Resilience of coastal bridges under extreme wave-induced loads

Records of wave-induced damage on coastal bridges during natural hazards have been well documented over the past two decades.It is of utmost importance to decipher the loading mechanism and enhance the resilience of coastal bridges during extreme wave-inducing events.Quantification of vulnerability of these structures is an essential step in designing a resilient bridge system.Recently,considerable efforts have been made to study the force applied and the response of coastal bridge systems during extreme wave loading conditions.Although remarkable progress can be found in the quantification of load and response of coastal superstructures,very few studies assessed coastal bridge resiliency against extreme wave-induced loads.This paper adopts a simplified and practical technique to analyze and assess the resilience of coastal bridges exposed to extreme waves.Component-level and system-level fragility analyses form the basis of the resiliency analysis where the recovery functions are adopted based on the damage levels.It is shown that wave period has the highest contribution to the variation of bridge resiliency.Moreover,this study presents the uncertainty quantification in resiliency variation due to changes in wave load intensity.Results show that the bridge resiliency becomes more uncertain as the intensity of wave parameters increases.Finally,possible restoration strategies based on the desired resilience level and the attitude of decision-makers are also discussed.

Analysis of Wave Loads on A Semi-Submersible Platform

For the global and structural fatigue strength analysis of a semi-submersible platform, wave loads under design conditions are calculated by use of the three-dimensional boundary element method. Methods for calculating the forward-speed free-surface Green function are discussed and a computer program with this Green function is developed. According to the special rules, the wave loads under several typical design conditions of the platform are calculated. The maximum vertical bending moment, torsion moment and horizontal split force are determined from a series of contour maps of wave loads for the wave period of 5 to 18 seconds at a certain interval and the wave phase of 0degrees to 360degrees at a certain interval. The wave height is determined by the function of wave period with a given exceedance probability. The maximum wave loads under the combination of wave parameters are used as the input of hydrodynamic pressure in the three-dimensional finite element analysis process. The transfer functions of wave loads on the platform are used for the fatigue strength analysis of the K-tubular joint and the sub-model of the structure.

Wave load computation in direct strength analysis of semi-submersible platform structures

A wave load computation approach in direct strength analysis of semi-submersible platform structures was presented in this paper. Considering the differences in shape of pontoon, column and beam, the combination of accumulative chord length cubic parameter spline theory and analytic method was adopted for generating the wet surface mesh of platform. The hydrodynamic coefficients of platform were calculated by the three-dimensional potential flow theory of the linear hydrodynamic problem for platform with low forward speed. The equation of platform motions was established and solved in frequency domain, and the responses of wave-induced loads on the platform can be obtained. With the interpolation method being utilized, the pressure loads on shell elements for finite element analysis (FEA) were converted from those on the hydrodynamic computation mesh, which pave the basis for FEA with commercial software.A computer program based on this method has been developed, and a calculation example of semi-submersible platform was illustrated.Analysis results show that this method is a satisfying approach of wave loads computation for this kind of platform.

3-D computational method of wave loads on turret moored FPSO tankers

A three-dimensional method of calculating wave loads of turret moored FPSO (Flo ating Production Storage and Offloading) tankers is presented. The linearized restoring forces acting on the ship hull by the mooring system are calculated according to the catenary theory, which are expressed as the function of linear stiffness coefficients and the displacements of the upper ends of mooring chains. The hydrodynamic coefficients of the ship are calculated by the three-dimensional potential flow theory of the linear hydrodynamic problem for ships with a low forward speed. The equations of ship motions are established with the effect of the restoring forces from the mooring system included as linear stiffness coefficients. The equations of motions are solved in frequency domain, and the responses of wave-induced motions and loads on the ship can be obtained. A computer pro gram based on this method has been developed,and some calculation examples are illustrated. Analysis results show that the method can give satisfying prediction of wave loads.

