## 4 Results and Discussions
### Dynamic Behaviors under Extreme Wave Excitations  
Dynamic simulations under the 100-year-strom condition (Hs = 11.7 m and Tp = 13.0 s) are performed for three hours. As mentioned before, the same wave time histories are inputted to both programs to directly compare the dynamics results. Both computer programs produce almost identical results. Figure 6 shows the envelopes of maximum and minimum for SFT displacements and mooring tension. The maximum horizontal and vertical responses and mooring tension occur in the middle location. The horizontal responses are larger than the vertical responses since the 1 st natural frequency of horizontal motion is closer to the input wave spectrum than that of vertical motion. Mooring-tension results show that shorter mooring lines (Line #3) have higher mooring tension than longer mooring lines (Line #1). The maximum mooring tension at the middle section is smaller than the MBL (minimum breaking load) divided by the SF (safety factor), which is presented in Figure 6b as a pink line. Recall that the MBL is 30,689 kN for Grade R5, which is obtained by DNV regulation [33]. The SF 1.67 is used as recommended by API RP 2 SK [47]. Even if the extreme 100-year-storm condition is considered, the maximum mooring tension is still smaller than the allowable tension.  
Figures 7-9 show the time histories and corresponding spectra of horizontal/vertical responses of the tunnel and mooring tension at the middle section. The spectra of responses indicate that wave-induced motions are dominant since the lowest natural frequencies in both directional motions (1.92 and 3.12 rad/s for horizontal and vertical directions) are away from the dominant input-wave spectral range of Figure 3. It means that there is negligible contribution from the structural elastic resonances. In case of mooring tension, under the given BWR = 1.3, snap-loadings characterized by extraordinary high peaks do not occur, as shown in the time series. However, it should be noted that the snap-loadings tend to occur at lower BWRs [28]. Obviously, smaller dynamic motions and mooring tensions can be obtained by further increasing submergence depth [28]. The relevant statistics obtained from the time series are summarized in Table 3.  
Figure 5: Submerged floating tunnel (SFT) vertical displacement (**a**) and mooring tension (**b**) in the static condition.  
Figure 6: Envelopes of the maximum and minimum displacements of the tunnel (**a**) and mooring tension (**b**) in the 100-year-strom condition.  
Figure 8: Time histories (**a**) and spectrum (**b**) of vertical displacement of the tunnel in the middle location under the 100-year-strom waves.  
Figure 9: Time histories (**a**) and spectrum (**b**) of mooring tension (#3) in the middle location under the 100-year-strom waves.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Maximum** & **Minimum** & **Standard Deviation** & **Unit** \\ \hline Horizontal displacement & 0.243 & \(-\)0.261 & 0.059 & m \\ Vertical displacement & 0.058 & \(-\)0.066 & 0.014 & \\ \hline Mooring tension (line \#1) & 14,765.75 & 885.56 & 1917.55 & \\ Mooring tension (line \#2) & 15,276.12 & 902.94 & 1919.01 & kN \\ Mooring tension (line \#3) & 17,334.93 & 1206.64 & 2015.53 & \\ Mooring tension (line \#4) & 16,542.11 & 953.24 & 2014.32 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistics of the SFT motions and mooring tensions at the middle location under 100-yr irregular wave excitations (from the time series of Figures 7–9).  
Figure 7: Time histories (**a**) and spectrum (**b**) of horizontal displacement of the tunnel in the middle location under the 100-year-strom waves.