Coupled dynamic analysis method for wave action on a submerged floating tunnel

Coupled dynamic analysis for wave action on a tension leg-type submerged floating tunnel in time domain

Numerical modeling of the interaction between submerged floating tunnel and surface waves

A global review for the hydrodynamic response investigation method of submerged floating tunnels

In the previous study, the optimal performance of a two-dimensional (2D) floating breakwater shape was obtained. The performance of this shape was also confirmed with a model experiment in a towing tank. Moreover, the shape’s performance in three dimensions (3D) was investigated in a subsequent study. However, to predict the shape’s performance in a real application more accurately, the shape’s characteristics in oblique waves must also be evaluated. In this study, the performance and characteristics of the model (hydrodynamic forces, body motions, wave elevations, and drift forces) are computed using a higher-orderboundary element method (HOBEM). The HOBEM, which is based on the potential flow theory and uses quadratic representation for quadrilateral panels and velocity potentials, can be used to obtain more accurate results with fewer panels compared to the conventional panel method (CPM). The computational accuracy is confirmed by using Haskind-Newman and energy conservation relations. In thisstudy, 3D wave effects were verified, and the body motions were much smaller compared to the 2D case. In addition, although the performance in terms of wave elevations depends on the measurement positions, the optimal performance obtained in the 2D case can be realized for a longer body length. 

Geotechnical investigation and tension-pile solution for foundation of SFT prototype at Qiandao Lake

This paper presents the comparison between SFT response with linear and nonlinear cables. The dynamic response analysis of submerged floating tunnel (SFT) is presented computationally with linear and nonlinear tension legs cables. The analysis is performed computationally for two wave directions one at 90 degrees (perpendicular) to tunnel and other at 45 degrees to the tunnel. The tension legs or cables are assumed as linear and non- linear and the analysis is also performed by assuming one tension leg or cable is failed. The Response Amplitude Operators (RAO\'s) are computed for first order waves, second order waves for both failure and non-failure case of cables. For first order waves- the SFT response is higher for sway and heave degree of freedom with nonlinear cables as compared with linear cables. For second order waves the SFT response in sway degree of freedom is bit higher response with linear cables as compared with nonlinear cables and the SFT in heave degree of freedom has higher response at low time periods with nonlinear cables as compared with linear cables. For irregular waves the power spectral densities (PSD\'s) has been computed for sway and heave degrees of freedom, at 450 wave direction PSD\'s are higher with linear cables as compared with nonlinear cables and at 900 wave direction the PSD\'s are higher with non-linear cables. The mooring force responses are also computed in y and z directions for linear and nonlinear cables.

Global response of submerged floating tunnel against underwater explosion

A high-order boundary element method (BEM) for the analysis of the steady two-dimensional full-potential transonic equation is presented. The use of a high-order (piecewise cubic on the boundary and piecewise bi-cubic in the field) numerical formulation, the main novelty of the present work, is important in two respects: first, the convergence of the solution as h vanishes is faster than the zeroth-order (the piecewise constant) one, yielding more accurate results with coarser grid resolutions. In addition, in supercritical flows, the derivation of the velocity field from the high-order representation for potential gives, in the vicinity of the shock, a sharper discontinuity, and allows for an in-depth analysis of the shock properties. Both aspects are analyzed in the present paper through applications to steady, two-dimensional, full-potential flows. All the results obtained using the present method are validated through comparison to other computational fluid dynamics (CFD) solutions of the full-potential flows and, when applicable, Euler equations. A comparison to a zeroth-order BEM, based on the same integral formulation is also included.