Nonlinear Random Motion Analysis of Coupled Heave-Pitch Motions of a Spar Platform Considering lst-Order and 2nd-Order Wave Loads

In this study, the coupled heave-pitch motion equations of a spar platform were established by considering lst-order and 2nd-order random wave loads and the effects of time-varying displacement volume and transient wave elevation. We generated random wave loads based on frequency-domain wave load transfer functions and the Joint North Sea Wave Project （JONSWAP） wave spectrum, designed program codes to solve the motion equations, and then simulated the coupled heave-pitch motion responses of the platform in the time domain. We then calculated and compared the motion responses in different sea conditions and separately investigated the effects of 2nd-order random wave loads and transient wave elevation. The results show that the coupled heave-pitch motion responses of the platform are primarily dominated by wave height and the characteristic wave period, the latter of which has a greater impact. 2nd-order mean wave loads mainly affect the average heave value. The platform＇s pitch increases after the 2nd-order low frequency wave loads are taken into account. The platform＇s heave is underestimated if the transient wave elevation term in the motion equations is neglected.

Experimental study on the wave loads of twin-plate breakwaterunder oblique waves

In this study, systematic physical model tests were performed to investigate the wave forces on the twin-plate breakwater under irregular waves. Based on the experimental results, the effects of the relative plate width B/L,wave height Hs/D and incident angle θ0 on the wave forces were analyzed and discussed. The results showed that:(1) The envelopes of the total wave pressure were generally symmetrical along the direction of plate width under the incident angles(θ0) being 0°, 15°, 30°, 45° and 60°. In particular, the envelopes of wave pressure atθ0=30° were larger than all other cases.(2) The synchronous pressure distribution of the breakwater under oblique wave action was more complicated comparing to the normal incident waves.(3) Based on data analysis, an empirical formula was obtained to estimate the total vertical force of the twin-plate breakwater.This empirical formula can be a good reference for the design basis of engineering applications under specified wave conditions.

Experimental Investigation of Wave Load and Run-up on the Composite Bucket Foundation Influenced by Regular Waves

In the design of wind turbine foundations for offshore wind farms, the wave load and run-up slamming on the supporting structure are the quantities that need to be considered. Because of a special arc transition, the interaction between the wave field and the composite bucket foundation(CBF) becomes complicated. In this study, the hydrodynamic characteristics, including wave pressure, load, upwelling, and run-up, around the arc transition of a CBF influenced by regular waves are investigated through physical tests at Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China. The distributions of the wave pressures and upwelling ratios around the CBF are described, and the relationship between the wave load and the wave parameters is discussed. New formulae based on the velocity stagnation head theory with linear wave theory and the second-order Stokes wave theory for wave kinematics are proposed to estimate the wave run-up. Moreover, the multiple regression method with nonlinear technology is employed to deduce an empirical formula for predicting run-up heights. Results show that the non-dimensional wave load increases with the increase in the values of the wave scattering parameter and relative wave height. The wave upwelling height is high in front of the CBF and has the lowest value at an angle of 135? with the incoming wave direction. The performance of the new formulae proposed in this study is compared using statistical indices to demonstrate that a good fit is obtained by the multiple regression method and the analytical model based on the velocity stagnation head theory is underdeveloped.

Numerical study on wave loads and motions of two ships advancing in waves by using three-dimensional translating-pulsating source

A frequency domain analysis method based on the three-dimensional translating-pulsating （3DTP） source Green function is developed to investigate wave loads and free motions of two ships advancing on parallel course in waves. Two experiments are carried out respectively to mea- sure the wave loads and the free motions for a pair of side-by- side arranged ship models advancing with an identical speed in head regular waves. For comparison, each model is also tested alone. Predictions obtained by the present solution are found in favorable agreement with the model tests and are more accurate than the traditional method based on the three dimensional pulsating （3DP） source Green function. Numer- ical resonances and peak shift can be found in the 3DP pre- dictions, which result from the wave energy trapped in the gap between two ships and the extremely inhomogeneous wave load distribution on each hull. However, they can be eliminated by 3DTP, in which the speed affects the free sur- face and most of the wave energy can be escaped from the gap. Both the experiment and the present prediction show that hydrodynamic interaction effects on wave loads and free motions are significant. The present solver may serve as a validated tool to predict wave loads and motions of two ves- sels under replenishment at sea, and may help to evaluate the hydrodynamic interaction effects on the ships safety in replenishment operation.

