## 4 Numerical Simulation and Results  
The parameters of rock mechanics required for the numerical simulation were obtained after the aforementioned evolutionary law and geomechanical qualitative analysis (Table 3). The boundary conditions of the rock body of the roof slab of Yuanjue Cave are very clear, and this chapter analyzes them from the perspective of 3D modeling and numerical simulation for a precise quantitative perspective [46]. Combined with the aforementioned stratigraphic distribution characteristics and physical and mechanical parameters of the rock body [47; 48], the final stability study was conducted by finite difference software for the effect of overhanging, crushing, and damage of the roof slab on the overall top slab of Yuanjue Cave, respectively. In the aforementioned study, it is given that the top plate of the Yuanjue Cave has formed a relatively independent block structure in the form of a \"triangular thick plate\" (Figure 3), in which the J10 fissure forms a natural cutting boundary on the east side, so the model boundary on the east side can be extended 5 m eastward as the boundary of the J10 fissure. The rock body of the top slab on the west side forms a fracture boundary along the L6 fissure, but this boundary intersects the axis of the cave chamber horizontally at a large angle to accommodate the space of the cave chamber, so the west side extends westward to the end of the cliff wall of the L6 fissure with the west boundary of the cave chamber. The northern boundary is the hollow surface of the cliff wall, and the entrance of the cave canal can be used as the boundary; the southern side is bounded by the convergence angle of the roof slab. The rock supporting the top slab is the image formation, which is relatively stable and intact, so it can be extended below the top slab to the bottom part of Yuanjue Cave, and the three-dimensional model is shown in Figure 9. The model of the top slab of the Yuanjue Cave was established with 109,524 units and 19,856 nodes. \begin{table}
\begin{tabular}{c c c c} \hline
**Grouping** & **K(N/m)** & **Grouping** & **K(N/m)** \\ \hline TS01 & \(3.42\times 10^{10}\) & TS38 & \(5.22\times 10^{9}\) \\ TS04 & 0 & TS39 & \(6.94\times 10^{9}\) \\ TS10 & \(1.55\times 10^{10}\) & TS40 & \(5.16\times 10^{9}\) \\ TS11 & 0 & TS41 & \(5.69\times 10^{9}\) \\ TS12 & \(3.56\times 10^{10}\) & TS42 & \(1.19\times 10^{9}\) \\ TS13 & \(9.38\times 10^{9}\) & TS43 & \(9.10\times 10^{9}\) \\ TS14 & \(6.00\times 10^{9}\) & TS46 & \(1.01\times 10^{7}\) \\ TS15 & 0 & TS49 & \(1.12\times 10^{10}\) \\ TS16 & \(9.99\times 10^{9}\) & TS51 & \(1.81\times 10^{10}\) \\ TS20 & 0 & TS52 & \(2.14\times 10^{10}\) \\ TS25 & \(8.51\times 10^{9}\) & TS55 & 0 \\ TS29 & \(2.68\times 10^{10}\) & TS56 & 0 \\ TS30 & \(6.86\times 10^{9}\) & TS57 & 0 \\ TS34 & \(5.00\times 10^{9}\) & TS59 & \(3.07\times 10^{10}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Equivalent support stiffness of cracked boulders. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Sequence** & **Formation** & **Bulk** & **Shear** & **Cohesion** & **Friction** & **Density** & **Strength** \\
**Stratigraphy** & **Lithology** & **(GPa)** & **(GPa)** & **(MPa)** & **Angle (\({}^{\circ}\))** & **(kg/m\({}^{3}\))** & **(MPa)** \\ \hline
1 & Fine sandstone & 10 & 5 & 1.38 & 38.14 & 2230 & 0.2 \\
2 & Slate & 10 & 7 & 1.5 & 30 & 2300 & 0.2 \\ \end{tabular}
\end{table} 
Table 3: Stratigraphic lithological parameters. During the numerical simulation, the vertical displacement and the maximum principal stress location distribution of the roof slab were monitored at the four edge measurement points above the roof slab of Yuanjue Cave. By comparing and analyzing the vertical displacement and the maximum principal stress development trend of the roof slab at the four measurement points, the effect of the number of overhanging, broken, and damaged boulders on the force deformation characteristics and stability of the roof slab of Yuanjue Cave was revealed.