## 4 Simulation Analysis of Key Roof-Cutting Parameters for GSER
### Analysis of Simulation Results  
The deformation and stress distribution of the surrounding rock along the gob-side entry retention under different roof-cutting schemes are shown in Figures 8 and 9. As can be seen from Figure 8, after the roof cutting and entry retaining, a distinct fracture line is formed along the cutting line of the roof, and there is a significant difference in vertical displacement between the two sides of the fracture line, indicating that the cantilever structure of the roadway roof has been effectively cut off through roof cutting and pre-splitting, thus playing a role in controlling the displacement of the surrounding rock of the roadway. Among them, the subsidence of the roadway roof near the goat side is significantly greater than that of the solid coal side, showing a trapezoidal subsidence state. Therefore, reinforcement support is needed on the side of the gob-side entry retention near the goat to achieve overall stability control of the roadway roof. As shown in Figure 9, after top-cutting and gob-side entry retaining, the vertical stress in the roof of the roadway is significantly released, and the stress is transferred towards the deep part of the solid coal side as a whole. Locally, affected by the deflection of the roof strata, the stress is concentrated at the top of the top-cutting crack, thereby avoiding the shallow stress concentration on the solid coal side of the roadway caused by the untimely cutting and collapse of the roof on the goat side. If the supporting capacity of the solid coal side is insufficient to cope with the concentrated stress, it will lead to rib spalling and extrusion deformation on the solid coal side of the roadway during the process of gob-side entry retention. In severe cases, the concentrated release of accumulated energy on the solid coal side or rockburst accidents may occur, thereby threatening the stability and safety of the gob-side entry retention. Therefore, the numerical simulation indicates that reasonable top-cutting parameters can effectively cut off the mechanical connection between the roof of the retained roadway and the goat side, reduce the vertical stress on the roadway roof, and force the concentrated stress on the solid coal side to transfer towards the deep part, significantly optimizing the stress state of the surrounding rock of the retained roadway and facilitating long-term stability control of the retained roadway roof. Figure 8: Vertical displacement nephogram of the surrounding rock in the gob-side entry retaining section corresponding to different numerical simulation schemes. Figure 9: Vertical stress nephogram of the surrounding rock in the gob-side entry retaining section corresponding to different numerical simulation schemes. In the numerical simulation, measuring lines were arranged above the coal seam using the built-in commands of FLAC3D to monitor the vertical stress, vertical displacement, and lateral supporting stress of the gob-side entry retaining roof. Specifically, the monitoring lines for roof stress and lateral supporting stress of the roadway were horizontally arranged at the intersection of the basic roof and the immediate roof of the roadway, i.e., 5.3 m above the coal seam. The displacement monitoring line was horizontally arranged below the immediate roof, i.e., on the surface of the roadway. The peak values of roof vertical displacement and vertical stress from each numerical simulation scenario were extracted and plotted in Figure 10. An analysis of Figure 10 reveals that within the same burial depth range, achieving complete roof cutting is more feasible by increasing the cutting height and decreasing the cutting angle. Comparing scenarios 3, 4, and 5, as the cutting height increases, the selectable range of cutting angles gradually widens, and the displacement and stress peak of the retained roadway roof gradually decrease, albeit with diminishing returns. Therefore, the benefits gained from increasing the cutting height gradually diminish.