Experimental Study on Hydrodynamic Load Characteristics for A Typical Cross-Section of A Submerged Floating Tunnel

The typical cross-sectional form of a submerged floating tunnel plays a significant role in the dynamic response of the tunnel itself,which directly affects the overall design.In this work,a series of experiments involving wave action on a submerged floating tube cross section is reported to study its hydrodynamic load characteristics.Two typical cross section tube cylinders,circular and rectangular,are chosen.Experiments are carried out in a wave flume with waves of relatively low Keulegan-Carpenter(KC)numbers.Three relative depths of submergence of 0,0.25 and 0.5 are chosen.The measured wave forces in regular waves are used to analyze the horizontal force,vertical force and torque,and then the drag coefficient(Cd)and inertia coefficient(Cm)are derived.The results show that the drag coefficients at low KC numbers are large and decrease sharply with increasing KC number.The inertial coefficient Cm values in the vertical direction are about 70%larger than those in the horizontal direction.With an increase in aspect ratio(the ratio of the height to width of the structure),the ratio of inertia coefficient in the horizontal direction to that in the vertical direction increases remarkably.The inertia force coefficient is very sensitive to the submerged water depth and aspect ratio.The existing results may overestimate the actual force value.

Global Dynamic Responses and Progressive Failure of Submerged Floating Tunnel Under Cable Breakage Conditions

The Submerged Floating Tunnel(SFT)relies on a tensioned mooring system for precise positioning.The sudden breakage of a single cable can trigger an immediate alteration in the constraint conditions of the tube,inducing a transient heave response within the structure along with a transient increase in cable tension experienced by adjacent cables.In more severe cases,this may even lead to a progressive failure culminating in the global destruction of the SFT.This study used ANSYS/AQWA to establish a numerical model of the entire length SFT for the hydrodynamic response analysis,and conducted a coupled calculation of the dynamic responses of the SFT-mooring line model based on Orca Flex to study the global dynamic responses of the SFT at the moment of cable breakage and the redistribution of cable internal forces.The most unfavorable position for SFT cable breakage was identified,the influence mechanism of cable breakage at different positions on the global dynamic response was revealed,and the progressive chain failure pattern caused by localized cable breakage are also clarified.

Research on the Dynamic Response of Submerged Floating Tunnels to Wave Currents and Traffic Load

Submerged floating tunnel(SFTs)are typically subjected to complex external environmental and internal loads such as wave currents and traffic load.In this study,this problem is investigated through a finite element method able to account for fluid-structure interaction.The obtained results show that increasing the number of vehicles per unit length enhances the transverse vibrational displacements of the SFT cross sections.Under ultimate traffic load condition,one-way and two-way syntropic distributions can promote the dynamic responses of SFTs whereas two-way reverse distributions have the opposite effect.

Comparison Study and Forensic Analysis between Experiment and Coupled Dynamics Simulation for Submerged Floating Tunnel Segment with Free Ends under Wave Excitations

This paper presents dynamic-behavior comparisons and related forensic analyses of a submerged floating tunnel(SFT)between numerical simulation and physical experiment under regular and irregular waves.The experiments are conducted in the 3Dwave tank with 1:33.3 scale,and the corresponding coupled time-domain simulation tool is devised for comparison.The entire SFT systemconsists of a long concrete tunnel and 12 tubular aluminummooring lines.Two numerical simulation models,the Cummins equation with 3D potential theory including second-order wave-body interaction effects and the much simpler Morison-equation-based formula with the lumped-massbased line model,are designed and compared.Forensic analyses for mooring-line adjustments in the simulation are carried out in view of the best representation of the physical system.After that,the measured pre-tension distribution and systemstiffness of twelvemooring lines arewell reproduced in the numericalmodel.Subsequently,the dynamic responses and mooring tensions of the SFT are compared under regular and irregular waves.The measured and simulated results coincide reasonably well for both regular-and irregular-wave conditions.

