## 4 Cutting Top Analysis and Constant Resistance Anchor Cable Support
### Determination of Important Parameters of the Cutting Top  
#### 4.1.1 Theoretical Calculation of Top Cutting Pressure Relief Angle  
From the mechanical model that can be introduced, cutting the top angle too large or too small will have an impact; if the angle is too small, rock friction is larger, which is not conducive to cut off the peripheral rock between the transfer of force; cutting the top angle too large will lead to cut off the length of the broken arm of the beam increases, resulting in the withdrawal of the roadway depressurization not being adequate [38].  
According to the masonry beam theory, and the principle of structural stabilizing the perimeter rock structure, it can be seen that when the fracture surface of the basic top rock layer is considered to be at a certain angle \(\theta\) to the vertical plane, the force relationship at the occlusion point of the rock block is shown in Figure 9.  
And at this time, the conditions under which the rock block undergoes slip destabilization are  
\[\tan\varphi(F\cos\theta-R_{\mathrm{T}}\mathrm{sin}\ \theta)\leq R_{\mathrm{T}} \cos\theta+F\mathrm{sin}\theta \tag{5}\]  
\[T=\frac{qL^{2}}{2(d-\Delta h)} \tag{6}\]  
\[R_{\mathrm{T}}=qL \tag{7}\]  
\(F\) is the horizontal thrust force on the rock mass (kN); \(R_{\mathrm{T}}\) is the shear force on the rock mass (kN); \(\varphi\) is the friction angle between the rock masses (\(\lx@math@degree\)); \(q\) is the load set of the basic top (kN/m); L is the length of the rock mass of the basic top, which is approximately equal  
Figure 8: Stress field distribution after roof cutting. 1: main retracement roadway; 2: auxiliary retracement roadway.  
Figure 7: Distribution of stress field before roof cutting. 1: main retracement roadway; 2: auxiliary retracement roadway.  
to the cyclic come-pressure step (m); d is the thickness of the direct top, m; and \(\Delta\)h is the subsidence of the rock mass B (m).  
At \(\theta=\varphi\), no matter how large the force of the horizontal push \(F\) is, the structure of the rock mass will undergo slip instability. Therefore, when the cutting angle \(\theta\) is equal to the friction angle \(\varphi\) between the rock blocks, the three-hinged arch rock block structure can not be balanced, and the basic top rock block can be smoothly cut down along the cut seam surface to form the lane gang, thus cutting off the path of lateral block to transmit force to the roof of the retaining lane to fully unloading the pressure and obtaining a good effect of forming the lane.  
It is equivalent to reducing the lateral cantilever length of the roof plate, which is beneficial for maintenance along the empty stay lane, and the roof-cutting angle ought to be reduced as much as possible under the condition of satisfying that the basic top rock mass can collapse smoothly. Therefore, the top-cutting angle should be taken to satisfy the following equation.  
\[\theta=\varphi-\tan^{-1}\frac{2(\mathrm{d}-\Delta\mathrm{h})}{\mathrm{L}} \tag{8}\]  
From the geological conditions measured on site at the 108 working face of Jinjiitan Mine, we can obtain the friction angle of the salt block, \(\varphi=22^{\circ}\); the length of the basic top rock block, \(L=18\) m; the sinking amount of the rock block B, \(\Delta h=1.6\) m; and the thickness of the direct top, \(d=2.8\) m. It can be obtained that \(\theta=14.4^{\circ}\). Taking into account the convenience and error of the process of construction, after comprehensive deliberation, the angle of cutting the top is taken as \(15^{\circ}\).