Wave run-up on bermed coastal structures

Reliable estimation of wave run-up is required for the effective and efficient design of coastal structures when flooding or wave overtopping volumes are an important consideration in the design process. In this study, a unified formula for the wave run-up on bermed structures has been developed using collected and existing data. As data on berm breakwaters was highly limited, physical model tests were conducted and the run-up was measured. Conventional governing parameters and influencing factors were then used to predict the dimensionless run-up level with 2% exceedance probability. The developed formula includes the effect of water depth which is required in understanding the influence of sea level rise and consequent changes of wave height to water depth ratio on the future hydraulic performance of the structures. The accuracy measures such as RMSE and Bias indicated that the developed formula is more accurate than the existing formulas. Additionally, the new formula was validated using field measurements and its superiority was observed when compared to the existing prediction formulas. Finally, the new design formula incorporating the partial safety factor was introduced as a design tool for engineers.     

堆石防波堤不规则波浪反射系数试验研究

结合物理模型试验,分析斜坡坡度、波陡、相对水深、护面类型和破波参数等因素对堆石防波堤不规则波浪反射系数的影响规律。将常用的Van der Meer公式,Seelig公式,Postma公式和Davison公式计算值和实测值进行比较,并结合试验数据,基于有效波高和平均周期定义的Iribarren数,得出堆石防波堤不规则波浪反射系数经验公式。结果表明,该公式能较好地计算不规则波作用下块石和扭王块体护面堆石防波堤波浪反射系数。     

Neural network modelling of wave overtopping at coastal structures

A method has been developed to estimate wave overtopping discharges for a wide range of coastal structures. The prediction method is based on Neural Network modelling. For this purpose use is made of a data set obtained from a large number of physical model tests (collected within the framework of the European project CLASH, see e.g. [Steendam, G.J., Van der Meer, J.W., Verhaeghe, H., Besley, P., Franco, L. and Van Gent, M.R.A. (2004). The international database on wave overtopping. World Scientific, Proc. 29th ICCE, vol. 4, pp. 4301–4313, Lisbon, Portugal.]). Moreover, a method was developed to obtain confidence intervals for the overtopping predictions of the neural network.     

Nonlinear surface fit stability formula without any transition region for conventional breakwater design

Determining the optimum weight of the armor blocks is of vital importance in the design of conventional breakwaters. The widely used formulae in the literature include the transition region from plunging to surging waves. In this paper, it is aimed to investigate a new design formula without any transition region as an alternative to widely used Van der Meer formulae. The dimensionless parameters of Van der Meer formulae as well as newly generated variables are used as inputs. Nonlinear surface fit best subset regression model is used to find the optimum input combination that keeps the nonlinear relationships. All the input parameters, their second powers, and their two-way interactions are included in the regression analyses to obtain a nonlinear surface fit. Various goodness of fit statistics are applied to check the different perspectives of the model accuracy. It is demonstrated that the proposed model gives a realistic prediction of the stability number for critical data range. Especially for high values of stability number the proposed formula outperforms the benchmark formulae of Van der Meer and Etemad-Shahidi and Bonakdar. The other advantage is that it does not contain any transition region that depends on wave conditions. Besides, there is no need to include “number of waves” and “permeability” parameters into the equation.     

Design of rubble-mound breakwaters using M5 ′ machine learning method

Predicting the stability of armor blocks of breakwaters and revetments is a very important issue in coastal and ocean engineering. Recently, soft computing tools such as artificial neural networks and fuzzy logic have been used to predict the stability number of armor blocks. However, these tools are not as transparent as empirical formulas. This study presents another soft computing approach, i.e. model trees for predicting the stability number of armor blocks. The main advantage of model trees is that, unlike the other data learning tools, they are easier to use and more importantly they represent understandable mathematical rules. A total of 579 experimental test data from Van der Meer 1988 are used for developing the model. The conventional governing parameters were selected as the input variables and the obtained results were compared with those of measurements, empirical and soft computing models. Using statistical measures, it was shown that the developed models are more accurate than previous empirical and soft computing models. Furthermore, some simple rules are given for armor blocks’ design.     

