Overtopping Rate Research Articles

Laboratory investigation of overtopping at a sloping structure with permeable shingle foreshore

The vast majority of overtopping data applied in EurOtop (2018) has been made from small-scale measurements with impermeable foreshore slopes. This article describes a comprehensive two-dimensional experimental study conducted in a small-scale 1:50 wave flume. Results are presented for the overtopping performance at a 1 to 2 sloping wall, undertaken on both impermeable and permeable foreshore slopes. Within experimental limitations, the results demonstrated that the mean overtopping rate is reduced by up-to a factor of 4, when compared to the predictions reported for the impermeable slope. However, when comparing maximum individual wave-by-wave overtopping volumes, no significant differences were observed. These results are intended for practitioners and researchers predicting wave overtopping characteristics at sloping structures with permeable gravel foreshores.

Analysis and prediction of storm water levels in Delaware inland bays

A simple approach based on an analytical model and available tide gauge data is proposed for the analysis of storm tide damping inside inland bays with complex bathymetry and for the prediction of peak water levels at gauge locations during storms. The approach was applied to eight tide gauges in the vicinity of inland bays in Delaware. Peak water levels at the gauge locations were analyzed for 34 storms during 2005-2017. A damping parameter in the analytical model was calibrated for each bay gauge. The calibrated model predicted the peak water levels within errors of about 0.2 m except for Hurricane Sandy in 2012. The analytical model including wave overtopping was used to estimate the peak wave overtopping rate over the barrier beach from the measured peak water level in the adjacent bay.

Effect of Sea Level Rise on the Wave Overtopping Rate at Berm Breakwater

This study quantitatively assessed the risk in the overtopping performance of berm breakwaters due to sea level rise (SLR). To achieve this, a recent overtopping prediction formula that includes the influence of water depth on the estimated overtopping rate was used for the analysis. Additionally, the probabilities of failure in terms of the overtopping rate for different SLR scenarios were estimated using the Monte Carlo simulations, and the optimal maintenance intervals were determined. The increase in the crest freeboard, required to maintain the design overtopping rate, was estimated to be less than the increase needed in berm width for the different sea level rise scenarios considered. Furthermore, the required crest freeboard was influenced less by the initial configuration of the berm width. Shorter maintenance intervals were required for structures with an initially wide berm compared to those with a high crest freeboard. The results indicated that the future design and maintenance of berm breakwaters need to consider the effects of SLR on the overtopping performance, especially in shallow water zones.

Distribution of individual wave overtopping volumes on mound breakwaters

Conventional mound breakwaters are usually designed to withstand low mean wave overtopping discharges and a low proportion of overtopping waves (Pow). Existing formulas to estimate Pow and maximum individual wave overtopping volume are usually based on tests with high Pow; this study is focused on mound breakwaters subjected to Pow < 0.2. The performance of the 2-parameter Weibull and Exponential distributions is examined in order to describe individual wave overtopping volumes of mound breakwaters in non-breaking wave conditions. A new methodology is applied to 164 small-scale 2D physical tests to identify the number of overtopping waves, and the corresponding individual wave overtopping volumes. Utility functions are used to consider the relative relevance of the observed data: in this study, a quadratic utility function depending on all the individual wave overtopping volumes and step utility functions with 10%, 30% and 50% of the highest volumes are used to fit the Weibull and Exponential distributions. In this study, a new estimator of Pow is proposed to improve the predictions required to estimate the maximum individual wave overtopping volume. Existing estimators of Pow underpredict the largest values of Pow measured in the physical tests. The parameters fitted to the Weibull and Exponential distributions using the quadratic utility function provide estimations of the dimensionless maximum individual wave overtopping volume with relative mean squared errors rMSE = 10.4% and 10.6%, respectively. When CLASH Neural Network-estimated mean overtopping rates are used to predict the maximum individual wave overtopping with the quadratic utility function, the 2-parameter Weibull and Exponential distributions provide rMSE = 31.6% and rMSE = 33.3%, respectively. The new estimators proposed in this study improve the predictions of Pow and maximum individual wave overtopping volumes on conventional mound breakwaters designed for low wave overtopping rates.

