## 3 Analysis of Key Strata Failure Structure and Movement Characteristics in Shallow Coal Seam Mining
### Key Strata-Bearing Structure and Surface Movement Characteristics  
(1) Trapezoidal-like hinged arch structure movement characteristics  
The key strata in the working face form a fracture-bearing structure, which undergoes periodic load movement as the working face advances. Based on the results of experimental simulations, it is evident that after the fracture of the sub-key stratum, a trapezoidal-like hinged arch structure is formed on the inclined section, and this structure's hinged support reduces the subsidence of the overlying strata. Calculations based on the working face inclined length and the sub-key stratum's position reveal that the sub-key stratum reaches a state of over-mining conditions. Monitoring lines A and B for sub-key stratum displacement show that the rock layers on the left side of the cutting section exhibit more significant subsidence compared to the right side; with the maximum subsidence occurring in the range of 0-22 m and 75-120 m on the left side of the working face, the load-bearing action of the sub-key stratum causes line B to move toward both sides of the working face. As line A has no load-bearing rock layer support at its position, the rock layers exhibit smaller horizontal displacement after compaction, confirming the controlling effect of the trapezoidal-like hinged arch structure on the subsidence of the overlying rock and soil layers. Analysis of the fitted curves for lines A and B reveals that the fitted curve for line B has a larger slope, indicating the presence of inflection points and stretching zones at both ends of the working face. The fitted curve for line A exhibits a funnel-like shape with no inflection points, demonstrating that the key strata-bearing structure has a certain control over the subsidence of the overlying rock layers, effectively reducing the amount of subsidence of the overlying strata, as shown in Figure 4 in the subsidence curve of the trapezoidal-like hinged arch structure;  
(2) Full-trapezoidal hinged arch structure and surface movement characteristics  
The fracture of the sub-key stratum results in an increased free movement space in the lower part of the main key stratum, forming a full-trapezoidal hinged arch structure on the inclined section. Based on the rock fracture angle and coal pillar support, the inclined length of the full-trapezoidal hinged arch structure is smaller than that of the trapezoidal-like hinged arch structure, with the difference being twice the thickness of the interlayer rock. Due to the supporting effect of the full-trapezoidal hinged arch structure, the subsidence of rock and soil layers in the inclined section ranges from 0 to 10 m and 94 to 120 m and is relatively small. In the range of 10-32 m and 69-94 m, the subsidence gradient of rock and soil layers is higher, leading to an intensified subsidence trend. Within the range of 32-69 m, the subsidence values for various monitoring lines are essentially the same, indicating that the maximum subsidence point has been reached. Comparing the fitted curves of rock and soil layers, only monitoring line C has an inflection point on the left side of the working face. Fitted curves for lines D and E exhibit a high degree of similarity, with inflection points and stretching zones on both sides of the working face. The subsidence gradient for the latter is gentler, indicating a higher degree of fit. The fitted curve for line E closely  
Figure 4: Subsidence curve graph of the trapezoidal-like hinged arch structure. resembles the surface subsidence curve in mining subsidence theory and is symmetric with the maximum subsidence point, indicating that the fracture-bearing structure of the key strata can effectively control and mitigate surface subsidence. It possesses self-repairing properties, resulting in a smoother surface subsidence curve and reducing the impact of mining-induced damage on the surface.