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

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 peak frequency period of waves.

Fig. 12. Frequency spectra of the cable tensions for different peak frequency periods of waves (*d*=30cm, *Hs*=3.0cm)

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

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.

Experimental Investigation on Motions of

August 26-30, 2003

31–June 5, 2009

7798

3839

2007), pp. 1067-1090, ISSN 1090-0241

010112-X, Beijing, China. (in Chinese)

Vol. 8, pp. 18-26, (March 2009), ISSN 1671-9433

10, (January 2006), pp. 1367-1377, ISSN 0141-0296

(October 1996), pp. 479-483, ISSN 0886-7798

1993), pp. 119-139, ISSN 0886-7798

21, No. 6, (December 2009), pp. 739-749, ISSN 1001-6058

**6. References** 

Immersing Tunnel Element under Irregular Wave Actions 213

Anastasopoulos, I., Gerolymos, N., Drosos, V., Kourkoulis, R., Georgarakos, Τ. & Gazetas, G.

Aono, T., Sumida, K., Fujiwara, R., Ukai, A., Yamamura K. & Nakaya, Y. (2003). Rapid

Chen, S. Z. (2002). *Design and Construction of Immersed Tunnel*, Science Press, ISBN 7-03-

Chen, Z. J., Wang, Y. X., Wang, G. Y. & Hou, Y. (2009a). Frequency responses of immersing

Chen, Z. J., Wang, Y. X., Wang, G. Y. & Hou, Y. (2009b). Time-domain responses of

Chen, Z. J., Wang, Y. X., Wang, G. Y. & Hou, Y. (2009c). Experimental Investigation on

Ding, J. H., Jin, X. L., Guo, Y. Z. & Li., G. G. (2006). Numerical Simulation for Large-scale

Gursoy, A., Van Milligen, P. C., Saveur, J. & Grantz, W. C. (1993). Immersed and Floating

Hakkaart, C. J. A. (1996). Transport of Tunnel Elements from Baltimore to Boston, over the

Ingerslev, L. C. F. (2005). Considerations and Strategies behind the Design and

Kasper, T., Steenfelt, J. S., Pedersen, L. M., Jackson P. G. & Heijmans, R. W. M. G. (2008).

Zhan, D. X. & Wang, X. Q. (2001a). Experiments of hydrodynamics and stability of

Zhan, D. X., Zhang, L. W., Zhao, C. B., Wu, J. P. & Zhang, S. X. (2001b) Numerical

*Ser. B*, Vol. 13, No. 2, (June 2001), pp. 121-126, ISSN 1001-6058

(2007). Nonlinear Response of Deep Immersed Tunnel to Strong Seismic Shaking, *Journal of Geotechnical and Geoenviron-mental Engineering*, Vol. 133, No 9, (September

Stabilization of the Immersed Tunnel Element, *Proceedings of the Coastal Structures 2003 Conference*, pp. 394-404, ISBN 978-0-7844-0733-2, Portland, Oregon, USA,

tunnel element under wave actions, *Journal of Marine Science and Application*, 2009,

immersing tunnel element under wave actions, *Journal of Hydrodynamics, Ser. B*, Vol.

Immersion of Tunnel Element, *28th International Conference on Ocean, Offshore and Arctic Engineering*, pp. 1-8, ISBN 978-0-7918-4344-4, Honolulu, Hawaii, USA, May

Seismic Response Analysis of Immersed Tunnel, *Engineering Structures*, Vol. 28, No.

Tunnels, *Tunnelling and Underground Space Technology*, Vol.8, No.2, (December

Atlantic Ocean, *Tunnelling and Underground Space Technology*, Vol. 11, No. 4,

Construction Requirements of the Istanbul Strait Immersed Tunnel, *Tunnelling and Underground Space Technology*, Vol. 20, (October 2005), pp. 604-608, ISSN 0886-

Stability of an Immersed Tunnel in Offshore Conditions under Deep Water Wave Impact. *Coastal Engineering*, Vol. 55, No. 9, (August 2008), pp. 753-760, ISSN 3783-

immersed tube tunnel on transportation and immersing. *Journal of Hydrodynamics,* 

simulation and visualization of immersed tube tunnel maneuvering and immersing, *Journal of Wuhan University of Technology (Transportation Science* 

Moreover, corresponding to the wave-frequency peak and low-frequency peak of the frequency spectra of the cable tensions, there occur the wave-frequency motions and lowfrequency motions in the tunnel element. This also reflects directly the interrelation of the tunnel element motions and the cable tensions.
