Cheng Cui

The motion responses, mooring tensions, and submergence depth are the dominant factors for the arrangement of the Submerged Floating Tunnel (SFT) subjected to waves. Generally, the maximum values of motion responses, mooring tensions, and absolute submergence depth are mainly focused on. In the present study, experiments are implemented to measure the motion responses and mooring tensions of the SFT with different mooring patterns and submergence depths under waves with different characteristic wave heights and periods. In order to evaluate the arrangement of the SFT more effectively and comprehensively, besides the maximum values, several new characteristic parameters are introduced. Such parameters account for the motion responses in the frequency domain, the uniformity of the tension distribution, the length of time during which the cable reaches a relaxed condition during wave action, the KC number, the dimensionless period, the wave height, and the submergence depth. The results from the optimization analysis show the following: according to the characteristic values of motion responses and mooring tensions, the pattern of diagonal cables is better than that of diagonal cables + vertical cables; and within the range of the present experiments, there are optimal dimensionless parameters—the dimensionless submergence depth d₀/L_P ≥ 0.15, the KC number ≤ 0.8, or the dimensionless wave height Hs/d₀ ≤ 0.10—for the condition of which the dynamic responses and mooring tensions vary slightly.

The dynamic response characteristics of a two-dimensional submerged floating tunnel (SFT) under random and freak waves were investigated in the present study. The results demonstrate that (1) the dynamic responses of the SFT under the freak wave are significantly larger than those under the largest wave in the wave train excluding the freak wave, particularly for the motion response. The maximum values of the motion responses induced by the freak wave were several times larger than those induced by the largest wave in the wave train excluding the freak wave, far exceeding the proportion of the corresponding wave height. (2) The freak wave parameter α₁ has a significant effect on the amplification coefficients of surge, heave and pitch; all increase nonlinearly as α₁ increases. Within α₁ = 1.90~2.59, the amplification coefficients of the surge, heave and pitch vary in the ranges of 1.91~6.46, 1.53~3.87 and 1.73~5.32, respectively. (3) Amplification coefficients of tension increase almost linearly as α₁ increases. Additionally, the amplification effect of the freak wave on the mooring tension is much smaller than that on motion responses. Within α₁ = 1.90~2.59, the amplification coefficients of tension vary from 1.15 to 1.35. (4) Generalised amplification coefficients of motion responses increase as α₁ increases and are all greater than 1.0, indicating that growth rates for motion responses under the freak wave exceed the growth rates for maximum wave height. Moreover, motion responses show a significantly nonlinear growth as maximum wave height increases. The generalised amplification coefficients of the mooring tension decrease as α₁ increases, and are all less than 1.0, indicating that the dynamic amplification effect of the freak wave on the mooring tension is much smaller than that on motions. On the other hand, growth rates of the mooring tension under freak waves are smaller than the linear growth rate of the height of freak waves.

A freak wave is a spike in a random wave series and hence the local characteristics in the time-domain are of key importance. When freak waves act on moored floating structures, the dynamic responses of the structures in the time and frequency domains change interdependently in a short period of time. It is difficult to comprehensively and accurately describe this physical process using a single-dimensional analysis method, such as time-domain statistical analysis or frequency-domain spectral analysis. The wavelet analysis method, which can simultaneously provide the time-domain and frequency-domain joint information of the physical process, is used to discuss the time-frequency joint variation characteristics of the dynamic responses of a two-dimensional submerged floating tunnel under a freak wave. The time-frequency characteristics of the dynamic responses induced by the freak wave and the differences from the action under random waves are investigated, with a particular emphasis on the ‘convex variation’ characteristics of the dynamic responses under a freak wave. The results show that: (1) The wavelet analysis method can effectively describe the basic characteristics of the dynamic responses of the SFT under a freak wave and clearly distinguish the differences in dynamic responses under freak and random waves. (2) Freak waves have dynamic amplification effects, which are related to the freak wave parameter α₁, on a two-dimensional SFT. Following the action of freak waves on a two-dimensional SFT, significant energy concentration occurs in the time-frequency spectrum of the dynamic response in a certain time and frequency range. The degree of energy concentration increases nonlinearly with an increase in α₁, and a certain high-frequency energy appears in the time-frequency spectrum of the motion response. The maximum values of the time-frequency spectra of the dynamic responses under a freak wave are much larger than those under a random wave with the identical wave spectrum. (3) Following the action of a freak wave on a two-dimensional SFT, the generalised energy spectra of surge, heave, pitch, and mooring tensions have convex peak values, which occur simultaneous with the occurrence of the freak wave, and the convex parts significantly increase as α₁. (4) The time lengths of the influence of a freak wave on the dynamic responses exceeded the freak wave period. With an increase in α₁, the time ranges of the large values of the time-frequency spectra of surge, heave, pitch, and mooring tensions increase nearly linearly.