Nonlinear hydrodynamic modeling of an offshore stationary multi-oscillating water column platform

A comprehensive two-dimensional (2D) time-domain numerical model is established to investigate the interaction of irregular waves and submerged structures with different sections. The model specifically focuses on the dual-lane submerged floating tunnel (SFT) designs, encompassing elliptical, twin-circular, and round rectangular sections. For the hydrodynamic analysis, we adopt the second-order potential flow theory, while for the mooring line simulations, we employ the slender rod theory, taking into account the entire hydrodynamic load acting on it. In the coupled dynamic analysis, the fourth-order Adams–Bashforth–Moulton method, Newmark-β method, and Newton–Raphson iteration scheme are utilized for the coupled motion equation of the floating body and the dynamic equation of the mooring riser system. Experimental free decay tests are conducted to determine the damping coefficients of various section shapes in different directions. Our analysis delves into the detailed motion responses and mooring tensions of the SFTs with different section forms under irregular waves. We compare and contrast these responses in both time and frequency domains, particularly focusing on movement trends. The elliptical section structure emerges as the most stable design based on our comparisons. These findings provide valuable insights for the selection of optimal section shapes for dual-lane SFTs.

Analysis of wave force induced dynamic response of submerged floating tunnel

A submerged floating tunnel (SFT) is considered an innovative alternative to conventional bridges and underground or immersed tunnels for passing through deep water. Assessment of hydrodynamic performance of SFT under regular wave loading is one of the important factors in the design of SFT structure. In this paper, a theoretical hydrodynamic model is developed to describe the coupled dynamic response of an SFT and mooring lines under regular waves. In this model, wave-induced hydrodynamic loads are estimated by the Morison equation for a moving object, and the simplified governing differential equation of the tunnel with mooring cables is solved using the fourth-order Runge–Kutta and Adams numerical method. The numerical results are successfully validated by direct comparison against published experimental data. On this basis, the effects of the parameters such as the cable length, buoyancy-weight ratio, wave period, wave steepness, and water/submergence depth on the dynamic response of the SFT under wave loading are studied. The results show that tunnel motions and cable tensions grow with wave height and period and decrease with submergence depth. The resonance of the tunnel will be triggered when the wave period is close to its natural vibration period, and the estimation formula of wave period corresponding to tunnel resonance is proposed in this paper.

Coupled dynamic analysis for wave interaction with a truss spar and its mooring line /riser system in time domain

A complete semi-analytical solution is given for second-order diffraction of monochromatic waves by a truncated vertical circular cylinder in water of uniform finite depth. The methodology presented in detail elsewhere (Eatock Taylor & Huang 1996) is adopted to find a particular solution which exactly satisfies the governing equation, the inhomogeneous free-surface condition and the seabed condition. In order to satisfy the boundary condition on the cylinder bottom, the fluid domain around the cylinder is divided into two regions. First- and second-order velocity potentials are described separately in the two regions and matched on the interface by the pressure and normal-velocity continuity conditions. Based on the formulation, the second-order wave field in the vicinity of the cylinder and the corresponding wave forces and overturning moments on the cylinder are studied in detail. Numerical results for the double frequency forces obtained by using the present semi-analytical approach are compared with those computed with a higher-order boundary element method (Eatock Taylor & Chau 1992). As well as the exact solution, an approximate solution is also given for the second-order potential and the corresponding forces. Numerical results show that the approximate solution possesses excellent accuracy for the total second-order heave force over a wide range of conditions. When kb > 1.2 (where k, b are the incident wavenumber and the draught of the cylinder respectively), the accuracy for total second-order surge force and pitch moment is also satisfactory. These results could lead to the development of very efficient solutions and corresponding algorithms for the analysis of second-order wave diffraction by more complicated structures such as tension leg platforms. Numerical results based on the present solution show that in many cases, both the first- and the second-order-free surface elevation in the vicinity of a truncated cylinder is very close to that of a bottom-seated cylinder. For waves with larger amplitudes, the maximum free-surface elevation around a vertical cylinder predicted with the second-order theory can significantly exceed that given by linear theory. There is also a considerable difference in the location of the maximum elevation predicted by the linear and nonlinear theories.

New higher-order boundary element methods for wave diffraction/radiation