# Numerical Simulation on the Leakage-Induced Collapse of Segmental Tunnels
## 4 Tunnel Collapse Process Analysis
### Structural Response  
#### 4.2.1 Distribution of Earth Pressure  
Based on the results of the strata analysis, the contact forces applied to the tunnel were extracted. The loads applied to the tunnel are shown in Figure 12. The opening is located at the angles of 270\({}^{\circ}\) and 300\({}^{\circ}\), so the loads of these two monitoring points are zero due to the opening. Figure 11: Displacement distribution of strata at different heights above the tunnel: (**a**) Leakage started; (**b**) Initial soil cave; (**c**) Secondary soil cave; (**d**) Third soil cave; (**e**) Surface subsidence. The loads applied to the top of the tunnel (\(0^{\circ},30^{\circ}\), and \(330^{\circ}\)) are shown in Figure 12a. The load at the top of the tunnel first shows an increase after the leakage. Then, the load decreases rapidly. After that, several sudden increases in load occur due to impact loads. Three main impact loads were observed in the numerical simulation, and the magnitude of the three impact loads increases with the increase in the height of the destabilized soil, and the third impact load reaches 18.68 kPa. The loads applied to the tunnel waist (\(60^{\circ}\), \(90^{\circ}\), \(120^{\circ}\), and \(240^{\circ}\)) are plotted in Figure 12b. Two different load trends can be observed. The measurement points at \(60^{\circ}\), \(90^{\circ}\), and \(120^{\circ}\) are located at the backside compared to the opening of the tunnel, are less affected by the leakage, and show a more stable trend of the load in the simulation. The measurement point at \(240^{\circ}\) is located at the lower side of the tunnel opening, and the load decreases rapidly due to soil loss and then stabilizes. The loads applied to the bottom of the tunnel (\(150^{\circ}\), \(180^{\circ}\), and \(210^{\circ}\)) are shown in Figure 12a. The loads applied at the angle of \(150^{\circ}\) and \(180^{\circ}\) show a sharp decrease after the leakage, while the loads at \(210^{\circ}\) show a relatively stable trend. The reason for this is that, with the supports of the soil arch located at the angle of \(210^{\circ}\), the loads remain stable even with some of the surrounding soil loss. Based on the aforementioned loads calculated from the strata model, the loads at key moments were extracted and applied to the FEM tunnel model to investigate the response of the tunnel structure and the cause of the tunnel collapse. The external load distributions at the tunnel at the six critical moments were extracted, and their distributions are shown in Figure 13. The load characteristics of the six key moments were analyzed as follows:  
Figure 12: Comparison of external load in model tests and simulation: (**a**) Loads applied to the top of tunnel (\(0^{\circ},30^{\circ},330^{\circ}\)); (**b**) Loads applied to the waist of tunnel (\(60^{\circ}\), \(90^{\circ}\), \(120^{\circ}\), and \(240^{\circ}\)); (**c**) Loads applied to the bottom of tunnel (\(150^{\circ}\), \(180^{\circ}\), and \(210^{\circ}\)). 1. Moment 1: The moment when the leakage started was chosen as the moment 1. The initial pressure is shown in Figure 13a. From the load distribution, it can be seen that the external load distribution of the tunnel at moment 1 was relatively uniform, with larger loads at the top and bottom of the tunnel and smaller loads at the waist. 2. Moment 2: the moment when the initial soil arch formed was chosen as moment 2. The load at the top and bottom of the tunnel increased significantly due to the soil arching effect, as shown in Figure 13a. 3. Moment 3: the moment when the initial soil arch was destabilized was chosen as moment 3. At this moment, the top of the tunnel was completely within the soil cave, and the loads were decreased to the lowest value. Since the soil erosion had not yet progressed to other locations of the tunnel, the loads at other locations of the tunnel were relatively stable. The supports of the arch were at the 210\({}^{\circ}\) location, and the loads were larger than those at other locations, as shown in Figure 13a. 4.