Numerical simulation of irregular wave overtopping against a smooth sea dike

Based on the filtered Navier-Stokes equations and Smagorinsky turbulence model,a numerical wave flume is developed to investigate the overtopping process of irregular waves over smooth sea dikes.Simulations of fully nonlinear standing wave and regular wave’s run-up on a sea dike are carried out to validate the implementation of the numerical wave flume with wave generation and absorbing modules.To model stationary ergodic stochastic processes,several cases with different random seeds are computed for each specified irregular wave spectrum.It turns out that the statistical mean overtopping discharge shows good agreement with empirical formulas,other numerical results and experimental data.     

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.     

Effect of Berm Width and Elevation on Irregular Wave Run-Up

This paper discusses the effect of berm width and elevation of composite slope on irregular wave run-up. Based on the data obtained from model tests, the formula and distribution of irregular wave run-up on composite slope are derived. The changing of wind speed, width and elevation of the berm are considered comprehensively. The wave run-up with various exceedance probability can be es-timated utilizing the distribution curves of irregular wave run-up.     

陡墙式海堤平台对波浪爬高影响

通过物理模型试验研究陡墙式海堤复坡平台高程和宽度对波浪爬高的影响。平台越宽对波浪爬高影响越大,平台位于静水位处对波浪爬高影响最大,并得出了受平台影响的波浪爬高折减系数计算公式,可供工程参考使用。     

Effect of Wave Groups on Wave Run-up

-The effect of wave group on wave run-up on a slope dike is mainly discussed in this paper. Two simulating methods of wave group and their applications in laboratory are introduced. Synthesizing the research results of wave run-up on a slope dike, the effect of wave group on wave run-up on a slope dike in coastal protection engineering is studied as the main point.     

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.     

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。     

孤立波低顶海堤越浪的数值模拟研究

灾害性波浪是中国沿海地区最具破坏性的自然灾害之一。采用开源程序OpenFOAM中interFoam求解器,对低顶海堤（在风暴潮和海平面上升情况下所面临的不利工况）的孤立波越浪特性开展数值模拟研究。通过孤立波冲击海堤的基准算例,验证模型在模拟波浪爬升和越浪过程中大变形波面以及剧烈波浪力方面的精度。基于验证的数值模型,对孤立波在低顶海堤上的越浪特征以及防浪墙高度对越浪的影响开展参数化研究。结果表明堤顶超高减小导致更为剧烈的越浪。针对尚无低顶海堤孤立波越浪量经验公式的问题,提出新的适用于堤顶超高小或为0的孤立波越浪量经验公式。此外,研究发现增加防浪墙高度可有效减少越浪,但防浪墙所受的波浪力也增大。综合考虑防浪墙减少越浪以及自身所受波浪力,针对文中研究采用的海堤截面和波浪条件,建议无量纲防浪墙高度取为1.00。     

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.     

Stable-thickness study of masonry block on the inner slope of dikes

Dike failure caused by overtopping is likely to result in major casualties and property losses.Aiming at this fact,a series of physical model experiments were conducted on stable thickness of masonry block on the inner slope of the dike.According to the erosion of block embankment with different thicknesses,the relation between the stable thickness of masonry block pitching of the inner slope and the average overtopping discharge is discussed.New equations subject to irregular waves are presented for average overtopping discharge,based upon the analysis of mean overtopping discharge and comparison of present overtopping discharge formulas at domestic and abroad.Finally,a calculation equation of the stable thickness of the dry masonry block stone of inner slope subject to irregular waves is given.In conclusion,the formula matches well with the experiment result,which is capable of functioning as an important reference for structure designs of the dike in China.     

