# Risk Identification Method and Application of Roof Water Inrush Under Multi-Working Face Mining
## 2 The Theory of Key Strata and Full Mining Disturbance
### Identification of Key Strata  
In mining areas with multiple hard strata in the overburden, the strata that significantly influence the overall or partial movement of the rock mass are termed the key strata. When multiple strata undergo synchronous and coordinated deformation and failure, leading to surface subsidence, the lowest hard stratum is designated as the main key stratum. In  
Figure 1: Development of the water-conducting fracture zone and its relationship with repeated disturbances induced by multi-working face mining. contrast, if only a few strata within the rock mass experience coordinated deformation and failure without affecting the surface, the lower hard stratum is classified as a sub-key stratum. When the key strata fracture, the subsidence deformation of the overlying strata occurs in a coordinated and consistent manner [29; 30]. The fracture of the key strata will result in the overall movement of all or a significant portion of the overlying strata. While multiple sub-key strata may exist within the overlying strata, there is only one main key stratum. Due to its superior strength, the main key stratum does not fracture concurrently with the sub-key strata. Fracturing of the main key stratum occurs only when its exposed area is sufficiently large enough to induce maximum stress that exceeds its strength limit. According to the key strata theory, when the main key stratum in the overburden fractures, a water-conducting fracture zone develops, extending to the top of the bedrock, with the height of this zone being equal to or greater than the thickness of the bedrock. Consequently, under similar geological conditions, the greater the distance of the main key stratum from the coal seam roof, the lower the risk of water inrush from the roof during mining operations [31; 32]. The positions of the key strata are determined based on the load characteristics of the strata and their influence on the fracture sequence. This is achieved through a comprehensive stiffness and strength analysis of the strata [33; 34]. The formula for identifying the position of the key strata based on stiffness is presented in Equation (1). In the identification process, calculations using \(E_{m+1}h_{m+1}^{2}\sum_{i=1}^{m}h_{i}\gamma_{i}\) and \(\gamma_{m+1}\sum_{i=1}^{m}E_{i}h_{i}^{3}\) are performed stratum by stratum, starting from the first stratum above the coal seam. When the \(m\)-th stratum satisfies Equation (1), the calculation process is terminated, and the \((m+1)\)-th stratum is designated as the first hard stratum. The position of the second hard stratum is then determined using the same method, and this procedure continues until the topmost hard stratum is identified. By identifying the positions of the hard strata, the locations of the overlying hard strata and the soft strata they influence are also determined. \[E_{m+1}h_{m+1}^{2}\sum_{i=1}^{m}h_{i}\gamma_{i}>\ \ \gamma_{m+1}\sum_{i=1}^{m}E_{i}h_{i}^{3} \tag{1}\]  
In the equation, \(h_{i}\), \(\gamma_{i}\), and \(E_{i}\) represent the thickness, unit weight, and elastic modulus of the \(i\)-th stratum (m, KN\(\cdot\)m\({}^{-3}\), GPa) (\(i=1,\,2,\ldots,\,m,\,m+1\)). Strength identification primarily involves comparing the rupture distances of the hard strata to assess whether they will fracture simultaneously with the underlying key strata. Taking into account the influence of the stratum's height relative to the coal seam and the fracture angle of the rock, the rupture distance for the \(j\)-th hard stratum is expressed using Equation (2). \[S_{j}=s_{j}+2H_{j}\cot\alpha \tag{2}\]  
In the equation, \(s_{j}\) represents the ultimate span of the \(j\)-th hard stratum (m); \(H_{j}\) denotes the distance from the \(j\)-th hard stratum to the upper surface of the coal seam (m); and \(\alpha\) is the fracture angle of the stratum (\({}^{\circ}\)) (\(j=1,\,2,\ldots,\,m,\,m+1\)).