## 4 Simulation Analysis on Stability of the Withdrawal Space in the Final Mining Stage
### Study on the Stability of the Withdrawal Space under Different Fracture Positions of the Main Roof  
3.1 Migration Characteristics of the Overlying Rock Structure in the Withdrawal Space Under Different Fracture Positions of the Main Roof  
The distance of stopping coal cavity at the end of mining is 30 m, and the structural characteristics of overlying strata in the withdrawal space under different fracture positions are shown in Figure 11. With the continuous advancement of the working face, the influence of different fracture positions on the deformation of the withdrawal space is significant. 1. When the fracture position is located above the stopping coal pillar (Figure 11a), the dynamic and static loads of the rotary sinking parts of B and C\({}_{1}\) are concentrated on the upper part of the whole withdrawal space, and the plasticizing damage of the shallow coal body of the stopping coal pillar is serious, which leads to the serious extrusion deformation in the section of the withdrawal space; consequently, the support crushing accident occurs in the support area of the support, and the section space of the withdrawal channel area cannot withdraw the support normally. 2. When the fracture position is located above the withdrawal space (Figure 11b), the dynamic and static loads of the B and C\({}_{1}\) rotary sinking parts are concentrated above the partial withdrawal space. Compared with Figure 11a, it is found that the deformation of the support area of the hydraulic support is more serious, and the roof of the area is completely crushed but the section of the withdrawal channel area is relatively complete. 3. When the fracture position is located above the goaf (Figure 11c), the dynamic and static loads of B and C\({}_{1}\) rotary subsidence are concentrated on the stopping coal cavity filling area behind the support, and the withdrawal space is placed under the stable A region. The overall section control effect of the withdrawal space is good. This arrangement is conducive to the safe and efficient withdrawal of the final mining. Figure 10: The evolution law of maximum shear stress in withdrawal space under different stopping coal cavity distances: (**a**) \(L_{\text{C}}\) = 0 m; (**b**) \(L_{\text{C}}\) = 10 m; (**c**) \(L_{\text{C}}\) = 20 m; (**d**) \(L_{\text{C}}\) = 30 m; (**e**) \(L_{\text{C}}\) = 40 m; (**f**) \(L_{\text{C}}\) = 50 m. In the figure, the red dotted line delineates the low value area of the maximum shear stress, and the black dotted line delineates the high value area of the maximum shear stress. In order to facilitate readers to read, the corresponding line color indicates the regional characteristics. 3.2 Evolution Characteristics of Vertical Stress and Maximum Shear Stress of Overlying Strata in the Withdrawal Space under Different Fracture Positions of the Main Roof  
The evolution law of vertical stress and maximum shear stress of overlying strata in the withdrawal space under different fracture positions of the main roof is shown in Figure 12. The evolution analysis of vertical stress and maximum shear stress also introduces the above evaluation and analysis indexes. Figure 11: The structural characteristics of overlying strata in the withdrawal space under different fracture positions: (**a**) the fracture position is located above the stopping coal pillar; (**b**) the fracture position is located above the withdrawal space; (**c**) the fracture position is located above the goat. The blue dotted line on the left side of the figure delineates the buffer support range of the stopping coal cavity area to the overlying key rock blocks. The red dotted line and the downward arrow indicate the dynamic and static load disturbance of the unstable rock strata in the rear of the goat on the underlying stopping coal cavity area. The red explosion shape indicates the serious mine pressure disaster in the underlying area under the influence of different fracture positions. The arrows and related marks in the right sketch correspond to the information in the left sketch.