Study on Effectiveness of Solitary-Wave-Like Form Based on Overtopping Data from Irregular Wave Tests

The previous study conducted by Li(2022)demonstrates that the Goda graph can be adequately represented by a solitary-wave-like form across the entire range of relative water depth,with the exception of the extremely shallow zone.However,it remains uncertain whether this form is equally effective when applied to test data generated by irregular waves,as the Goda graph was initially developed based on overtopping data from regular wave tests.Additionally,it is unclear whether this form is suitable for formulating overtopping discharge at composite vertical walls.In order to address these questions,a 2D overtopping experiment was conducted,incorporating both simple and composite types of vertical walls,with various relative water depths across the entire range,excluding the extremely shallow zone.A novel analysis procedure was developed,which proved to be highly productive and can be considered a general method for data fitting.Ultimately,the study yielded two conclusions:(1)the solitary-wave-like form is remarkably effective in formulating overtopping test data generated by irregular waves,regardless of whether the vertical wall is simple or composite,and(2)the resulting formulas exhibit definitely better performance compared with existing formulas.

Centrifugal model tests and numerical simulations for barrier dam break due to overtopping

The present study focuses on the breaching process and failure of barrier dams due to overtopping. In this work, a series of centrifugal model tests is presented to examine the failure mechanisms of landslide dams. Based on the experimental results, failure process and mechanism of barrier dam due to overtopping are analyzed and further verified by simulating the experimental overtopping failure process. The results indicate that the barrier dam will develop during the entire process of overtopping in the width direction, whereas the breach will cease to develop at an early stage in the depth direction because of the large particles that accumulate on the downstream slope. Moreover, headcut erosion can be clearly observed in the first two stages of overtopping, and coarsening on the downstream slope occurs in the last stage of overtopping. Thus, the bottom part of the barrier dam can survive after dam breaching and full dam failure becomes relatively rare for a barrier dam. Furthermore, the remaining breach would be smaller than that of a homogeneous cohesive dam under the same conditions.

Numerical model for homogeneous cohesive dam breaching due to overtopping failure

Based on the large-scale model tests, a simplified dam breach model for homogeneous cohesive dam due to overtopping failure is put forward. The model considers headcut erosion as one of the key homogeneous cohesive dam breaching mechanisms and we calculate the time-averaged headcut migration rate using an energy-based empirical formula. A numerical method is adopted to determine the initial scour position at the downstream slope in terms of the water head and dam height, and the broad-crested weir equation is utilized to simulate the breach flow. The limit equilibrium method is used to analyze the stability of breach slope during the breach process. An iterative method is developed to simulate the coupling process of soil and water at each time step. The calculated results of three dam breach cases testify the reasonability of the model, and the sensitivity studies of soil erodibility show that sensitivity is dependent on each test case's soil conditions. In addition, three typical dam breach models, NWS BREACH, WinDAM B, and HR BREACH, are also chosen to compare with the proposed model. It is found that NWS BREACH may have large errors for cohesive dams, since it uses a noncohesive sediment transport model and does notconsider headcut erosion, WinDAM B and HR BREACH consider headcut erosion as the breaching mechanism and handle well homogeneous cohesive dam overtopping failure, but overall, the proposed model has the best performance.

Risk analysis for earth dam overtopping

In this paper, a model of overtopping risk under the joint effects of floods and wind waves, which is based on risk analysis theory and takes into account the uncertainties of floods, wind waves, reservoir capacity and discharge capacity of the spillway, is proposed and applied to the Chengbihe Reservoir in Baise City in Guangxi Zhuang Autonomous Region. The simulated results indicate that the flood control limiting level can be raised by 0.40 m under the condition that the reservoir overtopping risk is controlled within a mean variance of 5×10-6. As a result, the reservoir storage will increase to 16 million m3 and electrical energy generation and other functions of the reservoir will also increase greatly.