Wave Loads and Protective Techniques of An On-Shore Wave Power Device

In this paper, the extreme wave loads on an on-shore wave power device are investigated. First, boundary element method is applied to solve the three dimensional potential problem based on the small amplitude wave assumption. Then the motion of the Oscillating Water Column (OWC) inside the device and its laods on the device are calculated in time domain. Several protective techniques often applied are simulated by changing the constraint of the upper end of the chamber of the device. Numerical results are used to judge the effectiveness of these techniques. The investigation shows that damping can not effectively restrain the motion of OWC when the period of incident wave is long, which may cause dangerous loads on the structure. The shut chamber can effectively restrain the motion of OWC, but alternatively cause high pressure in the chamber. A Contracting opening with a Taper (CT) can exhaust a great amount of kinetic energy of OWC, and significantly decrease the loads. It is a promising protective technique.

Influence of structural factors on the strength properties of aluminum alloys under shock wave loading

The results of measurements of the strength characteristics-Hugoniot elastic limit and spall strength of aluminum and aluminum alloys in different structural states under shock wave loading are presented.Single-crystals and polycrystalline technical grade aluminumА1013 and aluminum alloysА2024,АА6063Т6,А1421,A7,А7075,А3003,A5083,АА1070 in the initial coarse-grained state and ultrafine-grained or nanocrystalline structural state were investigated.The refinement of the grain structure was carried out by different methods of severe plastic deformation such as Equal Chanel Angular Pressing,Dynamic Channel Angular Pressing,High-Pressure Torsion and Accumulative Roll-Bonding.The strength characteristics of shock-loaded samples in different structural states were obtained from the analysis of the evolution of the free surface velocity histories recorded by means of laser Doppler velocimeter VISAR.The strain rates before spall fracture of the samples were in the range of 10^(4)-10^(5 )s^(-1),the maximum pressure of shock compression did not exceed 7 GPa.The results of these studies clearly demonstrate the influence of structural factors on the resistance to high-rate deformation and dynamic fracture,and it is much less than under the static and quasi-static loading.

Characteristics of Pore Water Pressure of Saturated Silt Under Wave Loading

The characteristics of dynamic stress in the seabed under wave loading are constant principal stress and continuous rotation of the principal stress direction. Cyclic triaxial-torsional coupling shear tests were pefformed on saturated silt by the hollow cylinder apparatus under different relative densities, deviator stress ratios and vibration frequencies to study the development of pore water pressure of the saturated silt under wave loading. It was found that the development of pore water pressure follows the trend of ＂fast - steady - drastic＂. The turning point from fast to steady stage is not affected by relative density and deviator stress ratio. However, the turning point from steady to drastic stage relies on relative density and deviator stress ratio. The vibration cycle for the liquefaction of saturated silt decreases with increasing deviator stress ratio and increases with relative density. The vibration cycle for the liquefaction of the saturated silt increases with vibration frequency and reaches a peak value, after which it decreases with increasing vibration frequency for the relative density of 70%. But the vibration cycle for the liquefaction of saturated silt increases with vibration frequency for the relative density of 30%. The development of pore water pressure of the saturated silt is influenced by relative density and vibration frequency.

