## 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
#### 4.2.3 Evolution Law of Maximum Shear Stress in the Final Mining Withdrawal Space  
The maximum shear stress can characterize the deformation and failure of coal and rock mass under the combined action of complex stress. In this paper, the maximum shear stress index is introduced to study the complex stress environment and deformation and failure mechanism of surrounding rock in the large-section withdrawal space under different stopping caving distances. The evolution law of maximum shear stress of overlying rock in the withdrawal space under different stopping caving distances is shown in Figure 10. The evolution of the maximum shear stress is introduced into the following evaluation indexes: the maximum shear stress peak \(\tau_{\rm w}\) of the middle coal in front of the retreat space; \(\tau_{\rm w}\) from the withdrawal space coal wall distance \(D_{\rm w}\); [\(\tau_{\rm w}(L_{\rm C})\) \(-\)\(\tau_{\rm w}(L_{\rm C}=0)\)] \(\times\) 100% (the percentage of the peak difference between \(\tau_{\rm w}(L_{\rm C})\) and \(\tau_{\rm w}(L_{\rm C}=0)\) in front of the withdrawal space under different stopping coal caving distances); [(\(D_{\rm w}(L_{\rm C})\)\(-\)\(D_{\rm w}(L_{\rm C}=0)\))/\(D_{\rm w}(L_{\rm C}=0)\)] \(\times\) 100% (the percentage of the range difference between the withdrawal space \(D_{\rm w}(L_{\rm C})\) and \(D_{\rm w}(L_{\rm C}=0)\) under different stopping distances). 1. It can be seen from Figure 10 that with the increase in the stopping coal caving distance (\(L_{\rm C}\)), the range of maximum shear stress low-value area of surrounding rock in withdrawal space is shrinking, and the range of the maximum shear stress increase area is expanding. The range of stress increase area first extends longitudinally to the direction of the withdrawal space (0 m\(\rightarrow\)20 m), and then extends laterally to the depth of the stopping coal pillar (20 m\(\rightarrow\)30 m). When \(L_{\rm C}\geq 30\) m, there is no obvious expansion of the stress increase area (30 m\(\rightarrow\)50 m). 2. The maximum shear stress peak \(\tau_{\rm w}\) of the central coal in front of the withdrawal space at different stopping caving distances is 1.48 MPa, 1.52 MPa, 1.70 MPa, 1.82 MPa, 2.01 MPa, and 1.96 MPa, respectively. The percentage of the difference between the peak values of \(\tau_{\rm w}\) (\(L_{\rm C}\)) and \(\tau_{\rm w}\) (\(L_{\rm C}=0\)) [(\(\tau_{\rm w}(L_{\rm C})\)\(-\)\(\tau_{\rm w}(L_{\rm C}=0)\))/\(\tau_{\rm w}(L_{\rm C}=0)\)] \(\times\) 100% in the central coal in front of the withdrawal space is 2.70%, 14.86%, 22.97%, 35.81%, and 32.43%, respectively. When \(L_{\rm C}=40\) m, the maximum shear stress peak \(\tau_{\rm w}\) of the middle coal body in front of the withdrawal space reaches the maximum value of 2.01 MPa, which is 35.81% higher than that of \(L_{\rm C}=0\) m.
3. The distance \(D_{\rm w}\) between \(\tau_{\rm w}\) and the coal wall in the withdrawal space is 27 m, 12.5 m, 6 m, 5 m, and 5 m, respectively, under different stopping coal caving distances. The percentage of the range difference between the withdrawal space \(D_{\rm w}(L_{\rm C})\) and \(D_{\rm w}(L_{\rm C}=0)\) [(\(D_{\rm w}(L_{\rm C})-D_{\rm w}(L_{\rm C}=0)\))/\(D_{\rm w}(L_{\rm C}=0)\)] \(\times\) 100% is \(-53.7\%\), \(-77.8\%\), \(-81.5\%\), \(-81.5\%\), and \(-81.5\%\), respectively. When \(L_{\rm C}=30\) m, the distance between \(\tau_{\rm w}\) and the coal wall in the withdrawal space \(D_{\rm w}\) reaches the minimum value of 5 m, which is 81.5% less than that of \(L_{\rm C}=0\) m.
4. Through the analysis of quantitative results, it can be seen that with the increase in stopping coal caving distance, the maximum shear stress peak of the middle coal body in front of the withdrawal space is greatly transferred to the shallow coal body of the stopping coal pillar.