Estimation and Prediction of Typhoons and Wave Overtopping in Qingdao, China

This study aims to estimate and predict the impact of climate change on typhoons and wave overtopping during typhoon progresses in Qingdao, China. The SWAN wave model is used to simulate wave elements. The scale coefficients of wave overtopping are estimated using an empirical prediction formula. A total of 75 tropical cyclones affected Qingdao from 1949 to 2019. These tropical cyclones can be grouped into eight categories according to typhoon tracks. Typhoon wind speed during Track G is projected to decrease, and those of the other seven typhoon progresses will increase by 0.35% – 0.75% in 2025, 0.69% – 1.5% in 2035, and 1.38% – 3.0% in 2055. The significant wave height and wave overtopping outside the bay are greater than those inside the bay. Among the 506 typical points selected, the maximum values of the significant wave height and wave overtopping inside the bay are mainly distributed in the range of 0 – 2 m and 0 – 60 m^3 km^(-1) s^(-1), respectively. The increments of the significant wave height and wave overtopping of Track F are most obvious. The significant wave height of Track F will increase by 50.5% in 2025, 51.8% in 2035, and 53.4% in 2055. In the 2℃ scenario, the maximum value of wave overtopping of Track F will increase by 21.9% in 2025, 24.3% in 2035, and 29.5% in 2055. In the 4℃ scenario, the maximum value of wave overtopping of Track F will increase by 21.9% in 2025, 24.3% in 2035, and 29.5% in 2055.

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.

Experimental Study on Mean Overtopping of Sloping Seawall Under Oblique Irregular Waves

In this paper, domestic and abroad research progresses and related calculation formulae of the mean overtopping discharge are summarized. Through integral physical model experiments, the relation between the wave direction and the overtopping discharge on the top of the sloping dike is focused on and put into analysis and discussion; and a modified formula for mean overtopping discharges under oblique irregular waves is proposed. The study shows that the mean overtopping discharge generally goes down as the relative wave obliquity fl increases for a fixed measurement point and the mean overtopping discharge generally increases as the wave steepness H/L decreases （the cycle increases） for a fixed relative wave obliquity.

Modelling Wave Transmission and Overtopping Based on Energy Balance Equation

Wave transmission and overtopping around nearshore breakwaters can have significant influence on the transmitted wave parameters,which affects wave conditions and sediment transportation and becomes the focus of design in engineering.The objective of this paper is to present a simplified model to estimate these important wave parameters.This paper describes the incorporation of wave transmission and overtopping module into a wave model for multi-directional random wave transformation based on energy balance equation with the consideration of wave shoaling,refraction,diffraction,reflection and breaking.Wen's frequency spectrum and non-linear dispersion relation are also included in this model.The influence of wave parameters of transmitted waves through a smooth submerged breakwater has been considered in this model with an improved description of the transmitted wave spectrum of van der Meer et al.(2000) by Carevic et al.(2013).This improved wave model has been validated through available laboratory experiments.Then the verified model is applied to investigate the effect of wave transmission and overtopping on wave heights behind low-crested breakwaters in a project for nearshore area.Numerical calculations are carried out with and without consideration of the wave transmission and overtopping,and comparison of them indicates that there is a considerable difference in wave height and thus it is important to include wave transmission and overtopping in modelling nearshore wave field with the presence of low-crested breakwaters.Therefore,this model can provide a general estimate of the desired wave field parameters,which is adequate for engineers at the preliminary design stage of low-crested breakwaters.

