Field and laboratory measurements of mean overtopping discharges and spatial distributions at vertical seawalls

Within the CLASH project, wave overtopping at the vertical seawall at Samphire Hoe was measured by HR Wallingford (HRW), and compared laboratory tests in 2 & 3 dimensions carried out at the University of Edinburgh and HRW. At Samphire Hoe, overtopping volumes were captured in three volumetric tanks capable of measuring wave-by-wave and total overtopping volumes. The three tanks were placed progressively farther back from the seawall edge so that the spatial distribution of the overtopping discharges could be determined. The field measurement equipment was successfully deployed on three occasions, and measured overtopping discharges ranged from that barely considered to be hazardous to the public to over q = 3.0 l/s/m. The 2d testing at Edinburgh was modelled at a scale of 1:40, and the 3d model at HRW was modelled at 1:20. For both sets of laboratory tests, a range of conditions, representative of the storm wave conditions and water levels, was reproduced in addition to a set of parametric conditions. The storm conditions allowed a direct comparison between the field and laboratory measurements, and the parametric conditions were used to test the generic overtopping behaviour of the structure. For both sets of laboratory tests, mean overtopping discharges and the spatial distribution were measured separately. Analysis of the distribution data relates the proportion of the discharge that has landed as a function of (x / L_o); where x is the distance behind the crest, and L_o is the offshore wavelength. Analysis of the field, 2d & 3d laboratory data, and empirical prediction methods have not identified any scale effects for overtopping discharges at vertical and near-vertical seawalls.     

Exceedance probability for wave overtopping on a fixed deck

Detailed laboratory measurements were made of the instantaneous free surface elevation in front of a fixed deck and the instantaneous free surface elevation, velocity, and overtopping rate at the leading edge of the deck. The study showed that the exceedance probabilities for the normalized maximum instantaneous overtopping rate and the normalized overtopping volume were predicted by a simple exponential curve. The measured exceedance probability seaward of the deck compared well with the nonlinear theory of Kriebel and Dawson (Kriebel D.L., Dawson T.H., 1993. Nonlinearity in wave crest statistics. In: Proceedings Ocean Wave Measurement and Analysis. American Society of Civil Engineers, pp. 61–75). Conditional sampling of the crest heights seaward of the deck gave a normalized probability distribution similar to that of the maximum water level measured on the deck for each overtopping event. However, the values used to normalize each distribution were not the same.     

Dynamic properties of green water event in the overtopping of extreme waves on a fixed dock

A statistical model is developed to predict wave overtopping volume and rate of extreme waves on a fixed deck. The probability density function for the volume and rate of overtopping water are formulated based on the truncated Weibull distribution with the assumption of local sinusoidal profile for small amplitude waves. Sensitivity to the wave nonlinearity parameter and deck clearance is discussed. The statistical model is compared to laboratory data of the instantaneous free surface elevation measured in front of a fixed deck, and overtopping volume and overtopping rate measured at the leading edge of the deck. The statistical theory compared well with the measured exceedance probability seaward of the deck. The model prediction of the exceedance probability of deck overtopping gave qualitatively good agreement for large overtopping values.     

Random wave runup and overtopping a steep sea wall: Shallow-water and Boussinesq modelling with generalised breaking and wall impact algorithms validated against laboratory and field measurements

