Overtopping Discharge Research Articles

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).

INFLUENCE FACTORS FOR CREST WIDTH, ROUGHNESS AND WAVE PERIOD ON OVERTOPPING OF RUBBLE MOUND STRUCTURES

New data was collected in the wave flumes of Ghent University and Aalborg University on wave overtopping discharges over rubble mound structures, focusing on the influence of (large) crest width and surface roughness in combination with wave period. Combining these new data with existing data, analysis has led to the improvement of the guidance for wave overtopping prediction. The data and full analysis are presented in Eldrup et al. (2022). The present extended abstract adds a comparison of this improved guidance to the Neural Network prediction by Formentin et al. (2017), and to the EurOtop (2018) prediction.

THE EFFECT OF WIND STRESS ON WAVE OVERTOPPING ON VERTICAL SEAWALL

Onshore wind can significantly affect wave overtopping process and increase mean overtopping discharge. Thus, the wind should be an important variable in coastal design process. However, despite many researches have analyzed the influence of wind on the overtopping, there is still a lack of exhaustive knowledge about this phenomenon. To further analyze the wind effects, the CFD model FLOW-3D has been used to investigate wave overtopping at vertical seawalls. The single-fluid approach has been adopted, i.e. the presence of wind has been simulated via the wind shear stress on the sea surface. The main aim of this work is to verify the ability of this simplified numerical modelling to capture the macro-processes involved in the phenomenon of wave overtopping. The presence of wind shear stress has led to physically consistent results. It confirmed that as the mean overtopping discharge decreases, as the wind effect increases. Furthermore, numerical results have shown that the advection of water droplets behind the structure by the wind is the key mechanism for the enhancement of wave overtopping. Finally, by gathering numerical results and laboratory data carried out by Durbridge (2021), a new predictive formula to estimate the wind factor is provided.

INVESTIGATION OF DIRECTIONAL SPREADING EFFECT ON WAVE RUN-UP USING SWASH

In order to keep optimal safety of coastal lines, it is necessary to maintain an appropriate crest level of coastal dikes. This is designed based on wave run-up height and/or wave overtopping discharge. Therefore, it is important to estimate wave run-up and overtopping as accurate as possible. However, the influence of directional spreading on wave run-up and overtopping has not been fully understood yet. In this study, non-hydrostatic model SWASH (Zijlema et al., 2011) is used. First, we implemented a wave run-up model in SWASH in 2DV (flume like) and 3D (basin like). Then wave run-up are simulated for some different cases and compared to the existing empirical wave run-up formulas in literature (e.g. Holman, 1986 and Mase, 1989).

2DH modelling and mapping of surfbeat-driven flooding in the shadow of a jettied tidal inlet

Near estuaries and harbours, submerged shoals and defence structures impact the exposure to overtopping. These features may be accounted for in two-dimensional horizontal (2DH) numerical models, either based on phase-resolving or phase-average solvers for wave propagation. In between, surfbeat solvers, such as in XBeach, combine an affordable computational cost with the ability to generate and propagate the longer infragravity (IG). However, surfzone wave characteristics and the overtopping exposure modelled with XBeach are sensitive to settings such as the shape of the forcing wave spectra and the numerical scheme for wave propagation. The present paper explores this sensitivity and assesses the performance of different inundation models built with the 2DH surfbeat solver of XBeach. These models were forced with downscaled water levels and directional wave spectra and the results fuelled a discussion bounded by data collected downdrift of the entrance to the harbour of Figueira da Foz (Portugal). The original second-order upwind scheme, which propagates short-waves with a lower numerical diffusion improved the model performance in terms of long-wave height, and an unconventional breaking criterion better represented the cross-shore distribution of short-wave height near the shore. A calibrated model was validated through the hindcast of an overtopping event observed under moderate swell forcing, and was used to map the overtopping exposure during a hypothetical combination of an energetic swell with a water level having a return period of ∼70 years. Compared to the default wave spectra shape and model settings, using an appropriate representation of the short-wave directional spectrum at the open boundary was necessary to reproduce the observed overtopping extent. Refining the cross-shore resolution of the model helped to better represent the observed inundation extents, as also did the reduction of the friction coefficient. Additional phase-resolving simulations in 1DH overestimated IG wave energy and produced higher and more frequent overtopping discharges. However, differences with the calibrated 2DH surfbeat model increased with the proximity of the inlet and with short-wave height and angle of incidence. Overall, required calibration steps were provided. They aim at making 2DH XBeach surfbeat a credible tool for 1) predicting short and IG wave characteristics until the shoreline, as well as for 2) providing first estimates of exposure to overtopping in areas with shallow and alongshore-irregular morphologies.

