# Study on the Co-Evolution Mechanism of Key Strata and Mining Fissures in Shallow Coal Seam Mining
## 3 Fracture Structure of Key Strata and Evolution Characteristics of Mining Fissures  
### Physical Similarity Simulation Experiment Design  
The experimental prototype is based on the geological data of the No.2-2 coal seam working face of the Hanjiawan Coal Mine in northern Shaanxi to build a near-horizontal physical model. In the experiment, a 3 m plane model frame made by Xi'an University of Science and Technology was selected. The thickness of the coal seam was 4.3 m, and the thickness of the coal seam was 4.5 m. It is known that the bearing capacity of the loose soil layer is insufficient, and it breaks simultaneously with the key strata and the bedrock layer. Therefore, this study focused on the bedrock layer. The bedrock layer was built to 41 m, and the equivalent load was applied to the unbuilt part.  
According to the research content, the geometric similarity constant was selected as 1:100, and the model construction size was 300 cm (length) \(\times\) 20 cm (width) \(\times\) 44 cm (height). Based on the similarity law, the bulk density similarity constant was selected as 1.56; the stress similarity constant was selected as 156; and the time similarity constant was selected as 10. River sand, fly ash, gypsum, and large white powder were used as similar model building materials, among which river sand and fly ash were used as model aggregates, gypsum and large white powder were used as cement, and mica powder was used as joint division material. The test process was recorded by a total station and a digital camera, and the relevant mechanical properties of similar simulated test materials are shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Observed Time (d)**} & **Working Face Position (m)** & **Maximum Mining Fissure Location (m)** & **Daily Footage (m)** & **Lag Distance (m)** & **Lag Angle (\({}^{\circ}\))** \\ \hline
1.3 & 204.3 & 167.48 & 11.4 & 36.8 & 65.0 \\
1.5 & 219.5 & 187.59 & 9.7 & 31.91 & 68.9 \\
1.3 & 236.6 & 203.05 & 12.4 & 33.5 & 66.9 \\
1.4 & 252.4 & 221.84 & 11.2 & 30.5 & 68.8 \\
1.5 & 271.2 & 241.37 & 12.2 & 29.8 & 69.2 \\
2.0 & 285.9 & 254.48 & 7.2 & 31.4 & 68.2 \\
1.9 & 302.3 & 270.12 & 8.4 & 32.1 & 67.7 \\
1.0 & 314.5 & 285.59 & 12.1 & 28.9 & 69.8 \\
1.3 & 331.7 & 299.86 & 13.1 & 31.8 & 68.0 \\
2.2 & 350.4 & 321.0 & 8.4 & 29.4 & 69.5 \\  & Average value & & 10.63 & 31.61 & 68.2 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Space–time relationship between surface mining fissures and working surfaces.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **Lithology** & **Thickness** & **Model** & **Tensile** & **Cohesion** & **Bulk Modulus** & **Shear Modulus** & **Volumetric Weight** \\  & **(m)** & **Thickness (m)** & **Strength (MPa)** & **(MPa)** & **(MPa)** & **(MPa)** & **(MPa)** & **(kN-m\({}^{-3}\))** \\ \hline
13 & Loading layer & \(\backslash\) & \(\backslash\) & \(\backslash\) & \(\backslash\) & \(\backslash\) & \(\backslash\) \\
12 & Fine-grained & 3.7 & 4 & 1.77 & 1124 & 512 & 24.1 \\  & sandstone & 2.8 & 3 & 1.04 & 1.38 & 752 & 435 & 25.3 \\
11 & Mudstone & 2.8 & 3 & 1.04 & 1.38 & 752 & 435 & 25.3 \\
10 & Fine-grained & 0.8 & 1 & 2.02 & 1.50 & 998 & 488 & 22.7 \\  & sandstone & & & & & & \\
9 & Sandy mudstone & 1.69 & 2 & 2.12 & 1.34 & 715 & 472 & 22.4 \\  & Fine-grained & & & & & & \\
8 & sandstone & 4.8 & 5 & 1.78 & 1.90 & 1180 & 641 & 23.4 \\
7 & Sandy mudstone & 2.6 & 3 & 2.12 & 1.32 & 780 & 467 & 24.1 \\
6 & Mudstone & 2.8 & 3 & 1.25 & 1.24 & 731 & 412 & 27.4 \\
5 & Medium-grained & & & & & & \\  & sandstone & 16.04 & 16 & 2.32 & 0.8 & 1269 & 620 & 21.6 \\  & Fine-grained & & & & & & \\
4 & sandstone & 2.8 & 3 & 1.94 & 2.50 & 1531 & 832 & 23.0 \\
3 & Sandy mudstone & 0.97 & 1 & 2.35 & 1.22 & 750 & 450 & 25.6 \\
2 & No.2-2 coal seam & 4.3 & 4.5 & 0.35 & 1.18 & 612 & 333 & 13.4 \\
1 & Siltst one & 2.78 & 3 & 1.53 & 0.15 & 141 & 510 & 23.4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The main mechanical properties of each material in the model.