Development of Wave Overtopping Formulas for Inclined Seawalls using GMDH Algorithm

Since wave overtopping is a very complex phenomenon and is sensitive to hydraulic and structural parameters, hydraulic model tests have been used to estimate the wave overtopping rates at coastal structures. Efforts have also been made toward developing empirical formulas and machine learning models based on a large amount of accumulated data, e.g., the EurOtop formulas and Artificial Neural Network (ANN) models based on the CLASH database. In this study, new machine learning formulas for inclined seawalls are derived by using the Group Method of Data Handling (GMDH) algorithm with the CLASH and new EurOtop datasets. Because the GMDH formulas are more complex than other empirical formulas, an EXCEL calculator is provided so that engineers can easily use the formulas. The GMDH formulas are shown to be more accurate than other empirical formulas and equally accurate as the EurOtop-ANN model. The estimation errors of 95% confidence interval and the range of 95% prediction error are also given. The sensitivity analysis of the derived formulas shows that the parameters that more influence the wave overtopping rate are in the order of crest freeboard, structure slope, wave period, and seabed slope.

Coastal flooding from wave overtopping and sea level rise adaptation in the northeastern USA

In the northeastern United States, flooding arising from wave overtopping poses a constant threat to coastal communities during storm events. The purpose of this study is to construct a novel integrated atmosphere-ocean-coast and overtopping-drainage modeling framework based on the coupled tide, surge and wave model, SWAN+ADCIRC, to assess risk and facilitate coastal adaptation and resilience to flooding in a changing climate in this region. The integrated modeling system was validated against the field observations of water level, wave height and period during the January 2015 North American blizzard. The water level collected by a sensor in the Avenues Basin behind the seawall in Scituate, Massachusetts were combined with the basin relationship between basin area and water level given by the USGS LIDAR data to obtain the field measurements of wave overtopping water volume in order to verify the model predictions. At the storm peak, the significant wave height was increased by 0.7 m at the coast by tide and surge. The wave setup along the coast varied from 0.1 m to 0.25 m depending on the coastline geometry. The interaction between tide-surge and waves increased the wave overtopping rate by five folds mainly due to the increased wave height at the toe of the seawall. The wave overtopping discharge would approximately double in an intermediate sea level rise scenario of 0.36 m by 2050 for a storm like the January 2015 North American blizzard. The wave overtopping discharge would increase by 1.5 times if the seawall crest elevation was raised by the same amount as sea level rise as an adaptation strategy. An increase of 0.9 m in the seawall crest elevation instead of 0.6 m currently planned by the town is required to bring the wave overtopping discharge to the current level under a 0.36 m sea level rise scenario. This result is primarily due to larger waves arriving at the seawall without breaking in the presence of larger water depth.

INFLUENCE OF CROWN-WALL ON WAVE OVERTOPPING PROBABILITY AND PROBABILITY DISTRIBUTION OVER A SEAWALL

In the past decades, the crest height of the seawall was determined by the allowable average wave overtopping rate q. Franco (1994) concluded that individual wave overtopping，particularly the maximum individual volume, provided a better design method than q, considering the stability of the seawall and the safety of vehicles and people along the coastal area protected by the coastal defense structures. Shanghai, located on the west bank of the Pacific Ocean, is quite sensitive to the risk of storm surges and violent wave overtopping. The crown-wall serves as an engineering measure to reduce the wave overtopping effectively.