Numerical Analyses of Caisson Breakwaters on Soft Foundations Under Wave Cyclic Loading

A caisson breakwater is built on soft foundations after replacing the upper soft layer with sand. This paper presents a dynamic finite element method to investigate the strength degradation and associated pore pressure development of the intercalated soft layer under wave cyclic loading. By combining the undrained shear strength with the empirical formula of overconsolidation clay produced by unloading and the development model of pore pressure, the dynamic degradation law that describes the undrained shear strength as a function of cycle number and stress level is derived. Based on the proposed dynamic degradation law and M-C yield criterion, a dynamic finite element method is numerically implemented to predict changes in undrained shear strength of the intercalated soft layer by using the general-purpose FEM software ABAQUS, and the accuracy of the method is verified. The effects of cycle number and amplitude of the wave force on the degradation of the undrained shear strength of the intercalated soft layer and the associated excess pore pressure response are investigated by analyzing an overall distribution and three typical sections underneath the breakwater. By comparing the undrained shear strength distributions obtained by the static method and the quasi-static method with the undrained shear strength distributions obtained by the dynamic finite element method in the three typical sections, the superiority of the dynamic finite element method in predicting changes in undrained shear strength is demonstrated.

Variational Solution of Coral Reef Stability Due to Horizontal Wave Loading

This paper proposes a theoretical method that can be used in calculating the stability of coral reefs or artificial islands.In this work,we employ the variational limiting equilibrium procedure to theoretically determine the slope stability of coral reefs covered with hard reef shells as a result of horizontal wave loads.A reasonable functional is proposed and its extremum is calculated based on the conservation of energy.Then,we deduce the stability factor Ns of coral reefs under combined vertical self-gravity and horizontal wave loads,which is consistent with the published results.We compare some classic examples of homogeneous slopes without hard shells in order to analyze the accuracy of results generated by this variational procedure.The variational results are accurate and reliable according to the results of a series of detailed calculations and comparisons.Simultaneously,some other influence parameters on the reef stability,including the top-layer tensile strength of coral reef,the amplitude of wave loading,and the tensile crack,are calculated and discussed in detail.The analysis results reveal that the existence of a hard reef shell could enhance the stability of reef slope and that there is a nonlinear relationship between the stability factor Ns,the shear strength,and the thickness Ds of the covered coral reef shell.Furthermore,the emergence of top-layer tensile cracks on the coral reefs reduces their stability,and the action of horizontal wave loads greatly decreases the stability of coral reefs.Thus,the hard shell strength and its thickness Ds,surface tensile crack,and wave loading require more careful attention in the field of practical engineering.

Effects of the shape and size of a mooring line surface buoy on the mooring load of wave energy converters

This paper describes the physical model testing of a wave energy converter (WEC) undertaken in the Heriot-Watt wave basin during October 2010 as part of the SUPERGEN2 project funded by the British government,and provides a preliminary analysis of the extreme mooring loads.Tests were completed at 1/20 scale on a single oscillating water column device deployed with a 3-line taut mooring configuration.The model was fully instrumented with mooring line load cells and an optical motion tracker.The tests were preceded by calibration of instrumentation and the wave test environment,and carried out in long crested waves regimes with 12 combinations of peak period T p and significant wave height H s.The main objective for these experiments was to examine the effect of shape and size of the tethered buoy on the leading mooring line on the maximum mooring loads and the excursion of the device.Comparison of the loads at different configurations of the tethered buoy suggests that the results are consistent with the hypothesis that the mooring forces should depend on the change in stiffness of the mooring system.In particular,the results indicate that with the spectral peak period close to the natural period of the moored device of 8 s,peak loads in a configuration with a smaller buoy may be considerably higher than those with a larger buoy.However,when T p was dissimilar,a harder mooring with a smaller spherical buoy appears to result in lower peak loads.The exact configuration should,therefore,be chosen according to the prevalent conditions of any particular location,and will also depend on the design and expected maintenance schedule,as well as matters related to the risk to navigation,environmental effects and the conservation status of the area.

