Wave Loading Research Articles

Optimization Analysis of the Shape and Position of a Submerged Breakwater for Improving Floating Body Stability

Submerged breakwaters can be installed underneath floating structures to reduce the external wave loads acting on the structure. The objective of this study was to establish an optimization analysis framework to determine the corresponding shape and position of the submerged breakwater that can minimize or maximize the external forces acting on the floating structure. A two-dimensional frequency-domain boundary element method (FD-BEM) based on the linear potential theory was developed to perform the hydrodynamic analysis. A metaheuristic algorithm, the advanced particle swarm optimization, was newly coupled to the FD-BEM to perform the optimization analysis. The optimization analysis process was performed by calling FD-BEM for each generation, performing a numerical analysis of the design variables of each particle, and updating the design variables using the collected results. The results of the optimization analysis showed that the height of the submerged breakwater has a significant effect on the surface piercing body and that there is a specific area and position with an optimal value. In this study, the optimal values of the shape and position of a single submerged breakwater were determined and analyzed so that the external force acting on a surface piercing body was minimum or maximum.

Floating bridge global responses to slowly varying wave loads

The global responses of a 5530-m-long floating bridge under linear and slowly varying wave loads were studied. The bridge has modes from seconds to around 2 min. A comparative study was carried out applying full Quadratic Transfer Functions (QTFs) or Newman's approximation (Newman, 1974) for slowly varying loads. Four groups of QTFs were computed: one fixed pontoon, one pontoon with specified stiffnesses, three fixed pontoons, and three pontoons with stiffnesses for the mid-pontoon. The importance of damping to the global response was demonstrated by a sensitivity check on the viscous damping. The study showed the importance of hydrodynamic interaction in both first and second order wave loads and responses. Hydrodynamic interaction led to more ‘distributed’ QTF peak values away from the diagonal, which may reduce the correctness of Newman's approximation. Parametric study showed that the floating bridge responses were sensitive to wave direction, wave height and period. This study suggested that full QTFs based on three fixed pontoons provided the most conservative results for the base case. Newman's approximation provided reasonable levels of overall responses but underpredicted specific responses in this study. Though the full QTFs method is preferred in a detailed analysis, the efficient Newman's approximation is considered as a valuable tool for large-scale screening analysis during the early design phase of practical engineering.

Dynamic response of subsea tunnel in liquefiable layered seabed under combined earthquake and wave action

Liquefaction poses a potential threat to the safety of subsea tunnel during the earthquake. In the ocean environment, wave pressure is considered as a normal loading applied at the seabed surface. This study proposed a fully coupled dynamic effective stress finite element model for subsea tunnel in liquefiable layered seabed under combined earthquake and wave action. Biot u-p formulation integrated with a modified generalized plasticity model was adopted for liquefaction analyses of the seabed. The proposed model was validated through a wave flume model test in terms of excess pore water pressure (EPWP). The results showed that the tunnel – soil dynamic interaction significantly increased EPWP near the tunnel. Increasing the wave height significantly increased the liquefaction depth of the seabed; however, the wave loading can either suppress the displacement of the tunnel during the earthquake or increase the uplift of the tunnel during the subsequent wave loading. When investigating seismic response of subsea tunnels in liquefiable soils under combined earthquake and wave action, the ground motion was suggested to be input simultaneously with the wave pressure. This study also highlights the effect of the thickness of liquefiable layer and frequency content of earthquakes on dynamic responses of subsea tunnels.

CFD analysis of wave loading on a 10 MW TLP-type offshore floating wind turbine in regular waves

This paper aims to study the higher-harmonics wave-induced surge force on the CENTEC-TLP platform in regular head waves with non-breaking assumptions, using a CFD-based numerical wave tank model, which is a useful tool for the analysis of the nonlinear interaction of waves and structures. Moreover, the influence of change in the wave diffraction and the incident wave angle on the surge force subject to operational and extreme wave conditions is investigated. The numerical analysis is conducted using the CFD toolbox OpenFOAM. The link between Secondary Load Cycle and the wave scattering Type2 is apparent and it is concluded that they are all inertia-driven and that 2nd harmonics play an important role.

