Maximum Wave Force Research Articles

Investigations on the second-order transient gap resonance induced by focused wave groups

Two or more marine structures deployed side by side may encounter strong water-body resonances within narrow gaps between them. It may cause significant wave loads on structures and the green water phenomenon on the deck. In this article, the transient fluid motion within a narrow gap formed by two fixed boxes suffered from incident focused wave groups is investigated using a two-dimensional viscous flow numerical wave flume. The focused wave groups adopted have the spectral peak frequency equal to half the fluid resonant frequency inside the gap. The wave fields both inside the gap and around the two-box system, the response/damping time of the transient wave surfaces inside the gap, the maximum wave forces and the ratios of the 2nd-order to the corresponding 1st-order wave surfaces/forces are investigated. It is revealed that the most dangerous place to green water is always the front edge of the two-box system. The damping time of the 2nd-order wave surface is significantly larger than that of the 1st-order one. As the incident wave amplitude rises, the ratios of the 2nd-order to the first-order wave surfaces/forces becomes increases gradually and can even exceed 100% for the wave surface, the horizontal wave force and the moment.

Numerical study of the effect of wind above irregular waves on the wave-induced load statistics

A wind-forcing model is implemented into a fully nonlinear potential flow solver for water wave propagation. The model is suited for simulations of a large number of waves and for generation of fully nonlinear wave kinematics. The direct effect of wind is achieved through Jeffreys sheltering mechanism, which models the form drag on steep waves by a varying surface pressure. We detail the implementation and examine the effect of the model parameters, which consist of a sheltering coefficient and a threshold of the spatial slope of the wave for activation of the wind model. Next, we present the calibration and application of the model for reproduction of a test campaign for the effect of wind over waves on the wave-induced loads on a vertical surface piercing cylinder. The experimental study has been reported in ( Kristoffersen et al., 2021 ) and consisted of four storm sea states, each run with a duration equivalent to 30 h (full scale), with and without a simultaneous scaled wind field above the waves in the flume. After calibration, the numerical model is able to reproduce many of the findings from the experimental study. When wind forcing is added and the significant wave height is kept fixed, the crest statistics are slightly suppressed in the tail by the presence of wind. The wind, however, leads to a pronounced increase in the wave steepness and to a larger number of breaking waves. Despite the increased number of breaking waves, the depth integrated inline force was only found to increase slightly for the most extreme events at small exceedance probabilities. In contrast, the local force in the vicinity of the free surface was found to increase significantly, at short term exceedance probabilities up to 10 −2 , which is consistent with the measured pressures. For the numerical force profile along the vertical direction of the pile, we found that the altitude of maximum wave force is lowered with the introduction of wind. All of these findings are consistent with the experimental observations. Further for the numerical wave-induced local force at short term exceedance probability of 10 −4 , an increase by a factor of 1.8 was found from the introduction of wind. Although the effect on the global inline force was less strong, this local effect is important for design. The present numerical approach offers a direct way to establish such design loads.

3D Numerical Modeling and Quantification of Oblique Wave Forces on Coastal Bridge Superstructures

Simply supported bridges comprise the majority of bridge systems in coastal communities and are susceptible to severe damage from extreme waves induced by storms or tsunamis. However, the effects of oblique wave impacts have been less investigated due to the lack of appropriate numerical models. To address this issue, this study investigates the effects of wave incident angles on coastal bridge superstructures by developing an advanced computational fluid dynamics (CFD) model. Different wave scenarios, including wave height, relative clearance, incident angle, and wavelength are tested. It is found that the maximum wave forces in the horizontal and longitudinal directions could reach 1901 and 862 kN under extreme conditions, respectively, destroying bearing connections. Three surrogate models, i.e., the Gaussian Kriging surrogate model, the Artificial Neural Network (ANN), and the Polynomial Chaos Expansion (PCE), are established by correlating the wave parameters with the maximum wave forces. Through comparisons among the three surrogate models, it is found that the 3-order PCE model has better performance in predicting loads in vertical and horizontal directions, while the ANN model is more suitable for results in the longitudinal direction. This study contributes to the optimized design of coastal bridges and also offers an opportunity for future studies to investigate hazard damage-mitigation measures.

