## 3 Numerical Model and Calculation Scheme
### PFC Simulation Results Analysis
#### 3.3.1 Overburden Rock Failure Characteristics
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Lithologic Characters** & **E\({}_{\text{mod}}\)** & **K\({}_{\text{att}}\)** & **Kn** & **Ks** & **K\({}_{\text{npb}}\)** & **K\({}_{\text{spb}}\)** \\  & **/GPa** & **/Gpa** & **/Gpa** & **/Gpa** & **/Gpa** & **/Gpa** \\ \hline Medium sandstone & 28.60 & 2.4 & 51.4 & 21.4 & 49.6 & 20.7 \\ Mudstone & 12.10 & 2.9 & 30.3 & 10.4 & 22.4 & _7.7_ \\ Fine sandstone & 26.40 & 1.8 & 56.4 & 31.3 & 45.6 & 25.3 \\ Mudstone & 10.30 & 2.9 & 30.3 & 10.4 & 19.8 & 6.8 \\ Silstone & 25.60 & 2.6 & 53.1 & 20.4 & 43.6 & 16.8 \\ Mudstone & 8.90 & 2.9 & 30.3 & 10.4 & 18.2 & 6.3 \\ Fine sandstone & 23.60 & 1.8 & 56.4 & 31.3 & 41.6 & 23.1 \\ Sandy mudstone & 2.86 & 1.8 & 11.5 & 6.6 & 7.7 & 4.3 \\
2\#Coal & 4.2 & 3.1 & 14 & 4.5 & 9.7 & 3.1 \\ Mudstone & 8.2 & 2.9 & 30.3 & 10.4 & 16.4 & 5.7 \\ Silstone & 21.20 & 2.6 & 53.1 & 20.4 & 39.7 & 15.3 \\ Medium sandstone & 26.05 & 2.4 & 51.4 & 21.4 & 44.9 & 18.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Particle model microphysical and mechanical parameters. time, the overlying strata in the goat are arched as a whole, and the load capacity of each rock stratum in the arch is greatly reduced. The load of the overlying strata is transferred from the side of the arch to the deep rock mass, and there is no separation between the upper strata of the vault. In summary, when the advancing distance of the working face is small (advancing 40 m), the immediate roof directly fills the goat due to its low strength. As the working face continues to advance, the exposed span of the overlying main roof strata continues to increase after the direct roof collapses, forming a fixed beam structure at both ends of the coal wall at the open-off cut. When the fixed beam reaches the limit span, the fixed beam is destroyed, and the first pressure occurs at the working face (as shown in Figure 18e). As the working face continues to advance, a new load structure, namely the plate structure, is formed after the main roof beam breaks (as shown in Figure 18f). With the increase of the exposed area of the plate, the plate is prone to break and form periodic weighting. At the same time, the repeated breaking of the plate is the periodic weighting process of the working face. Most of the collapsed rock masses are arranged regularly, and the rock masses are stacked at the coal wall position; one end of the rock mass is at the coal wall, and the other end is on the coal gangue in the goat. Moreover, in the process of continuous advancement of the work, the roof spans develop upward and forward, the height of the span zone increases, the deformation and failure of the rock mass increases, and the rock mass of the goat span is slowly compacted. At the same time, the fracture position of the rock stratum at the coal wall is shown in the figure. The rock stratum is close to the direction of the goat from the position of the coal wall, and the rock stratum presents a step-like fracture. The whole structure gradually evolves from the plate structure to the arch structure (as shown in Figure 18i).