# Characteristics of the Deformation and Fracture of Overlaying Slopes in Roof Cutting
## 4 Analysis of the Influence of the Height of Roof Cutting on Displacement  
### Analysis of the Displacement of the Overlaying Rock Formations in Mining Without Roof Cutting  
The displacement cloud diagram of the overlaying rock formations in mining is shown in Figure 4. Due to horizontal stress and self-weight, the surrounding rock formations moved horizontally and vertically toward the goaf zone. The vertical displacement was toward the goaf zone, and the horizontal displacement was toward the goaf zone or the free surface. This resulted in the crushing of the internal rock mass of the slope to a certain extent and reduced its mechanical strength and stability, leading to deformation, fracture and instability-induced slippage. As shown in Figure 4a, the area with the largest vertical displacement was located in the arched area above the goaf zone, forming a distinct arched collapse zone; as can be seen from the horizontal displacement cloud diagram in Figure 4b, the rock formation displacement at the upper left arched collapse zone (the area between the ab lines) was downward vertical displacement and rightward horizontal displacement, which was comprehensively manifested as rotation to the goaf zone where there was concentrated triangular horizontal displacement; the rock formation at the upper right collapse zone was manifested as downward vertical displacement and minor horizontal displacement; on the left side of the arched collapse zone (that is, the left side of the a line), there was a minor horizontal and vertical displacement, and the rock formation tends to stabilize. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Rooof-Cutting Angle/\({}^{\circ}\)** & **Rooof-Cutting Height/m** & **Remarks** \\ \hline  & 0 & \\
0 & 20 & The 12.3 m thick limestone stratum above the working face was severed. \\  & 40 & The 15.39 m thick fine sandstone stratum above the working face was severed. \\  & 60 & The 16.45 m thick medium sandstone stratum above the working face was severed. \\  & 80 & sandstone stratum above the working face was severed. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental design. The overlaying rock formation is divided into three areas by the displacement with movement and the collapse boundaries as the dividing lines, as shown in Figure 5. The movement boundary was the dividing line with horizontal displacement close to 0. The collapse boundary is composed of the left half of the arched collapse zone and its extension. The subsidence area was below the collapse boundary, mainly characterized by vertical displacement with minor horizontal displacement towards the goat zone; the rotation area was within the collapse and the movement boundaries, where there was large vertical and horizontal displacement. The reason for the large deformation was the traction of the collapsed rock formations in the subsidence area, and therefore, the overall displacement was the rotation to the goat zone; the stable area was located in the rock formation on the left side of the movement boundary, characterized by minor horizontal and vertical displacement. The rock formations in the stable area were overall stable without large deformation. Analysis of the Influence of the Height of Roof Cutting on the Displacement of Overlaying Rock Formations  
Blasting roof cutting was performed at the 10101 working face. The displacement simulation results of the overlaying rock formation under different heights of roof cutting are shown in Figures 6 and 7. When the height of the roof cutting was 20 m, the 12.30 m thick limestone top plate above the coal seam was cut off. There were all thin or soft rock formations within close adjacency to the limestone top plate, and their strength was much weaker than that of limestone rock formations. The collapse of the top plate along the cutting line is shown in Figure 6b. There was a triangular area with concentrated horizontal displacement in the rotation area, with the ends of cutting lines as the vertexes.