Non-Linear Response of Tethers Subjected to Parametric Excitation in Submerged Floating Tunnels

For the study of the non-linear response of inclined tethers subjected to parametric excitation in submerged floating tunnels, a theoretical model for coupled tube-tether vibration is developed. Upon the assumption that the static equilibri- um position of the tether is a quadratic parabola, the governing differential equations of the tether motion are derived by use of the Hamihon principle. An approximate numerical solution is obtained by use of Galerkin method and Runge-kutta method. The results show that, when the static equilibrium position of the tether is assumed to be. a quadratic parabola, the tether sag effect on its vibration may be reflected; the tether sag results in the asymmetry of tether vibration amplitude ; for the reduction of the tether amplitude, the buoyant unit weight of the tether should approach to zero as far as possible during the design.

Feasibility study on buoyancy-weight ratios of a submerged floating tunnel prototype subjected to hydrodynamic loads

The research progress of a novel traffic solution,a submerged floating tunnel（SFT）,is reviewed in terms of a study approach and loading scenario.Among existing publications,the buoyancy-weight ratio（BWR） is usually predefined.However,BWR is a critical structural parameter that tremendously affects the dynamic behaviour of not only the tunnel tube itself but also the cable system.In the context of a SFT prototype（SFTP） project in Qiandao Lake（Zhejiang Province,China）,the importance of BWR is illustrated by finite element analysis and subsequently,an optimized BWR is proposed within a reasonable range in the present study.In the numerical model,structural damping is identified to be of importance.Rayleigh damping and the corresponding Rayleigh coefficients are attained through a sensitivity study,which shows that the adopted damping ratios are fairly suitable for SFTP.Lastly,the human sense of security is considered by quantifying the comfort index,which helps further optimize BWR in the SFTP structural parameter design.

Parametric Vibration of Submerged Floating Tunnel Tether Under Random Excitation

For the study of the parametric vibration response of submerged floating tunnel tether under random excitation, a nonlinear random parametric vibration equation of coupled tether and tube of submerged floating tunnel is set up. Subsequently, vibration response of tether in the tether-tube system is analyzed by Monte Carlo method. It may be concluded that when the tube is subjected to zero-mean Gaussian white noise random excitation, the displacement and velocity root mean square responses of tether reach the peak if the circular frequency of tube doubles that of tether; the displacement and velocity root mean square responses of tether increase as the random excitation root mean square increases; owing to the damping force of water, the displacement and velocity root mean square responses of tether decrease rapidly compared with tether in air; increasing the damping of the tether or tube reduces the displacement and velocity root mean square responses of tether; the large-amplitude vibration of tether may be avoided by locating dampers on the tether or tube.

Effects of fundamental structure parameters on dynamic responses of submerged floating tunnel under hydrodynamic loads

This paper investigates the effects of structure parameters on dynamic responses of submerged floating tunnel （SFT） under hydrodynamic loads. The structure parameters includes buoyancy-weight ratio （BWR）, stiffness coefficients of the cable systems, tunnel net buoyancy and tunnel length. First, the importance of structural damp in relation to the dynamic responses of SPT is demonstrated and the mechanism of structural damp effect is discussed. Thereafter, the fundamental structure parameters are investigated through the analysis of SFT dynamic responses under hydrodynamic loads. The results indicate that the BWR of SFT is a key structure parameter. When BWR is 1.2, there is a remarkable trend change in the vertical dynamic response of SFT under hydrodynamic loads. The results also indicate that the ratio of the tunnel net buoyancy to the cable stiffness coefficient is not a characteristic factor affecting the dynamic responses of SFT under hydrodynamic loads.

