# Numerical Simulation on the Leakage-Induced Collapse of Segmental Tunnels
## 2 Model Tests  
### Test Design  
The accident at Shanghai Metro Line 4 was selected as the background for the reduced-scale model tests [7]. At 6:00 a.m. on 1 July 2003, when the excavation of the connecting passage was still 0.8 m away from penetration, the freezing system broke down, resulting in the melting of the frozen soil, and a large amount of soil and water rushed from the excavated surface of the connecting passage through the openings of the connecting passage and into the tunnel. This eventually caused the collapse of part of the tunnel and ground subsidence in the surrounding area, resulting in severe tilting of surrounding buildings.  
The tests were carried out in a model box at a reduced scale with a geometrical similarity ratio of 50. The model box is shown in Figure 1a, and has dimensions of 1400 mm \(\times\) 400 mm \(\times\) 1000 mm. The model box consists of a soil box in the center and water tanks on both sides. The colored sand layers were used to visualize the displacement of the strata. The tunnel is buried in the soil box, which is separated from the water tanks on both sides by a permeable plate to provide water sources for the tunnel leakage and to control the water level at the same time. To ensure constant water levels throughout the tests, overflow outlets were set on both sides of the water tanks. Throughout the test, continuous water was refilled into the water tanks. The presence of overflow outlets ensured that the water level remained stable, as any excess water would flow out once it surpassed the height of these outlets.  
When leakage accidents occur at the location of the connecting passage, a longitudinal symmetry condition is assumed to be satisfied along the direction of the tunnel, so the tunnel and the soil can be taken as a semi-structure to carry out the tests. Before the tests, an opening (20 mm \(\times\) 20 mm) was made in the tunnel-connecting passage and sealed with a rubber plug. Then, the plug was removed at the beginning of the tests to trigger the water and sand inrush, as shown in Figure 1b, which illustrates a side view of the test setup. A total of 18-ring model tunnels were employed, with the leakage point located at the first ring.  
In the model tests, different proportions of sand and clay were mixed to obtain model soil with obvious differences in key parameters, from which the soil that had the parameters close to the background case was selected for the tests. The raw material of sand is quartz sand. The clay material was selected from natural clay. Percentages of 0%, 5%, 10%, and 20% content of clay were added into sand. The soil parameters were then compared with the key parameters in the background case in Table 1. It can be seen that, when the clay content is 5%, the parameters of the soil are the closest to that of the background case. Therefore, the soil mixture with 5% clay addition was chosen as the model soil for the tests.  
Figure 1: Model test device: (**a**) Model box; (**b**) Illustration of the tests (side view).  
Gypsum was used as the material for the reduced-scale model tunnel. The dimensions of the model tunnel meet the geometric similarity ratio of 50 when compared with the prototype. Also, the compressive strength of gypsum material in the model tunnel is 1.1 MPa, which meets the similarity ratio for compressive strength, which is 55 MPa in the actual tunnel. The model tunnel is shown in Figure 2.