## 2 Model Test
### Test Results  
During the test, the phenomena of tunnel leakage-induced seepage erosion in different strata differed significantly, and, in order to facilitate the comparison and analysis, the phenomena were processed by the Particle Image Velocimetry (PIV) technique [18]. The phenomena of erosion in soil A are shown in Figures 4 and 5, where the green arrows in Figure 4 indicate the direction of displacement, and Figure 5 shows the velocity distribution field. The erosion process in soil A can be summarized as follows. (1) Stage 1: after leakage occurred at the top of the tunnel, the water and soil mixture rapidly poured through the opening. (2) Stage 2: an apparent displacement appeared in the soil above the tunnel, and developed upward to the soil top. (3) Stage 3: a slip surface appeared in the soil, and the soil top within the slip surface subsided. From the above observation, it can be seen that the soil loss in soil type A was continuous during the whole process. The strata response in soil B is shown in Figures 6 and 7. The process can be summarized into four stages. (1) Stage 1: after leakage initiates, soil and water start to rush into the tunnel, and seepage erosion of the surrounding soil starts. (2) Stage 2: due to the loss of soil and water at the top of the tunnel, an initial soil cave was formed above the tunnel, which temporarily remained stable. (3) Stage 3: the initial soil cave destabilized, and the soil above the cave collapsed rapidly. Subsequently, a secondary soil cave was formed and stabilized again. (4) Stage 4: the secondary soil cave destabilized and the soil above the cave, including the soil surface, subsided instantly and impacted the tunnel. In the test of soil B, the phenomena of the soil cave were observed after the erosion occurred. The surface was stable during the development of the erosion. However, the soil cave was unstable and continued to develop. Eventually, when the soil cave reached a critical height, the soil surface destabilized and fell. Regarding the discussion of soils C and D, it was observed that in the test, soil C showed the same phenomena as soil D. Therefore, soil C is taken as an example for the discussion of soils C and D.  
Figure 3: Model tunnel. 120 min, the soil cave remained stable without any further development, which indicated that the stratum stabilized itself spontaneously. Figure 6: Displacement of soil B: (**a**) leakage at the tunnel top; (**b**) initial soil cave; (**c**) secondary soil cave; (**d**) surface subsidence. Figure 7: Velocity distribution of soil B (m/s): (**a**) leakage at the tunnel top; (**b**) initial soil cave; (**c**) secondary soil cave; (**d**) surface subsidence. It can be summarized that the seepage erosion in the four different types of soil showed three completely different development processes:  
(1) For soil A, a slip surface developed rapidly after the tunnel leakage, which extended to the soil top and caused the surface to subside. No soil cave was observed during the whole process. In what follows, soil A is referred to as the no soil cave (NSC) soil. (2) For soil B, after the tunnel leakage, soil caves were observed. However, the soil caves were unstable and continued to destabilize and reappear with seepage erosion. The soil surface remained stable until the soil cave reached a critical height. In what follows, soil B is referred to as the unstable soil cave (USC) soil. (3) For soil C and D, after the tunnel leakage, a stable soil arch was observed near the leakage point and the soil stabilized spontaneously. In what follows, soil C is referred to as the stable soil cave (SSC) soil. For other soil with a clay addition higher than 10%, an experimental study by [PERSON] et al. [17] has provided compelling evidence of the correlation between clay content and the stability of the soil. [PERSON] conducted a series of seepage experiments specifically targeting clay content, demonstrating that as the clay content increases, the soil exhibits greater stability and resistance against seepage erosion.