AVERAGE AND WAVE-BY-WAVE OVERTOPPING PERFORMANCE OF STEEP LOW-CRESTED STRUCTURES

Wave overtopping is a key process in coastal protection. The assessment of the wave overtopping rates is an important aspect in the design of coastal structures. In this paper, the focus is on steep low-crested structures, which include structures with steep slopes up to the limit case with vertical structures, with small relative freeboards up to the case with zero freeboards. This type of structures is of use for coastal protection in the case of sea level rise within climate change process and for overtopping wave energy converters. A literature review of the overtopping knowledge available for steep low-crested structures is carried out, identifying a knowledge gap. To fill this knowledge gap, 2D hydraulic model tests were performed at the wave flume of the Department of Civil Engineering at Ghent University, measuring wave conditions and the overtopping performance. Average and individual wave overtopping were analysed and compared to existing prediction formulae. Inaccuracies in the existing prediction formulae are detected and studied, and enhanced prediction formulae are presented for the average overtopping and the probability distribution of the individual overtopping volumes. The new prediction formulae improve the accuracy of wave overtopping volumes for steep low-crested structures range while maintaining the accuracy for other types of structures. The improved understanding of the overtopping behaviour allows a safer design of coastal structures.

Hydraulic Stability of the Armor Layer of Overtopped Breakwaters

Mound breakwaters with significant overtopping rates in depth-limited conditions are common in practice due to social concern about the visual impact of coastal structures and sea level rise due to climatic change. For overtopped mound breakwaters, the highest waves pass over the crest producing armor damage, not only to the front slope, but also to the crest and the rear slope. To guarantee the breakwater stability, it is necessary to limit the armor damage in the three parts of the structure: Front slope, crest, and rear slope. This paper describes the hydraulic stability of the armor layer of medium and low-crested structures in wave breaking conditions. Small-scale physical model tests were carried out with different relative crest freeboards and three armor units: Rocks, cubes, and Cubipods. The armor damage progression in the front slope, crest, and rear slope was analyzed using the Virtual Net method to consider the heterogeneous packing and porosity evolution along the armor slope. A comparison is provided between the hydraulic stability of the different armors and their relationship with the measured overtopping volumes.

Wave overtopping and toe scouring at a plain vertical seawall with shingle foreshore: A physical model study

This paper describes a physical model study to investigate the wave overtopping and toe scouring at a plain vertical wall with a shingle foreshore. A matrix of 180 experimental test conditions were performed in a 2D wave flume, with an approximate scale of 1:50. The study investigates the baseline overtopping characteristics at a plain vertical wall on an impermeable 1:20 foreshore slope and compares the results with two permeable 1:20 shingle beach foreshores with prototype d50 values of 13 mm, and 24 mm respectively. For impulsive wave conditions, it was found that the mean overtopping rate was reduced by factor 3 for the d50 of 13 mm, and a factor of 4 for the d50 of 24 mm. For non-impulsive waves, the reduction factors were 1.5 for d50 of 13 mm and 2 for d50 of 24 mm. Prior to this study, limited design guidance was available to predict the mean overtopping discharges and mean sediment rates at vertical seawalls on permeable shingle foreshores. Therefore, a new set of prediction formulae are proposed in this study, based on the new laboratory test results, and a comparison with the available prediction methods in literature for vertical seawalls subjected to both impulsive and non-impulsive wave conditions.

Effect of the armor crest freeboard relative to the crown wall freeboard on wave overtopping for simple rubble mound slopes

Several studies have been carried out to investigate the effect of crest parameters on the wave overtopping for armored slopes with crown walls. However, the effect of the armor crest freeboard is still under question. In this study, for the first time, a series of hydraulic model experiments are conducted specifically to investigate how the armor crest freeboard relative to the crown wall freeboard affects the wave overtopping rate. Experimental results indicate that while the armor crest freeboard lower than the crown wall freeboard is giving larger overtopping, higher armor crest freeboard is reducing the overtopping. However, this reduction is not same as the reduction due to the increase in the crown wall freeboard. The reason may be the porosity of the armor crest. For the first time, a new correction factor is proposed to describe the change in the wave overtopping due to the armor crest freeboard by using experimental results. The correction factor CAc is applied to cover the effect of armor crest freeboard in the predictions of EurOtop (2016). The verification study present that overtopping rate predictions of corrected EurOtop (2016) are more consistent with the measured rate results compared to the predictions of the original formula, if the armor crest freeboard is not equal to the crown wall freeboard.

