## 3 Pressure Relief Mechanism of Roof Cutting
### Analysis of Roof Cutting Effect
Figure 6 shows the vertical displacement of the roadway surrounding rock with different roof cutting angles, and Figure 5b shows the vertical displacement curve. From the perspective of roadway roof displacement, in the absence of roof cutting, both roof subsidence and floor have are observed. The largest roof subsidence occurs in the center of the roadway, sinking to about 1.58 cm. When the angle is 10\({}^{\circ}\), the subsidence of the roadway roof near the kerf side gradually increases, and peak displacement is 1.85 cm. When the roof is cut at an angle of 15\({}^{\circ}\), the roadway's roof sinking rises, and peak displacement is 3.54 cm. When the roof is 20\({}^{\circ}\), the peak displacement of roof subsidence is 3.58 cm, which does not considerably differ from that of 15\({}^{\circ}\). Combining the theoretical calculation results, numerical simulation results, and engineering practice, a conclusion is drawn that the cutting angle scheme is 20\({}^{\circ}\). Figure 4: Vertical stress distribution diagram of the roadway with different roof cutting angles: (a) uncut roof; (b) 10\({}^{\circ}\); (c) 15\({}^{\circ}\); (d) 20\({}^{\circ}\). Figure 5: (a) Vertical stress curve of the roadway with different roof cutting angles; (b) vertical displacement curve of the roadway with different roof cutting angles. The cutting height is then established. Figure 7 shows the vertical stress distribution in the rock surrounding the roadway for various roof cutting angles, and the vertical stress curve is depicted in Figure 8a. Based on the aforementioned theoretical calculations and simulation outcomes, the cutting angle for this section is determined to be 20\({}^{\circ}\), and four schemes, namely, uncut roof and cutting heights of 9, 13.5, and 18 m, are implemented. When the vertical stress variations in the rock around the roadway are compared and analyzed, it can be shown that the highest vertical stress, without roof cutting, is 22.01 MPa. Following roof cutting, the peak vertical stress significantly decreases, as seen by the vertical stress curve. The vertical stress peak, which is 1.54 m from the roadway, is lowered to 14.02 MPa when the roof cutting height is 9 m. This is roughly 36% less than when the roof is left uncut. When the cutting height is 13.5 m, the vertical stress peak is further reduced to 13.63 MPa, which is approximately 38% lower. When cutting height is 18 m, the vertical stress peak is reduced to 12.77 MPa, which is about 42% lower. The vertical stress peak under the three distinct roof cutting heights stays comparatively steady, according to the vertical stress curve generated from the numerical simulation data, with a fluctuation range of less than 1.5 MPa. Therefore, analyzing and considering the actual construction amount and the roof rock structure are necessary. When the cutting height reaches 9 m, the roof cutting seam remains confined within the basic roof area of the rock layer. Consequently, this scenario fails to effectively disrupt the integrity of the hard rock layer, resulting in a suboptimal pressure relief effect. Improving the roadway's overall stability is difficult and could possibly cause stress concentration in the roof rock layer, which could lead to catastrophic dynamic disasters. The cutting seam penetrates deeply into the main roof at a height of 18 m, the real construction amount is excessive, and the enhancement of the roof cutting pressure relief effect is not noticeable, which can easily result in resource waste. Figure 6: Vertical displacement distribution map of the roadway with different roof cutting angles: (**a**) uncut roof; (**b**) 10\({}^{\circ}\); (**c**) 15\({}^{\circ}\); (**d**) 20\({}^{\circ}\). Figure 9 shows the vertical displacement curve of the roadway surrounding rock with different roof cutting angles, and Figure 8b shows the vertical displacement curve. From the standpoint of roadway roof displacement, when the cutting height is 9 m, the subsidence of the roadway roof near the cutting side increases, and peak displacement is 3.53 cm.