Physical Model Experiment for Estimating Wave Overtopping on a Vertical Seawall under Regular Wave Conditions for On-Site Measurements

Apart from implementing hardware solutions like raising the crest freeboard of coastal structures to efficiently counter wave-overtopping, there is a simultaneous requirement for software-driven disaster mitigation strategies. These tactics involve the swift and accurate dissemination of wave-overtopping information to the inland regions of coastal zones, enabling the regulation of evacuation procedures and movement. In this study, a method was proposed to estimate wave-overtopping by utilizing the temporal variation of wave heights exceeding the structure’s crown level, with the aim of developing an on-site wave measurement system for providing wave-overtopping information in the field. Laboratory model experiments were conducted on vertical seawall structures to measure wave-overtopping volumes and wave runup heights under different wave conditions and structural freeboard variations. By assuming that the velocity of water inundation on the top of the structure during wave-overtopping events is equivalent to the long-wave velocity, an overtopping discharge coefficient was introduced. This coefficient was utilized to estimate the rate of wave-overtopping based on the temporal changes in wave runup heights measured at the top of the structure. Upon reasonably calculating the overtopping discharge coefficient, it was verified that the estimation of wave-overtopping could be achieved solely based on the wave runup heights.

Influence of Van Gent Parameters on the Overtopping Discharge of a Rubble Mound Breakwater

The choice of the values of the friction parameters may strongly influence the numerical modeling of the interaction between waves and porous media. Here, an assessment of such an influence is carried out using the OpenFOAM solver IhFoamV1 to simulate the response of the Catania harbor breakwater under extreme wave attack. The numerical model was validated by comparison with an experimental dataset, and a sensitivity analysis of the overtopping discharge estimate to van Gent parameter β was carried out testing values suggested by previous studies. A discussion on the importance of a careful estimate of such a parameter when dealing with the numerical modeling of porous coastal structures is presented. Indeed, variations in the non-dimensional overtopping discharge higher than 150% were observed as a consequence of a small variation (10–20%) in the absolute value of β.

Development of a Bayesian networks-based early warning system for wave-induced flooding

Coastal flooding prediction systems can be an efficient risk-reduction instrument. The goal of this study was to design, build, test, and implement a wave-induced flooding early warning system in urban areas fronted by sandy beaches. The system utilizes a novel approach that combines Bayesian Networks and numerical models (SWAN + XBeach) and was developed in two phases. In the development phase, firstly, the learning information was generated including the creation of oceanic conditions, modeling overtopping discharges, the characterization of the associated impacts (no, low, moderate and high) in pedestrians, urban components and buildings, and vehicles, and secondly, the Bayesian Networks were designed that surrogated the previously generated information. After their training, the conditional probability tables were created representing the foundation to make predictions in the operational phase. This methodology was validated for several historical events which hit the study area (Praia de Faro, Portugal), and the system correctly predicted the impact level of around 80% of the cases. Also, the predictive skills varied depending on the level, with the no and high impact levels overcoming the intermediate levels. In terms of efficiency, one simulation (deterministic) of coastal flooding for 72 h by running SWAN + XBeach operationally would take more than two days on a one-logical processor workstation, while the current approach can provide quasi-instantaneously predictions for that period, including probability distributions. Moreover, the two-working phase approach is very flexible enabling the inclusion of additional features such as social components representing a powerful tool for risk reduction in coastal communities.