Comparison of the Effect of Tetrapod Block and Armor X block on Reducing Wave Overtopping in Breakwaters

As the Armor shape has a significant effect on the reduction of wave overtopping, this study compares the performance of various shapes of concrete armored blocks of X block and Tetrapod as the most suitable armors. In this study, a three-dimensional numerical model was used for simulation of the effects of waves on the armors of Tetrapod and X Block breakwaters. In this regard, in order to calibrate the numerical model, a sample of conventional stone armor has been selected and using available experimental data on the design of armor such as wave overtopping, wave height, period of waves and energy density of the required spectral range of wave verification was conducted on a numerical model. In this regard, it is necessary to calibrate all the conditions of the model including boundary conditions, numerical modeling, initial conditions, numerical solvers and other parameters in the numerical model and simulation error rate is determined. The maximum error of the numerical model for the relative height values of the impact waves on the structure of breakwater is 7.87% for different conditions. Accordingly, the maximum error of the numerical model in determining overtopping values is 7.81%. The average fluctuation value of overtopping in the X block armor has dropped by about 31% compared to the tetrapod armor.

Formula of Overtopping Discharge of Vertical Seawall with A Form Similar to Solitary Wave Function

An empirical formula to predict overtopping discharge of vertical wall is presented,in which an expression similar to the solitary wave function is proposed to describe the rule of the influence of relative water depth.The formula is derived from performing an investigation to the well-known overtopping graphs of Goda,and for the sake of interest,the process of the derivation is detailed.To make clear the formula’s performance,relevant test datasets in the CLASH database are extracted to examine the error levels of the formula.As a result,an overall good agreement has been found between the predictions of the formula and the extracted datasets in a wide range outside the extreme shallow region,i.e.,the range of relative water depth smaller than 0.6,in which the water depth near the wall is so shallow that nearly all the incoming waves have been broken before reaching the wall.

Overtopping Discharge of Wind-Waves on Simple Slope Dikes

An empirical formula for estimating the overtopping discharge of wind-waves on a smooth-impermeable-simple slope dyke is derived through model tests in this paper, it can be adopted by related design departments in the determination of the crest elevation of the dyke.

Probabilistic Assessment of Wave Overtopping of Nampo Dikein 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.

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 labo-ratory 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 investi-gated.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.

Experimental Study of Irregular Wave Reflection by a Perforated Caisson Breakwater Under Wave Overtopping Conditions

The characteristics of irregular wave reflection by a perforated caisson breakwater under wave overtopping conditions were investigated using physical model tests.The effects of various parameters,especially the mean overtopping discharge that was mainly determined by the relative crest freeboard,on the reflection coefficient of perforated caisson breakwater were analyzed using experimental data.The results showed that the wave overtopping occurrence had no appreciable effect on the reflection coefficient when the mean overtopping discharge was less than 0.2 m^(3)(m s)^(−1).Under the wave overtopping condition,the reflection coefficient of the perforated caisson breakwater in this study was reduced by 20%-50% compared with that of the non-perforated caisson breakwater.A predictive formula of the reflection coefficient for perforated caisson breakwaters in terms of relative water depth,relative chamber width,and porosity of the caisson front wall,was developed for practical engineering design.

Numerical Simulation of Random Wave Overtopping of Rubble Mound Breakwater with Armor Units

Based on the open source code OpenFOAM,a three-dimensional model is presented for simulation of the interaction between waves and rubble mound breakwater with armor units.The armor units with their real geometries are depicted through computational grids.The volume-averaged RANS equation and the seepage equation containing nonlinear term are used to describe the percolation in the core and underlayer of the breakwater.Grids independence analysis are carried out,the horizontal and vertical grid size are recommended to take as one-fifteenth of the mean nominal diameter D_(50) of the armor units and one-fifteenth of the wave height respectively.Random wave overtopping of rubble mound breakwater with armor units is simulated through the proposed model.The results show good agreement between the simulated and measured overtopping discharge rates for different types of armor units.The developed numerical model can be used to evaluate the random wave overtopping in design of rubble mound breakwater with artificial armor blocs.

Prediction 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 the 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 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 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.

