# 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 the Fracture Structure and Bearing Characteristics of the Key Strata
Stepped rock beam structure-(I-II) type mining fissure  
When the key strata form a stepped rock beam structure, the stress characteristics of the key block and the migration characteristics of the overlying rock can be simplified, as shown in Figure 7. Due to the breakage of the key block, the rock and soil layer formed a relative up-and-down movement and rotary subsidence based on the key block D and E, which prompted the downward cutting and turning of the overlying rock and loose soil layer. At this time, the overlying rock and soil layer is subjected to the shear stress acting up and down at a certain angle and the tensile stress of reverse rotation, forming opening type (type I) and sliding type (type II) mining fissures, which are collectively referred to as type I-II mining fissures. According to the S-R standard and deflection principle, with the increase of the radius of curvature \(r\) based on the F\({}_{1}\) point, the type I mining fissures caused by the tensile stress gradually dominate. Similarly, for mining fissures near the F\({}_{1}\) point, shear stress is the main action. Under the action of shear stress, the upper overlying rock produces shear failure to form type II mining fissures that develop upward from the key strata. When the shear strength of overlying rock \([\sigma_{\text{t}}]\geq\) the maximum shear stress \(\sigma_{\text{tmax}}\) or the lower broken rock mass is full of free movement space, type II mining fissures stop developing upwards. The type I mining fissures produced by rock formation rotation are similar to the downward mining fissures formed by the hinged rock beam structure, so no further details are given. Figure 6: Mechanical model of hinged rock beam-(I-I) mining fissure. Regarding the development height of mining fissures, it can be divided into two cases. One is that the key strata do not break. At this time, the height of fracture development is the distance between the coal seam and the key strata. It is the sum of the depth of the developed down-going production fissures and the height of the up-going production fissures developed upward from the key strata. If the depth of the mining fissure exceeds the buried depth of the key strata, it indicates that the mining fissure on the surface is connected to the working face, and it is easy to cause the water-bearing body or aeolian sand in the surface and the overlying rock and soil layer to collapse into the underground, accompanied by air leakage, which is harmful to the mine. Mining is hazardous. On the contrary, if the mining fissures are not penetrated, the working face mining will not be affected by the above factors. The above analysis is the situation when the broken structure of the key strata is in a stable state. The stability of the hinged rock beam structure or stepped rock beam structure generated by the key strata can be calculated by using the S-R stability theory [14]. The broken structure of the key strata has strong self-stability and bearing capacity, but there is still the possibility of instability, so a certain supporting force needs to be provided for it. For the hinged rock beam structure to maintain stability, the required supporting force \(R_{\text{J}}\) is  
\[R_{\text{J}}=\frac{4i_{\text{J}}(1-\sin\theta_{\text{J}})-3\sin\theta_{\text{J }}-2\cos\theta_{\text{J}}}{4i_{\text{J}}+2i_{\text{J}}\sin\theta_{\text{J}}( \cos\theta_{\text{J}}-2)}\times(P_{\text{SJ}}+P_{\text{J}})+P_{\text{n}} \tag{2}\]  
where \(i_{\text{J}}\) is the degree of the key block B of the hinged rock beam; \(P_{\text{SJ}}\) is the upper load of the hinged rock beam, MPa; \(P_{\text{J}}\) is the self-weight load of the hinged rock beam, MPa; and \(P_{\text{n}}\) is the rock load of the lower part of the key strata, MPa.