## 3 Simulation Experiment of Overlying Strata Movement  
### Experimental Model  
With the above real conditions as the engineering background, a two-dimensional plane model was established. Figure 2 presents a schematic diagram of the experimental model. The height of the model was 750 mm, and the coal seam was 70 mm. The materials were mainly composed of aggregate and cementing material, whereby fine sand was selected as the aggregate, and lime and gypsum were used as the cementing material. The basic parameters are shown in Table 1. To simulate the strata pressure, a counterweight was applied at the top of the model. Stress sensors were laid on the floor of the coal seam to monitor the stress distribution along the gob side of the coal seam. Points a-e at the top of the coal seam were set to calculate the interlayer friction sliding displacement. The orange dashed line represents the calculation area of the coal seam deformation field along the goat.  
According to mechanical similarity, the geometric similarity ratio, \(\alpha_{L}\), time similarity ratio, and stress similarity ratio were obtained from the perspectives of geometric similarity, \(\alpha_{t}\), motion similarity, and dynamic similarity, \(\alpha_{r}\). The similarity ratios were 150:1, 12:1, and 140:1, respectively, and the calculation process was as shown in Equations (1)-(3):  
\[\alpha_{L}=\frac{L_{h}}{L_{m}} \tag{1}\]  
\[\alpha_{L}=\sqrt{\alpha_{L}} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**Materials**} & **Specific Gravity** & **Compressive Strength** & **Elastic** & **Poisson’s** & **Stratification \(\times\)** & & & & \\  & **/g** \(\times\)**cm\({}^{3}\) & **/MPa** & **/MPa** & **Ratio** & **Layer** & **Proportion** & **Sand** & **/kg** & **/kg** & **Gypsum** & **Water Consumption** \\ \hline Sandy soil & - & - & - & - & 1 \(\times\) 7 & 8:1:1 & 26.1 & 3.2 & 3.2 & 5\% \\ Mudstone & 2.75 & 71.8 & 1186 & 0.36 & 3 \(\times\) 3 & 9:7:3 & 6.6 & 5.2 & 2.2 & 5\% \\ Fine sandstone & 2.71 & 72.8 & 4507 & 0.23 & 10 \(\times\) 4 & 8:7:3 & 8.2 & 7.2 & 3.1 & 5\% \\ Silstone & 2.73 & 81.2 & 3439 & 0.26 & 1 \(\times\) 2 & 8:6:4 & 4.1 & 3.1 & 2.1 & 5\% \\ Coal & 1.43 & 20.5 & 1008 & 0.33 & 1 \(\times\) 7 & 9:9:1 & 17.1 & 17.1 & 1.9 & 5\% \\ \hline \end{tabular}
\end{table}
Table 1: Main physical parameters and material ratios of each rock formation.  
Figure 1: Location of the Liuxiang Coal Mine.  
\[a_{\sigma}=\frac{\gamma_{h}}{\gamma_{m}}a_{L} \tag{3}\]  
where \(L_{h}\) is the actual size, \(L_{m}\) is the model size, \(\gamma_{h}\) is the actual material bulk density, and \(\gamma_{m}\) is the model material bulk density.  
Each layer of material was laid in turn, according to the preset parameters. After the model was dry, a 400 kg weight was uniformly placed on the top of the model. Marking points were laid on the working face, and artificial speckle spraying was carried out in the coal seam area and the overlying strata. In order to prevent the weight from falling and prevent off-plane displacement during excavation, a transparent plexiglass plate was fixed in front of the model for restraint.  
Figure 2: Schematic diagram of the model size and the analysis area. (**a**) presents the model’s schematic diagram, while (**b**) illustrates the analysis area diagram of the sliding displacement between layers.