Relative Freeboard Research Articles

Empirical Predictions on Wave Overtopping for Overtopping Wave Energy Converters: A Systematic Review

Over the past three decades, the development and testing of various overtopping wave energy converters (OWECs) have highlighted the importance of accurate wave run-up and overtopping predictions on those devices. This study systematically reviews the empirical formulas traditionally used for predicting overtopping across different types of breakwaters by assessing their strengths, limitations, and applicability to OWECs. This provides a foundation for future research and development in OWECs. Key findings reveal that empirical formulas for conventional breakwaters can be categorized as mild or steep slopes and vertical structures based on the angle of the slope. For the same relative crest freeboards, the dimensionless average overtopping discharge of mild slopes is larger than that of vertical structures. However, the formula features predictions within a similar range for small relative crest freeboards. The empirical formulas for predicting overtopping in fixed and floating OWECs are modified from the predictors developed for conventional breakwaters with smooth, impermeable and linear slopes. Different correction coefficients are introduced to account for the effects of limited draft, inclination angle, and low relative freeboard. The empirical models for floating OWECs, particularly the Wave Dragon model, have been refined through prototype testing to account for the unique 3D structural reflector’s influence and dynamic wave interactions.

Computational Study of Overtopping Phenomenon over Cylindrical Structures Including Mitigation Structures

Wave overtopping occurring in offshore wind renewable energy structures such as tension leg platforms (TLPs) or semi-submersible platforms is a phenomenon that is worth studying and preventing in order to extend the remaining useful life of the corresponding facilities. The behaviour of this phenomenon has been extensively reported for linear coastal defences like seawalls. However, no referenced study has treated the case of cylindrical structures typical of these applications to a similar extent. The aim of the present study is to define an empirical expression that portrays the relative overtopping rate over a vertical cylinder including a variety of bull-nose type mitigation structures to reduce the overtopping rate in the same fashion as for the linear structures characteristic of shoreline defences. Hydrodynamic interaction was studied by means of an experimentally validated numerical model applied to a non-impulsive regular wave regime and the results were compared with the case of a plain cylinder to evaluate the expected improvement in the overtopping performance. Four different types of parapets were added to the crest of the base cylinder, with different parapet height and horizontal extension, to see the influence of the geometry on the mitigation efficiency. Computational results confirmed the effectivity of the proposed solution in the overtopping reduction, though the singularity of each parapet geometry did not lead to an outstanding difference between the analysed options. Consequently, the resulting overtopping decrease in all the proposed geometries could be modelled by a unique specific Weibull-type function of the relative freeboard, which governed the phenomenon, showing a net reduction in comparison with the cylinder without the geometric modifications. In addition, the relationship between the reduced relative overtopping rate and the mean flow thickness over the vertical cylinder crest was studied as an alternative methodology to assess the potential damage caused by overtopping in real structures without complex volumetric measurements. The collection of computational results was fitted to a useful function, allowing for the definition of the overtopping discharge once the mean flow thickness was known.

Full-scale experiments on wave transmission and stability of oyster shell-filled bag berms

Oyster shell-filled bags have been used in engineered reefs and living shorelines as a nature-based solution to attenuate wave energy and stabilize shorelines. However, due to limited scientific data, uncertainties persist in accurately predicting the performance of these reefs, which can hinder a more widespread adoption. In particular, there is a lack of information on wave transmission through, and the stability of, oyster shell-filled bag berms with different configurations and relative freeboards. To address this knowledge gap, a full (1:1) scale experimental flume study was conducted to measure the wave transmission and stability of six different oyster shell-filled bag berms under a range of incident wave conditions and water levels. The findings from the experimental tests were used to propose empirical equations for wave transmission and stability, which can assist practitioners in predicting the performance of these engineered reefs.

