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

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

Experimental Investigation on Motions of

side, *C*22: back cable at the offshore side)

0 0.5 1 1.5 2 2.5 3 3.5

onshore side

frequency (s-1)

onshore side

0 0.5 1 1.5 2 2.5 3 3.5

frequency (s-1)

0 0.5 1 1.5 2 2.5 3 3.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

spectral density (kg2·s)

spectral density (kg2·s)

F(kg)

Immersing Tunnel Element under Irregular Wave Actions 209

0 20 40 60 80 100 120 140 160 180

Fig. 9. Time series of tensions acting on the cables (*d*=30cm, *Hs*=4.0cm, *Tp*=1.1s, *C*11: front cable at the onshore side, *C*12: back cable at the onshore side, *C*21: front cable at the offshore

*a. d*=10cm

spectral density (kg2·s)

b. *d*=30cm

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

spectral density (kg2·s)

0 0.5 1 1.5 2 2.5 3 3.5 t(s)

C22

0 0.5 1 1.5 2 2.5 3 3.5

offshore side

frequency (s-1)

offshore side

0 0.5 1 1.5 2 2.5 3 3.5

frequency (s-1)

than that of the cables at the onshore side. It is also shown that in the figure there are at least two peaks in the curves of the frequency spectra of the cable tensions, which are respectively corresponding to the wave-frequency motions and low-frequency motions of the tunnel element. When the tunnel element is at the position of a relatively small immersing depth, the frequency spectra of the cable tensions have other small peaks besides the two peaks at the wave frequency and the low frequency. It illustrates that the case of the forces generating in the cables is more complicated for the comparatively strong motion responses of the tunnel element under the wave actions when the immersing depth is relatively small.

than that of the cables at the onshore side. It is also shown that in the figure there are at least two peaks in the curves of the frequency spectra of the cable tensions, which are respectively corresponding to the wave-frequency motions and low-frequency motions of the tunnel element. When the tunnel element is at the position of a relatively small immersing depth, the frequency spectra of the cable tensions have other small peaks besides the two peaks at the wave frequency and the low frequency. It illustrates that the case of the forces generating in the cables is more complicated for the comparatively strong motion responses of the tunnel

0 20 40 60 80 100 120 140 160 180

0 20 40 60 80 100 120 140 160 180

0 20 40 60 80 100 120 140 160 180

t(s)

t(s)

t(s)

C11

C12

C21

element under the wave actions when the immersing depth is relatively small.

0 0.5 1 1.5 2 2.5 3

0 0.5 1 1.5 2 2.5 3 3.5

0 0.5 1 1.5 2 2.5 3 3.5

F(kg)

F(kg)

F(kg)

Fig. 9. Time series of tensions acting on the cables (*d*=30cm, *Hs*=4.0cm, *Tp*=1.1s, *C*11: front cable at the onshore side, *C*12: back cable at the onshore side, *C*21: front cable at the offshore side, *C*22: back cable at the offshore side)

Experimental Investigation on Motions of

peak frequency period of waves.

0 0.5 1 1.5 2 2.5 3

waves (*d*=30cm, *Hs*=3.0cm)

spectral density(kg

 2·s)

Immersing Tunnel Element under Irregular Wave Actions 211

The results of the frequency spectra of the cable tensions for different peak frequency periods of waves in the test conditions *d*=30cm and *Hs*=3.0cm are shown in Fig. 12. It is seen that the cable tensions are largely influenced by the peak frequency period. The peak values of the frequency spectra of the cable tensions increase rapidly as the peak frequency period increases. Corresponding to the case of the motion responses of the tunnel element for different peak frequency periods, the larger is the peak frequency period, the larger are also the cable tensions. For different peak frequency periods, the frequency spectra of the cable tensions all have a peak at the corresponding frequency. Besides, from the figure, it can be observed that the peaks of the frequency spectra at the lower frequency are obvious when the peak frequency period *Tp*=1.4s. This reflects that the low-frequency motions of the tunnel element become large with the increase of the

**3.2.4 Influence of the peak frequency period on the cable tensions** 

onshore side

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

The tunnel element moves under the irregular wave actions, and at the same time, the tunnel element is restrained by the cables in the motions. So the wave forces and cable tensions together result in the total effect of the motions of the tunnel element. On the other hand, the restraint of the cables from the movement of the tunnel element makes the cables bear forces. Hence, the motions of the tunnel element and the cable tensions are coupled. According to the discussion in the above context, in the case when the immersing depth is small and the significant wave height and the peak frequency period are large comparatively, the motion responses of the tunnel element are relatively large. And in the case of that, the variations of the cable tensions are accordingly more complicated.

Fig. 12. Frequency spectra of the cable tensions for different peak frequency periods of

**3.3 Relation between the tunnel element motions and the cable tensions** 

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

spectral density(kg

 2·s) offshore side

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

0 0.5 1 1.5 2 frequency(s-1)

0 0.5 1 1.5 2 frequency(s-1)

Fig. 10. Frequency spectra of the cable tensions for different immersing depths (*Hs*=4.0cm, *Tp*=1.1s)

#### **3.2.3 Influence of the significant wave height on the cable tensions**

Fig. 11 gives the results of the frequency spectra of the cable tensions for different significant wave heights in the test conditions *d*=30cm and *Tp*=1.1s. It is shown that the area under the frequency spectrum of the cable tensions for the significant wave height *Hs*=4.0cm is larger than that for *Hs*=3.0cm. Therefore, the larger is the significant wave height, the larger are the cable tensions accordingly. This is corresponding to the case that the motion responses of the tunnel element are larger for the larger significant wave height. When the significant wave height increases, the wave effects on the tunnel element increase. Accordingly, the forces acting on the cables also become larger.

Fig. 11. Frequency spectra of the cable tensions for different significant wave heights (*d*=30cm, *Tp*=1.1s)

spectral density (kg2·s)

c. *d*=50cm Fig. 10. Frequency spectra of the cable tensions for different immersing depths (*Hs*=4.0cm,

Fig. 11 gives the results of the frequency spectra of the cable tensions for different significant wave heights in the test conditions *d*=30cm and *Tp*=1.1s. It is shown that the area under the frequency spectrum of the cable tensions for the significant wave height *Hs*=4.0cm is larger than that for *Hs*=3.0cm. Therefore, the larger is the significant wave height, the larger are the cable tensions accordingly. This is corresponding to the case that the motion responses of the tunnel element are larger for the larger significant wave height. When the significant wave height increases, the wave effects on the tunnel element increase. Accordingly, the

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

0 0.5 1 1.5 2 2.5 3 3.5

offshore side

frequency (s-1)

0 0.5 1 1.5 2 frequency(s-1)

offshore side

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

0 0.005 0.01 0.015 0.02 0.025 0.03

spectral density (kg2·s)

*Tp*=1.1s)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

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

spectral density(kg2·s)

0 0.5 1 1.5 2 2.5 3 3.5

onshore side

frequency (s-1)

forces acting on the cables also become larger.

0 0.5 1 1.5 2 frequency(s-1)

**3.2.3 Influence of the significant wave height on the cable tensions** 

onshore side

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

Fig. 11. Frequency spectra of the cable tensions for different significant wave heights

0

0.5

1

1.5

spectral density(kg2·s)

2

2.5