On front slope stability of berm breakwaters

The short communication presents application of the conventional Van der Meer stability formula for low-crested breakwaters for the prediction of front slope erosion of statically stable berm breakwaters with relatively high berms. The method is verified (Burcharth, 2008) by comparison with the reshaping of a large Norwegian breakwater exposed to the North Sea waves. As a motivation for applying the Van der Meer formula a discussion of design parameters related to berm breakwater stability formulae is given. Comparisons of front erosion predicted by the use of the Van der Meer formula with model test results including tests presented in Sigurdarson and Van der Meer (2011) are discussed. A proposal is presented for performance of new model tests with the purpose of developing more accurate formulae for the prediction of front slope erosion as a function of front slope, relative berm height, relative berm width, method of armour stone placement, and hydraulic parameters. The formulae should cover the structure range from statically stable berm breakwaters to conventional double layer armoured breakwaters.     

Prediction of wave pressures on smooth impermeable seawalls

Simple prediction methods are proposed to estimate the wave induced pressures on smooth impermeable seawalls. Based on the physics of the wave structure interaction, the sloped seawall is divided into a total of five zones (zones 1, 2 and 3 during run-up (corresponding pressures are called as positive pressures) and zones 4 and 5 during run-down (corresponding pressures are called negative pressures)) (Fig. 1). Zone 1 (0<z<d−H_i/2), where the wave pressure is governed by the partial reflection and phase shift; Zone 2 (d−H_i/2<z<d), where the effect of wave breaking and turbulence is significant; Zone 3 (d<z<Run-up height), where the pressure is induced by the run-up water; Zone 4 (Run-down<z<d), where the wave pressure is caused by the run-down effect and Zone 5 (0<z<d-Run down), where the negative wave pressures are due to partial reflection and phase shift effects. Here d is the water depth at the toe of the seawall, H_i is the incident wave height and z is the vertical elevation with toe of the seawall as origin and z is positive upward. For wave pressure prediction in zones 1 and 5, the empirical formula proposed by Ahrens et al. (1993) to estimate the wave reflection and Sutherland and Donoghue's recommendations (1998) for the estimation of phase shift of the waves caused by the sloped structures are used. Multiple regression analysis is carried out on the measured pressure data and empirical formulas are proposed for zones 2, 3 and 4. The recommendations of Van der Meer and Breteler (1990) and Schüttrumpf et al. (1994) for the prediction of wave run-down are used for pressure prediction at zone 4. Comparison of the proposed prediction formulas with the experimental results reveal that the prediction methods are good enough for practical purposes. The present study also shows a strong relation between wave reflection, wave run-up, wave run-down and phase shift of waves on wave pressures on the seawalls.     

Managing local coastal inundation risk using real-time forecasts and artificial dune placements

Uncertainty in the behaviour of future storm events and extreme water levels means that the introduction of Early Warning Systems for coastal inundation risk at vulnerable local sites becomes increasing paramount. In this study the coupled hydro-morphodynamic model XBeach is used at two sites along the Emilia-Romagna coastline in northern Italy to predict coastal inundation risk in the presence of coastal structures and temporary artificial dunes. These dunes are typically formed by beach scraping and are used on this coastline to protect beach-front infrastructure during the winter period. Coastal inundation risk is defined by the cross-shore distance between the seaward edge of the building and the time-varying waterline predicted by XBeach. A series of synthetic storm events as well as a real-world scenario that caused dune failure at one of the sites are tested. Comparisons between XBeach results and the Van Der Meer empirical formula for wave transmission behind offshore structures show a very strong agreement, while the real-world scenario indicates promising model prediction performance of dune failure at least one day in advance. A new model tool known as DuneMaker is developed that modifies XBeach model grids to simulate the impacts of scraped/placed artificial dunes of varying size, shape and configuration. The use of this tool is demonstrated on the same model test runs, where it is shown that improved dune design can reduce the predicted coastal inundation risk at critical points of vulnerability identified by the model.     

