## 3 Mechanical Analysis of Stress Optimization Induced by Roof Structure in GSER
### Analysis of Mechanical Model Results  
The sources of the parameters in the mechanical model are listed here. According to the geological conditions of Anshun Coal Mine, the directly obtainable parameters are the following: the working face length \(b\) is 180 m, the coal seam thickness \(m\) is 1.8 m, the gob-side entry retaining width \(x_{2}\) is 6 m, the thickness of the immediate roof \(m_{1}\) is 5.3 m, and the thickness of the main roof \(m_{2}\) is 4.8 m. Laboratory experiments were conducted on coal and rock samples obtained from on-site borehole coring to determine the coal cohesion \(C\) as 1 MPa and the internal friction angle \(\varphi\) of coal as 20\({}^{\circ}\). Based on empirical values and references, the friction coefficient \(f\) was determined as 0.1, and the unit weight of rock \(\gamma\) was 25 kN/m\({}^{3}\). Finally, through data collection and analysis from on-site hydraulic-support-pressure sensors and surrounding-rock-stress sensors, the average periodic weighting interval \(l\) was obtained as 18 m, the resistance of the support to the coal rib \(p_{1}\) was 0.1 MPa [35; 41], the stress concentration factor \(K\) was 2.5, the load \(q_{2}\) was 0.12 MPa, the load \(q_{3}\) was 0.4 MPa, and the load \(q_{4}\) was 1 MPa. By substituting the aforementioned parameter values into Equations (9)-(14), the relationships between the tensile stress in the uncut roof section and the cutting height, cutting angle, and coal seam burial depth were obtained as follows:  
\[\left\{ \begin{array}{l}x_{4}=14.31-4.41 ln(0.01076H+0.47307)-h\cdot tan\theta \\ \sigma_{\text{t}}=\frac{0.48x_{2}^{3}+0.25x_{3}^{3}}{\left(10.06-h\right)^{2}} \end{array} \right. \tag{15}\]  
Affected by the unique geological characteristics of karst mountainous areas, the working face will continuously pass through multiple independent peaks during the mining process, resulting in significant changes in the buried depth of the working face. The resulting characteristics of roof-stress distribution will significantly impact the selection of roof-cutting parameters and the stability of the retained roadway. The coal seam burial depth of the 9306 working face in Anshun Coal Mine ranges from 385 to 537 m, and the sum of the thickness of the overlying immediate roof and the main roof is 10.06 m. Therefore, the coal seam burial depths are set at 350 m, 400 m, 450 m, 500 m, and 550 m; the roof-cutting heights are set at 4 m, 5 m, 6 m, 7 m, and 8 m; and the roof-cutting angles are set at 0\({}^{\circ}\), 5\({}^{\circ}\)\(10^{\circ}\), \(15^{\circ}\), \(20^{\circ}\), \(25^{\circ}\), \(30^{\circ}\), \(35^{\circ}\), \(40^{\circ}\), \(45^{\circ}\), and \(50^{\circ}\). The coal seam burial depth (\(H\)), roof-cutting height (\(h\)), and roof-cutting angle (\(\theta\)) are substituted into Equation (14) to plot the evolution characteristics of the tensile stress in the uncut part of the main roof under the influence of burial depth and roof-cutting parameters (Figure 5), where the tensile strength of the main roof is 7.2 MPa. As can be seen from Figure 5a, there is a relatively clear positive correlation between the tensile stress in the uncut part of the main roof and the cutting height. As the cutting  
Figure 5: Evolution characteristics of tensile stress in the uncut part of the main roof under the influence of burial depth, cutting height, and cutting angle: (**a**) contour of tensile-stress distribution under the influence of multiple factors; (**b**) relationship between characteristic values of tensile stress and tensile strength under the influence of multiple factors. height increases, the length of the uncut part gradually decreases, resulting in a decrease in the bending-section coefficient of the cantilever beam and a gradual increase in tensile stress. However, when the cutting angle exceeds 30\({}^{\circ}\), the effect of further increasing the cutting height on the tensile stress is no longer significant.