# Characteristics of the Deformation and Fracture of Overlaying Slopes in Roof Cutting
## 6 Conclusions  
This paper presents a case study of the 10101 working face of Xinyuan Coal Mine and its overlying slope. With the adoption of numerical simulation, a numerical simulation calculation model for different roof-cutting heights was constructed to study the influence of roof-cutting height on slope deformation and damage. The main conclusions are as follows:  
1. During mining, the overlaying rock formation can be divided into three zones by displacement, namely, the subsidence area, the rotatory zone and the stable area. The subsidence area is below the collapse boundary, mainly characterized by vertical displacement with minor horizontal displacement towards the goat zone; the rotation area is within the collapse and movement boundaries, where there is large vertical and horizontal displacement and the overall displacement was the rotation to the goat zone; and the stable area is in the rock formation on the left side of the movement  
Figure 15: Collapse angle of overlying rock formation at different heights of roof cutting: (a) 0 m; (b) 20 m; (c) 40 m; (d) 60 m; (e) 80 m. The gray lines represent the fractures.  
boundary, characterized by minor horizontal and vertical displacement, and the rock formations are overall stable.
2. A reasonable roof-cutting height should allow the cutting of hard rocks in overlaying formations without destroying the integrity of the control layer. The control layer supports the overlaying formation, especially the slope.
3. With the increase in the height of roof cutting, the movement boundary offsets towards the cutting line, and the stable area expands. When the roof-cutting height is 60 m, the movement boundary is outside the slope, which puts the slope within the stable area, and the slope deformation and failure are controlled; when the roof-cutting height is 80 m, the control layer is cut off, which exacerbates the slope deformation and failure.
4. With the increase in the roof-cutting height, the collapse angle of the overlaying rock formation decreases, and the growth rate of tensile stress at the slope bottom is not reached. However, at a roof-cutting height of 80 m, the ground experiences increased subsidence due to the removal of the control layer. As a result, the fractures at the surface and top of the slope are connected to increase the risk of landslides.
5. The control effect of roof cutting on the slope is mainly reflected in expanding the stable zone to cover the slope. After being cut and crushed, the overlaying formation in the roof-cutting area fully collapses along the cutting line, and the movement boundary also offsets toward the cutting line, so that the slope is within the stable area. At the same time, the collapse angle and the stress at the slope bottom are reduced to the development of cracks, thereby reducing the rotation of the rotation area to the goat zone.  
Conceptualization, Z.C. and C.W.; methodology, M.W. and C.W.; software, Z.C.; validation, Z.C., C.W. and M.W.; formal analysis, Z.C.; investigation, Y.Y.; resources, Y.Y.; data curation, Z.C.; writing--original draft preparation, Z.C.; writing--review and editing, Z.C.; visualization, Z.C.; supervision, M.W.; project administration, M.W.; funding acquisition, Y.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant No. 42302202) and the Shanxi Natural Science Foundation Project (Grant Nos. 20210302123124 and 202303021211057). The authors are grateful for this financial support.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflicts of interest.