Experimental study of wave force on breakwater head under oblique waves

The head of a breakwater warrants special consideration to achieve the necessary stability at vulnerable part of its structure. To widen the entrance to a harbour, a caisson is used for the breakwater head. Therefore, the wave force on the caisson head under oblique waves was analysed in this study. Physical model tests were performed in a wave tank, where wave loads on two weathering sections (S1 and S2) of the caisson head were measured under oblique-regular and irregular wave attacks. The results have shown that the improved Goda’s method can predict the wave forces on the caisson head. The wave forces on the two sections increased with an increase in the period under different incident angles. The phase lag between the horizontal forces on S1 and S2 was evidently influenced by the incident angle. The relationship between the maximum wave force on one section and its accompanying wave force on another section was described, and the results have demonstrated that under the same incident angle, as the period increased, the maximum wave force of S1/S2 is gradually equal to its accompany wave force of another section.

SPH study of wave force on simplified superstructure of open-type sea access road

A numerical study is performed on the horizontal and uplift wave forces acting on open-type sea access roads. Numerical simulations are performed using the 2D δ-SPH model. In boundary condition, the static pressure difference between the fixed ghost particle and its interpolation point is calculated considering the distance between the interpolation node and the free surface. To avoid improper dynamic pressure measurements, an improved pressure measurement technique is incorporated with the numerical model. To increase the calculation accuracy for the upper region of the sea access road under wave conditions involving a large wave height with overtopping, Adaptive Particle Refinement (APR) is performed. Comparison of the numerical and experimental results demonstrates the high accuracy of the SPH scheme. Based on the numerical results, the characteristics of the wave force on the sea access road are investigated. Furthermore, the maximum horizontal and uplift wave forces on the sea access road are presented for cases involving different water depths, wave heights and wave periods. In this manner, the effects of the wave period on the wave force are clarified. Finally, the influence of the seaside slope on the wave force is examined.

Experimental Study of Forces Influencing Vertical Breakwater under Extreme Waves

In order to understand the extreme wave acting on the vertical breakwater, a series of experiments were constructed in the wave tank to measure the variations of pressure on the front, rear faces, and below the caisson due to overtopping waves. The front and backward horizontal forces and the uplift forces were estimated by integrating the dynamic wave pressure distributions. The COBRAS numerical model was also used to calculate the wave loads under various overtopping waves. The measured wave pressures and wave forces were compared with the predictions of numerical results and showed good agreement. It was found that the forces acting on the backward side of the vertical structure induced by the wave overtopping should be considered. From the experimental data, new semi-empirical equations for calculating the maximum wave forces are proposed using a least squares approximation.

Experimental and numerical investigation on wave impacts on box-girder bridges

Climate change could result in more extreme weather events and induce increasing challenges to the low-lying coastal bridges. The structural performance of box-girder bridges under wave impacts was seldom investigated. In this paper, a three-dimensional (3D) computational fluid dynamics (CFD) model is established to simulate the wave-bridge interactions, and laboratory experiments are conducted to investigate wave impacts on a bridge. The experiments and 3D CFD simulations are unique as compared with other relevant studies since they provide the complex wave-bridge interactions through dynamic and spatial analyses. Specifically, time histories of vertical and horizontal wave forces are measured through experiments. The time-dependent pressure distributions, wave-induced forces, and overturning moments on the bridge model are computed with the CFD model. The effects of different parameters on the maximum wave forces are discussed. Also, comparisons of the differences between two-dimensional (2D) and 3D CFD models are conducted. Then, the results are converted to a prototype scale to explore the effects of wave impacts, and prediction formulas are proposed accordingly. This study combining experimental and 3D numerical investigations could help improve understanding of the wave-bridge interaction mechanism, and further aid the optimal and robust designs of coastal bridges.

Assessment of dynamic pressure and wave forces on vertical-caisson type breakwater

The design and construction of coastal structures such as breakwaters, at great water depths is rapidly increasing as a result of the increasing draught of large vessels and off-shore land reclamations. Vertical caisson breakwaters may be the best alternative compared to ordinary rubble mound breakwaters in larger water depths, in terms of performance, total costs, environmental aspects, construction time and maintenance. To fulfilling the functional utility and impact of the structure on the sea environment, it is necessary to study the hydraulic performance. This can be found by field investigation, numerical simulations and by physical modelling. Scale modelling techniques are used to study various coastal engineering problems. This article presents the results obtained by conducting series of experiments in two-dimensional wave flume to assess the hydrodynamic performance of vertical-caisson breakwater, which is made of concrete, with the protection of toe. The dynamic pressure distribution, wave runup, wave reflection, wave forces and stability parameter on the vertical caisson breakwater are discussed. The maximum wave force on the wall breakwater is calculated from measured pressure values and is compared with the forces calculated by Goda’s and Sainflou wave theories.