Rock stability of rubble mound breakwaters with a berm

Breakwaters with a berm can significantly reduce overtopping and reduce the required rock size compared to straight slopes without a berm. Here, the stability of rock slopes with a horizontal berm has been studied by means of physical model tests to provide information on the required rock size. The tests and analysis are focussed on the slope above the berm as well as the slope below the berm. Also the stability of the rock at the berm is addressed. The influence of the slope angle (1:2 and 1:4), the width of the berm, the level of the berm, and the wave steepness has been investigated. Based on the test results prediction formulae have been derived to quantify the required rock size for rubble mound breakwaters with a berm. Especially for the slope above the berm, the rock size can be reduced significantly compared to straight slopes.     

基于随机森林的复坡堤越浪量预测研究

针对复坡堤越浪量的计算问题,提出了采用随机森林算法预测越浪量的方法。首先,通过对欧洲CLASH数据集进行筛选,挑选出符合复坡堤越浪量预测的数据;其次,对数据做无量纲化处理,建立以随机森林为基础的复坡堤越浪量预测模型,并通过网格搜索(GridSearchCV)方法对模型进行调参以改善模型的性能;最后,利用决定系数R~2来评估模型的精度,并将随机森林模型与集成神经网络模型做了预测能力的对比,同时还给出了随机森林模型各个特征参数对预测精度的重要性。结果显示,随机森林模型的决定系数为92.7%,集成神经网络模型的决定系数为87.7%,表明随机森林模型对越浪量具有更强的学习和预测能力。通过对特征重要性的分析,墙顶高程对模型预测精度的影响最大,堤顶高程次之,堤脚宽度影响最小。     

Probabilistic Assessment of Wave Overtopping of Nampo Dike in the West Coast of Korea

The Nampo dike, which is located at the west coast of Korea, was destroyed by wave overtopping during the storms on 30 August and 17 September in 1959. In this paper, is performed the probabilistic assessment of wave overtopping of Nampo dike by use of Owen model, Van der Meer ＆ Janssen model and Hedges ＆ Reis model for wave overtopping of seawall. Based on the available tidal and wave data for storm surges in 1989, the risk assessment of wave overtopping of the Nampo dike has been carried out by both Level Ⅱ and Level Ⅲ reliability methods. The calculated resuhs show the general agreement of failure probability between the two methods. By utilizing the rehabilitated cross section of Nampo dike, the failure probability of wave overtopping for the Nampo dike after rehabilitation will be rapidly reduced to that of initial design at crest level of 9.0 m with the improved slope from 1 ： 2 to 1 ： 4 at seaside. Since the sea level may only rise 1.0 m in the next few decades, the failure probability of Nampo dike will be still in the safe range.     

Core made of geotextile sand containers for rubble mound breakwaters and seawalls: Effect on armour stability and hydraulic performance

A systematic armour stability and the hydraulic performance, including wave reflection, wave transmission, experimental study in the twin-wave flumes of Leichtweiss-Institute (LWI) is performed on a geocore breakwater and a conventional rubble mound breakwater in order to comparatively determine the wave run-up and wave overtopping. The geocore breakwater consists of a core made of sand-filled geotextile containers (GSC) covered by an armour made of rock. The geocore is more than an order of magnitude less permeable than the quarry run core of a conventional breakwater. As expected, the core permeability substantially affects the armour stability on the seaside slope, the wave transmission and the wave overtopping performance. Surprisingly, however, wave reflection and hydraulic stability of the rear slope are less affected. Formulae for the armour stability and hydraulic performance of the geocore breakwater are proposed, including wave reflection, transmission, run-up and overtopping.     

