# Numerical Simulation of a Submerged Floating Tunnel: Validation and Analysis
## 3 Numerical Study of Shaking Table Model for Scaled-Down SFT
### Numerical Modelling  
Using the CEL method, a numerical simulation analysis was conducted based on the aforementioned model test. The SFT tube body was set as a rigid body and was simulated  
Figure 5: Experimental diagram of the submerged floating tunnel (SFT) model.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Physical Indicators** & **Dimensional System** & **Similarity Constant** \\  & & **[L][\(\rho\)][\(\epsilon\)][g]** & **(N = 50)** \\ \hline \multirow{4}{*}{Geometric features} & Geometric dimension & \([L]\) & \(1/N\) \\ \cline{2-3}  & Area & \([L]^{2}\) & \(1/N^{2}\) \\ \cline{2-3}  & Inertia moment & \([L]^{4}\) & \(1/N^{4}\) \\ \hline \multirow{4}{*}{Material behavior} & Density & \([\rho]\) & \(1\) \\ \cline{2-3}  & Elasticity modulus & \([L][\rho][g][\epsilon]^{-1}\) & \(1\) \\ \cline{2-3}  & Mass & \([\rho][L]^{3}\) & \(1/N^{3}\) \\ \hline \multirow{4}{*}{Dynamic characteristics} & Input vibration acceleration & \([g]\) & \(1\) \\ \cline{2-3}  & Field acceleration & \([g]\) & \(1\) \\ \cline{2-3}  & Force & \([\rho][L]^{3}[g]\) & \(1/N^{3}\) \\ \cline{2-3}  & Input vibration time & \([L]^{0.5}[\epsilon]^{0.5}[\epsilon]^{-0.5}\) & \(1/N^{0.5}\) \\ \cline{2-3}  & Vibrational frequency & \([L]^{-0.5}[\epsilon]^{-0.5}[g]^{0.5}\) & \(N^{0.5}\) \\ \cline{2-3}  & Dynamic response acceleration & \([g]\) & \(1\) \\ \cline{2-3}  & Dynamic response stress & \([\rho][L][g]\) & \(1/N\) \\ \cline{2-3}  & Dynamic response strain & \([\epsilon]\) & \(1\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Model test similarity constants.  
using Lagrangian solid elements. The water body was simulated using Eulerian elements, with a density of 1000 kg/m\({}^{3}\), a viscosity of 0.001 Pa\(\cdot\)s, and a speed of sound of 1480 m/s. The ground containing the shaking table was simulated using rigid shell elements, and the anchor cable system was simulated using simplified spring elements. The anchor cable and the shaking table surface were hinged, as was the submerged floating tunnel section. To simulate the relaxation of the anchor cable, bilinear stiffness was introduced.  
\[K_{i}(\Delta L_{i})=\left\{\begin{matrix}k=\frac{EA}{L_{n}},&\Delta L_{i}\geq 0 \\ 0,&\Delta L_{i}<0\end{matrix}\right. \tag{6}\]  
The anchor cable tensile stiffness, denoted as \(L_{n}\), is a constant which is determined using the anchor cable modulus of elasticity (\(E\)) and its cross-sectional area (\(A\)). When the instantaneous length (\(L_{i}\)) of the anchor cable was greater than the unstretched length (original length), \(L_{n}\) remained constant. However, when the transient length was less than the original length, the anchor cable relaxed, and \(L_{n}\) became zero.  
The contact between the SFT tube and the fluid was defined as a smooth hard contact, which meant that no mutual intrusion was allowed in the normal direction. The tangential friction coefficient was set to 0.1. A fluid-free surface boundary was used on the surface of the water body, and the fluid velocity on all four sides of the water body was set to zero, ensuring that the fluid flowed only within the grid. An energy dissipation treatment was applied around the water body, and a fixed boundary was applied at the bottom of the water tank. The model dimensions and other physical parameters were the same as those reported by [PERSON] and [PERSON] [17,18]. The model comprised 158,006 elements and 169,020 nodes, and is shown in Figure 6.