A semi-implicit shallow-water and Boussinesq model has been developed to account for random wave breaking, impact and overtopping of steep sea walls including recurves. At a given time breaking is said to occur if the wave height to water depth ratio for each individual wave exceeds a critical value of 0.6 and the Boussinesq terms are simply switched off. The example is presented of waves breaking over an offshore reef and then ceasing to break as they propagate inshore into deeper water and finally break as they run up a slope. This is not possible with the conventional criterion of a single onset of breaking based on rate of change of surface elevation which was also found to be less effective generally. The runup distribution on the slope inshore of the reef was well predicted. The model is tested against field data for overtopping available for Anchorsholme, Blackpool and corresponding 1:15 scale wave flume tests. Reflection of breaking waves impacting a steep sea wall is represented as a partial reversal of momentum flux with an empirically defined coefficient. Offshore to nearshore significant wave height variation was reasonably predicted although nearshore model spectra showed distinct differences from the experiments. The breaking wave shape described by a shape parameter was also not well represented as might be expected for such a simple model. Overtopping agreement between model, field and flume was generally good although repeatability of two nominally identical flume experiments was only within 25%. Different distributions of random phase between spectral components can cause overall overtopping rates to differ by up to a factor of two. Predictions of mean discharge by EurOtop methods were within a factor of two of experimental measurements.     

The applicability of the shallow water equations for modelling violent wave overtopping

The shallow water equations (SWE) have been used to model a series of experiments examining violent wave overtopping of a near-vertical sloping structure with impacting wave conditions. A finite volume scheme was used to solve the shallow water equations. A monotonic reconstruction method was applied to eliminate spurious oscillations and ensure proper treatment of bed slope terms. Both the numerical results and physical observations of the water surface closely followed the relevant Rayleigh probability distributions. However, the numerical model overestimated the wave heights and suffered from the lack of dispersion within the shallow water equations. Comparisons made on dimensionless parameters for the overtopping discharge and percentage of waves overtopping between the numerical model and the experimental observations indicated that for the lesser impacting waves, the shallow water equations perform satisfactorily and provide a good alternative to computationally more expensive methods.     

The new wave overtopping database for coastal structures

Significant effort has been made to generate a homogeneous database on wave overtopping consisting of more than 10,000 irregular wave overtopping tests from more than 160 independent projects or test series, each described by means of 31 parameters. Many coastal structures, including dikes, rubble mound breakwaters, berm breakwaters, caisson structures and combinations have been considered and have been schematised for inclusion in the database. All these overtopping tests are represented by over 300,000 numbers in the database.     

Laboratory study of combined wave overtopping and storm surge overflow of a levee

Combined wave overtopping and storm surge overflow of a levee with a trapezoidal cross section was studied in a two-dimensional laboratory wave/flow flume at a nominal prototype-to-model length scale of 25-to-1. The goal of this study was to develop design guidance in the aftermath of Hurricane Katrina. Time series of water depth at two locations on the levee crown and flow thickness at five locations on the landward-side slope were measured along with horizontal velocity near the landward edge of the crown. New equations are presented for average overtopping discharge, distribution of instantaneous discharge, and distribution of individual wave volumes. Equations are also given for mean flow thickness, RMS wave height, mean velocity, and velocity of the wave front down the landward-side slope.     

Predictions on Irregular Wave run-up and Overtopping

A series of hydraulic model tests are carried out to investigate random wave run-up and overtopping on smooth, impermeable single slope and composite slope. Based on analysis of the influences of wave steepness, structure slope, incident wave angle, width of the berm and water depth on the berm and the wave run-up, empirical formulas for wave run-up on dike are proposed. Moreover, empirical formula on estimating the wave run-up on composite slope with multiple berms is presented for practical application of complex dike cross-section. The present study shows that the influence factors for wave overtopping are almost the same as those for wave run-up and the trend of the wave overtopping variation with main influence parameters is also similar to that for wave run-up. The trend of the wave overtopping discharge variations can be well described by two main factors, i.e. the wave run-up and the crest freeboard of the structure. A new prediction method for wave overtopping discharge is proposed for random waves. The proposed prediction formulas are applied to case study of over forty cases and the results show that the prediction methods are good enough for practical design purposes.     

