## 2 Engineering Background
### Stability Analysis of Key Blocks of Overlying Strata in the Withdrawal Space
#### 3.2.1 Theoretical Analysis of Reasonable Stopping Coal Caving Distance  
Reasonable stopping coal caving distance can slow down the rotation angle of fractured rock mass, weaken the influence of the dynamic and static load's combined disturbance on the stable overburden environment of underlying withdrawal space during the rotation and subsidence of key blocks, and ensure the safe and efficient withdrawal of final mining hydraulic support. The selection principle of reasonable stopping coal caving distance is as follows: on the one hand, ensure that the goat area below B is fully filled, and the rotation angle of B is small; on the other hand, the uncaving top coal and the caving direct roof collapse and slip to the lower part of C\({}_{1}\) under the action of the B rotary extrusion and fill part of the goat space below C\({}_{1}\). The rotation angle of C\({}_{1}\) is larger than that of B to a certain extent but it can ensure the transition to B and C\({}_{2}\) and ensure the stable hinge between the key blocks. Therefore, the selection of stopping coal caving distance is closely related to the strike length (\(L_{Z}\)) of the fractured rock mass of the final mining. In this paper, the \(L_{Z}\) approximate the cycle weighting interval distance of the final mining period (26 m). The distance of stopping coal caving is summarized into the following four types--a: \(L_{C}\) = 0 m; b: 0 \(<L_{C}<L_{Z}\); c: \(L_{Z}\leq L_{C}<2L_{Z}\); d: \(L_{C}\geq 2L_{Z}\). Under the four typical stopping coal caving distances, the migration of the key blocks of the overlying basic roof in the withdrawal space is shown in Figure 4.  
Figure 4: Overburden rock migration characteristics of withdrawal space in different stopping coal caving spans: (**a**) \(L_{C}\) = 0 m; (**b**) 0 \(<L_{C}<L_{Z}\); (**c**) \(L_{Z}\leq L_{C}<2L_{Z}\); (**d**) \(L_{C}\geq 2L_{Z}\). 1. When \(L_{\rm C}\) = 0 m (Figure 4a), B has a large rotation angle. After the hinges of B and C1 are stable, there is still a large area of goaf space below B. In order to facilitate the subsequent corresponding regional analysis, according to the migration of the main roof fracture rock mass in the withdrawal space, the overlying rock in the withdrawal space can be divided into a stopping coal pillar area, a support area of the hydraulic support, withdrawal channel area, suspended roof area, and direct roof caving filling area. 2. When \(0<L_{\rm C}<L_{Z}\) (Figure 4b), the rotation angle of B gradually decreases with the increase in stopping coal caving distance. However, due to the limited stopping coal caving distance, the range of top coal slow collapse and sliding filling goat is limited, and the vertical dislocation difference between B and C1 is large. There are still some suspended roof areas in the goaf below B and C1. With the continuous advancement of the final mining face, the hinged structure cannot maintain a stable state for a long time, which is not conducive to the stable migration of the final mining overburden. According to the migration of the main roof fracture rock mass in the withdrawal space, the overlying strata in the withdrawal space are divided into a stopping coal pillar area, support area of the hydraulic support, withdrawal channel area, top coal smooth-out collapse filling area, top coal sliding filling area, suspended roof area, and a direct roof caving filling area. 3. When \(L_{\rm Z}\leq L_{\rm C}<2L_{\rm Z}\) (Figure 4c), the rotation angle of B is obviously slowed down under the buffer support of the caving coal and rock mass. Due to the effect of the rotary extrusion pressure of B, the caving top coal slips and fills the goat below C1, and the rotation angle of C1 slows down. The B rotation subsidence is supported by C1, and the C1 rotation is buffer supported by the rear C2.