Prediction of wave overtopping discharges at coastal structures using interpretable machine learning

ABSTRACT Appropriate estimation and prediction of wave overtopping discharges are very important in terms of economics, port structure stability, and port operation. In recent years, machine learning (ML) techniques, which predict by finding statistical structures from input/output data using computers, have generated interest. However, as the complexity of ML models increases, interpreting their results becomes increasingly difficult. Interpretation of ML results is an important part in developing an efficient structure design strategy for improved wave overtopping discharge estimation. Therefore, in this study, eight linear/nonlinear ML models were applied to the same data, and a pipeline model for selecting an ML model suitable for data characteristics was developed. In addition, the importance of variables related to the prediction of wave overtopping discharges and their correlations were analyzed by interpretable ML. The research results showed that the extreme gradient boosting model had the highest prediction accuracy and significantly reduced the error. Accordingly, a data-based model can be a new alternative for analyzing the complex physical relationships in the field of coastal engineering and used as a starting point toward structure design and development for coastal disaster prevention.

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.

Extending the Design Life of the Palm Jumeirah Revetment Considering Climate Change Effects

This paper presents potential upgrades to the Palm Jumeirah Island’s outer revetment to extend its design life for 50 years, considering the sea level rise (SLR) associated with climate change. The paper proposes several upgrade options to ensure that the hydraulic stability and wave overtopping discharges of the Palm Jumeirah revetment comply with the recommended design criteria based on industry guidelines. The performance of the existing revetment, in terms of the hydraulic stability and wave overtopping discharge criteria, is assessed using design wave heights (1- and 100-year events) extracted from an extreme wave analysis study on the Dubai coast. The results show that, based on the new design conditions, the existing structure should be upgraded to meet the armor stability criteria and recommended overtopping discharge values. Three different upgrade solutions are designed and analyzed to satisfy the required hydraulic stability and overtopping conditions. The suggested upgrade options are an extra armor layer, a flat berm, and a submerged breakwater offshore. The proposed upgrade solutions are preliminary designs that would require verification in terms of their geotechnical stability and physical model testing to evaluate their performance.

Conceptual and quantitative categorization of wave-induced flooding impacts for pedestrians and assets in urban beaches

Beaches combined with sloping structures are frequently the first element of defense to protect urban areas from the impact of extreme coastal flooding events. However, these structures are rarely designed for null wave overtopping discharges, accepting that waves can pass above the crest and threat exposed elements in hinterland areas, such as pedestrians, urban elements and buildings, and vehicles. To reduce risks, Early Warning Systems (EWSs) can be used to anticipate and minimize the impacts of flooding episodes on those elements. A key aspect of these systems is the definition of non-admissible discharge levels that trigger significant impacts. However, large discrepancies in defining these discharge levels and the associated impacts are found among the existing methods to assess floodings. Due to the lack of standardization, a new conceptual and quantitative four-level (from no-impact to high-impact) categorization of flood warnings (EW-Coast) is proposed. EW-Coast integrates and unifies previous methods and builds on them by incorporating field-based information. Thus, the new categorization successfully predicted the impact level on 70%, 82%, and 85% of the overtopping episodes affecting pedestrians, urban elements and buildings, and vehicles, respectively. This demonstrates its suitability to support EWSs in areas vulnerable to wave-induced flooding.

Effect of data normalisation in estimating wave overtopping discharge parameter of semicircular breakwater using ANN and Random Forest.

Breakwaters are the structures constructed in the coastal areas to maintain calm inside the port or prevent beach erosion. Semi-circular Breakwater (SCB) is an innovative type of Breakwater made of hollow caisson on a base slab with or without perforations. In this study, the wave overtopping discharge parameter of an SCB is estimated using Artificial Neural Network and Random Forest. The data is collected and used in the current research from an experimental investigation conducted in the Wave Mechanics Laboratory of the Department of Water Resources and Ocean Engineering (WROE), NITK Surathkal. Using this experimental data, the ANN and Random Forest models are developed for the prediction of the wave overtopping discharge parameter of an SCB. The performance of the models is evaluated using different statistical parameters. Data with and without normalisation are used separately to check the effect of normalisation in the prediction of wave overtopping discharge parameter using ANN and Random Forest. From the results, it is found that ANN gives better results when the data is normalised. The performance of Random Forest is independent of the data normalisation.

