## 3 Research Methods and Process
### Numerical Simulation Test (Flac\({}^{3\text{D}}\)6.0)
#### 3.1.2 Model Type Design  
According to the research results of [PERSON] [28,30], the sand layer coefficient (defined as the ratio of the total number of sandstone layers to the total number of strata in the coal seam overburden) and the sand-mud ratio (defined as the ratio of the total thickness of sandstone to the total thickness of mudstone in the coal seam overburden) are the key characteristics of the coal seam overburden structure in the study area. Because this paper is to study the influence of the relationship between the number and thickness ratio of sandstone and mudstone in the overlying bedrock section on the water-flowing fracture rather than the morphological changes of the rock layer and the slope, the model is simplified according to the study area. The number of sandstone layers in the bedrock section of the numerical model is designed as 6 layers, 8 layers, 10 layers, 20 layers, 30 layers, and 40 layers. The number of sandy mudstone layers is designed as 4 layers, and the sand-mud ratios are designed as 6:4 and 8:2. The single layer thickness of fine sandstone and siltstone is treated as equal thickness, and the mining thickness is designed as 3 m and 5 m. After permutation and combination of the above variables, 24 different types of numerical models are obtained, as shown in Table 2.  
Figure 3: Three-dimensional geological model diagram.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**Loose Layer Characteristics**} & \multicolumn{6}{c}{**Bedrook Layered Structure Characteristics**} \\ \cline{3-11}
**Numbering** & **Deep** & **Height** & **Mining/m** & **Thichess of** & **Red Soil** & **Total Number** & **Sand-Mud** & **Sandstone** & **Sandstone** & **Sandstone** & **Sandy Mudstone** \\  & & & & **Sand** & **Layer** & **of Rock** & **Ratio** & **Layer Coefficient/** & **Number of** & **Thickness/** & **Number of** & **Thickness/m** \\  & & & & **Layer/m** & **Thickness/m** & **Stata/Layer** & **Ratio** & **cient/\%** & **Layers/Layer** & **m** & **Layer/Layer** & **Trichness/m** \\ \hline M1 & 300 & 5 & 30 & 20 & 10 & 6.4 & 60.0 & 6 & 25.00 & 4 & 25.00 \\ M2 & 300 & 5 & 30 & 20 & 12 & 6.4 & 66.7 & 8 & 18.75 & 4 & 25.00 \\ M3 & 300 & 5 & 30 & 20 & 14 & 6.4 & 71.4 & 10 & 15.00 & 4 & 25.00 \\ M4 & 300 & 5 & 30 & 20 & 24 & 6.4 & 83.3 & 20 & 7.50 & 4 & 25.00 \\ M5 & 300 & 5 & 30 & 20 & 34 & 6.4 & 88.2 & 30 & 5.00 & 4 & 25.00 \\ M6 & 300 & 5 & 30 & 20 & 44 & 6.4 & 90.9 & 40 & 3.75 & 4 & 25.00 \\ M7 & 300 & 3 & 30 & 20 & 10 & 6.4 & 60.0 & 6 & 25.00 & 4 & 25.00 \\ M8 & 300 & 3 & 30 & 20 & 12 & 6.4 & 66.7 & 8 & 18.75 & 4 & 25.00 \\ M9 & 300 & 3 & 30 & 20 & 14 & 6.4 & 71.4 & 10 & 15.00 & 4 & 25.00 \\ M10 & 300 & 3 & 30 & 20 & 24 & 6.4 & 83.3 & 20 & 7.50 & 4 & 25.00 \\ M11 & 300 & 3 & 30 & 20 & 34 & 6.4 & 88.2 & 30 & 5.00 & 4 & 25.00 \\ M12 & 300 & 3 & 30 & 20 & 44 & 6.4 & 90.9 & 40 & 3.75 & 4 & 25.00 \\ M13 & 300 & 5 & 30 & 20 & 10 & 82 & 60.0 & 6 & 33.33 & 4 & 12.50 \\ M14 & 300 & 5 & 30 & 20 & 12 & 82 & 66.7 & 8 & 25.00 & 4 & 12.50 \\ M15 & 300 & 5 & 30 & 20 & 14 & 82 & 71.4 & 10 & 20.00 & 4 & 12.50 \\ M16 & 300 & 5 & 30 & 20 & 24 & 82 & 83.3 & 20 & 10.00 & 4 & 12.50 \\ M17 & 300 & 5 & 30 & 20 & 34 & 82 & 88.2 & 30 & 6.67 & 4 & 12.50 \\ M18 & 300 & 5 & 30 & 20 & 44 & 82 & 90.9 & 40 & 5.00 & 4 & 12.50 \\ M19 & 300 & 3 & 30 & 20 & 10 & 82 & 60.0 & 6 & 33.33 & 4 & 12.50 \\ M20 & 300 & 3 & 30 & 20 & 12 & 82 & 66.7 & 8 & 25.00 & 4 & 12.50 \\ M21 & 300 & 3 & 30 & 20 & 14 & 82 & 71.4 & 10 & 20.00 & 4 & 12.50 \\ M22 & 300 & 3 & 30 & 20 & 24 & 82 & 83.3 & 20 & 10.00 & 4 & 12.50 \\ M23 & 300 & 3 & 30 & 20 & 34 & 82 & 88.2 & 30 & 6.67 & 4 & 12.50 \\ M24 & 300 & 3 & 30 & 20 & 44 & 82 & 90.9 & 40 & 5.00 & 4 & 12.50 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Types of numerical models and characteristics of overlying strata structure.