Testing device for aerodynamic alternating loads on a train cabin

In high-speed train operations, especially during the passage of two trains or when passing through tunnels, the surface of the train experiences intense transient alternating pressure. The resulting alternating aerodynamic loads can lead to fatigue damage in the train's structure. To address this issue, an experimental device is developed in this study to accurately replicate the alternating aerodynamic loads experienced by trains. In this research, a novel method for simulating variable loads using triangular pressure wave patterns is proposed. Validation tests are conducted to assess the effectiveness of the device in replicating the desired load profiles. Furthermore, a noise suppression mechanism is incorporated into the device design. By incorporating noise source analysis and optimization techniques, the device design effectively controls the noise level within 85 dBA during the loading process. The experimental results demonstrate that the proposed device can achieve a triangular wave loading frequency of 2.5 cycles per minute, with a pressure range of ±3000 Pa for a 250 m3 high-speed train cabin. The pressure load output stability has high consistency in the pressure‒time curves at various measurement points inside the tested object, with a maximum difference of 0.99%. The experimental device designed in this study meets the requirements for simulating the aerodynamic loads on the surface of high-speed trains travelling at speeds of up to 350 km/h.

Fragility assessment of sea-crossing cable-stayed bridge subjected to multi-hazard action via TKC and R-vine copula

Seismic fragility analysis methods commonly used for assessing structural components and systems have certain limitations. This paper introduces a new semi-parametric approach for structural component fragility analysis, the TKC method. This method is based on log-transformed kernel density estimation (log-TKDE) and copula functions, which establish the joint probability distribution (JPD) of a structural response value (d) and a disaster-inducing factor strength parameter (α) using log-TKDE and match the marginal cumulative distributions (MCDs) of d and a via bivariate copula functions. A novel method for evaluating structural system fragility is also proposed based on the R-vine copula function. This approach accounts for the intricate correlations among different components, providing a precise estimation of the multidimensional JPD. The reliability and accuracy of the proposed methods are demonstrated through a seismic fragility analysis of a sea-crossing cable-stayed bridge under earthquake load. Furthermore, a multi-hazard fragility analysis of bridge components and systems is conducted considering hazards such as earthquake, wind, and wave loads. A comparison is made with the seismic fragility of bridges subjected to earthquake loads alone. The results show that the median and 95% confidence of the damage probability of structural components calculated by the TKC method and Monte Carlo simulation (MCS) closely match, which validates the proposed method. The TKC method is also more accurate and computationally efficient than the MCS method with the same Bootstrap sample size and confidence level (95%). The proposed structural system fragility assessment method based on the R-vine copula accounts for complex correlations between components and yields more accurate results than the first-order boundary method. Load spectrum characteristics, structural component characteristics, and other factors cause the multi-hazard fragility of bridge components and systems to differ substantially from their seismic fragility. The difference rate of system damage probability can reach 28.82%. In evaluating the anti-disaster performance of sea-crossing bridges, it is necessary to incorporate the marine environmental load and consider the dynamic response coupling effect of the bridge excited by seafloor ground motions with extreme wind and wave loads. This approach can guide the optimization of bridge designs and facilitate multi-hazard fragility analysis in accordance with real damage probabilities.

Vibration Mitigation Using 3D-PSTMD for the Offshore Wind Turbine Considering Self-Excitation Behaviors

The self-excitation behaviors can be triggered by the blade rotation of the wind turbine. To mitigate the excessive vibration of offshore wind turbine (OWT) tower under this self-excitation addition with wind–wave loadings, a three-dimensional prestressed TMD (3D-PSTMD) is extended in this study. First, based on the Lagrange equation, the analytical formulations of 1P (rotor rotational speed) and 3P (blade passing frequency) loads from self-excitations are deduced, and more factors under real operational conditions of the OWT are further analyzed using theoretical derivation and numerical simulation. Then, structural aero-hydrodynamic loadings are modelled, and self-resonance phenomenon of the uncontrolled OWT and resonance dissipation capability of 3D-PSTMD are discussed at startup–operation–shutdown state. Finally, the energy harvesting competence of 3D-PSTMD is quantitatively calculated via the classical Wilson-[Formula: see text] algorithm under self-excitations with wind–wave loadings. Results indicate that this dashpot is remarkably able to mitigate the structural resonance responses over 61.3% and 40.5% respectively when under the 1P and 3P loadings, and it can also effectively reduce the bi-directionally horizontal vibrations of OWT under aero-hydrodynamic loadings.