Measured and modeled wave overtopping on a natural beach

The rate of wave overtopping of a barrier beach is measured and modeled. Unique rate of wave overtopping field data are obtained from the measure of the Carmel River, California, lagoon filling during a time when the lagoon is closed-off with no river inflow. Volume changes are based on measured lagoon height changes applied to a measured hypsometric curve. Wave heights and periods are obtained from directional wave spectra data in 15 m fronting the beach. Beach morphology was measured by GPS walking surveys. Three empirical overtopping models by Van der Meer and Janssen (1995), Hedges and Reis (1998) and Pullen et al. (2007) with differing parameterizations on wave height, period and beach slope and calibrated using extensive laboratory data obtained over plane, impermeable beaches are applied in a quasi-2D manner and compared with the field observations. Three overtopping events are considered when morphology data were available less than 2 weeks prior to the event. The models are tuned to fit the data using a reduction factor to account for beach permeability, berm characteristics, non-normal wave incidence and surface roughness influence. In addition, the run-up model by Stockdon et al. (2006) based on field data is examined and found to underestimate run-up as the calculated values were too small to predict any of the observed overtopping. The three overtopping models performed similarly well with values of 0.72–0.87 for the two narrow-banded wave cases, with an average reduction factor of 0.78. The European model (Pullen et. al., 2007) performed best overall and in particular for the case of the broad-banded, double peaked wave spectrum.     

Forecast of wave run-up on coastal structure using offshore wave forecast data

In this paper, first we introduce the wave run-up scale which describes the degree of wave run-up based on observed sea conditions near and on a coastal structure. Then, we introduce a simple method which can be used for daily forecast of wave run-up on a coastal structure. The method derives a multiple linear regression equation between wave run-up scale and offshore wind and wave parameters using long-term photographical observation of wave run-up and offshore wave forecasting model results. The derived regression equation then can be used for forecasting the run-up scale using the offshore wave forecasting model results. To test the implementation of the method, wave run-up scales were observed at four breakwaters in the East Coast of Korea for 9 consecutive months in 2008. The data for the first 6 months were used to derive multiple linear regression equations, which were then validated using the run-up scale data for the remaining 3 months and the corresponding offshore wave forecasting model results. A comparison with an engineering formula for wave run-up is also made. It is found that this method can be used for daily forecast and warning of wave run-up on a coastal structure with reasonable accuracy.     

Comparison between M5′ model tree and neural networks for prediction of significant wave height in Lake Superior

Prediction of wave height is of great importance in marine and coastal engineering. Soft computing tools such as artificial neural networks (ANNs) are recently used for prediction of significant wave height. However, ANNs are not as transparent as semi-empirical regression-based models. In addition, neural networks approach needs to find network parameters such as number of hidden layers and neurons by trial and error, which is time consuming. Therefore, in this work, model trees as a new soft computing method was invoked for prediction of significant wave height. The main advantage of model trees is that, compared to neural networks, they represent understandable rules. These rules can be readily expressed so that humans can understand them. The data set used for developing model trees comprises of wind and wave data gathered in Lake Superior from 6 April to 10 November 2000 and 19 April to 6 November 2001. M5′ algorithm was employed for building and evaluating model trees. Training and testing data include wind speed (U₁₀) as the input variable and the significant wave height (H_s) as the output variable. Results indicate that error statistics of model trees and feed-forward back propagation (FFBP) ANNs were similar, while model trees was marginally more accurate. In addition, model tree shows that for wind speed above 4.7 m/s, the wave height increases nonlinearly by the wind speed.     

