## 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
When the fracture position is located above the stopping coal pillar (Figure 12a), in terms of vertical stress, the overlying top coal and direct roof of the withdrawal space are almost all located in the depressor area, \(D_{\text{i}}\) is 19 m and \(D_{\text{o}}\) is 26.7 m. A \"Carillon shape\" stress-focused area is formed in front of the stopping coal pillar, and \(\sigma_{\text{w}}\) is 2.3 MPa. Due to the large plasticized area in front of the withdrawal space, \(\sigma_{\text{w}}\) is far away from the coal wall in front of the withdrawal space. In terms of maximum shear stress, the large-scale coal body in the shallow part of the stopping coal pillar is in the low-value area of maximum shear stress. When the fracture position is located above the withdrawal space (Figure 12b), in terms of vertical stress, the depressor area in front of the stopping coal pillar is greatly reduced and the depressor area above the withdrawal space is reduced to a certain extent, \(D_{\text{i}}\) is 12 m and \(D_{\text{o}}\) is 10.4 m. A \"string moon\" stress-focused area is formed in front of the stopping coal pillar, and \(\sigma_{\text{w}}\) is 2.8 MPa, which is close to the coal wall when the fracture position is located above the stopping coal pillar. In terms of maximum shear stress, the maximum shear stress peak \(\tau_{\text{w}}\) of the middle coal body in front of the withdrawal space is 1.7 MPa, and the distance between \(\tau_{\text{w}}\) and the coal wall in the withdrawal space \(D_{\text{w}}\) is 6 m.  
When the fracture position is located above the goal (Figure 12c), in terms of vertical stress, the depressor area in front of the withdrawal space and the stopping coal pillar is greatly reduced, \(D_{\text{i}}\) is 11 m and \(D_{\text{o}}\) is 9.4 m. A \"string moon\" stress-focused area is formed in front of the stopping coal pillar, and \(\sigma_{\text{w}}\) is 2.9 MPa. In terms of maximum shear stress, the maximum shear stress peak \(\tau_{\text{w}}\) of the middle coal body in front of the withdrawal space is 1.82 MPa, and the distance between \(\tau_{\text{w}}\) and the coal wall in the withdrawal space \(D_{\text{w}}\) is 5 m.  
Through the analysis of quantitative results, in terms of vertical stress, when the fracture position is above the goaf, the transverse and longitudinal range of the depressor area is the smallest, and \(D_{\text{i}}\) and \(D_{\text{o}}\) are 42.1% and 64.8% lower than those when the fracture position is above the stopping coal pillar, respectively. In terms of maximum shear stress, when the fracture position is located above the goaf, the maximum shear stress peak is the closest to the coal wall in the withdrawal space, and \(D_{\text{w}}\) is 5 m. When the fracture position is located above the stopping coal pillar, the stopping coal pillar is plasticized in a large range, the integrity of the coal body is poor, and the shallow coal body does not have good bearing and shear performance. When the fracture position is located above the withdrawal space, the plasticization range of the stopping coal pillar area is greatly reduced but the top coal and direct top plasticization above the withdrawal space is serious, the coal body integrity is poor, and the top coal does not have good bearing and shear performance; in contrast, when the fracture position is located above the goaf, the top coal above the stopping coal pillar and withdrawal space is greatly weakened by the mining disturbance of the working face. The surrounding rock integrity of the withdrawal space is good, and the coal and rock mass of the withdrawal space in the final mining stage has good bearing and shear resistance. In summary, the main roof fracture position is located above the goaf, and the withdrawal space is arranged under the A region. This arrangement form is most beneficial to the stop mining and withdrawal work.