Investigation of Wave Overtopping from Various Geometrical Configurations of Coastal Breakwater Ramps

Breakwater is often required for erosion protection. The effectiveness of breakwater structure as a coastal defence could be determined through overtopping wave surpass onto its crest freeboard structure. The common design practice of breakwater structure is using a linear ramp configuration. There is still a limited knowledge on the contribution of various configuration ramps shape into breakwater efficiency. Thus, this study attempts to investigate a few other's configuration of ramp geometries through overtopping discharge rate performance and identified its relationships with the crest freeboard. Three configurations of ramp geometries (convex, concave and cubic) have been investigated using numerical simulation of CFD-Flow 3D software. The result indicates that, there are significant influences of ramp configuration parameters on the overtopping rate and the highest overtopping rate is contributed from cubic shape ramp geometry. It is recommended that the detail study on cubic ramp shape geometry for determining its capability in increasing overtopping rate.

A Critical Analysis and Validation of the Accuracy of Wave Overtopping Prediction Formulae for OWECs

The development of wave energy devices is growing in recent years. One type of device is the overtopping wave energy converter (OWEC), for which the knowledge of the wave overtopping rates is a basic and crucial aspect in their design. In particular, the most interesting range to study is for OWECs with steep slopes to vertical walls, and with very small freeboards and zero freeboards where the overtopping rate is maximized, and which can be generalized as steep low-crested structures. Recently, wave overtopping prediction formulae have been published for this type of structures, although their accuracy has not been fully assessed, as the overtopping data available in this range is scarce. We performed a critical analysis of the overtopping prediction formulae for steep low-crested structures and the validation of the accuracy of these formulae, based on new overtopping data for steep low-crested structures obtained at Ghent University. This paper summarizes the existing knowledge about average wave overtopping, describes the physical model tests performed, analyses the results and compares them to existing prediction formulae. The new dataset extends the wave overtopping data towards vertical walls and zero freeboard structures. In general, the new dataset validated the more recent overtopping formulae focused on steep slopes with small freeboards, although the formulae are underpredicting the average overtopping rates for very small and zero relative crest freeboards.

A quantitative model for danger degree evaluation of staged operation of earth dam reservoir in flood season and its application

Based on the natural disaster risk evaluation mode, a quantitative danger degree evaluation model was developed to evaluate the danger degree of earth dam reservoir staged operation in the flood season. A formula for the overtopping risk rate of the earth dam reservoir staged operation was established, with consideration of the joint effect of flood and wind waves in the flood sub-seasons with the Monte Carlo method, and the integrated overtopping risk rate for the whole flood season was obtained via the total probability approach. A composite normalized function was used to transform the dam overtopping risk rate into the danger degree, on a scale of 0–1. Danger degree gradating criteria were divided by four significant characteristic values of the dam overtopping rate, and corresponding guidelines for danger evaluation are explained in detail in this paper. Examples indicated that the dam overtopping danger degree of the Chengbihe Reservoir in China was 0.33–0.57, within the range of moderate danger level, and the flood-limiting water level (FLWL) can be adjusted to 185.00 m for the early and main flood seasons, and 185.00—187.50 m for the late flood season. The proposed quantitative model offers a theoretical basis for determination of the value of the danger degree of an earth dam reservoir under normal operation as well as the optimal scheduling scheme for the reservoir in each stage of the flood season.