Prototype measurements and small-scale model tests of wave overtopping at shallow rubble-mound breakwaters: the Ostia-Rome yacht harbour case

The paper presents the comparison between the results of small-scale model tests and prototype measurements of wave overtopping at a rubble-mound breakwater. The specific structure investigated is the west breakwater of the yacht harbour of Rome at Ostia (Italy) and is characterized by a gentle seaward slope (1/4) and by a long, shallow foreshore. The laboratory tests firstly aimed at carefully reproducing two measured storms in which overtopping occurred and was measured. The tests have been carried out in two independent laboratories, in a wave flume and in a wave basin, hence using a two-dimensional (2-D) and a three-dimensional (3-D) setup. In the 2-D laboratory tests no overtopping occurred during the storm reproductions; in the 3-D case discharges five to ten times smaller than those observed in prototype have been measured. This indicates the existence of model and scale effects. These effects have been discussed on the basis of the results of several parametric tests, which have been carried out in both laboratories, in addition to the storm reproductions, varying wave and water level characteristics. Final comparison of all the performed tests with 86 prototype measurements still suggests the existence of scale and model effects that induce strong underestimation of overtopping discharge at small scale. The scale reproduction of wave breaking on the foreshore, together with the 3-D features of the prototype conditions and the absence of wind stress in the laboratory measurements, have been individuated as the main sources of scale and model effects. The paper also provides a comparison between the data and a largely used formula for wave overtopping discharges in the presence of structures similar to the one at hand. The suitable value of a roughness factor that appears in that formula is investigated and good agreement is found with other recent researches on rubble-mound breakwaters.     

Probability distributions for wave runup on beaches

Measured probability distributions of shoreline elevation, swash height (shoreline excursion length) and swash maxima and minima from a wide range of beach types are compared to theoretical probability distributions. The theoretical distributions are based on assumptions that the time series are weakly steady-state, ergodic and a linear sum of random variables. Despite the swash process being inherently non-linear, results indicate that these assumptions are not overly restrictive with respect to modeling exceedence statistics in the upper tail of the probability distribution. The RMS-errors for a range of exceedence level statistics (50, 10, 5, 2, and 1%) were restricted to < 10 cm (and often < 5 cm) for all of the swash variables that were investigated. The results presented here provide the basis for further refinement of coastal inundation modeling as well as stochastic-type morphodynamic modeling of beach response to waves. Further work is required, however, to relate the parameters of swash probability distributions to wave conditions further offshore.     

Layer thicknesses and velocities of wave overtopping flow at seadikes

Seadikes often fail due to wave overtopping and a failure of the landward slope. Therefore, these aspects have to be taken into account for the design of seadikes. In present design, the calculation of the crest height of seadikes is essentially based on using a design water level and the corresponding wave run-up height. An average overtopping rate is generally considered for wave overtopping which can not account for the stresses and other effects due to extreme individual overtopping events. Landward slope design is more or less based on experience. It can be concluded from failure analysis that dike failures on the landward slope are rather initiated by individual overtopping events, in particular by the related overtopping flow velocities and layer thicknesses which are relevant for the prediction of erosion, infiltration and slip failure. Therefore, overtopping flow velocities and layer thicknesses are required in addition to average overtopping rates as hydraulic boundary conditions for the geotechnical stability analysis of seadikes.The objective of the present paper is the theoretical and experimental determination of overtopping flow velocities and layer thicknesses on the seaward slope, the dike crest and the landward slope of a seadike. Overtopping parameters are derived on the basis of small scale model tests which are required for the design of the landward slope and to avoid dike failures by wave overtopping in the future. For the prediction of the layer thicknesses and the velocities of the overtopping flow on the seaward slope, the dike crest and the landward slope, a set of theoretical formulas is derived and validated by hydraulic scale model tests.     

Derivation of unified wave overtopping formulas for seawalls with smooth,impermeable surfaces based on selected CLASH datasets

A set of unified formulas for prediction of the mean rate of wave overtopping at coastal structures with smooth, impermeable surfaces have been derived through the analysis of the selected CLASH datasets. The mean wave overtopping rate is expressed as the function of the significant wave height at the structural toe and the relative freeboard. The formulas are applicable for both vertical walls and inclined seawalls with smooth transition between them. The formulas are simple but cover the full range of water depth from the shoreline to deep water. The effects of the toe depth and the seabed slope on wave overtopping rate are duly incorporated in the formulas. Prediction performance of the new formulas is better than the EurOtop formulas for both vertical walls and inclined seawalls.     