Experimental study on axial compression fatigue of grouted connection in jacket offshore wind turbines

The grouted connection (GC) of the offshore wind turbine (OWT) jacket foundation mainly bears axial loads, the wind and wave load in the working environment make the structure prone to fatigue problems. The construction environment of the OWT foundation is relatively harsh, so there will be vertical and horizontal errors during the construction process. In this paper, the fatigue test of 9 specimens were designed to analyze the influence of vertical and horizontal errors, water ingression and other factors on the axial fatigue performance of the GC section. The static ultimate bearing capacity test was carried out to determine the load ranges of the fatigue test. Results of fatigue tests indicate that the fatigue performance of the GC considerably degenerates with the load eccentricity, especially at the end sections of the inner and outer tubes. Water ingression has a significant negative influence on the fatigue performance of the GC section. The presence of water contributes to the propagation and development of cracks in the grout layer. Load range, vertical and horizontal errors and grout material have negligible effect on the fatigue performance of the structure.

Array analysis on a seawall type of deformable wave energy converters

There has been a significant interest in developing Flexible Wave Energy Converters (FlexWECs) that utilise structural deformations to generate electricity and mitigate destructive wave loads to the devices. In the meantime, FlexWECs are most likely to operate in an array format to enhance space usage and power output, as well as provide convenience for maintenance. In this context, the present paper develops a high-fidelity computational model to investigate the interaction of ocean surface waves with an array of seawall-type FlexWECs, which can meanwhile serve coastal engineering purposes. The fluid field is solved using the Navier-Stokes equations, and structural deformations are predicted using a nonlinear finite-element method. Hydroelastic interactions of up to seven deforming FlexWECs with the surrounding wave fields are demonstrated through systematic simulation cases. Based on the simulation results, analyses are conducted to investigate how the wave farm energy output is influenced by the gap between individual devices and the number of devices deployed. Accordingly, empirical design suggestions are provided. Overall, this work innovatively simulates the hydroelastic interactions between waves and multiple deforming structures, and the provided insights are useful for promoting the development of FlexWECs and their wave farms.

Gyroscopic effects of the spinning rotor-blades assembly on dynamic response of offshore wind turbines

An analytical solution for the gyroscopic effect of the spinning rotor-blades assembly on the dynamic response of offshore wind turbines (OWT) is presented. A continuous coupled model is rigorously developed to form the partial differential equations of fore-aft, side-side, and yaw motions. The gyroscopic moments caused by the angular momentum of the spinning rotor-blades assembly are formulated and handled into the three boundary conditions at the nacelle. The procedure for obtaining the operational natural frequencies of the structure including these coupled boundary conditions is developed. Furthermore, a response function for each fore-aft and yaw motions is obtained by solving the equations of motion under a wave load applied in only the fore-aft direction. Finally, the operational natural frequencies are calculated and compared to the idling ones for the considered example of OWT. The response of the structure under different values of the rotor-blades assembly's angular velocity is investigated. The proposed solution in this study unfolds a revelational procedure in capturing the gyroscopic effect in wind turbine industries which also can be a guideline for developing the floating OWT models.

Serviceability analysis of sea-crossing bridges under correlated wind and wave loads

With coupled wind and wave loads suffered by sea-crossing bridges, it is challenging to include uncertainties for assessing bridge serviceability. In this study, an efficient probabilistic peak response framework with surrogate models is developed for the serviceability analysis of sea-crossing bridges under coupled wind and wave loads. The joint probability distribution functions (JPDF) of the mean wind speed, significant wave height, and peak wave period are first derived based on long-term field measurement data and using a C-vine copula model. The JPDF serves as an input to the bridge to calculate the peak response of the bridge through finite-element analyses. To improve computational efficiency and make the problem manageable, the surrogate models are then generated by both the support vector machine and response surface method to predict the bridge peak responses. The exceeding probabilities for the serviceability assessment are finally obtained by the Monte-Carlo method using the pre-defined threshold values of bridge serviceability. A real long-span sea-crossing bridge is used as a case study to demonstrate the feasibility and effectiveness of the proposed framework. The results elucidate the effects of correlated wind and wave loads on bridge serviceability. Ignoring the correlation of wind and wave parameters will significantly overestimate the exceeding probability of bridge serviceability.

Hydro- and aero-elastic response of floating offshore wind turbines to combined waves and wind in frequency domain

An analytical approach and numerical solution to determine coupled aeroelastic and hydroelastic response of floating offshore wind turbines of arbitrary shape to combined wind and wave loads is presented. The model considers simultaneously the aerodynamic and hydrodynamic loads on an FOWT and integrates these with finite element method for structural analysis due to the combined loads. The hydrodynamic and aerodynamic loads are determined based on the linear wave diffraction theory and steady blade element momentum method, respectively, and the solution is obtained in frequency domain. The structure may be fixed or floating, located in arbitrary water depth, and may host single or multiple wind towers. The model captures the complete translational and rotational motions of the body in three dimensions, and the elasticity of the blades, tower and the floating platform. To assess the performance of the model, rigid and elastic responses of a FOWT to combined wave and wind loads are computed and compared with available laboratory measurements and other theoretical approaches where possible, and overall very good agreement is observed. The model developed in this study addresses directly three shortcomings of existing approaches used for the analysis of FOWTs, namely (i) determination of the elastic responses of the entire structure including the floating platform, (ii) analysis of the motion and elastic response of FOWTs in frequency domain, and (iii) assessment of responses of FOWTs with single or multiple wind towers.