Spatial Variation of Wave Force Acting on a Vertical Detached Breakwater Considering Diffraction

In this study, the analytical solution for diffraction near a vertical detached breakwater was suggested by superposing the solutions of diffraction near a semi-infinite breakwater suggested previously using linear wave theory. The solutions of wave forces acting on front, lee and composed wave forces on both side were also derived. Relative wave amplitude changed periodically in space owing to the interactions between diffracting waves and standing waves on front side and the interactions between diffracting waves from both tips of a detached breakwater on lee side. The wave forces on a vertical detached breakwater were investigated with monochromatic, uni-directional random and multi-directional random waves. The maximum composed wave force considering the forces on front and lee side reached maximum 1.6 times of wave forces which doesn’t consider diffraction. This value is larger than the maximum composed wave force of semi-infinite breakwater considering diffraction, 1.34 times, which was suggested by Jung et al. (2021). The maximum composed wave forces were calculated in the order of monochromatic, uni-directional random and multi-directional random waves in terms of intensity. It was also found that the maximum wave force of obliquely incident waves was sometimes larger than that of normally incident waves. It can be known that the considerations of diffraction, the composed wave force on both front and lee side and incident wave angle are important from this study.

Numerical investigation on the wave force characteristics of multi-cylinder with equilateral-triangular arrangement

Based on the open source program DualSPHysics, a numerical investigation is carried out on the hydrodynamic characteristics of multi-cylinder with equilateral-triangular arrangement and the wave field distribution characteristics under the action of regular waves. With the SPH method, the hydrodynamic response characteristics of multi-cylinder with equilateral-triangular arrangement are analyzed under different wave directions. The phase difference distribution characteristics of the wave force on multi-cylinder with equilateral-triangular arrangement are analyzed, as well as the wave field distribution characteristics under different wave angles. In addition, the wave force distribution characteristics and the phase difference distribution characteristics of multi-cylinder with equilateral-triangular arrangement are explored under different wave parameters (wave period and wave height). Through the observations of the hydrodynamic forces induced by the wave, the phase difference of these forces on upstream cylinder and downstream cylinder is the largest when the wave angle is 30°. The maximum wave force of the cylinder is roughly proportional to the distance between the center of the cylinder and the x-axis centerline of the wave field.

The influence of incident angles and length-diameter ratios on the round-ended cylinder under regular wave action

The round-ended cylinder is commonly applied in coastal engineering as foundation. While researches related to the round-ended cylinder are pretty limited. In the present study, the influence of the incident wave angles and length-diameter (LD) ratios is investigated through numerical simulation. An equation is then proposed to calculate the maximum horizontal wave force based on numerical solutions and verified by random cases. Additionally, results of numerical simulation, proposed equation, the Chinese design code and the American design code are compared with each other. The results show that the proposed equation has good accuracy and the product of a safety factor, in the range of 1.5–2.0, with the proposed equation result is recommended in practical engineering. Besides, small LD ratios are suggested to be adopted in the structure design.

Blind-Test Numerical Simulation of Tsunami Wave Pressure Acting on a Land Structure

The prediction performance of numerical models of tsunami wave pressure on land structures was investigated using blind tests. Two types of numerical models were used, based on the volume-of-fluid (VOF) method. Both models reproduced the experimental results well for water-level time series. For wave-pressure time series, some differences were observed between the two models in the vertical distribution of wave pressure during the initial rise. In both models, however, the experimental results showed that overall trends for total wave force were in good agreement. The experimental results produced a value slightly higher than the maximum wave force, suggesting that caution is needed when designing structures to ensure that wave force is not underestimated.