Wave run-up on slender piles in design conditions — Model tests and design rules for offshore wind

Wave run-up on foundations is a very important factor in the design of entrance platforms for offshore wind turbines. When the Horns Reef 1 wind turbine park in Denmark was designed the vertical wave run-up phenomenon was not well known in the industry, hence not sufficiently considered in the design of Horns Reef 1. As a consequence damage was observed on the platforms. This has been the situation for several sites and design tools for platform loads are lacking. As a consequence a physical model test study was initiated at Aalborg University to clarify wave run-up on cylindrical piles for different values of diameter to water depth ratios (D/h) and different wave heights to water depth ratios (H/h) for both regular and irregular waves. A calculation model is calibrated based on stream function theory for crest kinematics and velocity head stagnation theory. Due to increased velocities close to the pile an empirical factor is included on the velocity head. The evaluation of the calculation model shows that an accurate design rule can be established even in breaking wave conditions. However, calibration of a load model showed that it was necessary to increase the run-up factor on the velocity head by 40% to take into account the underestimation of run-up for breaking or nearly breaking waves given that they produce thin run-up wedges and air entrainment, two factors not coped with by the measurement system.     

强非线性规则波在防波堤上爬高公式研究

为了研究波浪非线性对爬高的影响,解决防波堤等工程设计的实际问题,通过对数学模型试验、物理模型试验、规范公式得到的防波堤波浪爬高对比分析,分析了非线性主要影响参数厄塞尔数、相对水深和波陡对波浪爬高的影响规律,指出规范公式计算时存在的缺陷,并对其计算公式、适用范围进行修正、拟合,得到了强非线性规则波浪爬高的计算方法,可适用于斜坡堤断面的波浪爬高计算,与物理模型试验和数学模型试验结果对比表明,新的波浪爬高计算公式具有较好的计算精度,研究结果可为防波堤等实际工程设计提供重要参考。     

Application of probabilistic neural network to design breakwater armor blocks

This study presents a probabilistic neural network (PNN) technique for predicting the stability number of armor blocks of breakwaters. The PNN is prepared using the experimental data of Van der Meer. The predicted stability numbers of the PNN are compared with those of previous studies, i.e. by an empirical formula and a previous neural network model. The agreement index between the measured and predicted stability numbers by PNN are better than those by the previous studies. The PNN offers a way to interpret the network's structure in the form of a probability density function and it is easy to implement. Therefore, it can be an effective tool for designers of rubble mound breakwaters.     

Prediction of scour depth at breakwaters due to non-breaking waves using machine learning approaches

Coastal structures may cease to function properly due to seabed scouring. Hence, prediction of the maximum scour depth is of great importance for the protection of these structures. Since scour is the result of a complicated interaction between structure, sediment, and incoming waves, empirical equations are not as accurate as machine learning schemes, which are being widely employed for the coastal engineering modeling. In this paper, which can be regarded as an extension of Pourzangbar et al. (2016), two soft computing methods, a support vector regression (SVR), and a model tree algorithm (M5′), have been implemented to predict the maximum scour depth due to non-breaking waves. The models predict the relative scour depth (S_max/H₀) on the basis of the following variables: relative water depth at the toe of the breakwater (h_toe/L₀), Shields parameter (θ), non-breaking wave steepness (H₀/L₀), and reflection coefficient (Cr). 95 laboratory data points, extracted from dedicated experimental studies, have been used for developing the models, whose performances have been assessed on the basis of statistical parameters. The results suggest that all of the developed models predict the maximum scour depth with high precision, the M5′ model performed marginally better than the SVR model and also allowed to define a set of transparent and physically sound relationships. Such relationships, which are in good agreement with the existing empirical findings, show that the relative scour depth is mainly affected by wave reflection.     