Experimental Study on Surge Overtopping Process of Earthen Embankments and Calculation of First Surge Wave Discharge

The landslide-induced surge overtopping of embankments not only causes damage to the dam body but also poses a threat to downstream life and property. This paper explored the process of surge overtopping caused by landslides through model experiments, calculated the first surge wave overtopping discharge using empirical formulas, and evaluated the overtopping discharge at Vajont Dam in Italy. The study revealed that the first wave of landslide-induced surge carried higher energy than subsequent waves, and the surge waves action on the downslope of the embankment was non-uniform. The subsequent surge waves will cause localized "rills" on the dam body, and if there were enough subsequent surge waves, these "rills" may connect and ultimately lead to the failure of the embankment. The first surge wave overtopping discharge per unit width obtained in the experiments was 0.274 m2/s. According to geometric similar, the overtopping discharge of the Italian dam was as high as 682,830 m3/s.

Wave Overtopping at Sea Dikes on Shallow Foreshores: A Review, an Evaluation, and Remaining Challenges

Wave overtopping is a critical parameter in the design of coastal defense structures. Nowadays, several empirical formulations based on small-scale experiments are available in the literature to predict the mean overtopping discharge at dikes on shallow foreshores. Although the accuracy of the predictions has improved due to each approach’s contributions, the formulations’ performance depends on their range of applicability. In engineering applications, it is important to know the performance and limitations of the different formulas. This work presents a new experimental dataset focused on very shallow and extremely shallow foreshore conditions for a range of foreshore slopes (i.e., 1/20, 1/35, 1/50, and 1/80) and relative water depths. The recent developments in wave overtopping research on very shallow and extremely shallow foreshore conditions have been reviewed using this dataset to reflect the existing uncertainties and challenges in the wave-overtopping literature. We find that predicting wave overtopping for extremely shallow foreshore conditions still requires improvement. Additional research is needed to understand the (residual) influence on the wave overtopping of the foreshore slope and relative magnitude of the infragravity wave height to the sea-swell wave height at the dike toe, especially for extremely shallow foreshore conditions. The variation in performance of the formulas for different foreshore slopes is demonstrated. Finally, some of the remaining uncertainties that need further exploration are discussed.

Comparison of deep-water-parameter-based wave overtopping with wirewall field measurements and social media reports at Crosby (UK)

Wave overtopping formulae, which often underlie coastal hazard early warning systems, are typically parameterised using wave conditions at the toe of the structure. For very shallow conditions where significant wave breaking occurs over the foreshore, this usually requires computationally-demanding numerical models—and practitioners skilled in their application—to accurately transform offshore waves to the structure toe. An additional concern is that overtopping formulae are scarcely validated in the field due to the very limited availability of in-situ overtopping data obtained at actual structures. Here, we validate a set of deep-water-parameter-based formulae for mean overtopping discharge (q) at smooth slopes, which remove the need for nearshore measurements or additional numerical modelling but require that a single representative foreshore slope angle (m) be defined. The validation is carried out against field data gathered at Crosby (UK) using two novel approaches: i) a new overtopping measurement system called “WireWall”; and ii) crowd-sourced data in the form of overtopping images obtained from a community Facebook page (social media). A method is introduced to define m for irregular bathymetries, based on the location where the local water depth is equal to the offshore significant wave height. The overtopping formulae proved accurate—with estimates of q being within a factor of 4 of observations—when compared to both 1-h averaged and 15-min averaged overtopping data, suggesting that the approach can be used for both design and assessment and now-casting hazard information. Finally, hindcasts made using the newly validated formulae for the events reported by the community indicate that q can exceed 10 l/s/m under yearly winter conditions, posing a serious hazard to pedestrians. This highlights the pressing need to update the current hazard warning system at Crosby, which estimates q to be a factor of 3 lower than the deep-water-parameter-based approach, on average.