Variable Natural Frequency Damper for Minimizing Response of Offshore Wind Turbine: Effect on Dynamic Response According to Inner Water Level

Offshore wind turbines (OWTs) are exposed to cyclic loads resulting from wind, waves, and rotor rotation. These loads can induce resonance, thereby significantly increasing the amplitude of the structure and accelerating the accumulation of fatigue damage. Particularly, wave loads can induce the first mode of large turbines. While many studies have been conducted to suppress OWT vibrations due to external loads, research on variable natural frequency damper (VNFD), which control vibrations through changes in the natural frequency by adjusting the inner water level of the structure, is still in its infancy. Herein, the performance of a VNFD in controlling the vibration of monopile-type OWTs is analyzed by focusing on cyclic environmental loads. To analyze the amplitude minimization achieved using a VNFD, wave loads with the same period as that of the structure’s natural frequency were generated, and the structural response resulting from changes in the inner water level were analyzed. As a result, the peak displacement at the top of the tower decreased by 5.8% and 34% at the water depths of 20 m and 50 m, respectively. In terms of the peak intensity determined through Fast Fourier Transform of the displacement response, reductions of 33% and 65% were confirmed at the depths of 20 m and 50 m, respectively.

A CFD-FEA coupled model for simulating dynamic response of offshore jacket platform under earthquake considering wind, wave, current and aftershock loads

Offshore platforms as the key equipment in marine oil and gas exploitation are facing challenges from various environmental conditions, such as winds, waves, currents and even earthquakes. Due to the combined action of those concurrent loads, there is potential risk of accidents. The aim of this paper is to systematically study the dynamic response and safety assessment of the large scaled offshore structures against the concurrent loads considering the fluid-structure interaction (FSI) effects. Three-dimensional numerical wave flume including a jacket platform is established by CFD software Fluent, based on which the simulation of wave generation and propagation is carried out. Then the FSI effects between waves and platform are analyzed using the CFD- FEA coupling method. Subsequently, the seismic ground accelerations are inputted into the platform, correspondingly the structural response is analyzed. Moreover, multiple influencing factors including earthquake direction and mainshock-aftershock sequence are discussed. The results show that the structure response under concurrent loads is not a simple linear superposition of different load. The seismic response would be underestimated if wave action is ignored when the earthquake acts on certain angles. The methodology proposed could be regarded as an effective way to analyze the FSI problem under realistic offshore environment.

Experimental study on the effects of hydrodynamic loads on the seismic response of end-anchored floating bridges

This study focuses on seismic hydrodynamic testing and presents a 1:100-scaled experiment conducted on an end-anchored floating bridge. A series of underwater experiments with varying wave heights and wave periods were conducted to evaluate the effects of hydrodynamic properties on the dynamic behavior of floating bridges under the combined action of earthquakes and waves. The experimental results showed that sway motion resonance occurred when the wave period increased under a multihazard effect. The lateral motion of the pontoon is generated by the earthquake-induced lateral seismic radiation waves on both sides of the pontoon. However, as the wave height increased, the laterally expanding radiation waves on both sides of the pontoon were diminished by the incident waves, resulting in the fragmentation of the seismic radiation waves. Furthermore, independent of the wave height or earthquake, the roll motion of the pontoons induced by the earthquake steadily stabilized as the wave period increased. The effect of wave loads on the translational and rotational responses of floating structures under multihazard effects depends on the hydrodynamic properties of the input sea state.