Experimental Study of Overtopping on Sea Dikes and Coastal Flooding Under the Coupled Processes of Tides and Waves

Storm surges are cataclysmic natural disasters that occur along the coasts and are usually accompanied by large waves. The effects of coupled storm surges and waves can pose a significant threat to coastal security. Previous laboratory studies on the effects of storm surges and waves on coastal structures have typically utilized steady water levels and constant wave elements. An indoor simulation of the coupled processes of tides and waves is developed by adding a tide generation system to an existing laboratory wave basin to model continuous dynamic tide levels so that tide generation and wave-making occur synchronously in the pool. Specific experimental methods are given, which are applied to further study waves overtopping on artificial sea dikes and coastal flooding evolution under the coupled actions of tides and waves. The results of the overtopping discharge obtained by the test with a dynamic water level are compared with those obtained from steady water level tests and the existing empirical formula. In addition, the impacts of ecological coastal shelterbelts and structures on coastal flood processes and distributions are also investigated. The proposed simulation methods provide a new approach for studying the effects of storm surges and waves on coastal areas. The study also aims to provide a reference for coastal protective engineering.

     

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.     

Effect of open gap in coastal forest on tsunami run-up—investigations by experiment and numerical simulation

The objective of this study is to investigate the effects of an open gap, such as a road, in a coastal forest on tsunami run-up. A numerical model based on two-dimensional nonlinear long-wave equations was developed to account for the effects of drag and turbulence induced shear forces due to the presence of vegetation. Experiments were conducted on a forest simulated with vertical cylinders by changing the gap width. The numerical model was validated in good agreement with the experimental results. The numerical model was then applied to a wide forest of Pandanus odoratissimus, a tree species that is a dominant coastal vegetation on a sand dune in South and Southeast Asia. The effect of vertical stand characteristics of P. odoratissimus with aerial roots was considered on the drag resistance. A straight open gap perpendicular to the shoreline was used to investigate the effect of gap width. As the gap width increases, the flow velocity at the end of the open gap first increases, reaches a maximum, and then decreases, while the run-up height increases monotonously. The maximum velocity in the present condition is 1.7 times the maximum velocity without a coastal forest. The effects of different gap arrangements in the forest on tsunami run-up were also investigated in this paper. The flow velocity at the end of an open gap can be reduced by a staggered arrangement.     

大糙率礁面影响下珊瑚礁海岸附近规则波演化及爬高试验研究

本文通过波浪水槽试验研究了大糙率礁面影响下波浪沿礁的演化和爬高规律,测试了一系列规则波工况并对比了光滑礁面和粗糙礁面的情况。结果分析表明：二次谐波是礁坪上透射波的重要组成成分,粗糙礁面使主频波和二次谐波减小,对更高阶波的影响不显著;相对礁坪水深是描述礁坪上波浪透射的关键参数,礁面从光滑变为粗糙时海岸附近透射系数显著减小,能量衰减系数平均增大了8%,但礁前反射系数与礁面糙率之间无明显关系;礁后岸滩爬高随着透射波高的增大而增长,最后拟合了本文试验条件下珊瑚礁大糙率礁面预测规则波爬高的关系式。     

Coastal forest effects on tsunami run-up heights

An experimental study was carried out to determine the effects of a coastal forest on tsunami run-up heights. The beach was built as a natural sandy beach at laboratory scale. The coastal forest model was constructed using artificial trees (FM–I) and cylindrical timber sticks (FM–II). Artificial trees were placed on a 1:5 slope in three different layouts: rectilinear, staggered, and dense rectilinear. It was shown that in the case when the trees were placed in the dense rectilinear pattern and close to the still water level (SWL), the run-up height was reduced by approximately 45% compared with the case without trees. After evaluation of the experimental results, the parameters that affect the run-up height were determined. These parameters were written as a dimensionless group using Buckingham's Pi theorem. An extensive regression analysis was carried out and equations proposed. Furthermore, all experiments were repeated with a slope of 1:3.5 to verify the proposed equations. The experimental results were compared with the results of the proposed equations, and it was shown a good agreement between the results.