Numerical Simulation of Solitary Wave Forces on A Vertical Cylinder on A Slope Beach

Wave forces acting on a vertical cylinder at different locations on a slope beach in the near-shore region are investigated considering solitary waves as incoming waves. Based on the Reynolds-averaged Navier-Stokes equations and the k-ε turbulence model, wave forces due to the interaction between the solitary wave and cylinder are simulated and analyzed with different incident wave heights and cylinder locations. The numerical results are first compared with previous theoretical and experimental results to validate the model accuracy. Then, the wave forces and characteristics around the cylinder are studied, including the velocity field, wave surface elevation and pressure. The effects of relative wave height, Keulegan-Carpenter (KC) number and cylinder locations on the wave forces are also discussed. The results show that the wave forces exerted on a cylinder exponentially increase with the increasing incident wave height and KC number. Before the wave force peaks, the growth rate of the wave force shows an increasing trend as the cylinder moves onshore. The cylinder location has a notable effect on the wave force on the cylinder in the near-shore region. As the cylinder moves onshore, the wave force on the cylinder initially increases and then decreases. For the cases considered here, the maximum wave force appears when the cylinder is located one cylinder diameter below the still-water shoreline. Furthermore, the fluid velocity peaks when the maximum wave force appears at the same location.

Characteristics of wave forces on pile group foundations for sea-crossing bridges

The pile group foundation of sea-crossing bridges has various structural forms, and its wave force characteristics are complex. In this study, the Morrison equation and the boundary element method were utilized to establish a calculation model for predicting the maximum wave forces on the pile group foundation with a square pile cap. Moreover, hydrodynamic models of pile group foundations were designed according to the gravity similarity criterion. On this basis, the model test and analytical calculation were carried out to investigate the effect of pile spacings, pile slopes, conical slopes (on the top of the pile cap), and wave parameters on wave forces of pile group foundations. In addition, impact characteristics of waves on the foundation were also analyzed. The results shown that larger pile spacings and pile slopes reduced the wave forces on the foundation, but this relationship weakened with the rise of the water level. The inclined pile could be regarded as a vertical pile for calculating wave forces at high water level. The conical slope increased the water-blocking area on the pile cap, which led to the increase of wave forces on the foundation. When the wave only acted on the pile group, the wave forces on the single pile firstly decreased then increased with the increase of frequencies, and lower wave frequencies (larger periods) induced stronger nonlinear factors of the waves. When the water level was near the bottom of the pile cap, larger wave periods increased the vertical wave forces on the pile cap. The wave impact mainly occurred in the time range from the pile cap first contacting with the wave to the wave crest reaching the middle of the pile group foundation.

Experimental investigations on wave impact pressures under the deck and global wave forces and moments on offshore jacket platform for partial and full green water conditions

The wave induced dynamic pressures under the deck and the global wave forces and moments on an offshore platform model were measured for three different model orientations and for partial and full green water conditions in random wave fields of different energy levels. It is found that for partial and full green water conditions, the global vertical wave force dominates when compared to horizontal wave forces. The orientation of the structure to wave direction has some effect, only for 22.5° orientation of the deck to wave direction. Shoreward maximum wave force can reach 3 times the maximum seaward wave force. For zero air gap condition, the highest value of normalized peak vertical force can reach a value of 42, which is 5 times higher than the normalized significant uplift force value. The normalized downward peak force value can reach as high as 8 for full green water condition due to the weight of overrunning water staying on the top of deck slab. For zero air gap condition, the normalized peak impact pressure under the deck can reach as high as 13.2 and 21.5 near the leading and trailing bottom side of the deck.

Interaction between oblique waves and arc-shaped breakwater: Wave action on the breakwater and wave transformation behind it

The hydrodynamic interaction between oblique waves and an arc-shaped breakwater and the wave field behind it. A three-dimensional computational fluid dynamic model was used to simulate the interaction between the oblique waves and arc-shaped breakwater. The pressure distribution and wave force in the different sections under different wave directions were measured by experiments to validate the numerical results. The pressure distribution and wave force in the arc-shaped vertical part of the breakwater along the central axis were further analysed using numerical model. The maximum positive and negative forces in each section along the central axis were compared. The results indicated that the arc curvature exerted little effect on the maximum wave force in the different sections. The wave height behind the breakwater was obviously smaller than that at the front. With the decrease in the incident angle, the influence of diffraction on the wave field gradually decreased. Under east–southeast waves, the maximum wave height behind the breakwater caused by overtopping was approximately 0.7 times the incident-wave height. In the spatial distribution of the wave period behind the breakwater, some areas with smaller periods existed, which may be caused by the overtopping flow that broke behind the breakwater.