欧洲北海海域波高区间分布概率研究

为了研究欧洲北海海域的波高全区域概率分布情况,从而为海洋平台等海洋浮式结构物的选址和结构设计提供依据。首先基于Global Waves Statistics(GWS)提供的实测数据,确定典型计算工况的发生概率;同时考虑实测数据中极端波浪环境下的数据缺失导致大波高分布概率偏小的问题,利用三参数Weibull分布确定不同重现期下的极值风速,作为典型计算工况的补充。以不同风速、风向的定常风场为输入项,利用第三代海浪数值模型SWAN模型,对北海全区域波高进行数值模拟。将数值模拟的稳态形式依照各工况的发生概率进行归一化累加处理,认为其结果可以表征全区域的波高概率分布情况。以波高概率分布的计算结果为依据,分析北海海域波浪环境的统计学特征,发现有效波高为7 m以上的大波高频发区在北海北部区域有大范围分布;有效波高4～5 m为北海东北区域的多发海况,极端海况下的有效波高主要分布于7～14 m区间,在地形突变区域的波高发生显著变化。     

Three-dimensional investigations of wave overtopping on rubble mound structures

To study the influence of wave obliquity and directional spreading on wave overtopping of rubble mound breakwaters a total of 736 three-dimensional model tests were carried out at Aalborg University. The results of these tests are presented and analysed in this paper yielding a new empirical reduction factor to describe the influence of wave obliquity and directional spreading on the average wave overtopping discharges. The study shows that perpendicularly incident, long-crested waves result in conservative values of the overtopping discharge for the tested cross-section.     

Wave run-up and overtopping on smooth and rough slopes of coastal structures

A series of hydraulic model tests has been carried out in a glass wave flume to investigate the influences of wave height, wave period, wave steepness, surf similarity parameter, roughness, layer thickness and porosity on wave run-up and overtopping of 1:2 sloped impermeable and permeable breakwaters fronted by a 1:10 gentle, smooth beach slope. The analysis of results involves the correlation between the overtopping energy transfer with the relative wall height and the relationship between wave run-up and overtopping rate. Further, measured wave run-up and overtopping rates are compared with the results given in the Shore Protection Manual (1984), Automated Coastal Engineering System (1992)and results of other investigators.     

Empirical parameterization of setup,swash, and runup

Using shoreline water-level time series collected during 10 dynamically diverse field experiments, an empirical parameterization for extreme runup, defined by the 2% exceedence value, has been developed for use on natural beaches over a wide range of conditions. Runup, the height of discrete water-level maxima, depends on two dynamically different processes; time-averaged wave setup and total swash excursion, each of which is parameterized separately. Setup at the shoreline was best parameterized using a dimensional form of the more common Iribarren-based setup expression that includes foreshore beach slope, offshore wave height, and deep-water wavelength. Significant swash can be decomposed into the incident and infragravity frequency bands. Incident swash is also best parameterized using a dimensional form of the Iribarren-based expression. Infragravity swash is best modeled dimensionally using offshore wave height and wavelength and shows no statistically significant linear dependence on either foreshore or surf-zone slope. On infragravity-dominated dissipative beaches, the magnitudes of both setup and swash, modeling both incident and infragravity frequency components together, are dependent only on offshore wave height and wavelength. Statistics of predicted runup averaged over all sites indicate a − 17 cm bias and an rms error of 38 cm: the mean observed runup elevation for all experiments was 144 cm. On intermediate and reflective beaches with complex foreshore topography, the use of an alongshore-averaged beach slope in practical applications of the runup parameterization may result in a relative runup error equal to 51% of the fractional variability between the measured and the averaged slope.     