Experimental Study on Hydrodynamic Performance of Partially Perforated-Wall Caisson Breakwaters Designed for the Southeast Coast of Korea

Lee, B.W.; Baek, D.; Ha, T.; Lee, K.J., and Yoon, J.-S., 2023. Experimental study on hydrodynamic performance of partially perforated-wall caisson breakwaters designed for the southeast coast of Korea. Journal of Coastal Research, 39(1), 167–174. Charlotte (North Carolina), ISSN 0749-0208. If a perforated wall is installed on the front and rear surfaces of the caisson, then it is possible to reduce the wave reflection and the discharge of wave overtopping caused by energy dissipation. Consequently, the energy dissipation helps reduce the transmitted wave and improve the stability of the breakwater. This paper discusses the hydraulic performance (i.e. the wave reflection, wave transmission, discharge of wave overtopping, and stability of breakwater) of four perforated breakwaters as measured by physical experiments in a wave flume. The irregular wave was generated by the wave condition of the target site. Three breakwaters were designed: a perforated wall with a single chamber for a 50-year return period and two perforated walls with double chambers for a 100-year return period. Based on experimental results, the breakwater with a double chamber showed the best performance of 0.612, 0.102, and 0.076 m3/(m · s) for the reflection, transmission coefficient, and overtopping discharge, respectively. In particular, in the stability experiment of the armor units and perforated caissons, the breakwater with double chamber has not experienced any failure in any of the test cases.

Statistical analysis and prediction of force and overtopping rates on large-scale vertical walls using support vector machine and random forest regression

This study provides a statistical basis to determine the most influencing parameters on forces and overtopping over vertical walls, as well as to showcase the usability of machine learning modelling in coastal engineering. To this end, horizontal force and overtopping data for regular waves of varying height (0.63–1.65 m), period (4–8 s), and water depth (3.37–3.97 m) over a vertical wall were studied using redundancy analysis (RDA) and regressed using multiple linear regression, support vector regression (SVR), and random forest regression (RFR). The RDA showed that about 60% of the output variable variance can be explained by the structure dimensions and 15% by the incoming wave characteristics. The SVR approach better predicted the average force (mean relative error (MRE) = 39.9% and R2 = 0.346), whereas the RFR technique better predicted overtopping discharges (MRE = 46.7% and R2 = 0.802). By expanding the database, the error on overtopping prediction was reduced to 22.1% and 27.5%, respectively, for the SVR and RFR.

Application of SWASH to Compute Wave Overtopping in Ericeira Harbour for Operational Purposes

This work aimed at testing the capability of the numerical model SWASH to be implemented in the prototype of the overtopping and flooding forecast system HIDRALERTA for Ericeira harbour. In contrast to the neural network NN_OVERTOPPING2, which is currently implemented in HIDRALERTA, SWASH is able to estimate the flood extension and wave propagation along the domain, which makes it a possible improvement to NN_OVERTOPPING2. The one-dimensional version of the SWASH model was implemented to simulate overtopping at two different profiles (antifer and tetrapods) and calibrated for three storms in 2019 by comparing the simulated overtopping discharge to NN_OVERTOPPING2 results. For the calibration, the Manning coefficient was used to represent the friction of the armour layer. Then, for operational purposes, four expressions to calculate the Manning coefficient were developed based on: the relative crest freeboard, the wave steepness, the incident wave angle and the type of armour layer. The expressions showed small errors between the calculated and calibrated Manning coefficients and highlighted the importance of the incident wave angle to obtain an accurate calibration. Despite an underestimation of the overtopping discharge in some cases, the SWASH model was found to provide overall good results when applied with calculated Manning coefficients and suitable to be implemented in HIDRALERTA.

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.