## 3 Results and Discussion  
### The Fracture Law of the Overlying Rock  
The caving of the immediate roof is shown in Figure 5, which illustrates the stratat-caving conditions when the working face is advanced by 40 m and 50 m. Due to its low strength and the softness of the rock strata, during the early stage of the working face advancement, the phenomenon of caving as the coal is mined occurs. The immediate roof, with a relatively large thickness, can effectively fill the goal after caving, which is conducive to the formation of a stable structure in the overlying rock strata. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Lithology**} & \multirow{2}{*}{**Elastic Modulus**} & \multirow{2}{*}{\begin{tabular}{c} **Tensile** \\ **Strength** \\ **/MPa** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Cohesion** \\ **/MPa** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Internal Friction** \\ **Angle** \\ _f\({}^{\circ}\)_ \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Poisson** \\ **Ratio** \\ \end{tabular} } \\ \hline Sandy mudstone & 3.2 & 2.1 & 3.5 & 25 & 0.31 \\ Packsand & 4.2 & 2.3 & 4.4 & 22 & 0.24 \\ Mudstone & 2.5 & 1.3 & 2.2 & 24 & 0.17 \\ Medium sandstone & 4.2 & 2.9 & 5.9 & 26 & 0.27 \\ No. 2-1 coal & 0.5 & 0.1 & 1.5 & 22 & 0.24 \\ Limestone & 27.7 & 6.2 & 45.8 & 12.6 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical parameters of overburden rock. Figure 4: Schematic diagram of the model. Figure 5: Early collapse diagram. When the working face advanced to the critical position of 70 m, the primary roof experienced its initial fracture instability. As shown in Figure 5, illustrating overburden movement, distinct stratification occurred in the upper strata, with the main roof reaching its critical span and initiating collapse. The fracture location demonstrated minimal relative error compared with theoretical calculations, validating the computational rationality. The analysis of fracture position proves crucial for understanding intense strata pressure manifestations post-fracture. The observed fracture occurring on the goal side effectively reduced the probability of severe ground pressure disasters, providing significant guidance for safe mining practices [19]. Moreover, the substantial thickness of the immediate roof provided partial backfilling in the mined-out area, restricting sufficient rotational space. Temporary V-shaped articulated structures formed after preliminary contact between collapsed roof strata and gangue. The overlying strata subsequently collapsed with asynchronous settlement, creating bed separation fractures. The measured initial weighting interval of 70 m showed 7.9% deviation from field observations, demonstrating reasonable agreement with actual mining conditions. As advancement continued to 80 m, the fractured main roof fully compacted with goaf gangue, forming a stable V-shaped articulated structure exhibiting remarkable mechanical stability during strata movement. At 90 m advancement, the first periodic weighting occurred, accompanied by distinct bed separation between collapsed strata and key stratum, while only minor fractures developed in the key stratum without evident collapse. The overburden collapse configuration transitioned to trapezoidal morphology, with central strata gradually compacting and expanding along both advancing and vertical directions. The third periodic weighting at 120 m advancement witnessed vertical fracture propagation reaching maximum height, with Figure 5 illustrating final collapse morphology at 250 m advancement. Upon reaching the 100 m critical position, the principal key stratum underwent initial fracture instability with subtle yet measurable subsidence, as shown in Figure 6. Subsequent advancement triggered complete rupture of the principal key stratum, fundamentally altering load transfer mechanisms within the overburden and inducing progressive instability that ultimately manifested as surface subsidence.