**3. Experimental results and discussion**

#### **3.1 Motion responses of the tunnel element**

The significant wave height and the peak frequency period of waves are the main influencing factors on the motion responses of the tunnel element under irregular wave actions. Moreover, in the different immersing depth positions, the motions of the tunnel element make differences. In this experiment, the different immersing depths, significant wave heights and peak frequency periods are considered to explore their impacts on the motions of the tunnel element.

#### **3.1.1 Time series of the tunnel element motion responses**

As an example, the time series of the tunnel element motion responses in the wave conditions *Hs*=3.0cm, *Tp*=0.85s and *d*=10cm within the time 80s are shown in Fig. 5. Under the normal incident wave actions, the tunnel element makes two-dimensional motions, i.e. sway, heave and roll.

simulation of the physical wave spectra. Fig. 4 shows the results of the comparison between

The significant wave height and the peak frequency period of waves are the main influencing factors on the motion responses of the tunnel element under irregular wave actions. Moreover, in the different immersing depth positions, the motions of the tunnel element make differences. In this experiment, the different immersing depths, significant wave heights and peak frequency periods are considered to explore their impacts on the

As an example, the time series of the tunnel element motion responses in the wave conditions *Hs*=3.0cm, *Tp*=0.85s and *d*=10cm within the time 80s are shown in Fig. 5. Under the normal incident wave actions, the tunnel element makes two-dimensional motions, i.e.

0 10 20 30 40 50 60 70 80

(a) *Hs*=3.0cm, *Tp*=1.4s (b) *Hs*=4.0cm, *Tp*=1.1s

*S* (*f*)

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004 0.00045

> 0123 *f*(Hz)

target spectrum physical spectrum

t(s)

sway

the target spectrum and physical spectrum. It is seen that they agree very well.

target spectrum physical spectrum

0123 *f*(Hz)

**3.1.1 Time series of the tunnel element motion responses** 

0

Fig. 4. Measured and target spectrum

motions of the tunnel element.

sway, heave and roll.

ξ (cm)


**3. Experimental results and discussion 3.1 Motion responses of the tunnel element** 

0.00005 0.0001 0.00015 0.0002 0.00025 0.0003

*S* (*f*)

Fig. 5. Time series of the tunnel element motion responses (*d*=10cm, *Hs*=3.0cm, *Tp*=0.85s)

#### **3.1.2 Motion responses of the tunnel element in the different immersing depth**

Fig. 6 gives the results of the frequency spectra of the tunnel element motion responses 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, it is obvious that the motion responses of the tunnel element are comparatively large for the comparatively small immersing depth. Comparing the motions of the tunnel element of sway, heave and roll, the area under the heave motion response spectrum is larger than that under the sway motion response spectrum when the immersing depths are 10cm and 30cm, as indicates that the motion of the tunnel element in the vertical direction is predominant. In addition, it can be observed that there are two peaks on the curves of the sway and heave motion responses spectra. This illuminates that the low-frequency motions occur in the tunnel element besides the wave-frequency motions. The low-frequency motions are caused by the actions of cables. For the sway, the low-frequency motion is dominant, while the wave-frequency motion is relatively small. From the figure, it can be seen that the low-frequency motion is always larger than the wave-frequency motion for the sway as the tunnel element is in the different immersing depths. It reveals that the low-frequency motion is the main of the tunnel element movement in the horizontal direction. This can also be obviously observed from the curve of time series of the sway in Fig. 5. However, for the heave, as the immersing depth increases, the motion turns gradually from that the low-frequency motion is dominant into that the wave-frequency motion is dominant.

Experimental Investigation on Motions of

0 0.5 1 1.5 2

spectral density (degree2·s)

frequency (s-1)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

sway

0 0.2 0.4 0.6 0.8 1 1.2 1.4

depths (*Hs*=4.0cm, *Tp*=1.1s)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

spectral density(cm2·s)

spectral density (cm2·s)

Immersing Tunnel Element under Irregular Wave Actions 205

spectral density (cm2·s)

012

*c. d*=50cm Fig. 6. Frequency spectra of the tunnel element motion responses for different immersing

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

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

tunnel element are correspondingly large for the large significant wave height.

sway

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

0 0.2 0.4 0.6 0.8 1 1.2 1.4

spectral density(cm2·s)

0 0.5 1 1.5 2 frequency(s-1)

frequency (s-1)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

roll

012

frequency (s-1)

heave

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

0 0.5 1 1.5 2 frequency(s-1)

heave

0 0.5 1 1.5 2

a. *d*=10cm

0 0.2 0.4 0.6 0.8 1 1.2 1.4

roll

spectral density (cm2·s)

0 0.5 1 1.5 2

*b. d*=30cm

frequency (s-1)

frequency (s-1)

roll

spectral density (cm2·s)

0 0.5 1 1.5 2

0 0.5 1 1.5 2

frequency (s-1)

heave

frequency (s-1)

heave

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

spectral density (cm2·s)

spectral density (cm2·s)

0 0.5 1 1.5 2

spectral density (degree2·s)

frequency (s-1)

sway

0 0.5 1 1.5 2

spectral density (degree2·s)

frequency (s-1)

sway

Fig. 6. Frequency spectra of the tunnel element motion responses for different immersing depths (*Hs*=4.0cm, *Tp*=1.1s)
