## 4 Results and Discussions
### Dynamic Behaviors under Severe Seismic Excitations  
Regular and irregular seismic excitations are utilized for SFT dynamic analysis. Since the fixed-fixed boundary condition is applied at both ends of the tunnel, both ends as well as all anchoring points are assumed to move together with seismic motions. As a result, seismic time histories are inputted to every anchor location of mooring lines and both ends of the tunnel. The hydrodynamic forces generated by sea-water fluctuations under vertical seismic motions are computed by using modified Morison equation (e.g., [PERSON] and [PERSON] [41], [PERSON] et al. [24], [PERSON] et al. [42], and [PERSON] et al. [25]). The effect is well known and called seaquake. As a result, there are two mechanisms causing SFT dynamics under seabed seismic motions. First, the seismic motions are transferred through mooring lines. Second, sea-water fluctuations in the vertical direction. In this paper, the former will be called earthquake effect and the latter will be called seaquake effect. To investigate the seaquake effect, regular seismic cases only in the vertical direction are simulated and the resulting SFT dynamics are analyzed. Subsequently, strong real seismic displacements are applied to the SFT system to check the global performance and structural robustness. Figure 10 shows tunnel's vertical motion amplitudes at the mid-section and the corresponding vertical responses of mooring line #1 at its center under regular (sinusoidal) seismic excitations. Vertical motions of tunnel are largely amplified at 3.12 rad/s and 4.89 rad/s, the 1 st and 3 rd natural frequencies. The amplified tunnel motions at those frequencies directly influence high mooring dynamics, as shown in Figure 10b. A small peak can also be observed at 5.78 rad/s, the lowest natural frequency of mooring lines #1 itself. The hydrodynamic force by seaquake directly acts on the tunnel with earthquake frequencies. Whereas, the seismic excitations are delivered to the tunnel through mooring lines, as discussed earlier. Then, the resulting tunnel response also causes hydrodynamic force on the tunnel. Therefore, there exist phase effects between the two components. We can see that the tunnel dynamics are significantly reduced after including the seaquake effect when compared to the earthquake-only case. The reason can be found from Figure 11 by plotting the contribution of each constituent component separately. In the figure, the phase of the tunnel response induced by earthquake is opposite to that induced by seaquake at the tunnel's natural frequencies, 3.12 rad/s and 4.89 rad/s. Therefore, there is cancellation effect between the two components so that the total vertical response amplitude can be reduced compared to the earthquake-only case. On the other hand, when earthquake frequency is greater than 5.7 rad/s, the two components become in phase, so the tunnel vertical responses are increased compared to the earthquake-only case although the resulting increment is small. The seaquake effects are not generated by the horizontal seismic motions if the seabed is flat since the horizontal seabed motions do not influence seawater fluctuating motions. Figure 10: Amplitudes of vertical displacements of the tunnel (**a**) and mooring line #1 (**b**) at the middle location under regular seismic excitations of various frequencies (Eq: earthquake only considered; Eq + Sq: both earthquake and seaquake considered). Figures 12-14 show the time histories of horizontal/vertical responses of the tunnel and the corresponding mooring tensions at the tunnel's middle section under the real seismic excitations, as given in Figure 4. The case of earthquake effect only is compared with that of earthquake plus seaquake. Firstly, in the earthquake-only case, the tunnel responses are greater than the input seismic motions, horizontally about 3 times and vertically about twice larger.