## 4 Model Test
### Test Device  
It should be underlined that the length is defined as the extent along the tunnel axial orientation, and the width refers to the extent perpendicular to the tunnel axis in the same plane. Based on the geometric similarity ratio, the inner length of the test device is 1 m, the tunnel buried depth is 3 m, the tunnel diameter is 0.15 m, and the distance between the two tunnel centers is 0.45 m. Furthermore, to reduce boundary effects in the model tests, the distance from the device boundary to the tunnel boundary is set to be at least triple the tunnel diameter (0.45 m). As a result, the theoretical width and height of the test device should be 1.5 m and 3.6 m, respectively. Accordingly, a model test device was developed, consisting of a test container, stress loading facilities, water supply facilities, and data acquisition facilities, as illustrated in Figure 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Similarity Relationship** & **Similarity Ratio** \\ \hline Geometric size \(C_{l}\) & — & 60 (set) \\ Density \(C_{\gamma}\) & — & 1 (set) \\ Displacement \(C_{\delta}\) & \(C_{\delta}=C_{l}\) & 60 \\ Stress \(C_{\sigma}\) & \(C_{\sigma}=C_{l}C_{\gamma}\) & 60 \\ Strain \(C_{\epsilon}\) & \(C_{\epsilon}=C_{\delta}/C_{l}\) & 1 \\ Compression strength \(C_{\sigma_{\epsilon}}\) & \(C_{\sigma_{\epsilon}}=C_{\sigma}\) & 60 \\ Elastic modulus \(C_{E}\) & \(C_{E}=C_{\sigma}/C_{\epsilon}\) & 60 \\ Permeability coefficient \(C_{K}\) & \(C_{K}=\sqrt{C_{l}}/C_{\gamma}\) & 7.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The similarity relationship and ratio adopted in the model test. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Density/(g\(\cdot\)cm\({}^{-3}\))** & \begin{tabular}{c} **Permeability** \\ **Coefficient/(cm\(\cdot\)s\({}^{-1}\))** \\ \end{tabular} & \
\begin{tabular}{c} **Compression** \\ **Strength/MPa** \\ \end{tabular} &
\begin{tabular}{c} **Elastic** \\ **Modulus/GPa** \\ \end{tabular} \\ \hline Normal rock & 2.4–2.6 & 4.9 \(\times\) 10\({}^{-3}\)–1.0 \(\times\) 10\({}^{-2}\) & 15–20 & 3–5 \\ Fault rock & 1.9–2.1 & 5.8 \(\times\) 10\({}^{-4}\)–2.5 \(\times\) 10\({}^{-3}\) & 8–12 & 1–1.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Main physical and mechanical properties of surrounding rocks. The test container with inner dimensions of 1.0 m \(\times\) 1.6 m \(\times\) 1.7 m (length \(\times\) width \(\times\) height) was used for filling the medium, and it served as the location where the disasters occurred. To restrict lateral deformations, stress-bearing columns and beams were installed around the outside of the container. Additionally, a load-bearing plate was placed at the bottom of the container to enhance its structural stability. The entire test container was constructed using 20 mm thick steel and assembled with high-strength bolts, ensuring excellent tightness, stability, and safety. Significantly, the height of the test container was limited to 1.7 m due to constraints in test space and material cost, whereas ideally, it should have been 3.6 m to match the design value. As a result, the simulated tunnel buried depth in the model test was only 1.1 m, which was significantly less than the intended value of 3 m. To account for this discrepancy, stress loading facilities including hydraulic cylinder, controller, and pipe were used to provide an additional stress of 0.04 MPa based on engineering parameters and similarity ratios. The water supply facilities consisted of a water storage barrel, support tank, and other ancillary equipment such as a pump and reservoir, as shown in Figure 6. To provide a constant water pressure for the test, an overflow pipe connecting with the conversation tank was installed inside the water storage barrel at a height of 1.6 m. Different constant water pressures could be achieved by adjusting the height of the support. The support tank had a size of 1.0 m \(\times\) 1.6 m \(\times\) 0.1 m (length \(\times\) width \(\times\) height) and was fixed at the top of the test container.