## 4 Simulation Analysis on Stability of the Withdrawal Space in the Final Mining Stage
### Study on the Stability of the Withdrawal Space under Different Stopping Coal Caving Distances
#### 4.2.2 Evolution Law of Vertical Stress in the Final Mining Withdrawal Space  
The evolution law of vertical stress in the withdrawal space under different stopping coal caving distances is shown in Figure 9. In order to facilitate the analysis and comparison, the original rock stress of the coal seam where the withdrawal space is located is marked in the diagram. Taking the boundary between the goat and the withdrawal space as the starting line, the withdrawal space, and the stopping coal pillar in front of it are divided into a depressor area and pressurized area along the direction of the stopping coal pillar. The vertical stress distribution is introduced into the following evaluation and analysis indicators: The lateral extension range \(D_{\text{i}}\) of the depressor area in the withdrawal space. Due to the fact that there is little difference in the degree of coal plasticization at the edge of the support area of the hydraulic support under different stopping coal caving distances during the rotation and sinking of B, in order to intuitively and fairly reflect the influence of the change in stopping coal caving distance on the longitudinal extension range of the depressor area of withdrawal space, \(D_{\text{o}}\) is used to represent the longitudinal extension range of the depressor area of the withdrawal channel. The peak stress \(\sigma_{\text{w}}\) of the middle coal body in front of the withdrawal space: \([(D_{\text{i}}(L_{\text{C}})-D_{\text{i}}(L_{\text{C}}=0))/D_{\text{i}}(L_{ \text{C}}=0)]\times 100\%\) (the percentage of the difference between \(D_{\text{i}}(L_{\text{C}})\) and \(D_{\text{i}}(L_{\text{C}}=0)\) in the withdrawal space at different stopping distances); \([(D_{\text{o}}(L_{\text{C}})-D_{\text{o}}(L_{\text{C}}=0))/D_{\text{o}}(L_{ \text{C}}=0)]\times 100\%\) (percentage of difference between \(D_{\text{o}}(L_{\text{C}})\) and \(D_{\text{o}}(L_{\text{C}}=0)\) at different stopping coal caving distances); \(\sigma_{\text{w}}(L_{\text{C}})/\sigma_{\text{w}}(L_{\text{C}}=0)\) (under different stopping coal caving distances, the increase coefficient of the peak stress in front of the withdrawal space). Figure 8: The migration characteristics of the overlying rock structure in the withdrawal space under different stopping coal caving 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.  
Figure 9: _Cont._1. When \(L_{\rm C}=0\) m (Figure 9a), the overlying top coal and pseudo-top of the withdrawal space are all located in the depressor area, \(D_{\rm i}\) is 21 m, \(D_{\rm o}\) is 20.4 m. A \"shuttle shape\" stress-focused area is formed in front of the stopping coal pillar, and \(\sigma_{\rm w}\) is 2.4 MPa. Due to the large plasticizing area in front of the withdrawal space, \(\sigma_{\rm w}\) is far away from the coal wall in front of the withdrawal space. 2. When \(L_{\rm C}=10\) m (Figure 9b), the top coal and its direct roof in the support area of the hydraulic support are all located in the depressor area, and the depressor area in front of the withdrawal space and the stopping coal pillar is reduced, \(D_{\rm i}\) is 13 m, \(D_{\rm o}\) is 16.4 m. A \"string moon\"-type stress-focused area is formed in front of the coal pillar, and \(\sigma_{\rm w}\) is 2.5 MPa. Due to the decrease in the plasticizing area in front of the withdrawal space, \(\sigma_{\rm w}\) is close to the coal wall in front of the withdrawal space. 3. When \(L_{\rm C}=20\) m (Figure 9c), the range of the depressor area in front of the withdrawal space and stopping coal pillar is further reduced, \(D_{\rm i}\) is 11.5 m and \(D_{\rm o}\) is 12.4 m. A \"string moon\" stress-focused area is formed in front of the stopping coal pillar, and \(\sigma_{\rm w}\) is 2.8 MPa. \(\sigma_{\rm w}\) is closer to the coal wall in front of the withdrawal space than \(L_{\rm C}=0\) m.
4.