# Characteristics of the Deformation and Fracture of Overlaying Slopes in Roof Cutting
## 5 Analysis of the Influence of Height of Roof Cutting on Crack Development
### The Influence of the Height of Roof Cutting on the Angle of Collapse  
As shown in Figure 14, the collapse angle is angle \(\alpha\) formed between the fracture surface and the top plate level in the direction of the goat zone after the collapse of the top plate.  
As shown in Figure 15, with the increase in the height of the roof cutting, the overlaying rock formation fully collapsed. When the height of roof cutting was 0, 20 m, 40 m, 60 m and  
Figure 14: Schematic diagram of collapse angle at different heights of roof cutting.  
Figure 12: Tensile stress chains at different heights of roof cutting: (**a**) 0 m; (**b**) 20 m; (**c**) 40 m; (**d**) 60 m; (**e**) 80 m. The blue lines represent the tensile force chains.  
Figure 13: Fractures development 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.  
80 m, the collapse angle was 70\({}^{\circ}\), 70\({}^{\circ}\), 53\({}^{\circ}\), 35\({}^{\circ}\) and 55\({}^{\circ}\), respectively, and the collapse angle first decreased and then increased. When the height of the roof cutting was less than 60 m, as the height of the roof cutting increased, the collapse angle decreased, which resulted in a decrease in the rotation angle of rock formation from the rotation area to the goat zone and the control of the slope. When the height of the roof cutting was 80 m, the integrity of the sandstone rock formation in the control layer was damaged, which exacerbated the collapse of the overlaying rock formation. As both the collapse angle and rotation angle of the slope within the rotation area increased, the control effect on the slope decreased.  
According to the above analysis, the control effect of roof cutting on the overlaying rock formation and fracture development first increased and then decreased with the increase in the height of roof cutting. When the height of the roof cutting was less than 60 m, the overlaying rock formation fully collapsed, and the medium sandstone rock formation supported the slope, which effectively controlled the development of slope cracks. When the height of the roof cutting exceeded 60 m, the integrity of the medium sandstone rock formation was destroyed, and the support for the slope was weakened, which resulted in a weakened control effect on the slope. Judging from the development of slope cracks, the best effect was achieved when the height of the roof cutting was 60 m.  
Hence, it can be learned that roof cutting controls the slope mainly by suppressing the rotation of the rock mass from the rotary zone to the goat zone. With the increase in the height of roof cutting, the overlaying rock formation fully collapses and the collapse angle decreases, which reduces the rotation angle of the slope within the rotation area. In addition, there is slowed growth of tensile stress at the slope bottom, reduced peak tensile stress and suppressed development of cracks at the slope bottom, where the slope is controlled. When the integrity of the control layer is destroyed due to excessively high roof cutting, the fractures of the surface and top of the slope are easily connected to increase the risk of landslides.