Hydraulic Model Experiments and Performance Analysis of Existing Empirical Formulas for Overtopping Discharge on Tetrapod Armored Rubble Mound Structures with Low Relative Freeboard

In coastal structure design incorporating revetments, the assessment of wave overtopping discharge relies on hydraulic model experiments. Numerous empirical formulas have been developed to predict overtopping discharge based on quantitative data from these experiments. Typically, for revetment structures aimed at mitigating wave overtopping, crest height is determined by considering the maximum amplitude of the design wave, resulting in a relatively high freeboard compared to wave heights. However, achieving complete prevention of all wave overtopping would require the crown wall to have substantial crest heights, rendering it economically impractical. Therefore, the concept of limiting discharge has been introduced in the design of revetment structures, aiming to restrict wave overtopping discharge to an acceptable level. Consequently, many coastal structures in real-world settings feature relatively lower freeboard heights than incident wave heights. This study investigated wave overtopping discharge on rubble-mound breakwaters with relatively low freeboard heights through hydraulic model experiments. Furthermore, it conducted a comparative analysis of the predictive capabilities of existing empirical formulas for estimating overtopping discharge using experimental data.

Wave Pressures Acting On The Pavement Behind The Sloping Revetment

A physical experiment was performed to seek an empirical equation predicting the wave force acting on the upper surface of the pavement behind the revetment parapet due to wave overtopping as well as the uplift force acting on the underlayer of the pavement induced by the wave pressure passing through the core layers of the revetment. The experiment was carried out by installing pressure transducers along the upside and downside of the pavement with different configuration of the parapet, water depth, relative freeboard, and armor layer thickness. Then, the wave pressure and force on the pavement was analyzed under various incoming wave conditions. Based on the analysis results, major parameters affecting the wave forces were identified and an empirical equation for evaluating the forces on the pavement is suggested.

Experimental Study On The Effect Of The Wavelength On Wave Overtopping Over Recurved Walls

Wave overtopping phenomenon on vertical breakwaters is influenced by various physical parameters, encompassing wave height, period, water depth at the breakwater, breakwater freeboard, and foreshore steepness. Existing equations for estimating overtopping rates predominantly rely on the relative freeboard (Rc/Hm0) as the key parameter. This study highlights a significant deviation from this conventional approach when utilizing a recurved wall instead of a plain vertical wall, emphasizing the necessity to consider additional parameters, particularly wave period. In our quest for enhanced accuracy in estimating wave overtopping over recurved breakwaters, we have used F'=Rc/ (Hm02 Lp)1/3, as a replacement for the conventional relative freeboard. Comparative analyses reveal that the proposed formulas for both impulsive and non-impulsive waves exhibit superior accuracy compared to existing formulas. Nevertheless, it is noteworthy that, for larger relative freeboards, a robust formula for estimating wave overtopping remains elusive.

Estimate of Wave Overtopping Rate on Armoured Slope Structures Using FUNWAVE-TVD Model

In this study, the program was modified by adding the empirical formula of EurOtop (2018) to enable calculation of wave overtopping on armoured slope structures in the FUNWAVE-TVD model using the fully nonlinear Boussinesq equation. The validity of the modified numerical model was verified by comparing it with CLASH data and experiment data for the rubble mound structure. This model accurately reproduced the change in wave overtopping rate according to the difference in the roughness factor of the armoured block, and well reproduced the rate of decrease in wave overtopping rate due to the increase in relative freeboard. The overtopping rate of the armoured slope structures showed significant differences depending on the positioning condition of the armoured blocks. When Tetrapods were placed with regular positioning, the overtopping rate increased significantly compared to when they were placed with random positioning, and it was consistent with when they were placed with Rocks. Meanwhile, when rocks were placed in one row, the wave overtopping rate was greater than when rocks were placed in two rows, which is believed to be due to the influence of the roughness and permeability of the structure’s surface.