Wave-Induced Loads on Very Large FPSOs at Restricted Water Depth

The effects of water depth on the wave-induced vertical bending moment and shearing force on a very large FPSO are studied by experiments and computations for regular and irregular waves. The restricted water depth composite Green function is employed to develop a program for the computation of the hydrodynamic coefficients of the very large FPSO at shallow water. A three-segment model with 1∶100 scale is tested in the State Key Laboratory of Ocean Engineering at Shanghai Jiao Tong University for the verification of the numerical method. The experimental and computational results show that the water depth has a substantial effect on wave-induced loads. The wave-induced vertical loads increase with the decrease of water depth for shallow water. Especially, for ultra-shallow water these loads increase very evidently with the decrease of water depth. The long-term prediction values of wave-induced vertical loads increase with the decrease of the ratio of water depth to draught. The long-term prediction values of wave-induced vertical loads are about 8% larger than those for deep water when the ratio of water depth to draught is 3.0. However, water depth hardly affects the long-term prediction values of wave-induced loads when the ratio of water depth to draught is larger than 5.0.

Wave Loading on Concentric Porous Cylinders with Varying Porosity

Wave diffraction of two concentric porous cylinders with varying porosity was studied by using an analytical method based on eigenfunction matching.The fluid domain around the cylinders is divided into three sub-domains and in each sub-domain an eigenfunction expansion of the velocity potential is obtained by satisfying the Laplace equation,the boundary conditions on the free surface and on the sea bed.The unknown coefficients of eigenfunction expansions are determined by boundary conditions on the porous hulls.In the paper,the boundary conditions are based upon the assumption that the flow in the porous medium is governed by Darcy's law.Two porous-effect parameters applied on two porous cylinders are functions of the vertical coordinate instead of the constant.Wave loading on the outer and inner cylinder is presented in the numerical results.

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.

Risk Analysis of Breakwater Caisson Under Wave Attack Using Load Surface Approximation

A new load surface based approach to the reliability analysis of caisson-type breakwater is proposed. Uncertainties of the horizontal and vertical wave loads acting on breakwater are considered by using the so-called load surfaces, which can be estimated as functions of wave height, water level, and so on. Then, the first-order reliability method（FORM） can be applied to determine the probability of failure under the wave action. In this way, the reliability analysis of breakwaters with uncertainties both in wave height and in water level is possible. Moreover, the uncertainty in wave breaking can be taken into account by considering a random variable for wave height ratio which relates the significant wave height to the maximum wave height. The proposed approach is applied numerically to the reliability analysis of caisson breakwater under wave attack that may undergo partial or full wave breaking.

Torsionally coupled dynamic performance analysis of asymmetric offshore platforms subjected to wave and earthquake loadings

The dynamic equations of motion of asymmetric offshore platforms under three different environmental conditions:seismic action,wave action and their combination are established in this paper. In establishing these motion equations,three typical eccentricity types including mass eccentricity,rigidity eccentricity and their combination were considered,as are eccentricities that occur un-idirectionally and bi-directionally. The effects of the eccentricity type,the dynamic characteristics and the environmental conditions on the torsional coupling response of platforms are investigated and compared. An effort has also been made to analyze the inffluence of accidental eccentricity on asymmetric platforms with different eccentricity in two horizontally orthogonal directions. The results are given in terms of non-dimensional parameters,accounting for the uncoupled torsional to lateral frequency ratio. Numerical results reveal that the eccentricity type has a great inffluence on the torsionally coupled response under different environmental conditions. Therefore,it is necessary to consider the combination of earthquake and wave action in the seismic response analysis of some offshore platforms.

AN EXPERIMENTAL-NUMERICAL METHOD FOR MEASURING CRACK PROPAGATING VELOCITIES UNDER STRESS WAVE LOADING

An experimental-numerical method for measuring dynamic crack propagatingvelocities under stress wave loading is established in this paper. The experiments of thethree-point bend specimen are done on the improved Hopkinson bar. Deflection of loading point,dynamic load and instantaneous crack length are measured, then crack propagating velocities arecalculated. Experiments on 40Cr steel show that the results given by this method have a goodagreement with that obtained by the resistance fracture gage method. Therefore this method isfeasible for measuring crack propagating velocities under high loading rate and will have wideapplication.