maximum of 22.01 MPa at 2.45 m from the roadway. As the distance increases, the vertical stress gradually returns to the original rock stress levels. After the roof is cut, the pre-splitting blasting, roof cutting, and pressure-relief effects are clearly visible because the peak vertical stress is noticeably lower than when the roof is left uncut. When the angle is set to \(10^{\circ}\), the vertical stress peak is reached at 2.31 m away from the roadway and is reduced to 15.85 MPa, which is about 28% lower than that without roof cutting. With an increase in distance, vertical stress gradually decreases until it reaches the lowest value at 3.85 m away from the roadway, i.e., about 14.20 MPa. The vertical stress peak is 1.54 m from the roadway and is roughly 15.00 MPa when the angle is \(15^{\circ}\). This is about 32% less than the stress peak without roof cutting. The vertical stress peak further diminishes as the roof cutting angle increases. As distance increases, vertical stress decreases, and the minimum stress is 12.47 MPa. Then, vertical stress gradually increases and returns to the original rock stress. When the angle is \(20^{\circ}\), the vertical stress peak is 13.63 MPa and 1.67 m from the roadway. This is roughly 38% less than the vertical stress peak when the roof is left uncut. Vertical stress drops to 11.30 MPa with increasing distance. A study of the three roof cutting angle schemes' impacts on pressure relief and roof cutting shows that a \(20^{\circ}\) angle produces the best roof cutting and the largest decrease in the vertical stress peak. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Rock Name**} & **Volumetric** & **Bulk** & **Shear** & **Cohesion** & **Angle of** & **Compressive** & **Tensile** \\  & **Weight** & **Modulus** & **Modulus** & **/MPa** & **Internal** & **Strength** & **Strength** \\  & **d/(kg/m\({}^{3}\))** & **K/GPa** & **G/GPa** & **Friction/\({}^{c}\)** & **/MPa** & **/MPa** \\ \hline Fine sandstone & 2800 & 7.00 & 3.50 & 6.20 & 31 & 126.5 & 6.70 \\ Sandy mudstone & 2510 & 5.70 & 4.30 & 2.90 & 36 & 40.3 & 3.80 \\ Mudstone & 2250 & 4.39 & 2.20 & 2.60 & 28 & 38.6 & 3.20 \\ Carbon mudstone & 2310 & 5.10 & 2.70 & 2.42 & 33 & 34.7 & 2.90 \\
11-2 coal & 1420 & 2.30 & 1.30 & 1.25 & 30 & 12.5 & 2.30 \\ Silstone & 2700 & 6.50 & 4.00 & 6.00 & 35 & 80.5 & 5.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical simulation parameters of major coal and rock strata.