An experimental study on wave transmission by engineered plain and enhanced oyster reefs

This study examines the interaction between random waves and an oyster reef, both in its plain state and when enhanced by energy dissipating macro-roughness. The investigation was carried out using wave flume experiments, incorporating different water levels and wave conditions. The primary focus of the study revolves around two key parameters: freeboard and wave steepness. Additionally, the study explores the influence of macro-roughness arrangement on the wave energy transmission. Empirical relationships were established to determine the wave transmission coefficient for both the plain reef and the reef enhanced by macro-roughness. These relationships highlight the significance of the relative freeboard and wave steepness for the plain oyster reef. Moreover, a correction factor was introduced to account for the impact of macro-roughness configuration on the wave transmission coefficient. The findings of this study suggest that the incorporation of macro-roughness can effectively attenuate wave energy through dissipation and reflection, thereby serving as an additional measure for wave energy mitigation through nature-based solutions.

WAVE OVERTOPPING REDUCTION BY MODULAR CONCRETE ARMOUR UNITS

This paper describes a new armour unit called XP-Overtop which is applied together with XblocPlus armour units in a modular armour layer in order to reduce wave overtopping. This unit is placed close to the crest of the structure. Physical model tests have been performed to study the hydraulic stability and the overtopping reduction of the XP-Overtop as a function of the relative freeboard. Based on the model tests performed, the following conclusions can be drawn: 1) XPOvertop generates substantial overtopping reduction which increases with increasing relative freeboard; 2) because of the limited effectiveness and hydraulic stability for a low relative freeboard, it is not recommended to apply XP-Overtop for structures with a relative freeboard below Rc/Hm0=1; 3) the roughness factor γf for a structure with XP-Overtop is a function of the relative freeboard and varies between γf=0.42 and γf=0.41; 4) XP-Overtop enables a designer to reduce the crest level of a structure; 5) this reduction translates to significant reductions in the construction materials, costs and CO2 emissions.

VIOLENT AND IMPULSIVE WAVE OVERTOPPING AT VERTICAL WALLS WITH LARGE FREEBOARDS

Vertical walls are designed and built to protect coastal areas or harbours. Typically, these structures are installed in relatively deep water where incoming waves are reflected without breaking. In such cases the available prediction methods for wave overtopping discharge are well established. When the relative water depth h/Hm0 becomes smaller, waves start shoaling on the foreshore and breaking can occur leading to impulsive conditions. The present overtopping prediction methods (EurOtop, 2018) under impulsive conditions have been proposed by Van der Meer and Bruce (2014) including data from the VOWS project (Bruce et al.; 2001). Wave overtopping is strongly related to the relative freeboard Rc/Hm0, and for impulsive overtopping EurOtop suggests that for Rc/Hm0 greater than 3 there still might be significant overtopping but there is no data to validate such an extrapolation. Also the well-known overtopping graphs of Goda (2000) show that overtopping could be present for very large freeboards and impulsive waves. The objective of the present research is to investigate the mean discharge and volumes per wave from impulsive and violent overtopping at vertical walls with very large freeboards (up to Rc/Hm0 = 10).

Physical Model Tests for Mean Wave Overtopping Discharge of Rubble-mound Structure Covered by Tetrapods: <i>R<sub>C</sub>/A<sub>C</sub></i> = 1 and cot<i>a</i> = 1.5 Conditions

The allowable mean overtopping discharge is used as a design parameter for coastal structures. The crest elevation of coastal structures should ensure the wave overtopping discharge within acceptable limits for structural safety and the safety of pedestrians, vehicles, operations, and so on. In this study, two-dimensional physical model tests on typical rubble-mound structure geometries were performed and the the mean wave overtopping discharges under various water depth and wave conditions were measrued. The various test conditions were applied to the tests with the change of the wave steepness, relative freeboard and relative wave height. An empirical formula from the experimental data was proposed to predict the mean wave overtopping volumes.

