**3.1.3 Influence of the significant wave height on the tunnel element motions**

The results of the frequency spectra of the tunnel element motion responses for different significant wave heights in the test conditions *d*=30cm and *Tp*=1.1s are shown in Fig. 7. From the figure, it is seen that the shapes of the frequency spectrum curves of the tunnel element motion responses are very similar for different significant wave heights, while just the peak values are different. Corresponding to the large significant wave height, the peak value is large, as well large is the area under the motion response spectrum. Apparently, the motion responses of the tunnel element are correspondingly large for the large significant wave height.

Experimental Investigation on Motions of

spectral density(degree

frequency periods of waves (*d*=30cm, *Hs*=3.0cm)

**3.2 Cable tensions** 

**3.2.1 Time series of cable tensions** 

 2·s)

Immersing Tunnel Element under Irregular Wave Actions 207

0 0.5 1 1.5 2 frequency(s-1)

Furthermore, in the figure it is shown that the frequency spectra of the tunnel element motion responses all have a peak at the frequency corresponding to the respective peak frequency period of waves, besides a peak corresponding to the low-frequency motion of the tunnel element. For the sway, the peak frequency corresponding to the low-frequency motion of the tunnel element is the same in the cases of different peak frequency periods. However, for the heave, the peak frequency corresponding to the tunnel element low-frequency motion varies with the peak frequency period. It increases as the peak frequency period increases. The reason may be that there occurs slack state in the cables during the movement of the tunnel element when the peak frequency period increases, for which there is no more the restraint from the motion of the tunnel element in the vertical direction from the cables at this time.

As a typical case, Fig. 9 shows the time series of the cable tensions in the wave conditions *Hs*=4.0cm, *Tp*=1.1s and *d*=30cm within the time 160s. In the figure, *C*11 represents the front cable at the onshore side, *C*12 the back cable at the onshore side, *C*21 the front cable at the offshore side and *C*22 the back cable at the offshore side. It can be seen that the time series of tensions of the cables *C*11 and *C*12 at the onshore side are very similar, as well similar are those of the cables *C*21 and *C*22 at the offshore side. It shows that under the normal incident irregular wave actions the tunnel element does only two-dimensional motions. This can also

Fig. 10 shows the results of the frequency spectra of the cable tensions in the wave conditions *Hs*=4.0cm and *Tp*=1.1s for different immersing depths of the tunnel element. From the peak values of the frequency spectra curves and the areas under the frequency spectra, it is seen that the tensions acting on the cables are comparatively large in the case of comparatively small immersing depth, as is corresponding to the motion responses of the tunnel element. Furthermore, the peak values and the areas of the frequency spectra of the cable tensions at the offshore side are all larger than those of the cable tensions at the onshore side for different immersing depths. It indicates that the total force of the cables at the offshore side is larger

be observed in the experiment from the movement of the tunnel element.

**3.2.2 Cable tensions for the different immersing depth of the tunnel element** 

Fig. 8. Frequency spectra of the tunnel element motion responses for different peak

roll *Tp*=0.85s *Tp*= 1.1s *Tp*= 1.4s

Fig. 7. Frequency spectra of the tunnel element motion responses for different significant wave heights (*d*=30cm, *Tp*=1.1s)

#### **3.1.4 Influence of the peak frequency period on the tunnel element motions**

Fig. 8 shows the results of the frequency spectra of the tunnel element motion responses in the test conditions *d*=30cm and *Hs*=3.0cm for different peak frequency periods of waves. It can be seen that the peak frequency period has an important influence on the motion responses of the tunnel element. The peak values of the frequency spectra of the motion responses increase markedly with the increase of the peak frequency period. Thus, the larger is the peak frequency period of waves, the larger are the motion responses of the tunnel element.

0 0.5 1 1.5 2 frequency(s-1)

Fig. 7. Frequency spectra of the tunnel element motion responses for different significant

Fig. 8 shows the results of the frequency spectra of the tunnel element motion responses in the test conditions *d*=30cm and *Hs*=3.0cm for different peak frequency periods of waves. It can be seen that the peak frequency period has an important influence on the motion responses of the tunnel element. The peak values of the frequency spectra of the motion responses increase markedly with the increase of the peak frequency period. Thus, the larger is the peak frequency period of waves, the larger are the motion responses of the

**3.1.4 Influence of the peak frequency period on the tunnel element motions** 

sway

*T <sup>p</sup>*=0.85s *Tp*= 1.1s *Tp*= 1.4s

spectral density(cm

 2·s)

0 0.5 1 1.5 2 frequency(s-1)

spectral density(degree

wave heights (*d*=30cm, *Tp*=1.1s)

tunnel element.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

spectral density(cm

 2·s)

 2·s) roll

*Hs*=3.0cm *Hs*=4.0cm

heave

*Tp*=0.85s *Tp*= 1.1s *Tp*= 1.4s

0 0.5 1 1.5 2 frequency(s-1)

Fig. 8. Frequency spectra of the tunnel element motion responses for different peak frequency periods of waves (*d*=30cm, *Hs*=3.0cm)

Furthermore, in the figure it is shown that the frequency spectra of the tunnel element motion responses all have a peak at the frequency corresponding to the respective peak frequency period of waves, besides a peak corresponding to the low-frequency motion of the tunnel element. For the sway, the peak frequency corresponding to the low-frequency motion of the tunnel element is the same in the cases of different peak frequency periods. However, for the heave, the peak frequency corresponding to the tunnel element low-frequency motion varies with the peak frequency period. It increases as the peak frequency period increases. The reason may be that there occurs slack state in the cables during the movement of the tunnel element when the peak frequency period increases, for which there is no more the restraint from the motion of the tunnel element in the vertical direction from the cables at this time.
