## 4 Analysis of Fluid-Solid Coupling Disaster-Causing Mechanism
### Fluid-Solid Coupling Calculation Models on Inter-Layer Rock
#### 4.1.1 Network-Boundary Fluid-Solid Coupling Water Inrush Calculation Model  
The inter-layer rock forms a complete fracture structure after the mining disturbance of the upper and lower coal seams. The formed water-inrush fractures are not a single form of network water-inrush fractures or boundary water inrush fractures, they include boundary water-inrush fractures and network water-inrush fractures at the same time. The water accumulated in the upper part of the inter-layer rock enters the lower gob or working face through the water-inrush fractures of the inter-layer rock with time and space synchronization. When the upper water flows through the network fractures, the flow path is more complicated; the probability of lateral movement is the same as that of longitudinal movement. It mainly moves along the lateral separation fractures and longitudinal broken fractures formed by the fracture of different inter-layer rock strata. The state of water flow inside can be regarded as a high-density fracture flow state; the area of water flow in the inter-layer rock is a fracture medium. Because the upper water flows into the gob in the process of this fracture flow, the flow time is short, and the effect of water on the network fracture is not obvious. Therefore, it is assumed that the water flow process has no effect on the distribution and state characteristics of the network water inrush fracture; the effect of water on the network fracture is ignored. The network-boundary water inrush calculation model is shown in Figure 12.  
The flow of water accumulated in the upper part of the inter-layer rock in the network water-inrush fracture belongs to Darcy flow, it is not flowing outside the network water inrush fracture; that is, the pore flow between water and different inter-layer rock layers is ignored. Although the network water-inrush fractures are not completely evenly distributed among the inter-layer rock due to the high density of its distribution, it can be regarded as a connected uniform fracture network. The inter-layer rock area of the network water inrush fractures is a continuous rock medium; that is, the physical equation of water flow in the network fractures can be equivalently expressed by the seepage flow equation of the porous medium. Although its essence is different, the difference between the two is mainly manifested in the great difference in the permeability coefficient. The permeability coefficient of a continuous medium depends on the stress and strain value of the rock, while the water inrush coefficient of water inrush fracture in an inter-layer rock network is related to the characteristics of fracture, which can be expressed by Formula (11). The fluid flow in the water inrush fracture of the network can be equivalently expressed as Equation (12) [35]. \[(k(b,f)p,i),i=n\frac{\partial p}{\partial t}+\frac{\partial e}{\partial t}+W, \tag{11}\]  
Figure 12: Network-boundary fluid–solid coupling water inrush calculation model. \[k(b,f)=-\frac{1}{12}\sum_{i=1}^{n}b_{i}^{3}f_{i}. \tag{12}\]  
In the Formula, \(k\) is the equivalent permeability coefficient, and it can be calculated according to formula (12). \(b_{i}\) is the width of the fracture; \(f_{i}\) is the friction coefficient of the fracture; \(p\) is fracture water pressure; \(e\) is volume deformation; \(W\) is the source of water accumulation; \(t\) is time. The flow process of water in the upper part of the inter-layer rock in the boundary water-inrush fracture is instantaneous, and the water inflow is large. The distribution characteristics of water-inrush fractures at the boundary of inter-layer rock show that there are water-inrush channels longitudinally penetrating multiple inter-layer rock layers at the side of the open-off cut, the side of the stop-mining line, and the middle position of the strike in the lower coal seam. The distribution characteristics of water inrush fractures in inter-layer rock are obtained by the above similar simulation test. Multiple boundary water-inrush fracture channels can be found.