## 2 Model Test  
### Test Design  
A reduced scale model test was carried out based on recorded leakage accidents that occurred at the entrance and exit of shield tunnels. The test was carried out in a model box with a scale factor of 50:1. The model box is shown in Figure 1a, with dimensions of 1400 mm \(\times\) 400 mm \(\times\) 1000 mm. The colored sand layers were used to visualize the displacement of the strata. The model box consists of a soil box in the center and two water tanks on both sides to provide water for the tunnel leakage and to control the water level. The tunnel was buried in the soil box, which was separated from the two water tanks by permeable plates, which meet the requirements of water permeability and soil impermeability. Overflow outlets were set on both outsides of the tanks. Water was continuously refilled into the tanks during the test. Due to the presence of the overflow outlets, the water level was constant as it would flow out once it exceeded the height of the overflow outlets. In addition to this, the interior of the model box panels was coated with Vaseline to minimize friction between the soil and the boundary. A leakage may occur at different locations within the tunnel. In this research, leakage at the tunnel top is used as an example to compare the phenomenon of seepage erosion in different strata. During the test, an opening was made at the top of the tunnel in advance and sealed with a rubber plug. Then, at the beginning of the test, the plug was removed to trigger water and sand inrush, as shown in Figure 1b. The size of the openings is 2 cm \(\times\) 2 cm, which is large enough to ensure that the water and sand rush in continuously [11] since the focus of the study lies primarily on investigating the differencesin seepage erosion among different strata. Therefore, factors such as the shape or dimension of the opening were not explicitly considered, which will be investigated in future work. In order to study the difference in seepage erosion caused by tunnel leakage in different soil types, different proportions of sand and clay were mixed to obtain different model soils. These soils exhibit stability in their properties, with obvious differences in their physical-mechanical parameters. The raw material of sand is quartz sand, which is stable and free of impurities. In order to ensure that seepage erosion can occur in the soil, the sand used in the tests has the following characteristics: d\({}_{60}\) = 1 mm, d\({}_{10}\) = 0.1 mm. The grading curve is shown in Figure 2. The clay material was selected from natural clay with a cohesion of 20.4 kPa, a friction angle of 18.5\({}^{\circ}\), and a permeability coefficient of 1.26 \(\times\) 10\({}^{-7}\) cm/s. Clay percentages of 0%, 5%, 10%, and 20% were added to the quartz sand to make four types of soil (A, B, C, and D). The physical and mechanical parameters of the mixed soil with different mixing ratios are shown in Table 1.  
The seepage process involves the interaction of water and soil particles at the same time, which belongs to the fluid-solid coupling problem. [PERSON], et al. (2017) pointed out through \begin{table}
\begin{tabular}{c c c c c c} \hline
**Soil Type** & **Content of Clay** & **Unit Weight** & **Cohesion** & **Friction Angle** & **Permeability** \\  & **(\%)** & **(kN/m\({}^{3}\))** & **(kPa)** & **(\({}^{\circ}\))** & **Coefficient** \\ \hline A & 0 & 14.7 & 0 & 40.17 & \(2.21\times 10^{-5}\) \\ B & 5 & 15.1 & 1.81 & 35.56 & \(1.33\times 10^{-6}\) \\ C & 10 & 15.4 & 2.88 & 35.87 & \(8.04\times 10^{-7}\) \\ D & 20 & 15.8 & 4.28 & 34.16 & \(6.45\times 10^{-7}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of model soil. Figure 1: Model test device: (**a**) model test box (unit: mm); (**b**) illustration of the test process. Figure 2: Particle size distribution curve of sand. tests that the permeability coefficient of soil is a key parameter affecting the seepage erosion process.