## 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
When \(L_{\rm C}=30\) m (Figure 9d), the range of the depressor area in front of the withdrawal space and stopping coal pillar is greatly reduced, \(D_{\rm i}\) is 11 m, \(D_{\rm o}\) is 9.4 m. A \"string moon\" stress-focused area is formed in front of the stopping coal pillar, and \(\sigma_{\rm w}\) is 2.9 MPa. \(\sigma_{\rm w}\) is much closer to the coal wall in front of the withdrawal space than \(L_{\rm C}=0\) m.
5. When \(L_{\rm C}=40\), 50 m (Figure 9e,f), the range of the depressor area in front of the withdrawal space and stopping coal pillar are greatly reduced, \(D_{\rm i}\) is 11 m, \(D_{\rm o}\) is 9.1 m. A \"string moon\" stress-focused area is formed in front of the stopping coal pillar, and \(\sigma_{\rm w}\) is 3.2 MPa. \(\sigma_{\rm w}\) is much closer to the coal wall in front of the withdrawal space than \(L_{\rm C}=0\) m.
6. Under different stopping coal curing distances, [(\(D_{\rm i}(L_{\rm C})-D_{\rm i}(L_{\rm C}=0)\))/\(D_{\rm i}(L_{\rm C}=0)\)] \(\times\) 100% is \(-\)38.1%, \(-\)45.2%, \(-\)47.6%, \(-\)47.6%, \(-\)47.6%, respectively, compared with  
Figure 9: The evolution law of vertical stress in withdrawal space under different stopping coal curing distances: (**a**) \(L_{\rm C}=0\) m; (**b**) \(L_{\rm C}=10\) m; (**c**) \(L_{\rm C}=20\) m; (**d**) \(L_{\rm C}=30\) m; (**e**) \(L_{\rm C}=40\) m; (**f**) \(L_{\rm C}=50\) m.  
\(L_{\rm C}=0\) m. When \(L_{\rm C}=30\) m, \(D_{\rm i}\) reaches the minimum value, which is about 47.6% lower than that of \(L_{\rm C}=0\) m. [(\(D_{\rm o}(L_{\rm C})\)-\(D_{\rm o}(L_{\rm C}=0)\))/\(D_{\rm o}(L_{\rm C}=0)\)]\(\times 100\%\) is \(-19.6\%\), \(-39.2\%\), \(-53.9\%\), \(-55.4\%\), \(-55.4\%\), respectively, compared with \(L_{\rm C}=0\) m. When \(L_{\rm C}=40\) m, \(D_{\rm o}\) reaches the minimum value, which is about 55.4% lower than of \(L_{\rm C}=0\) m but the decrease is not obvious compared with \(L_{\rm C}=30\) m.
7. Under different stopping coal caving distances, \(\sigma_{\rm w}(L_{\rm C})/\sigma_{\rm w}(L_{\rm C}=0)\) is 1.04, 1.17, 1.21, 1.33, and 1.33, respectively, compared with \(L_{\rm C}=0\) m. The increase in \(\sigma_{\rm w}\) is smaller than that of \(L_{\rm C}=0\) m. When \(L_{\rm C}=30\) m, the increase coefficient of vertical stress peak is only 1.21. 8. Through the analysis of quantitative results, it can be seen that the increase in stopping coal caving distance has little influence on the peak stress in front of stopping coal pillar, and has significant influence on the range of the depressor area of surrounding rock in the withdrawal space. The increase in the stopping coal caving distance can reduce the horizontal and vertical extension range of the depressor area in the withdrawal space. At the same time, the plasticization range of the coal body and the direct roof in front of the stopping coal pillar is reduced, and the integrity is enhanced, which is beneficial to control the internal extrusion deformation of the coal wall of the stopping coal pillar. Therefore, according to the vertical stress evolution law of different stopping caving distances, the stopping caving distance \(L_{\rm C}\) is selected as 30 m.