## 4 Discussion
### Evolution Law of the Void Fraction While Advancing  
(1) Evolution of the void fraction  
First, we analyzed the evolution law of the overall void when the working face advanced from 20 m to 200 m. The development of the two zones and the voids in the working face advancement were analyzed. The detailed changes in the void fraction during the advancement are shown in Figure 10. With the advancement of the working face, the void area gradually increased, and the void ratio gradually decreased from 70.1% to 25.1%. At the beginning of the mining of the working face, there was a large void ratio behind the working face that was close to 70%. From this analysis, it could be seen that as the working face advanced, the overall void ratio gradually decreased, and the overall void area first increased and then decreased.  
In addition, during the advancement of the working face, the rear void was constantly in a changing state. For example, when the working face advanced by 50 m, the distribution of the voids within 20 m behind the working face was completely different from when the working face had advanced by 60 m. The following is an analysis of the distributions at different depths inside the goal during the advancement of the working face, as shown in Figure 11. According to the analysis in Figure 11a, before the working face was pushed to 100 m, the overall void was relatively large. At the same advancement, the voids in the goal behind the working face exhibited a pattern of more voids on both sides and less voids in the middle, similar to a U-shaped distribution. At different advancements, the maximum value of the void appeared 20 m behind the working face, and as the distance of the advancement increased, the void fraction at that location gradually decreased. Figure 11b shows that after the working face was pushed to 100 m, the void behind the working face gradually decreased.  
(2) Evolution of the void shape  
We analyzed the evolution law of the void shape in the goal using numerical and similarity models, as shown in Figure 12. Based on the analysis in Figures 7b and 12b, it could be seen that when the working face advanced to the initial breaking distance of the direct roof, a separation layer appeared, and at this time, the overall void fraction was extremely high, ranging from 95% to 100%. Afterwards, the direct roof periodically broke, and the void fraction decreased to below 88.9%. When the initial breaking distance of the basic roof was reached, it was obvious that the suspended roof and the masonry beam B block and masonry beam C block structures could be observed in the goal. The basic roof, the suspended roof, and the internal rock blocks intersected and overlapped into a triangular area, forming a natural accumulation area, and the overall void fraction further decreased to below 33.3%. After reaching the basic roof and the periodically  
Figure 10: Change trend in the overall void ratio in the goal during the process of advancing.  
breaking length, a natural accumulation area and a compaction area formed inside the goat. Under the gravity of the overlying rock, the internal voids in the re-compaction area were relatively small, accounting for 33.0% of the total goat, and the overall void fraction further decreased to below 27.8%. As the pushing distance further increased, the length of the natural accumulation area and the re-compaction area increased proportionally.  
Figure 11: Void distribution behind the working face. (**a**) Before the working face advanced 100 m. (**b**) After the working face advanced 100 m.  
Figure 12: Evolution of the void’s shape: (**a**) the numerical model and (**b**) the similarity model.