## 3 Knife Handle-Type Working Face Overlying Rock Breaking and Inducing Mechanism
### Analysis of Roof Breakage Induction Mechanism  
By constructing a mechanical model of the roof, the deflection expression is solved through the Galerkin method, and then the bending moment expression of the working surface roof is obtained, and through the bending moment function, the energy expression of the working surface roof is obtained. The formula of the bending moment and energy is obtained by simplifying the formula. Substituting \(a=27.5\) m, \(b_{1}=85\) m, and \(b_{2}=137.8\) m into Equations (9) and (10), we draw the bending moment diagram and energy diagram of the working surface roof and analyze the energy concentration law of the roof. The bending moment and energy distribution of the short fixed support edge of the working face are shown in Figure 3. The peak bending moment on the short fixed support edge is located at a position \(1/\sqrt{5}\)\(a\) away from the gob. When the working face width is \(85\) m and \(137.8\) m, the extreme bending moment values of the working face roof are \(1.34\)\(\times\)\(10^{4}\) kN\(\cdot\)m and \(5.47\)\(\times\)\(10^{3}\) kN\(\cdot\)m; the energy extreme values of the working surface roof are \(1.43\)\(\times\)\(10^{7}\) J and \(5.85\)\(\times\)\(10^{6}\) J respectively. As the width of the working face increases, the roof load further increases, and the load of the overlying rock layer is transmitted to the coal mass in front of the working face and the coal mass on the upper and lower sides of the working face. As the working face advances, the overlying rock layer reaches its ultimate strength and will fracture.  
\[M_{y|y=b}=\frac{121275 qb^{2}x(x^{2}-a^{2})^{2}}{4096a(45a^{4}+44a^{2}b^{2}+45b^{ 4})} \tag{11}\]  
\[U_{(x)}=\int\frac{M^{2}(y)}{2 EI}dx=-\frac{40425 qb^{2}(x^{6}-3 ax^{4}+3x^{2})}{16 384a(45a^{4}+44a^{2}b^{2}+45b^{4})EI} \tag{12}\]  
The sources of coal and rock dynamic disasters include static load stress and dynamic load stress after mining. The static load stress in the protected coal pillar area increases after mining on the working face. The dynamic load generated after mining is superimposed on the protected coal pillar area. When the coal and rock mass reaches the ultimate destructive strength, it will trigger a rock burst disaster. When the B2 coal seam is not mined, the middle rock layer of the I010408 working face of the B4-1 coal seam collapses and fills the gob. After mining the B2 coal seam, the I010206 working face forms a cantilever beam structure along the trough; as the working face continues to advance, the cantilever beam structure breaks and the beam structure rotates, causing the roof of the B2 coal seam to break. When the working face width is 85 m, the influence of mining disturbance on the working face after mining can be borne by the stable working space formed of the coal and rock mass. When the working face width increases to 137.8 m, the supporting pressure in the coal and rock mass around the stope increases, and the elastic energy accumulated in the protective coal pillar increases. When the roof of the I010206 working face was broken in the B2 coal seam, it further caused the masonry beam structure above the B4-1 coal seam to rotate at a larger angle, causing linkage instability between the B2 coal seam and the roof of the B4-1 coal seam. When overlying rock fractures induce dynamic loads, the superposition of dynamic and static loads makes it easier to induce rockburst.  
Figure 3: Characteristics of bending moment and energy distribution of short fixed support edge of working face.