## 4 Results
### Hydrodynamic Response
#### 4.1.3 Dynamic Response
In addition, the response shown by configuration C3 here is further reduced as compared to Section A, because Section B is supported by double inclined mooring cables. Figure 6: Comparison of the hydrodynamic response of the SFT at Section A: (**a**) \(Y\)-displacement; (**b**) bending moment M\({}_{\mathrm{Z}}\); (**c**) \(Z\)-displacement; and (**d**) bending moment M\({}_{\mathrm{Y}}\). Both Figures 6 and 7 show that the transient motions of the SFT are small and decay quickly with time, and the steady-state motions are more pronounced, especially in the traverse direction, as is clear from the \(Y\)-displacement and bending moment M\({}_{Z}\). In the vertical direction, the SFT vibrated under the effect of inertial force and buoyancy force like a beam on elastic supports, as shown by the \(Z\)-displacement and bending moment M\({}_{Y}\) in Figure 6c,d and Figure 7c,d, respectively. The SFT moored by tension leg mooring cables (C1) showed high peaks in the displacements and bending moments. The SFT moored by a tension leg and a single inclined mooring cable at the center (C2) provided better stiffness in the transverse direction, but lesser stiffness in the vertical direction. The SFT moored by double inclined mooring cables at the center (C3) showed the minimum response in the transverse direction. The response of SFT moored by the C1 and C2 configurations showed large peaks, due to very small restraining in the transverse direction. Therefore, C3 type configurations should be used at one or more locations at least, depending on the overall length of the SFT. It can be concluded that the C3 type cable configuration is more stable. The SFT moored by mooring cable configuration C3 is used for the analysis hereafter. Three-dimensional visualization of the SFT response in both time and space gives a very clear understating of the structural behavior of the SFT subjected to hydrodynamic waves and currents. The three-dimensional time histories of the displacements and bending moments are shown in Figures 8 and 9. The response of the SFT is plotted along the \(Z\)-axis; the tunnel longitudinal coordinates (\(x\)) are plotted along the \(X\)-axis; and time is plotted along the \(Y\)-axis. Figure 8 show the displacements along the length of the tunnel with time. Figure 8a illustrates that the SFT vibrates harmonically in the \(Y\)-direction both in the positive and negative extremities. Figure 7: Comparison of the hydrodynamic response of the SFT at Section B: (**a**) \(Y\)-displacement; (**b**) bending moment M\({}_{Z}\); (**c**) \(Z\)-displacement; and (**d**) bending moment M\({}_{Y}\). Figure 8b also shows a harmonic motion pattern, but only in the positive limit (this upward positive displacement is caused by the residual buoyancy acting on the SFT in this direction); which means that the cables were in taut conditions and did not permit slackness in this direction. Figure 9a shows the bending moment M\({}_{Y}\) distribution along the length of the tunnel with time. The shape of bending moments gives a clear picture of the mooring cables configuration (C3) used. The inclined mooring cables at the central location provided flexible elastic bilateral restraint to the transverse and almost unilateral restraint to the vertical motion. Figure 9b shows the bending moment M\({}_{Z}\) distribution along the length of the tunnel with time, and it is similar to the one related to a uniform beam vibrating in the first natural mode. It can be seen that only inclined cables, located at the center, provided significant restraining in the transverse direction (i.e., M\({}_{Z}\)), and the other two groups of vertical cables from left and right of the center provided almost no restraining in the transverse direction. Figure 8: Hydrodynamic displacements along the length of the SFT with time: (**a**) Y-displacement and (**b**) \(Z\)-displacement. Figure 9: _Cont._