The effect of variations in water level on wave overtopping discharge over a dike: An experimental model study

The water level during a storm event is never constant but variable in nature. A variable water level leads to varying crest freeboards at the coastal defense structure. A change in crest freeboards is directly linked to a changing average overtopping discharge q over the coastal defense structure. The existing prediction formulae for q are developed for constant water level ( C W L ) and do not take into account its variability ( V W L — variable water level) during a storm event. Hence, in this study the influence of the V W L on q was investigated experimentally. Model tests were conducted in the wave flume facility at Ghent University, where a range of V W L was modelled as representative for typical storm surges (total variation of the water level d h = 0.75–4.8 m) and a range of storm durations (time t = 2.7–22 h). During testing the q for these cases of V W L over a reference impermeable sloping (seaward slope of the structure cot( α ) = 2) dike structure was measured. Initial validation of model results for the C W L situation showed that the model setup was capable of reproducing the predicted q values from Eurotop (2018). For the V W L situation it was noted that the existing prediction formulae (Eurotop, 2018) are overestimating the measured q value, especially for smaller relative crest freeboards (relative freeboards R c / H m 0 < 1 . 5 ) when the smallest freeboard is considered. By using linear regression a new equivalent relative crest freeboard was derived to reduce the difference between q predicted by existing EurOtop (2018) and q measured during variable tests. The new equivalent freeboard is mainly dependant on the relative crest freeboard during the peak of the storm ( R c p e a k / H m 0 ), as well as the total storm surge variation ( d h). The existing formulation from EurOtop (2018) was kept by replacing R c by this new equivalent crest freeboard. The adapted formula for q is able to accurately predict the overtopping discharge for both, C W L and V W L situation. • 2D Physical model tests on wave overtopping performance of a smooth dike. • Influence of variable water level conditions on the average wave overtopping discharge. • New equivalent relative freeboard is determined to include this effect in the EurOtop formula for non-breaking waves. • Predictions are significantly improved with the new equivalent relative freeboard for the new data.

New insights in the probability distributions of wave-by-wave overtopping volumes at vertical breakwaters

Advances in the development of prediction tools for wave overtopping allow now for overtopping volumes to be estimated with good accuracy, with the combined use of mean overtopping rates and maximum wave by wave overtopping volumes in a sequence of wave overtopping events. While previous literature has tended to focus on mean overtopping rates at coastal structures, limited studies have investigated the wave by wave overtopping volumes at coastal sea defences; in particular, a paucity of studies have focussed on the prediction of the shape parameter in the Weibull distribution (i.e., Weibull b) of overtopping volumes. This study provides new insights on the probability distribution of individual wave overtopping volumes at plain vertical seawalls by analysing the measured Weibull b values derived from a series of laboratory experiments on seawalls performed on a wide range of wave conditions and crest freeboards. The influence of wave conditions (wave steepness, significant wave height), structural parameters (crest freeboard, toe water depth), impulsiveness, probability of overtopping waves, and overtopping discharge on Weibull b parameter were examined, and then compared with the well-established empirical formulae. For the conditions covered within this study, it was found that the probability distribution of wave-by-wave overtopping volumes follow a 2-parameter Weibull distribution. No apparent differences in Weibull b values were reported with the variation of incident wave steepness and impulsiveness parameter. Results of this study revealed that Weibull b values at vertical walls, subjected to non-impulsive wave conditions, can be predicted reasonably well using relative freeboard and relative overtopping rates. A new unified formula is proposed for the estimation of Weibull b values at vertical walls under impulsive and non-impulsive wave attack.

STUDY OF MODIFIED PERFORATED BREAKWATER AS RENEWABLE ENERGY DEVICE

Aim: This study investigates to determine the influence of wave steepness, relative freeboard, and breaker parameters on overtopping discharge at a perforated breakwater. Methodology and results: The research method used was using both a numerical model simulations on three-dimensional computational fluid dynamics (CFD) modelling software namely FLOW-3D; and empirical equation computation. The evaluation of both approaches were performed for understanding the characteristics of wave discharge that overtopping the perforated breakwater. The experimental results of modified perforated breakwater revealed that the lowest slope possible with the highest porosity possible can generate the highest value of dimensionless overtopping discharge for wave energy harvesting. Conclusion, significance and impact study: The findings of this study formulated the optimum slope and porosity to the highest wave energy harvested. Further studies recommend that data collection from onsite trials of modified perforated breakwater are performed.