Parametric Vibration Analysis of Submerged Floating Tunnel Tension Legs

According to the characteristics of submerged floating tunnel anchored by tension legs,simplifying the tube as point mass and assuming that the tension leg is a nonlinear beam model hinged at both ends,the nonlinear vibration equation of the tension leg is derived.The equation is solved by the Galerkin method and Runge Kutta method.Subsequently,numerical analysis of typical submerged floating tunnel tension leg is carried out.It is shown that,the parametric vibration response of the submerged floating tunnel tension leg is related to the amplitude and frequency of the end excitation.Without considering axial resonance and transverse resonance,it is reasonable that higher order modes are abandoned and only the first three modes are considered.The axial resonance amplitude of the second or third order mode is equivalent to the first order mode axial resonance amplitude,which should not be ignored.

Seismic Response of Submerged Floating Tunnel Tether

A mathematical equation for vibration of submerged floating tunnel tether under the effects of earthquake and parametric excitation is presented. Multi-step Galerkin method is used to simplify this equation and the fourth-order Runge-Kuta integration method is used for numerical analysis. Finally, vibration response of submerged floating tunnel tether subjected to earthquake and parametric excitation is analyzed in a few numerical examples. The results show that the vibration response of tether varies with the seismic wave type; the steady maximum mid-span displacement of tether subjected to seismic wave keeps constant when parametric resonance takes place; the transient maximum mid-span displacement of tether is related to the peak value of input seismic wave acceleration.

Effects of marine sediment on the response of a submerged floating tunnel due to p- wave incidence

Submerged floating tunnel (SFT) is a novel type traffic structure for crossing long strait and deep lakes. To investigate the dynamic pressure acting on an SFT under compression (P) wave incidence, a theoretical analysis model considering marine sediment effect has been proposed. Based on displacement potential functions, the reflection and refraction coefficients of P wave in different media are derived. Numerical examples are employed to illustrate the effects of the thickness of sediment layer, the incident P wave angle, the tether stiffness and spacing, and the permeability of the sediment on the dynamic pressure loading on the SFT. The results show that dynamic pressure is related to the saturation of sediment and affected by the thickness of sediment. The partially saturated sediment will amplify the dynamic pressure loading on the SFT, and the resonance frequency increases a little with the fully saturated sediment. Besides, increasing the tether stiffness and decreasing in the tether spacing will lead to a dynamic pressure falling. Deepening the SFT position and reducing the permeability of the sediment are effective measures to reduce dynamic pressure acting on the SFT.

The Effect of Key Design Parameters on the Global Performance of Submerged Floating Tunnel under Target Wave and Earthquake Excitations

This study presents a practical design strategy for a large-size Submerged Floating Tunnel(SFT)under different target environments through global-performance simulations.A coupled time-domain simulation model for SFT is established to check hydro-elastic behaviors under the design random wave and earthquake excitations.The tunnel and mooring lines are modeled with a finite-element line model based on a series of lumped masses connected by axial,bending,and torsional springs,and thus the dynamic/structural deformability of the entire SFT is fully considered.The dummy-connection-mass method and constraint boundary conditions are employed to connect the tunnel and mooring lines in a convenient manner.Wave-and earthquake-induced hydrodynamic forces are evaluated by the Morison equation at instantaneous node positions.Several wave and earthquake conditions are selected to evaluate its global performance and sensitivity at different system parameters.Different BuoyancyWeight Ratios(BWRs),submergence depths,and tunnel lengths(and mooring intervals)are chosen to establish a design strategy for reducing the maximum mooring tension.Both static and dynamic tensions are critical to find an acceptable design depending on the given target environmental condition.BWR plays a crucial role in preventing snap loading,and the corresponding static tension is a primary factor if the environmental condition is mild.The tunnel length can significantly be extended by reducing BWR when environmental force is not that substantial.Dynamic tension becomes important in harsh environmental conditions,for which high BWR and short mooring interval are required.It is underscored that the wet natural frequencies with mooring are located away from the spectral peaks of design waves or earthquakes.

