## 3 Analysis of Key Strata Failure Structure and Movement Characteristics in Shallow Coal Seam Mining
### Characteristics of Key Strata Fracture in Shallow Coal Seam Mining
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multirow{2}{*}{**Lithology**} & \multirow{2}{*}{**Thickness**} & \multirow{2}{*}{**Model**} & **Tensile** & **Compressive** & \multirow{2}{*}{**Cohesion** **(MPa)**} & **Bulk** & **Volumetric** \\  & & & **Thickness** & & **Strength** & & **Strength** & **Modulus** & **Weight** \\  & & & **(m)** & **(MPa)** & **(MPa)** & & **(MPa)** & **(\(\mathbf{k}\)N-\(\mathbf{m}^{-3}\))** \\ \hline \multirow{2}{*}{5} & Medium-grained & \multirow{2}{*}{0.53} & \multirow{2}{*}{0.5} & \multirow{2}{*}{2.33} & \multirow{2}{*}{27.3} & \multirow{2}{*}{165} & \multirow{2}{*}{1494} & \multirow{2}{*}{23.4} \\  & sandstone & & & & & & & \\ \multirow{2}{*}{4} & Fine-grained & \multirow{2}{*}{3.7} & \multirow{2}{*}{4} & \multirow{2}{*}{1.87} & \multirow{2}{*}{28.3} & \multirow{2}{*}{2.46} & \multirow{2}{*}{1548} & \multirow{2}{*}{23.5} \\  & sandstone & & & & & & & \\ \multirow{2}{*}{3} & Silstone & \multirow{2}{*}{4.65} & \multirow{2}{*}{4.5} & \multirow{2}{*}{2.2} & \multirow{2}{*}{29.8} & \multirow{2}{*}{0.64} & \multirow{2}{*}{746} & \multirow{2}{*}{23.1} \\  & & & & & & & & \\ \multirow{2}{*}{2} & No. 1–2 coal seam & \multirow{2}{*}{2.95} & \multirow{2}{*}{3} & \multirow{2}{*}{0.37} & \multirow{2}{*}{12.4} & \multirow{2}{*}{1.23} & \multirow{2}{*}{614} & \multirow{2}{*}{13.2} \\  & & & & & & & & \\ \multirow{2}{*}{1} & Silstone & \multirow{2}{*}{3.92} & \multirow{2}{*}{4} & \multirow{2}{*}{2.4} & \multirow{2}{*}{28.9} & \multirow{2}{*}{0.72} & \multirow{2}{*}{782} & \multirow{2}{*}{24.3} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._structures. When stepped beam structures are formed at both ends of the working face, the structural control of the overlying strata subsidence in the inclined section is referred to as the semi-trapezoidal hinged arch structure. If load-bearing structures at both ends of the working face are different, with one side forming a hinged beam structure and the other side forming a stepped beam structure, it is known as the trapezoidal-like hinged arch structure, which is commonly encountered in shallow coal seam mining, as shown in Figure 2 illustrating the trapezoidal-like hinged arch structure;  
(2) Breakage characteristics of main key strata  
After the fracture of the sub-key stratum in the working face recovery, it promotes the formation of free movement space in the lower part of the main key stratum, which, under the influence of the load from the overlying rock and soil layers, undergoes fracture to form a bearing structure. In comparison to the fracture-bearing structure of the sub-key stratum, the main key stratum exhibits a lagging behavior, meaning that the main key stratum fractures simultaneously with or after a certain delay relative to the sub-key stratum fracture. During this period, the main key stratum is supported by the sub-key stratum, resulting in a reduction in subsidence space. The fracture blocks of the bearing structure in the main key stratum are longer than those in the sub-key stratum, making it more likely to form a hinged beam structure. Detailed research on this phenomenon has been conducted in the literature [19]. When the sub-key stratum forms a hinged beam structure, the bearing structures in the main key stratum are often the same. If the former forms a stepped beam structure, the latter may develop both hinged beam and stepped beam structures. Due to differences in load bearing, free movement space, and lithology between the main key stratum and the sub-key stratum, periodic fractures of varying magnitudes can occur [37], resulting in smaller fracture block sizes in the main key stratum. This can lead to the formation of a hinged beam structure in the main key stratum, creating a bearing structure similar to that in the sub-key stratum, forming an inclined section full-trapezoidal hinged arch structure as shown in Figure 3.  
Figure 3: Full-trapezoidal hinged arch structure. Figure 2: Trapezoidal-like hinged arch structure.