# Design and Evaluation of Novel Submerged Floating Tunnel Models Based on Dynamic Similarity
## 3 Model Design
### Model Structure  
The model experiment is a critical research method for SFTs, playing a crucial role in validating the predictions of theoretical and numerical models. The model employed in the hydrodynamic test must satisfy the geometric similarity because the geometric  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Physical Properties** & **Name** & **Similarity Constant Symbol** & **Formula** & **Similarity** \\  & & length & \(S_{I}\) & \(S_{I}\) & \(\lambda_{I}\) \\  & cross-sectional area & \(S_{A}\) & \(S_{I}{}^{2}\) & \(\lambda_{I}{}^{2}\) \\ Geometric & displaced volume per meter & \(S_{A}\) & \(S_{I}{}^{2}\) & \(\lambda_{I}{}^{2}\) \\ Properties & moment of inertial & \(S_{I}\) & \(S_{I}{}^{4}\) & \(\lambda_{I}{}^{2}\) \\  & displacement & \(S_{I}\) & \(S_{I}\) & \(\lambda\) \\  & rotational angle & 1 & \(S_{\sigma}/S_{E}\) & 1 \\ \hline  & strain & 1 & \(S_{\sigma}/S_{E}\) & 1 \\  & elastic modulus & \(S_{E}\) & \(S_{E}\) & \(\lambda_{E}\) \\  & bending stiffness & \(S_{EI}\) & \(S_{E}S^{4}\) & \(\lambda_{E}\,\lambda_{I}{}^{4}\) \\ Material & stress & \(S_{\sigma}\) & \(S_{E}\) & \(\lambda_{E}\) \\ Properties & density & \(S_{\sigma}\) & \(S_{E}\)(\(S_{\sigma}\)) & \(\lambda_{E}/\lambda_{I}\) \\  & mass per meter & \(S_{A}\,  
shape of the structure has a significant influence on the fluid flow. However, most of the SFT model experiments ignored the elastic deformation of the tunnel and adopted simplified rigid models, such as the plexiglass tube model (Figure 2a) or the aluminum tube model (Figure 2b). The plexiglass tube model uses a plexiglass tube to satisfy the geometric similarity and employs counterweight steel blocks to maintain the buoyancy-weight ratio. The density of the aluminum tube is high, so there is no need to install additional counterweights. These rigid models cannot simulate the elastic deformation of the tunnel body, thereby they inadequately represent the hydrodynamic behavior of SFTs, such as the fluid-structure interaction and vortex-induced vibration. The hydroelastic model of the SFT can effectively make up for these shortcomings. The model tube can undergo elastic deformation and meet the elastic similarity. The steel pipe elastic model (Figure 2c) features a steel tube encased in foam plastic. However, foam plastic tends to absorb water, leading to an increase in the model's weight and a decrease in the buoyancy-weight ratio. These changes can significantly affect the dynamic characteristics of the model. Additionally, sensors can only be installed on the surface due to its solid structure, which will impact the external contour of the model and the flow field around the structure. Until now, SFTs have not been implemented in practical engineering applications. Many studies [31; 32] are dedicated to analyzing the effect of key design parameters such as the buoyancy-weight ratio (BWR), inclined mooring angle, and submerged depth, without yet reaching an agreement. Therefore, this paper extensively references a wide range of  
Figure 2: Schematic diagrams of SFT scale models. (**a**) Plexiglass tube model; (**b**) aluminum tube model; (**c**) steel pipe model. literature [13; 33] and considers the dimension of the experimental facility. The prototype of the SFT employed in this study was selected based on optimal parameters that minimize adverse phenomena such as tether slacking [34]. The SFT prototype discussed in this research features an external diameter of 12 m. The total length of the tunnel body is 360 m, with anchor cables spaced 84 m apart and inclined at an angle of 45 degrees. The total water depth where the tunnel is located is 60 m, with the geometric center of the tunnel body situated 18 m below the free surface. The tunnel is constructed from C60 reinforced concrete, which is characterized by a density of 2880 kg/m\({}^{3}\) and an elastic modulus of 36 GPa.