长江口横沙东滩典型海堤越浪量现场和试验研究

越浪量是允许越浪海堤设计的重要参数。在对以往相关研究成果进行回顾和分析基础上,结合长江口横沙东滩促淤圈围五期工程现场波浪和越浪量实测资料,通过对横沙东滩典型断面型式进行整体和断面物理模型试验,研究结构各参数对越浪量的影响,进而提出适合长江口海堤的越浪量计算公式。公式计算结果与试验数据吻合良好,与Van der Meer公式相比具有较好的一致性。     

A performance test of nearshore wave height prediction with CLASH datasets

The CLASH database was analyzed for extraction of a set of data having the measured wave heights at both the deep station and the toe of the structure for wave overtopping tests, yielding 1214 data from 29 datasets. Wave heights in front of the toe of the structure were estimated with the Goda formulas and compared with the measured ones. Comparison yielded the overall mean of 1.106 with the standard deviation of 0.155 for the ratio of the estimated to the measured heights, which support the use of the Goda formulas for prediction of nearshore wave heights. Another set of 1215 data having the measured wave heights at the deep station and the wave heights calculated with the SWAN model was also extracted from the CLASH database. A comparative test of the SWAN model using the wave height estimated with the Goda formulas in lieu of the measured height indicated the performance of the SWAN model being similar to that of the Goda formulas, but a tendency of underestimation was noticed in shallow water on a beach of very gentle slope.     

Characterizing random wave surface elevation data

The definition and subsequent use of dimensional and dimensionless parameters to characterize various nonlinear aspects of ocean surface waves has again become a matter of great interest to the offshore community. The desire to ascertain whether laboratory simulations are adequately representing the surface waves found in the oceans and the concern over the mechanisms behind platform response phenomena, like ringing, has driven this resurgence of interest. This paper presents a depth independent characterization of single design waves, from which improved estimates of localized wave crest front and back slopes follow that are consistent with discrete time series analysis. Characterization of the nature of the entire wave data recorded requires a combination of spectral parameters and probabilistic models in addition to those used in the design wave characterization. A new expression for the direct evaluation of the kurtosis from knowledge of the spectral bandwidth, the relationship between some of the common spectral parameters, and some modified spectral parameters are presented and discussed. Three illustrative examples are presented. The first example provides a detailed examination of wave data measured from a series of random amplitude and random phase tests in a large model basin. The second presents estimates of the various parameters for the Pierson-Moskowitz and Wallops wave spectrum models. The third example investigates the use of the spectral peakedness ratio for comparing data with selected wave spectrum models. The examples illustrate how the formulae can provide a comprehensive local and global parametric characterization of surface wave elevation data.     

Characterizing random wave surface elevation data

The definition and subsequent use of dimensional and dimensionless parameters to characterize various nonlinear aspects of ocean surface waves has again become a matter of great interest to the offshore community. The desire to ascertain whether laboratory simulations are adequately representing the surface waves found in the oceans and the concern over the mechanisms behind platform response phenomena, like ringing, has driven this resurgence of interest. This paper presents a depth independent characterization of single design waves, from which improved estimates of localized wave crest front and back slopes follow that are consistent with discrete time series analysis. Characterization of the nature of the entire wave data recorded requires a combination of spectral parameters and probabilistic models in addition to those used in the design wave characterization. A new expression for the direct evaluation of the kurtosis from knowledge of the spectral bandwidth, the relationship between some of the common spectral parameters, and some modified spectral parameters are presented and discussed. Three illustrative examples are presented. The first example provides a detailed examination of wave data measured from a series of random amplitude and random phase tests in a large model basin. The second presents estimates of the various parameters for the Pierson-Moskowitz and Wallops wave spectrum models. The third example investigates the use of the spectral peakedness ratio for comparing data with selected wave spectrum models. The examples illustrate how the formulae can provide a comprehensive local and global parametric characterization of surface wave elevation data.