Experimental analysis and numerical simulation of wave overtopping on a fixed vertical cylinder under regular waves

Wave overtopping phenomenon affects relatively narrow offshore marine structures different from shoreline linear structures, where there is not defined a precise prediction methodology as it is the case of the behaviour at long coastal defences. In the present study a combined experimental and numerical approach has been followed to obtain an empirical relation that represents the relative overtopping discharge over a fixed vertical cylinder exposed to non-impulsive wave conditions. The phenomenon follows a Weibull type dependence on the relative freeboard in a similar way as the case of vertical walls but reporting a decreasing overtopping rate at higher freeboards. In addition, a direct linear relationship between the relative mean flow thickness computed at the centre of the circular crest of the cylinder and the relative overtopping discharge has been observed. This methodology may be used as an indirect cost-effective method to characterize experimentally the wave overtopping phenomenon in cylindrical structures of full-scale prototypes without the need of accumulating and characterising huge amounts of overtopped water volumes. The present study contains a systematic analysis of the dispersion obtained in the experimental and computational results to evaluate the performance attributed to the proposed empirical expressions. • Overtopping has been characterized in a fixed vertical cylinder and compared with the behaviour of long shoreline defences. • A RANS-VOF Eulerian numerical model has been validated experimentally with a physical scaled model in a wave flume. • A new Weibull type expression predicts the overtopping discharge in a vertical cylinder for non-impulsive wave conditions. • The flow thickness measured at the crest has been proposed to determine the mean overtopping discharge over the structure.

Adaptation measures for seawalls to withstand sea-level rise

Sea level rise necessitates adaptation measures for coastal protection structures like seawalls as changes in the design conditions will generate higher wave overtopping discharges and coastal flooding. Although increasing crest height is a common measure, the recreational function of urban seawalls limits the applicability. In this paper, performance on overtopping control of crest modifications such as storm walls, parapets, promenade, and stilling wave basin (SWB), are studied for simple and composite vertical seawalls. Two independent physical model studies from Turkey and Italy that cover a wide range of hydrodynamic conditions focusing on low relative freeboard are presented. Reduction factors that can be integrated into EurOtop prediction formulae (2018) are proposed within the experiment boundaries. The results show that a simple promenade, extending landward of a vertical seawall, provides very little reduction, whereas a seaward storm wall, under low freeboard conditions, is not effective as a similar storm wall once located on the landward edge of the promenade. Parapets decrease the overtopping further, however, the increase in relative freeboard influences the effect of parapets. Basin width and storm wall heights are important design parameters for SWB. Although the performance of different SWB configurations converges to lower reduction factors as the relative freeboard decreases, they perform better overall. Further analysis showed that the multiplication of the two individual reduction factors, one for the parapet effects and one for the promenade effects could provide an accurate representation of the composite reduction factor to determine the total effect. However, for complex geometries, it is seen that the composite reduction factors should reflect the interdependency of components when different elements with different mechanisms that change the overtopping discharge exist such as an overtopping bore on the promenade overtopping a storm wall. However, for developing future design guidelines, it is also important to consider the influence of individual components on the composite reduction factors such as the influence of storm wall height for a storm wall at the end of a promenade.

Experimental Investigation of Wave Force on the Pavement behind Crown Wall of Rubble Mound Seawall

Physical experiments were conducted to establish an empirical formula that predicts the wave force on the upside of the pavement behind crown wall of rubble mound seawall due to wave overtopping as well as the uplift force on the downside of the pavement. The experiments were performed by different conditions of the parapet, water depth, relative freeboard, and thickness of the armour layer. Then, the wave force on the upside and downside of the pavement behind the crown wall was analyzed. The parameters that affect the wave overtopping force and the uplift force were identified and empirical formulae were suggested for evaluating the forces on the pavement.

