# Study on the Co-Evolution Mechanism of Key Strata and Mining Fissures in Shallow Coal Seam Mining
## 3 Fracture Structure of Key Strata and Evolution Characteristics of Mining Fissures
### Analysis of Mining FISSURE Activation Period
In order to obtain a single mining fissure evolution process, the statistical analysis of the advancing position and time of the working face during the five fissure evolution processes can be approximated as the calculation model of the mining fissure period and recovery distance shown in Figure 8. Point O in the figure is the position where mining fissures appear when the working face is recovered to point O\({}_{1}\), and the lagging distance of mining fissures is \(L_{1}\). When the working face is recovered to point O\({}_{2}\), the mining fissure at point O is close to closing for the first time, and the advancing length of the working face atthis time is \(L_{2}\). During the mining process from O\({}_{2}\) point to O\({}_{3}\) point in the working face, the key blocks rotate clockwise, and the mining fissures are activated. As the working face advances, the key blocks and mining fissures are closed again by horizontal extrusion, after which the mining fissures are no longer activated. In Figure 8, \(\beta_{\text{h}}\) is the hysteresis angle of the mining fissure, \({}^{\circ}\); \(\varphi\) is the first closure angle of the mining fissure, \({}^{\circ}\); \(\beta_{\text{h1}}\) is the activation angle of the mining fissure, \({}^{\circ}\); \(\varphi_{\text{1}}\) is the second closure angle of the mining fissure, \({}^{\circ}\); \(v\) is the average advancing speed of the working face, m/d; O is the first generation position of the mining fissure; \(L_{1}\) is the hysteresis distance of the mining fissure, m; \(L_{2}\) is the first closing distance of the mining fissure, m; \(L_{3}\) is the mining fissure activation expansion distance, m; \(L_{4}\) is the second closing distance of the mining fissure, m; \(H\) is the buried depth of the working face, m; and \(T\) is the evolution time of the mining fissure, d.  
According to the evolution characteristics of mining fissures [44], the fissure evolution time can be obtained as  
\[T=(L-L_{1})/v \tag{4}\]  
where \(L\) and \(L_{1}\) can be expressed as  
\[\left\{ \begin{array}{l}L=H/\tan\varphi_{\text{1}}\\ L_{1}=H/\tan\beta_{\text{h}}\end{array} \right. \tag{5}\]  
Substituting Formula (5) into Formula (4) can obtain  
\[T=\frac{H(\tan\beta_{\text{h}}-\tan\varphi_{\text{1}})}{v\cdot\tan\varphi_{ \text{1}}\tan\beta_{\text{h}}} \tag{6}\]  
To predict whether mining fissures can heal on their own, it is necessary to calculate the horizontal force between key blocks in the mining process. Assuming that the breaking length of the mining key block and the uniform load on the upper part of the working face remain unchanged, and the rock beam structure is not unstable, then when the mining fissure is closed for the second time, it is necessary to satisfy  
\[F_{\text{S}}\geq\frac{L_{\text{G}}^{2}\gamma H\zeta}{n-1} \tag{7}\]  
where \(F_{\text{S}}\) is the horizontal thrust of the key block, kN; \(L_{\text{G}}\) is the average breaking length of the key block, m; \(n\) is the number of breaking times of the key block from the secondary activation mining fissure to counterclockwise rotation; \(\gamma\) is the average bulk density of the rock and soil layer, kN/m\({}^{3}\); and \(\zeta\) is the friction coefficient between the key block and its underlying rock formation. Figure 8: The calculation model of the mining fissure cycle and mining distance. From the above analysis, it can be seen that the time \(T_{4}\) required for the second closure of mining fissures at this time is  
\[T_{4}=\frac{(n-1)L_{\text{G}}}{v} \tag{8}\]  
At this time, the mining fissure evolution time can be expressed as  
\[T=\frac{(n+1)L_{\text{G}}}{v} \tag{9}\]