## 4 Numerical Simulation and Results
### Analysis of the Effect of Slate Crushing on the Force Deformation of the Roof Slab  
The analysis scheme was used to increase the number of broken slates in sequence from the light hole to the direction of the J10 drainage place behind Yuanjue Cave and simulated the change of the number of broken- slates by changing the slate structure relationship. Figure 13 shows the vertical displacement of the roof slab of Yuanjue Cave under the action of different crushed rocks. With the increase in the number of crushed rocks, the roof slab of Yuanjue Cave underwent uneven settlement, and the maximum settlement position was shifted from the central area to the left front of Yuanjue Cave (the side of crushed rocks), and continuously developed to the left rear side. The above analysis shows that the number of broken boulders has a significant influence on the force deformation and stability of the roof slab of Yuanjue Cave. With the increase in the number of broken slate blocks, the settlement of Y6, Y8, and Y9 on the top plate of Yuanjue Cave gradually increased, the settlement of Y10 decreased, and the width of L6 cracks kept increasing. The settlement of the four monitored ones had the characteristics of Y6 \(>\) Y8 \(>\) Y9 \(>\) Y10 (Figure 14a), which is mainly since the monitoring points of Y6, Y9, and Y8 were closer to the broken slate area; when the broken slate exceeded 18 pieces (TS46), the settlement of Y6, Y8, and Y9 started to increase sharply and entered the stage of rapid change. The L6 crack still showed the characteristic of being \"wide at the top and narrow at the bottom\", and the width of the L6 crack increased with the increase of broken boulders, and when the number of broken boulders exceeded 18 (TS46), the width of the L6 crack stared to increase sharply and entered the rapid change stage (Figure 14b). According to the evolution law of vertical displacement and the L6 width change rate of measurement points, the change process can be divided into three stages: the initial uniform change stage (less than 11 pieces of broken slates), the middle stable change stage (the number of broken slates is between 11 and 18 pieces), and the late rapid change stage (broken slates have more than 18 pieces). When the broken slate exceeded 18 pieces, the vertical displacement and L6 crack width of each measurement point entered the late rapid change stage. Based on the principle  
Figure 12: Early warning point for instability of overhanging rocks. Figure 13: Vertical displacement clouds of the top slab when the number of broken slates varies. of preventive protection, the broken slate reaching 18 pieces can be taken as a sign that the top plate of the Yuanjue Cave has entered the destabilization warning state, i.e., the critical number of the broken slate is 18 pieces (Figure 15). Analysis of the Influence of the Degree of Damage to the Cracked Slates on the Force Deformation of the Top Slab  
Through the preliminary cave investigation, it was found that the single blocks of cracked boulders included TS01, TS02, TS03, TS04, TS07, TS08, TS10, TS11, TS12, TS14, TS17, TS31, TS32, TS36, TS52, and TS53. According to the contact area and grouping of the boulders, the groups where the cracked boulders are located were TS01, TS10, TS12, TS14, TS16, TS29, TS30, TS34, TS49, TS51, TS52, as shown in Figure 16. The cracked and damaged boulders were mainly distributed in the middle and front parts of the boulder-filled area. Figure 14: (**a**) Variation curve of vertical displacement of each measurement point with the number of broken slate blocks; (**b**) variation curve of the increase of L6 crack width with the number of broken slate blocks. Figure 15: Characteristic points of broken slates and destabilization warning points.