## 1 Introduction
### Double Key Layer Category 1 Direct Top
#### 3.3.2 Instance Validation  
For the Lime Tower N1200 working face, when mining the 2-2 coal seam, by arranging drill holes in the working face and the surrounding areas of the coal mine, detailed information regarding the coal and rock seams is obtained, and a comprehensive bar chart of the working face is drawn. The average mining height is 5.9 m, the depth is 140-150 m, the upper part of the 1-2 and 1-2 upper coal has been mined, the average spacing between the layers is 39 m, and the inter-seam mining ratio \(G=6.6\) (in accordance with the empirical formula for calculating the conditions of the double key layer, \(G\approx 6.9\)). There are two key strata above the coal seam, which conforms to the inter-layer mining conditions of the double key strata. The immediate roof is below the first key stratum. The immediate roof is composed of rock strata with the same lithology or different lithology but less mechanical difference, which conforms to the first type of immediate roof structure of the double key strata. The comprehensive histogram of the working face is shown in Figure 10.  
According to the comprehensive column diagram of the N1200 working face of Lime Tower, the mining conditions of the working face, and the breaking characteristics of the overlying rocks of the shallow buried coal seam, it can be seen that the support efficiency \(\mu=0.9\), the width of the support \(b=1.75\) m, the distance of the roof control \(l_{k}=5.0\) m, the depth of the slice of the gang \(l_{p}=1.2\) m, the cycle of the coming pressure step distance \(l=11.64\) m, the thickness of the direct roof \(\Sigma h=5.9\) m, and the length of the key block of the step rock beam \(L_{1}=12\) m. Lower key layer thickness \(h=12\) m; upper key layer thickness \(h2=18\) m; load layer capacity \(\rho_{1 up}g=\rho_{1 down}g=22\) kN\(\cdot\)m\({}^{-3}\); lower load layer thickness \(h_{1}=2.0\) m; key layer capacity \(\rho_{up}g=\rho_{down}g=25\) kN\(\cdot\)m\({}^{-3}\); masonry beam key block length \(L_{2}=24\) m; mining height \(m_{2}=5.9\) m; rock layer breaking angle \(\alpha=60^{\circ}\); load layer height \(h_{3}=0.8\) m; rock block end angle friction angle \(\varphi=27^{\circ}\); and load transfer factor \(K_{G}=0.4\).  
According to Equation (31), when the depth of the sheet gang \(l_{p}=0\) m,  
\[P_{1\text{m}}=11,810\text{ kN} \tag{32}\]  
When the depth of the sheet gang \(l_{p}=1.2\) m,  
\[P_{1\text{m}}=13,759\text{ kN} \tag{33}\]  
Figure 10: Comprehensive histogram of the N1200 working face at Lime Tower.  
According to the mining practice of the N1200 working face, there exist large and small cycles to pressure, small cycles to a pressure maximum working resistance of 12,515 kN/frame, and large cycles to a pressure maximum working resistance of the support up to 13,872 kN/frame. To pressure the coal wall sheet gang, the live column experiences downward shrinkage, and the safety valve opens. The rated working resistance of the working face is 12,000 kN/frame, which cannot meet the support requirements. The theoretical calculation results coincide with the actual measurement, which verifies its reliability.