Coupled dynamic analysis for wave action on a tension leg-type submerged floating tunnel in time domain
Introduction
A submerged floating tunnel (SFT) is a new traffic structure concept for crossing a strait, bay, or lake. The SFT has a large internal space that is sufficient for roads and even railways. There are harsh natural conditions in some fjords, and traditional spanning methods such as cross-sea bridges and immersed tunnels are not feasible due to environmental conditions and technical constraints. However, in such conditions, an SFT offers the possibility of crossing.
SFT support systems are generally categorized according to the buoyancy weight ratio (BWR): free type (BWR = 1), pressure-bearing pier type (BWR < 1), buoy type and tension leg type (BWR > 1). In a free system, there is no supporting connection system, the SFT floats freely in the sea, which has too many restrictions in use. A pressure-bearing pier system is similar to a submarine bridge and is stabilized by its own gravity. A tension leg system, which uses a mooring system to balance buoyancy and gravity, is generally more widely studied. The choice of the size and stiffness of the anchor chain is closely related to the overall force and motion response of the SFT.
An SFT is continuously exposed to wave effects from the free surface because the submerged depth is not sufficient to avoid free surface waves. Kunisu et al. (1994) addressed the wave force characteristics and dynamic behaviour of the SFT with numerical calculations using Morison's equation. Remseth et al. (1999) discussed the stochastic dynamic response of an SFT to wind driven waves and time domain earthquake analysis with particular emphasis on fluid structure interaction. Mai (2005) also applied Morison equation to solve the fluid force acting on the SFT, and established a static/dynamic finite element numerical model for the SFT structure in which the analysis of static/dynamic response could be conducted. Wang (2008) further considered the role of nonlinear lift force and simulated the overall motion response using finite element software. Long (2009) used fifth-order Stokes wave theory and Morison formula to calculate the dynamic response of an SFT under different BWRs and proposed an optimised range of BWR for the SFT prototype. Lu et al. (2011) investigated SFT dynamics with tether slacking and the related snap force under wave conditions, and provided an alternative philosophy for SFT structural design concerned with preventing the occurrence of tether slacking and snap force. Seo et al. (2015) proposed a simplified method for estimation of an SFT behaviour in waves, conducting physical model tests in a wave flume for variation.
For the wave-exciting force calculation of an SFT in waves, many scholars have applied high-precision numerical models in addition to empirical formulas. Full nonlinear potential numerical wave tank models have been used by Guerber et al. (2012), Hannan et al. (2014), and Bai et al. (2014) to examine the higher harmonics of wave forces on a horizontal submerged circular cylinder. Liu et al., 2016 and Teng et al. (2018, 2019) used the viscous flow theory to calculate the wave action on a submerged cylinder.
For tension leg-type floating bodies, previous research has focused on the tension leg platform (TLP). Adrezin and Benaroya (1999a, 1999b) investigated the coupled dynamic response of a TLP with a single tendon in which the hull was represented by a rigid cylindrical body and the tendon by a nonlinear elastic beam. Chandraekaran and Jain (2002a, 2002b) studied the dynamic responses of square and triangular configuration TLPs under random sea wave loads. Tabeshpour et al. (2006) focused on the comprehensive interpretation of structure responses in random sea in both time and frequency domains. However, the diffraction effects and second-order wave forces were not considered. Zeng et al. (2007) analysed the nonlinear behaviour of a TLP with finite displacement, in which multifold nonlinearities were considered. Subsequently, the dynamic responses of a TLP with a slack-taut tether were studied considering several nonlinear factors induced by large amplitude motions (Zeng et al., 2009). However, a tension leg-type SFT is different from a TLP. As the SFT must meet traffic requirements, its motion response must be controlled not only in the vertical direction but also in the horizontal direction through the mooring system, which results in the natural frequency increasing. Because the structure is submerged in water, its own radiation damping is small; viscous damping must be considered in the calculation to minimize calculation error.
Based on the previous research, this study fully considers the wave effects from the free surface on the mooring SFT, and use the HOBEM based on potential flow theory to simulate the wave load. The viscous damping is obtained from the physical model test. The mooring-line dynamics are simulated by the finite element method (FEM) based on the rod theory. In the coupled dynamic analysis, the motion equation for the hull of SFT and dynamic equations for the mooring-lines are solved simultaneously using the Newmark-β method. Numerical results including first- and second-order motion responses and tension at the top of the mooring-lines are presented, and some further suggestions for SFTs are proposed.
Section snippets
Second-order potential flow theory
Because the length of an SFT is much greater than the section size, two right-handed two-dimensional (2-D) coordinate systems (Fig. 1) can be established to investigate the interaction between waves and the SFT. One is a space-fixed coordinate system Oxz with its origin at the still water surface, with x measured horizontally and z measured vertically. The other is a body-fixed coordinate system O'x’z’. The water depth is defined as d and the submerged depth from the free surface to the centre
Experiment equipment and measuring instruments
The physical model experiments were conducted in the wave flume of TIWTE, China. The flume was 44 m long, 0.5 m wide and 1.2 m deep. The SFT element model was manufactured from plastic and concrete. The manufactured model of the SFT element is shown in Fig. 2. The two mooring lines are connected with springs and tighteners. The water depth d was 0.70 m, the submerged depth h was 0.30 m, and the diameter of the submerged cylinder D was 0.16 m. The BWRs were 1.20, 1.35, and 1.50 to confirm the
Conclusion
To fully consider the wave effects from the free surface on the SFT, the HOBEM based on potential flow theory was used to simulate the wave load in the time domain for every time step. For the mooring line dynamics, an FEM based on rod theory was developed. Motion equations for the hull and dynamic equations for its mooring line system were integrated by imposing appropriate boundary conditions at the connection points. In the coupled dynamic analysis, the motion equation for the hull and
CRediT authorship contribution statement
Ruijia Jin: Conceptualization, Methodology, Writing - original draft. Ying Gou: Validation, Writing - review & editing, Data curation. Baolei Geng: Writing - review & editing. Huaqing Zhang: Funding acquisition. Yong Liu: Writing - review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 51809133) and the China Postdoctoral Science Foundation (Grant No. 2019M652479).
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