Experimental and numerical analysis of submerged floating tunnel

As a new type of structure which has never been built, submerged floating tunnel was studied mainly by numerical simulations. To further study the seismic response of a submerged floating tunnel, the first model experiment of submerged floating tunnel （SFT） under the earthquake was carried out on the unique underwater shaking table in China. The experimental results show that vertical excitation induces larger response than horizontal and different inclination degrees of the tether also cause different seismic responses. Subsequently, based on the fluid-structure interaction theory, the corresponding numerical model is established. And comparing the numerical results with the experimental results, those of shaking table test. Numerical model adopted is effective for it is shown that the numerical results are basically identical with dynamic response of SFT.

Dynamic equations for curved submerged floating tunnel

In virtue of reference Cartesian coordinates, geometrical relations of spatial curved structure are presented in orthogonal curvilinear coordinates. Dynamic equations for helical girder are derived by Hamilton principle. These equations indicate that four generalized displacements are coupled with each other. When spatial structure degenerates into planar curvilinear structure, two generalized displacements in two perpendicular planes are coupled with each other. Dynamic equations for arbitrary curvilinear structure may be obtained by the method used in this paper.

波浪荷载作用下车辆-轨道-悬浮隧道动力响应研究

为实现波浪荷载作用下车辆-轨道-悬浮隧道系统耦合动力学行为模拟和分析,基于车辆-轨道耦合动力学理论,引入轮轨非线性时变单元矩阵法和结构单元多尺度耦合法,采用弹簧-阻尼单元模拟锚索系统,建立车辆-轨道-悬浮隧道动力相互作用模型;根据线性波浪理论和Morison方程,确定波浪荷载计算方法;最后,基于所建立的车辆-轨道-悬浮隧道动力相互作用模型开展数值仿真模拟,研究波浪荷载作用下锚索等效刚度、波浪高度、行车速度等参数变化时系统振动响应特性及传播规律。研究结果表明:锚索等效刚度变化对轨道-悬浮隧道系统结构位移的影响显著,提高锚索等效刚度能够有效抑制结构位移增大,且考虑部分锚索失效后系统结构位移变化较大,位移增幅均大于43%,不利于结构稳定;轨道-悬浮隧道系统结构的横向位移主要由波浪荷载引起,随着波浪高度增加,轨道-悬浮隧道系统结构位移整体上呈增大趋势;在工程设计过程中,应充分调研场地水环境,并合理设置轨道-悬浮隧道系统的结构参数,以确保系统的安全性和稳定性。

悬浮隧道地震动力响应及参数影响规律研究

为研究地震作用下悬浮隧道的动力响应问题,建立悬浮隧道二维截断有限元模型,基于Morison方程确定隧道管体和锚索上的水动力载荷,地震荷载的输入通过在锚索底部与海床铰接位置处输入地震加速度响应时程来实现,分别研究了不同地震类型、强度及双向地震动对悬浮隧道系统动力响应的影响,同时分析了隧道附加质量,结构阻尼与隧道、锚索拖曳力等参数对悬浮隧道系统响应的影响规律。结果表明:不同特性的地震动引发的隧道响应存在显著差异,能量较为集中的长周期地震动会引发较大的隧道响应,而能量较为分散的短周期地震动引发的隧道响应相对较小。当地震动引发隧道响应较小时,单向地震动单独作用仅能激发所对应方向的隧道响应;当地震动引发隧道响应较大时,水平方向地震动单独作用除了激发隧道的水平响应外还会激发一定的竖向响应,此时双向地震动作用下隧道加速度放大系数低于单向地震动单独作用,且放大系数随着地震强度的增大而减小。多数时间范围内,双向地震动的作用下锚索的张力波动稍大于单向地震动单独作用时的锚索张力;隧道附加质量、结构阻尼以及隧道、锚索拖曳力等参数均对隧道响应产生一定的抑制效果,但隧道附加质量会增大锚索张力。

