# Design and Evaluation of Novel Submerged Floating Tunnel Models Based on Dynamic Similarity
## 5 Foude Similarity Test
### Hydrodynamic Characteristics Test
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Indicator** & **Model** & **Parameter** \\ \hline Acceleration & YX 1211 & Sensitivity 0.5 mV/gal \\ Rotation & WT9011C4K & Precision 0.2\({}^{\circ}\) \\ Dynamic data acquisition & TST 3000 & Sampling rate 2000 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Sensor and data acquisition system. Figure 13: Experimental setup for assessing hydrodynamic characteristics. (**a**) Schematic diagram of experimental devices; (**b**) photograph of the wave tank setup. To verify whether the scale model satisfies the similarity relationships, a numerical model of the SFT was created using the hydrodynamic analysis software AQWA, as illustrated in Figure 15. In the hydrodynamic numerical model, the arrangement of the anchor cables and boundary conditions was the same as those in the wave experiment, and the physical parameters of the tunnel body were the theoretical values designed for the model, similar to the simplified numerical model of the tunnel body. Therefore, the difference in the hydrodynamic characteristics between the scale model and the theoretical values can be directly compared. After applying a Fourier transform to the time history data of the horizontal acceleration, vertical acceleration, and rotation angle of the tunnel tube, the frequency response of the model subjected to white noise wave excitation was obtained. The spectrum analysis in Figure 16 reveals that the natural frequency of the horizontal acceleration in the tunnel body is determined to be 0.95 Hz, the natural frequency of the vertical acceleration stands at 2.30 Hz, and the natural frequency of the rotation is identical to the horizontal acceleration, also at 0.95 Hz. The horizontal acceleration natural frequency (0.95 Hz) component exists in the vertical acceleration spectrum (Figure 16b). These findings demonstrate that, due to the constraint imposed by the anchor cables, there is a coupling between the horizontal movement, vertical movement, and rotation of the SFT with inclined cables. Figure 17 illustrates the motion pattern of the SFT with inclined cables, which can be simplified into a four-bar linkage model. The dashed line represents the initial shape of the structure. In this mechanism, the tunnel body itself acts as one linkage; the two mooring cables each act as another linkage; and the final linkage is a fixed line between two foundations on the seabed. Due to the buoyancy exceeding the weight, the tunnel body consistently experiences an upward force, enabling the entire system to maintain relative stability. This schematic diagram effectively explains the coupling relationship between the translational  
Figure 14: Schematic representation of wave incident, sensor distribution, and anchor cable arrangement for the SFT model. Figure 15: Hydrodynamic numerical model of the SFT. accurately simulate the elastic deformation of the tunnel body. Therefore, applying this model in SFT experiments can simulate complex hydrodynamic phenomena such as the fluid-structure interaction and vortex-induced vibration, thereby facilitating in-depth research on the structural characteristics of SFTs and enhancing their safety in harsh marine environments. Moreover, the design methodology used for this new model can be applied to other types of SFTs, which could promote technical progress in scale models and propel the development of hydrodynamic experiments related to SFTs. (1) Compared to previous models of SFTs, this new model addresses the challenge of simulating the elastic deformation of the tunnel body without changing the surface's fluid-structure interaction. The overall shape of the model is a hollow cylinder with the internal mass distribution of an actual tunnel, which replicates the structure without complicating the overall structure and fabrication process. The tunnel body itself satisfies both the Froude and Cauchy similarity criteria without attaching additional springs to simulate the elastic deformation, which is a major contribution of this study.