## 3 Numerical Model and Calculation Scheme
### PFC Simulation Results Analysis  
#### 3.3.1 Overburden Rock Failure Characteristics  
Simulate mining of the working face. The different color areas in the figure below represent different rock layers with different properties and record the deformation and failure process of the roof overburden. Now, the fracture morphology of the roof overburden with different advancing distances is studied. When the coal mining face began to advance 10 m, there were small cracks in the immediate roof, and the roof of the coal seam appeared slightly bending and sinking, but the cracks were small and did not penetrate the immediate roof, and the immediate roof did not collapse significantly. When the working face advances to 20 m, the small cracks inside the immediate roof of the coal seam gradually develop and penetrate, and the immediate roof collapses. The height of the caving zone is 4.45 m.  
When the working face continues to advance to 30 m, with the increase of the advancing distance, the roof hanging area above the goat gradually increases. Affected by the pressure of the overlying strata and its own gravity, the roof cracks increase, and the roof further collapses. At this time, the height of the caving zone is 4.45 m. When the working face advances to 40 m, the roof further ruptures and collapses with the advancement of the working face. However, due to the large structural strength of the upper basic roof, it can withstand the greater load capacity of the overlying strata. There is no obvious crack in the rock stratum, and the bending subsidence phenomenon is not obvious. At this time, the height of the caving zone is still 4.45 m.  
When the working face is advanced to 50 m, the initial pressure load capacity of the basic roof gradually decreases, and a large number of cracks appear at the roof boundary; that is, the 'beam' breaks, and the basic roof has a separation phenomenon, with the obvious sinking phenomenon. After the 'beam' is broken, the load on the center of the plate surface increases, and the center of the plate gradually produces unpenetrated small cracks. The plate does not break and does not collapse. At this time, the height of the collapse zone is 5.25 m. When the working face advances to 60 m, the main roof appears periodic weighting, and the cracks inside the plate gradually increase. The development of cracks leads to the fracture of the rock strata. After the main roof is broken by periodic weighting, many small cracks begin to appear in the rock strata with weak load capacity above it, and the separation phenomenon occurs. At this time, the caving height is 7.24 m.  
When the working face advances to 70 m, 80 m, and 90 m, due to the periodic weighting of the main roof, the load on the overlying strata becomes larger, and a large number of cracks are generated in the layer and bend and sink with the collapse of the main roof. When advancing to 90 m, the part of the goat has been gradually compacted in the front half of the working face due to the caving and sinking of the rock strata; the structure of the goat is more stable, the bending and sinking of the upper rock strata are obviously reduced, and the separation between the upper rock strata is no longer produced. At this