悬浮隧道支撑锚索在管体运动状态下的动频率与湿模态

悬浮隧道(submerged floating tunnel,SFT)是一种潜力巨大的水下交通结构,其支撑锚索频率、模态的精确获取对识别结构动力性能至关重要。该研究提出了一种管体运动状态下求解锚索“动频率”和“湿模态”的新颖方法,将锚索等效为梁或弦建立了四类考虑锚索抗弯刚度、湿重等因素的力学模型。在对运动悬浮隧道结构进行拟静态处理,及通过静平衡时锚索顶张力与该索支撑范围内净浮力相等的原则确定结构基本参数的前提下,研究了管体竖向周期运动过程中锚索动频率与湿模态的分布规律。获取了锚索动频率带及其上限、下限与管体浮重比、锚索倾角、竖向高度及管体运动幅值之间的对应关系与参数敏感区间,得到了锚索湿模态对湿重展向效应、竖向高度等因素的敏感程度,可为进一步深入研究锚索涡振频率锁定、参数振动提供新的处理思路。

悬浮隧道管体运动对锚索涡激振动的影响

根据锚索式悬浮隧道的运动特性,将锚索假设为两端铰接的非线性梁模型,在海流作用下,锚索会产生顺流向与横流向的涡激振动。当海流方向和管体轴向存在夹角时,管体运动可简化为作用在锚索上部端点的质点运动,并将质点运动沿锚索坐标系方向逐一分解。根据Hamilton原理建立锚索三向振动方程,并通过Galerkin方法和Runge-Kutta方法对该方程进行求解,选取典型悬浮隧道的结构进行数值分析。结果表明:当锚索上部端点的输入频率与锚索固有频率的比值为整数时,锚索会发生共振现象;如上部端点除锚索轴向方向外的某一方向质点运动与锚索振动方向一致,则锚索在该方向上的振动会出现显著变化,而对另一方向振动的影响较小;在多数情况下,锚索振动平衡位置的偏离与上部端点所输入的运动频率有紧密联系,但与幅值联系不大。

悬浮隧道管体运动对锚索涡激振动的影响规律

根据锚索式悬浮隧道的运动特性,假设锚索是两端铰接的非线性梁模型,并将管体运动简化为两自由度的质点运动,将其视作一种参数激励。考虑锚索长期处于海流环境下,其顺流向涡激力和管体横荡运动方向一致,锚索的运动响应可能会产生明显变化。建立锚索的非线性顺流向涡激振动方程,并通过Galerkin方法和Runge-Kutta方法对该方程进行求解,选取典型悬浮隧道的结构进行数值分析,结果表明:在锚索前三阶模态中,相比于一阶模态幅值,二阶和三阶模态幅值是一个很小的量,可以忽略不计;参数激励可以使锚索更快进入稳定状态,且对振动幅值的增加有显著影响;参数激励对顺流向涡激振动的影响程度与锚索顶端的端部激励幅值和频率有关。

悬浮隧道考虑竖向弹性约束的子结构模型与涡振响应特性

通过将跨内支撑锚索与连接边界条件简化为竖向弹性约束,采用尾流振子考虑均匀流作用下结构的流固耦合效应,研究多跨锚索支撑式悬浮隧道的涡振特性。基于Euler-Bernoulli梁理论建立可考虑跨内/边界竖向支撑刚度对涡振特性产生影响的悬浮隧道管体子结构模型,分析多组跨内锚索支撑刚度与边界约束刚度组合下管体的涡振响应规律。研究结果表明:当两类约束刚度增大、结构固有频率增大时,高阶模态越难以被激发,能有抑制涡振响应的作用;当锚索支撑刚度较小和较大时,靠近端部位置的涡振响应幅值随边界约束刚度的增大而减小,且跨度范围内的涡振响应峰值关于中点对称,当锚索支撑刚度中等且相邻阶次频率相差较大时,管体位移由单一模态主导,当相邻阶次频率接近时,在涡振锁定区间内可观察到由模态耦合所导致的“凹陷”和“凸起”的非线性现象;不同位置之间跨内位移响应的极大值在边界约束刚度较小、较大时分别出现在两端、中点位置。