## 2 Research Methods
### Verification Methods
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Strata** & **Normal Stiffness** & **Shear Stiffness** & **Cohesion (MPa)** & **Internal Friction** & **Tensile Strength** \\  & & **(Copa)** & **(Copa)** & **Angle (\({}^{\circ}\))** & **(MPa)** \\ \hline
1 & Mudstone & 2.5 & 1.5 & 0.6 & 17 & 0.6 \\
2 & Coal & 0.4 & 0.2 & 0.3 & 12 & 0.9 \\
3 & Sandy mudstone & 3.0 & 4.0 & 1.0 & 18 & 3.6 \\
4 & Fine sandstone & 6.0 & 5.0 & 2.0 & 20 & 5.8 \\
5 & Sandy mudstone & 3.0 & 4.0 & 1.0 & 18 & 3.6 \\
6 & Fine sandstone & 6.0 & 5.0 & 2.0 & 20 & 5.8 \\
7 & Sandy mudstone 1 & 3.0 & 4.0 & 1.0 & 18 & 3.6 \\
8 & Sandy mudstone 2 & 3.0 & 4.0 & 1.0 & 18 & 3.6 \\
9 & Fine sandstone & 6.0 & 5.0 & 2.0 & 20 & 5.8 \\
10 & Medium sandstone & 8.0 & 6.0 & 2.3 & 22 & 7.60 \\
11 & Coarse sandstone & 8.2 & 6.4 & 2.6 & 17 & 6.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Joint parameters. 2. Verification of the experimental method  
We further increased the similarity of the simulation validation to increase the reliability of the method. According to the similarity simulation rules, the geometric similarity ratio of the model was determined to be 80:1, the motion similarity ratio was 8.94:1, the stress similarity ratio was 100:1, and the mass similarity ratio was 0.64 \(\times\) 10\({}^{6}\):1, with a time similarity ratio of 15:1. The design model was 2.5 m \(\times\) 0.2 m \(\times\) 0.8125 m (length \(\times\) width \(\times\) height), and the specific material ratio parameters for the similarity simulation are shown in Table 3.  
We conducted design experiments to verify the distribution patterns of the voids and the formation process of the voids. A non-contact full-field strain measurement system, MatchID-2D, was used to monitor the voids. The system used a digital image correlation algorithm to provide displacement and strain data measurements in a two-dimensional field of view for the experiment. Using a digital image fixed-point capture analysis to  
Figure 4: Graph processing method for the void ratio. Figure 3: Numerical model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **Strata** & **Ratio Number** & **Thickness (cm)** & **Dry Weight (kg)** & **Sand (kg)** & **CaCo\({}_{2}\) (kg)** & **Gypsum (kg)** \\ \hline
1 & Mudstone & 555 & 12.5 & 182.81 & 152.34 & 15.23 & 15.23 \\
2 & Coal & 555 & 25 & 365.63 & 304.69 & 30.47 & 30.47 \\
3 & Sandy mudstone & 773 & 5 & 73.13 & 63.98 & 6.40 & 2.74 \\
4 & Fine sandstone & 337 & 2.5 & 36.56 & 27.42 & 2.74 & 6.40 \\
5 & Sandy mudstone & 337 & 3.75 & 54.84 & 41.13 & 4.11 & 9.60 \\
6 & Fine sandstone & 455 & 3.75 & 54.84 & 43.88 & 5.48 & 5.48 \\
7 & Sandy mudstone 1 & 337 & 3.75 & 54.84 & 41.13 & 4.11 & 9.60 \\
8 & Sandy mudstone 2 & 555 & 5 & 73.13 & 60.94 & 6.09 & 6.09 \\
9 & Fine sandstone & 555 & 7.5 & 109.69 & 91.41 & 9.14 & 9.14 \\
10 & Medium sandstone & 337 & 6.25 & 91.41 & 68.55 & 6.86 & 16.00 \\
11 & Coarse sandstone & 337 & 6.25 & 91.41 & 68.55 & 6.86 & 16.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Proportions of the materials. monitor the deformation of the physical model and taking photos every 10 min with a high-resolution camera at a fixed angle, we calculated and analyzed the displacement of each measuring point using image capture analysis software. The specific indicators that were monitored were 1 the displacement changes on the surface, basic roof, and floor of the model during the mining process and 2 the morphological changes in the development of the goal. The physical similarity model is shown in Figure 5. The void fraction was calculated as the ratio of the difference in the vertical displacement between the surface and the floor to the mining height.