Electric Potential Response Characteristics of Coal Under Stress Wave Loading

Electric Potential Response Characteristics of Coal Under Stress Wave Loading

Comparative study on dynamic responses of integrated installation process of a 5-MW and a 15-MW offshore wind turbine considering a pre-installed foundation

The integrated installation method for offshore wind turbines has the characteristics of high efficiency and low economic cost due to the small amount of construction work. However, the complexity of the entire system is exacerbated by environmental loads and mechanical couplings. Hence, it is urgent to investigate the dynamic response of OWTs during integrated installation procedures. This work compares the dynamic responses between NREL 5 MW and IEA 15 MW OWT installation systems. The hydrodynamics are calculated using the potential flow theory and the Morison equation, while the aerodynamics under wind turbine parked conditions are computed using the blade element momentum theory. Time domain simulations, considering various wind and wave conditions, are conducted via SIMA. This paper discusses the effects of wind and wave loads on the motion responses of catamaran installation vessel and spar, the relative motion at the mating point, and the sliding gripper forces, respectively. The results reveal that both the surge motions of the catamaran and the spar and the pitch motion of the spar exhibit sensitivity to wind loads. During installation, the motion response of the IEA 15 MW model is more dramatic than that of the NREL 5 MW system. Under wave-only conditions, the radial distances of the mating points for both NREL 5 MW and IEA 15 MW systems reach 1.65 m and 2.51 m, respectively. However, the influences of wind loads and wave incident angle are limited.

Submerged low-crested structures in front of coastal structures

Climate adaptation of coastal structures has become more important due to climate change, resulting in sea level rise and increased wave loading on coastal structures with depth-limited wave conditions. One of the climate adaptation measures to ensure that existing coastal structures continue to perform their function after unforeseen sea level rise, is to reduce the wave loading before the waves reach the existing coastal structure. This can be achieved by constructing a low-crested structure in front of the existing structure. Between the two structures, structure-induced wave set-up occurs. This structure-induced wave set-up has been studied based on wave flume tests. The effects of structure-induced wave set-up on wave transmission at the low-crested structures and the effects on wave overtopping at the emerged coastal structures were also measured and analyzed.The structure-induced wave set-up depends on the freeboard, wave steepness, and permeability of the low-crested structure. For configurations with impermeable low-crested structures, this wave-set-up does not depend on the distance between the two structures. Empirical expressions to estimate structure-induced wave set-up are derived for impermeable and permeable low-crested structures.The measurements indicate that the effect of structure-induced wave set-up on the wave transmission coefficients is negligibly small.The structure-induced wave set-up increases the wave overtopping discharges at the emerged coastal structure. This effect can be taken into account in wave overtopping estimates by reducing the freeboard with the structure-induced wave set-up.

Unravelling the excitation mechanism of very long-period (VLP) tremors in the Gulf of Guinea: evidence for vibrations of thin surface crustal plates

SUMMARY The Gulf of Guinea exhibits a continuous emission of narrow-band and long-period signals (16, 26 and 27 s) on teleseismic records, yet the underlying excitation mechanism remains unclear. This study establishes a connection between these tremors and the vibration of thin, decoupled crustal plates at unexplored volcanoes in the gulf. We first formulate the damped plate oscillation equation, by incorporating the vibration of the thin surface crustal plate and magma flow in the subsurface sill. The findings reveal that a fundamental-mode vibration with a period of several dozen seconds can be induced by a crustal plate that is less than 1.0 km thick but extends over tens of kilometres in both length and width, given a subsurface sill depth exceeding 10.0 cm. The thin plate hypothesis also allows for excitation of a few overtone modes, but such waves in higher frequencies diminish over long distances, leaving only the monotonous fundamental-mode vibration at teleseismic stations. The long duration of Guinea tremors at each recurrence is attributed to the presence of low viscosity basaltic magma, which influences the damping factor. Direct wave loads at the shallow gulf serve as the primary vibration source, accounting for seasonal variations and recurring patterns. Sporadic energy bursts may also occur due to large storms. Radiation patterns of Guinea tremors are linked to the geometric structure of the thin plate. Our theoretical estimates of tremor spectra closely align with observed data, confirming the model’s accuracy in capturing reported Guinea tremor characteristics. This study provides valuable insights into the origins of very long-period tremors at continental volcanoes.

Research on damage identification of jacket structure under wind and wave loads based on variational mode decomposition and chirplet transform

To conduct damage localization and damage quantification of jacket structure, a new damage identification approach based on variational mode decomposition (VMD) and chirplet transform (CT) is firstly introduced. Three kinds of environmental loads, namely, regular wave load, irregular wave load, and wind load, are set on the jacket structure to simulate the real environment of the jacket as much as possible. The acceleration response signals of each node of the damaged bar are extracted and analyzed by VMD and CT. The proposed method is used to analyze the time-frequency energy changes before and after damage for damage localization. Then, the time-frequency entropy of the damage location is further calculated for damage quantification. The feasibility of the introduced method is verified by setting different operating conditions, and the results show that the proposed method can locate and quantify the damage of the jacket under different environmental loads.