A numerical model of wave overtopping on seadikes

This paper describes the development of a numerical model for wave overtopping on seadikes. The model is based on the flux-conservative form of the nonlinear shallow water equations (NLSW) solved with a high order total variation diminishing (TVD), Roe-type scheme. The goal is to reliably predict the hydrodynamics of wave overtopping on the dike crest and along the inner slope, necessary for the breach modelling of seadikes. Besides the mean overtopping rate, the capability of simulating individual overtopping events is also required. It is shown theoretically that the effect of wave breaking through the drastic motion of surface rollers in the surfzone is not sufficiently described by the conventional nonlinear shallow water equations, neglecting wave setup from the mean water level and thus markedly reducing the model predictive capacity for wave overtopping. This is significantly improved by including an additional source term associated with the roller energy dissipation in the depth-averaged momentum equation. The developed model has been validated against four existing laboratory datasets of wave overtopping on dikes. The first two sets are to validate the roller term performance in improving the model prediction of wave overtopping of breaking waves. The last two sets are to test the model performance under more complex but realistic hydraulic and slope geometric conditions. The results confirm the merit of the supplemented roller term and also demonstrate that the model is robust and reliable for the prediction of wave overtopping on seadikes.     

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 0.117–0.424 m³/(m s) range of overtopping discharge and a 10 m/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.     

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.     

Analysis of overtopping flow on sea dikes in oblique and short-crested waves

Dike resilience against wave overtopping has gained more and more attention in recent years due to the effect of expected future climate changes. The overtopping flow velocities and flow depths on dikes have recently been studied in 2D small-scale experiments. This has led to semi-empirical formulae for the estimation of flow depths and flow velocities across a dike. The results have been coupled to the actual erosion of the landward dike slope determined by full-scale 2D tests using the so-called “Overtopping Simulator”. This paper describes the results from 96 small-scale tests carried out in a shallow water basin at Aalborg University to cover the so far unknown 3D effects from oblique long-crested and short-crested waves. Based on results from the laboratory tests, expansions are proposed to the existing 2D formulae so as to cover oblique and short-crested waves. The wave obliquity is seen to significantly reduce the overtopping flow velocities and flow depths on especially the landward slope of a sea dike. Moreover, the tests showed that the average flow directions on the dike crest from oblique long-crested and short-crested waves correspond approximately to the incident wave direction. Flow depths and the squared flow velocities on the dike are concluded to be Rayleigh-distributed in case of both long-crested and short-crested waves for all considered incident wave obliquities. Findings in the present paper are needed to obtain more realistic estimates of dike erosion caused by wave overtopping.     

Spatial distribution of wave overtopping water behind coastal structures

Spatial distribution of random wave overtopping water behind coastal structures was investigated using a numerical model based on Reynolds-Averaged Navier-Stokes solver (RANS) and Volume of Fluid (VOF) surface capturing scheme (RANS-VOF). The computed spatial distributions of wave overtopping water behind the structure agree well with the measurements by Pullen et al (2008) for a vertical wall and Lykke Andersen and Burcharth (2006) for a 1:2 sea dike. A semi-analytical model was derived to relate spatial distribution of wave overtopping water behind coastal structures to landward ground level, velocity and layer thickness on the crest. This semi-analytical model agrees reasonably well with both numerical model results and measurements close to coastal structures. Our numerical model results suggest that the proportion of wave overtopping water passing a landward location increases with a seaward slope when it is less than 1:3 and decreases with a seaward slope when it gets steeper. The proportion of wave overtopping water passing a landward location increases with landward ground level and overtopping discharge. It also increases with the product of incident wave height and wavelength, but decreases with increasing relative structure freeboard and crest width. We also found that the extent of hazard area due to wave overtopping is significantly reduced by using a permeable structure crown. Findings in this study will enable engineers to establish the extent of hazard zones due to wave overtopping behind coastal structures.     

珠江三角洲快速客船船行波模拟及其爬高研究

采用不规则波生波技术模拟珠江三角洲快速客船实测船行波,分别在波浪水槽和波浪水池中进行了船行波模拟试验研究。确定了不同波要素、不同入射角以及不同护岸坡比、平台宽窄、护面层结构等对船行波在斜坡护岸上的爬高影响,取得了船行波在斜坡式护岸上爬高的经验关系式。为珠江三角洲内河航道快速客船船行波作用下护坡的设计提供参考依据。