Estimate of Wave Overtopping Rate on Vertical Wall Using FUNWAVE-TVD Model

This study established a numerical model capable of calculating the wave overtopping rate of coastal structures by nonlinear irregular waves using the FUNWAVE-TVD model, a fully nonlinear Boussinesq equation model. Here, a numerical model was established by coding the mean value approach equations of EurOtop (2018) and empirical formula by Goda (2009), and adding them as subroutines of the FUNWAVE-TVD model. The verification of the model was performed by numerically calculating the wave overtopping rate of nonlinear irregular waves on vertical wall structures and comparing them with the experimental results presented in EurOtop (2018). As a result of the verification, the numerical calculation result according to the EurOtop equation of this model was very well matched with the experimental result in all relative freeboard (Rc/Hmo) range under non-impulsive wave conditions, and the numerical calculation result of empirical formula was evaluated slightly smaller than the experimental result in Rc/Hmo &lt; 0.8 and slightly larger than the experimental result in Rc/Hmo &gt; 0.8. The results of this model were well represented in both the exponential curve and the power curve under impulsive wave conditions. Therefore, it was confirmed that this numerical model can simulate the wave overtopping rate caused by nonlinear irregular waves in an vertical wall structure.

Prediction of Wave Transmission Characteristics of Low-Crested Structures with Comprehensive Analysis of Machine Learning.

The adoption of low-crested and submerged structures (LCS) reduces the wave behind a structure, depending on the changes in the freeboard, and induces stable waves in the offshore. We aimed to estimate the wave transmission coefficient behind LCS structures to determine the feasible characteristics of wave mitigation. In addition, various empirical formulas based on regression analysis were proposed to quantitatively predict wave attenuation characteristics for field applications. However, inherent variability of wave attenuation causes the limitation of linear statistical approaches, such as linear regression analysis. Herein, to develop an optimization model for the hydrodynamic behavior of the LCS, we performed a comprehensive analysis of 10 types of machine learning models, which were compared and reviewed on the prediction accuracy with existing empirical formulas. We found that, among the 10 models, the gradient boosting model showed the highest prediction accuracy with MSE of 1.0 × 10−3, an index of agreement of 0.996, a scatter index of 0.065, and a correlation coefficient of 0.983, which indicates a performance improvement over the existing empirical formulas. In addition, based on a variable importance analysis using explainable artificial intelligence, we determined the significant importance of the input variable for the relative freeboard (RC/H0) and the relative freeboard to water depth ratio (RC/h), which confirms that the relative freeboard was the most dominant factor for influencing wave attenuation in the hydraulic behavior around the LCS. Thus, we concluded that the performance prediction method using a machine learning model can be applied to various predictive studies in the field of coastal engineering, deviating from existing empirical-based research.

Spatial distribution of wave-by-wave overtopping behind vertical seawall with recurve retrofitting

Understanding the spatial distribution of wave overtopping water behind coastal protection structures is essential for assessing the safety level of coastal regions behind the coastal defences. The spatial distribution of wave overtopping volume determines the planning and arrangements of critical infrastructures (e.g., railways, roads and buildings) in coastal regions. This study presents a series of laboratory-scale physical modelling experiments to investigate the spatial distribution of wave overtopping volume behind plain vertical seawall and seawall with recurve retrofitting. The hydrodynamic conditions are designed to mimic both swell and storm sea conditions. Tests were conducted for a range of relative freeboard and empirical-based predictive equations were derived for both mean and extreme overtopping events under impulsive and non-impulsive wave conditions. Test results showed that overtopping impact hazard zone reduces up to 87% with the increase of relative freeboard (Rc/Hm0). The hazard zone for extreme overtopping events was found to be up to 3 times of the mean overtopping volumes. The effectiveness of recurve retrofitting on mitigating spatial distribution of wave overtopping were investigated with three recurve prototypes of varying overhang length and recurve's height. It was found that increase in overhang length provides higher reductions in the spatial distribution of hazard zone behind the wall and improve the climate resilience of the seawall. The results highlight that recurve retrofitting is more effective in reducing the length of hazard zone under impulsive wave conditions. The findings of this study provide key data and predictive formulae for robust assessments of the hazard zones behind the key coastal defence infrastructures during mild and extreme climatic events.