## 3 Prediction of Water-Storable Separation Layer Location
### Translation to English: Discrimination of Separation Layer Position Based on Key Stratum Theory  
The separation layer is caused by the way in which the shear force which acts between the layers--as a result of the weight of the stratified rock mass and the shear force acting on the contact surface--is greater than the bonding force on the contact surface of the rock layer itself under mining activities. The occurrence position of the separation layer is determined using the key stratum theory. The lowest hard and thick layer in the overlying strata is called the main key layer and it plays an important controlling role in the position and state of the separation layer formation. A composite key layer composed of multiple strata with different lithologies can be considered as a whole, and the lithology can be comprehensively judged based on the elastic modulus, specific gravity, and thickness of each stratum. On this basis, the overlying rock structure is abstracted as a plane strain problem, and the composite beam theory is applied to conduct a mechanical analysis. When there is a significant difference in flexural deformation among the composite beams, interlayer separation phenomenon will occur. In each group of composite beams, the load of the nth layer of rock on the bottommost 1 st layer of rock in that group is as follows:  
\[\mathfrak{q}_{n,1}=\frac{E_{1}h_{1}^{3}\sum\limits_{i=1}^{n}\gamma_{i}h_{i}}{ \sum\limits_{i=1}^{n}E_{i}h_{i}^{3}}=\frac{E_{1}h_{1}^{3}(\gamma_{1}h_{1}+ \gamma_{2}h_{2}+\cdots+\gamma_{n}h_{n})}{E_{1}h_{1}^{3}+E_{2}h_{2}^{3}+\cdots +E_{n}h_{n}^{3}} \tag{1}\]  
where \(E_{i}\) represents the elastic modulus of each layer, \(n\) is the number of layers in the group, \(h_{i}\) represents the thickness of each layer, and \(\gamma_{i}\) represents the unit weight of each layer. When q\({}_{n,1}\) is greater than q\({}_{n+1,1}\), the upper rock stratum no longer exerts a load on the lower rock stratum, which indicates the occurrence of a separation layer between these two layers. The discriminant is q\({}_{n,1}\) > q\({}_{n+1,1}\), as follows:  
\[\frac{E_{1}h_{1}^{3}\sum\limits_{i=1}^{n}\gamma_{i}h_{i}}{\sum\limits_{i=1}^{n}E _{i}h_{i}^{3}}>\frac{E_{1}h_{1}^{3}\sum\limits_{i=1}^{n+1}\gamma_{i}h_{i}}{ \sum\limits_{i=1}^{n+1}E_{i}h_{i}^{3}} \tag{2}\]  
After rearranging the formula, we find the following:  
\[E_{n+1}h_{n+1}^{2}\sum\limits_{i=1}^{n}\gamma_{i}h_{i}>\gamma_{n+1}\sum\limits _{i=1}^{n}E_{i}h_{i}^{3} \tag{3}\]  
Based on the comprehensive analysis results and the determination formula for separation layers, combined with the overlying rock mechanics parameters [20] (as shown in Table 1), the possible locations of separation layers in the study area are determined. According to Formula (3), we determine whether a separation occurs between the 1 st and 2 nd layers. We substitute the data of serial number 1 into the left side of the equation, as follows: 10.01 \(\times\) 182 \(\times\) 2480 \(\times\) 13 \(\approx\) 107. We substitute the data from entry 2 into the right side of the equation, as follows: 2490 \(\times\) 1.87 \(\times\) 133 \(\approx\) 106. When the left side is greater than the right side, a separation layer will form between the first and second layers. However, as mining continues, the first layer will quickly collapse, causing the separation layer to disappear rapidly. According to Formula (3), we determine whether a separation occurs between layer 2 and layer 3. Because separation has already occurred between layer 1 and layer 2, layer 2 will be considered as the first layer of this composite beam. We substitute the data of sequence 2 into the left side of the equation, as follows: 1.87 \(\times\) 162 \(\times\) 2490 \(\times\) 18 \(\approx\) 21 \(\times\) 106. We substitute the data from sequence number 3 into the right-hand side of the equation, as follows: 2480 \(\times\) 10.01 \(\times\) 183 \(\approx\) 14 \(\times\) 107. The left side is less than the right side, so no separation will occur between the second and third layers.