Characteristics of Breaking Wave Forces on Piles over a Permeable Seabed

Most offshore wind turbines are installed in shallow water and exposed to breaking waves. Previous numerical studies focusing on breaking wave forces generally ignored the seabed permeability. In this paper, a numerical model based on Volume-Averaged Reynolds Averaged Navier–Stokes equations (VARANS) is employed to reveal the process of a solitary wave interacting with a rigid pile over a permeable slope. Through applying the Forchheimer saturated drag equation, effects of seabed permeability on fluid motions are simulated. The reliability of the present model is verified by comparisons between experimentally obtained data and the numerical results. Further, 190 cases are simulated and the effects of different parameters on breaking wave forces on the pile are studied systematically. Results indicate that over a permeable seabed, the maximum breaking wave forces can occur not only when waves break just before the pile, but also when a “secondary wave wall” slams against the pile, after wave breaking. With the initial wave height increasing, breaking wave forces will increase, but the growth can decrease as the slope angle and permeability increase. For inclined piles around the wave breaking point, the maximum breaking wave force usually occurs with an inclination angle of α = −22.5° or 0°.

Numerical and experimental investigation of breaking wave forces on a monopile-type offshore wind turbine

Monopiles are the most commonly used foundation types for offshore wind turbines. This study investigates numerically and experimentally the effects of breaking wave impact on a monopile-type offshore wind turbine installed at different locations at the edge of a 1:25 slope. The numerical model uses a two-phase flow model based on solving the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations with using the volume of fluid method and the k-ω shear stress transport turbulence model. Typical environmental conditions from the East China Sea have been examined. The wave run-up around the monopile and the nonlinear total horizontal wave force on the monopile are examined and compared with relevant experimental data originally presented in the present paper in order to validate the accuracy of the developed numerical model. A good agreement between the experimental data and numerical predictions is observed. Moreover, the wave breaking evolution and impact kinematics are investigated numerically for the different monopile locations. The results show that there is a 23.5% interval between the maximum wave force in the breaking zone and the wave force at the beginning of breaking. The first-order energy proportion of the breaking wave force will decrease maximum 61.65%, while, the second-order and high-order energy proportion of the breaking wave force will increase maximum 25.92% and 17.57%, respectively, between the different examined monopile locations. The time of occurrence of the secondary load cycle has no great relation with the form of the breaking wave for all examined locations, and the duration time of secondary load cycle impact on the monopile lasts for approximately 16.2% of the wave period. The secondary load cycle is smaller compared to the total horizontal breaking force in a range between 16.37% and 8.5%. The pressure on the monopile increases along with the wave breaking gradually. Compared with the pressure impact on the monopile when the wave begins to break, the pressure exerted on the monopile after the wave is rolled increases by 149%.

Three-Dimensional Simulations of Offshore Oil Platform in Square and Diamond Arrangements

The interaction of the solitary wave with an oil platform composed of four vertical circular cylinders is investigated for two attack angle of the solitary wave β = 0 ° (square arrangement) and β = 45 ° (diamond arrangement). The solitary wave is generated using an internal source line as proposed by Hafsia et al. (2009). This generation method is extended to three-dimensional wave flow and is integrated into the PHOENICS code. The volume of fluid approach is used to capture the free surface evolution. The present model is validated in the case of a solitary wave propagating on a flat bottom for H / h = 0.25 where H is the wave height and h is the water depth. Compared to the analytical solution, the pseudowavelength and the wave crest are well reproduced. For a solitary wave interacting with square and diamond cylinders, the simulated results show that the maximum run-ups are well reproduced. For the diamond arrangements, the diffraction process seems to not affect the maximum run-ups, which approached the isolated cylinder. For the square arrangement, the shielding effect leads to a maximum wave force more pronounced for the upstream cylinder array.

Solitary Wave Diffraction with a Single and Two Vertical Circular Cylinders

This study investigates the three-dimensional (3-D) solitary wave interaction with two cylinders in tandem and side-by-side arrangements for two wave heights. The solitary wave generation and propagation are predicted using the volume of fluid method (VOF) coupled with the NavierStokes transport equations. The PHOENICS code is used to solve these transport equations. The solitary wave generation based on the source line developed by Hafsia et al. (2009) is extended in three-dimensional wave flow and is firstly validated for solitary waves propagating on a flat bottom. The comparison between numerical results and analytical solution for small wave height H / h = 0.1 and 0.2 shows good agreements. The wave crest and the pseudo-wavelength are well reproduced. Excellent agreements were found in terms of maximum run-up and wave forces by comparison with the present model and analytical studies. The present model can be tested for the extreme solitary wave to extend its application to a more realistic case study as the solitary wave diffraction with an offshore oil platform.