Numerical Simulation of Spatial Distribution of Wave Overtopping on Non-reshaping Berm Breakwaters

This study presents the results of a 2D numerical modeling investigation on the performance of non-reshaping berm breakwaters with a special look at the spatial distribution of irregular wave overtopping using FLOW-3D CFD code.The numerical model is based on Reynolds-Averaged Navier-Stokes solver(RANS)and volume of fluid(VOF)surface capturing scheme(RANS-VOF).The numerical model has been validated using experimental data.The armor and core porosities have been used as calibration factors to reproduce the wave overtopping distribution.The computed distributions of wave overtopping behind the structure agree well with the measurements for a non-reshaping berm breakwater.A formula is derived to relate the spatial distribution of wave overtopping water behind non-reshaping berm breakwaters to non-dimensional forms of wave height,wave period,berm width,berm height,and armor freeboard based on numerical results.This formula model agreed reasonably well with numerical model results.

Refined mathematical model for the breaching of concrete-face sand-gravel dams due to overtopping failure

Overtopping is one of the main reasons for the breaching of concrete-face sand-gravel dams(CFSGDs).In this study,a refined mathematical model was established based on the characteristics of the overtopping breaching of CFSGDs.The model characteristics were as follows:(1)Based on the Renormailzation Group(RNG)k-εturbulence theory and volume of fluid(VOF)method,the turbulent characteristics of the dam-break flow were simulated,and the erosion surface of the water and soil was tracked;(2)In consideration of the influence of the change in the sediment content on the dam-break flow,the dam material transport equation,which could reflect the characteristics of particle settlement and entrainment motion,was used to simulate the erosion process of the sand gravels;(3)Based on the bending moment balance method,a failure equation of the concrete face slab under dead weight and water load was established.The proposed model was verified through a case study on the failure of the Gouhou CFSGD.The results showed that the proposed model could well simulate the erosion mode of the special vortex flow of the CFSGD scouring the support body of the concrete face slab inward and reflect the mutual coupling relationship between the dam-break flow,sand gravels,and concrete face slabs.Compared with the measured values,the relative errors of the peak discharge,final breach average width,dam breaching duration,and maximum failure length of the face slab calculated using the proposed model were all less than 12%,thus verifying the rationality of the model.The proposed model was demonstrated to perform better and provide more detailed results than three selected parametric models and three simplified mathematical models.The study results can aid in establishing the risk level and devising early warning strategies for CFSGDs.

Wave Reflection Caused by Wave Overtopping and Sloping Top of Spructure

In this paper, the theoretical analysis and experimental studies are employed to investigate the reflection characteristics of partial standing waves caused by wave overtopping and sloping top of structures. Based on the principle of conservation of wave energy flux, the third-order Stokes wave theory is used to formulate the reflection coefficient at wave overtopping; the calculation results are regressed into an applied expression. A series of experiments of wave reflection for a vertical-wall structure with chamfered and overhanging upper sections are carried out to investigate the influence of top slope on wave reflection. The regularity of variation of wave reflection in this case is analysed based on the experimental results.

Bibliometric Study Applied to the Overtopping Wave Energy Converter Device

The present study aims to analyze the state of the art of scientific studies about the Overtopping device used to convert sea wave energy into electrical energy,by means the Bibliometric methodology.The development of this study took place through the selection of articles from conference proceedings,as well as national and international journals.The Bibliometric methodology consists of a statistical tool that allows quantifying the measurement of production indexes.Using selected keywords,it was conducted a survey of studies in the online databases of Science Direct,SciELO and Google Scholar.The works found then went through a filtering process,in order to limit the Bibliometric study only to studies about Overtopping devices as sea Wave Energy Converter(WEC).Finally,the investigation of these selected articles was carried out under the optics of production and authorship study,content study and study of bibliographic references.Where it was identified growth in publications related to the topic,methodologies used and,among other indicators,the authors most cited in the analyzed articles.The predominant keywords used were“Wave Energy Converter”and“Overtopping”.It was noted that Brazilian universities are leaders in the productivity,presenting more than 36%of the scientific production regarding Overtopping WECs.