## 4 Twin Tunnels Model in DEM  
The establishment process of the DEM model with small diameter (\(d\) = 6.2 m) and super-large diameter (\(D\) = 15.2 m) twin tunnels are similar. T1 and T2 represent the first and adjacent super-large (\(D\)) tunnels, and t1 and t2 are the first and adjacent small (\(d\)) tunnels. The outline of small and super-large diameter twin tunnels in DEM is shown in Figure 6. The size of the model is large enough to avoid the boundary effect. [3,28,30] The temperature influence is ignored since the whole time of the train passing the tunnel is 4.18 s. The parameters of the \(d\) and \(D\) twin tunnels are shown in Table 4. The steps of construction of super-large diameter (\(D\) = 15.2 m) twin tunnels model under train vibration is as follows:  
**Step 1:**: Four walls are generated as the model's boundary, and the particles with \(R_{1}\) = 0.12-0.2 m, \(R_{2}\) = 0.06-0.1 m, and \(R_{3}\) = 0.02-0.03 m are created inside the area. The particles near the twin tunnels (smaller than 2.0 m) are generated with particles (\(R_{2}\) = 0.06-0.1 m). Different sizes of particles used in different areas can save calculation time and obtain accurate results. The larger distance between the walls and the tunnel can weaken the boundary effect of the wall to the maximum extent to obtain accurate calculation results. The initial balance state of the model is achieved through calculation, and the initial model is shown in Figure 7a. At this time, all particles in the model adopt the parameters of silly sand.
**Step 2:**: The cross section of super-large diameter twin tunnels as shown in Figure 7b which will built in the red particle region in Figure 7a. First, the geometry, as shown in Figure 7b, was generated; second, redundancies particles inside the \(D\) twin tunnel liners are deleted according to the cross-section of the \(D\) twin tunnel (Figure 7b); third, micro-parameters of C60 concrete have been used in the red region, as shown in Figure 7c.
**Step 3:**: Gravity and water pressure are set. The lateral pressure coefficient is 0.4. The control conditions of the equilibrium state of the model will be stricter. If the maximum velocity of particles in the model is no more than 0.5 mm/s, the model is considered to reach a balanced state.
**Step 4:**: Measurement circles of the \(D\) twin tunnel model are generated as shown in Figure 7d, and the train vibration loads in T1 are simulated by the cosine functions (Figure 2).  
Figure 5: Curve fitting of shear force and shear displacement ratio of silly sand under 100–400 kPa pressure obtained from laboratory direct shear tests and DEM direct shear tests.  
The total time of the type A train passing through the twin tunnels at the speed of 120 km/h is 4.18 s.  
Figure 6: Small and super-large diameter twin tunnels in DEM: (**a**) Cross section of small tunnel (\(d\) = 6.2 m); (**b**) Outline of small twin tunnels DEM model; (**c**) The size of particles in the small twin tunnels; (**d**) Cross section of super-large tunnel (\(D\) = 15.2 m); (**e**) Outline of super-large twin tunnels DEM model; (**f**) The size of particles in the super-large twin tunnels.  
Figure 7: The process of DEM model setup of super-large diameter (\(D\) = 15.2 m) twin tunnels: (**a**) The initial model of super-large diameter twin tunnels; (**b**) the size of the geometry of super-large diameter twin tunnels; (**c**) the cross-section of super-large diameter twin tunnels; (**d**) detailed layout of monitoring points of the super-large diameter twin tunnels.