Reflection Coefficient and Overtopping Rate of Nonlinear Waves at a seawall in Shallow Water area

波の入・反射波の分離法には，Healy法をはじめとしていくつか存在する．非線形性の強い波に対するそれらの特性ついてはいまだ十分に議論されていない．CADMAS-SURFを用いた数値計算により，Healy法が小さめの反射率を与えること，その補正として合田によって提案された補正値も大幅な改善には至らないことが示されている．不規則波を対象として提案された合田の入・反射分離推定法の規則波への適用性を調べ，波の非線形性が入・反射分離に影響を及ぼすことを明らかにしている．疑似非線形波を対象とした久保田らの方法が検討され，波高値よりもrms値を用いた方が良い結果を与え，さらに離れた2点のデータを用いる方がより良い結果を与えることが明らかにされている．さらに，これらの結果は横山・水口らのデータと比較され，その有用性が示されている．

Estimations of wave forces on crown walls based on wave overtopping rates

In this study, seven input variables are used to estimate wave forces on the crown wall, and explanatory variables are ranked using neural network techniques. 274 small-scale 2D tests, including both wave overtopping and pressure on crown-wall measurements, were used to calibrate the wave force predictors. Wave overtopping (log Q) was the most relevant variable to estimate horizontal wave forces and overturning moments, while the relative foundation level (Fc/L0p) was the most relevant variable to estimate wave up-lift forces. The new wave force estimators showed prediction errors slightly higher than the formulas given in the literature, but using fewer parameters and explanatory variables. The range of application of the new formulas is 1.67 < Rc/(γfHm0) < 6.55, 1.39 < ξ0p < 7.77, 0.36 < γfRu0.1%/Rc < 1.41, 0.00 < (Rc-Ac)/Ch < 0.59, 2.64 < Lm/Gc < 6.54, 0.00 < Fc/L0p < 0.03 and −6.00 < logQ < −2.78. Compared to pressure on crown walls, the mean wave overtopping rate is relatively easy to measure in small-scale tests and prototypes. The new estimators of wave forces on the crown wall can be used to indirectly calculate forces on models when only overtopping rates are measured. If wave overtopping is one order of magnitude higher, the wave forces and overturning moments on the crown wall increase between 11% and 60%, considerably reducing the crown wall stability.

Wave overtopping at berm breakwaters: Experimental study and development of prediction formula

Prediction of overtopping rate plays a key role in the design and safety assessment of breakwater structures. In this study, the mean wave overtopping rate at hardly and partly reshaping berm breakwaters were investigated by means of small-scale physical model tests. The test program was designed to create a database with a wider range of wave steepness, berm width, berm level and crest level for the hardly/partly reshaping conditions with an initial slope of 1:1.50. The new formula was developed covering the comprehensive test conditions (including existing tests and newly-collected ones) using scaling arguments and data mining techniques. Dimensionless governing parameters were used in the development of the formulae, and it was found that the new formula represented the influence of relative water depth on the wave overtopping rate better than the other prediction models. Accuracy metrics such as RMSE and Bias indicated that the developed formula outperformed the existing prediction models within the range of significant overtopping rates. Moreover, the developed formula is simple and gives better insights into the physical significance of the variables in the overtopping process, and thus it is hoped it will be more appealing for engineering applications.

Experimental study on mechanism of sea-dike failure due to wave overtopping

This work, which was largely a fruit of China's national marine hazard mitigation service, explicitly reveals the major mechanism of sea-dike failure during wave overtopping. A large group of wave-flume experiments were conducted for sea dikes with varying geometric characteristics and pavement types. The erosion and slide of the landward slope due to the combined effect of normal hit and great shear from overtopping flows was identified the major trigger of the destabilization of sea dikes. Once the intermittent hydrodynamic load and swash caused any deformation (bump or dent) of the pavement layer, pavement fractions (slabs or rubble) on the slope started to be initiated and removed by the water. The erosion of the landward slope was then gradually aggravated followed by entire failure within a couple of minutes. Hence, the competent velocity would be helpful evaluate the failure risk if as well accounted in standards or criteria. However, the dike top was measured experiencing the largest hydrodynamic pressure with a certain cap while the force on the wall increased rapidly as the overtopping intensity approached the dike-failure threshold. The faster increase of the force on the wall than on the landward slope yielded the sequencing of loads reaching hypothetic limits before failure as: dike top – top-mounted wall – landward slope. Therefore, beside the slide failure, the fatigue damage due to the instantaneous hydrodynamic impact might be another mechanism of the dike failure, which did not appear in the experiment but should be kept in mind. Instead of the widely adopted tolerable overtopping rate, a 0.117–0.424m3/(ms) range of overtopping discharge and a 10m/s overtopping velocity for the failure risk of typical sea dikes along China's coastlines were suggested, which enables the possible failure risk prediction through empirical calculations. The failure overtopping rate was identified strongly dependent on the pavement material, the landward slope and the dike-mounted wall but showed little variation with the width of the dike top. The flat concrete pavement and gentle landward slopes are suggested for the dike design and construction. For given configurations and hydrodynamic conditions in the experiment, the dike without the wall experienced less overtopping volume than those with the 1-m top-mounted wall. Meanwhile, the remove of the wall increased the failure overtopping rate, which means a certain increase of the failure criterion. Thus, care must be taken to conclude that the dike-mounted wall seems not an entirely appropriate reinforcement for the stability and safety of coastal protections. This should be further checked and discussed by researchers and engineers in the future.

Improving predictions of swash dynamics in XBeach: The role of groupiness and incident-band runup

In predicting storm impacts on sandy coasts, possibly with structures, accurate runup and overtopping simulation is an important aspect. Recent investigations (Stockdon et al., 2014; Palmsten and Splinter, 2016) show that despite accurate predictions of the morphodynamics of dissipative sandy beaches, the XBeach model (Roelvink et al., 2009) does not correctly simulate the individual contributions of set-up, and infragravity and incident-band swash to the wave run-up. In this paper we describe an improved numerical scheme and a different way of simulating the propagation of directionally-spread short wave groups in XBeach to better predict the groupiness of the short waves and the resulting infragravity waves. The new approach is tested against field measurements from the DELILAH campaign at Duck, NC, and against video-derived runup measurements at Praia de Faro, a relatively steep sandy beach. Compared to the empirical fit by Vousdoukas et al. (2012) the XBeach model performs much better for more extreme wave conditions, which are severely underestimated by existing empirical formulations.For relatively steep beaches incident-band swash cannot be neglected and a wave-resolving simulation mode is required. Therefore in this paper we also test the non-hydrostatic, wave-resolving model within XBeach for runup and overtopping against three datasets. Results for a high-quality flume test show non-hydrostatic XBeach predicts the run-up height with good accuracy (maximum deviation 15%). A case with a very shallow foreshore typical for the Belgian coast at Wenduine was compared against detailed measurements. Overall the model shows correct behavior for this case. Finally, the model is tested against a large number (551) of physical model tests of overtopping from the CLASH database. For relatively high overtopping discharges the non-hydrostatic XBeach performs quite well, with increasing accuracy for increasing overtopping rates. However, for relatively low overtopping rates of less than 10–20 l/m/s, the model systematically underestimates measured overtopping rates.

WAVE OVERTOPPING AT MALECÃ’N TRADICIONAL, LA HABANA, CUBA

With the aim of redesigning the geometry of the Malecòn, a vertical face seawall protecting the northern waterfront of the city of La Habana, a wide experimental campaign was carried out. The latter was performed in the frame of a collaboration between the Government of the isle of Cuba and the CUGRI consortium, an Italian institution which joins the Universities of Salerno and Napoli “Federico II”. The different solutions investigated allowed both to detect the best solution for reducing the overtopping and to assess the role of wave setup and low frequency components of the incoming wave spectrum on the predictions of the mean overtopping rate. The stability of two nearshore structures designed to protect the seawall has also been assessed.