Crest Freeboard Research Articles

DISTRIBUTION OF INDIVIDUAL WAVE OVERTOPPING VOLUMES ON A SLOPING STRUCTURE WITH A PERMEABLE FORESHORE

Maximum wave overtopping volumes on sea defences are an indicator for identifying risks to people and properties from wave hazards. The probability distribution of individual overtopping volumes can generally be described by a two-parameter Weibull distribution function (shape and scale parameters). Therefore, the reliable prediction of maximum individual wave overtopping volumes at coastal structures relies on an accurate estimation of the shape factor in the Weibull distribution. This study contributes to an improved understanding of the distribution of individual wave overtopping volumes at sloping structures by analysing the wave-by-wave overtopping volumes obtained from physical model experiments on a 1V:2H sloped impermeable structure with a permeable shingle foreshore of slope 1V:20H. Measurements of the permeable shingle foreshore were benchmarked against those from an identical experimental set-up with a smooth impermeable foreshore (1V:20H) of the same geometry. Results from both experimental set-ups were compared to commonly used empirical formulations, underpinned by the assumption that an impermeable foreshore exists in front of the sea structure. The effect on the shape factor in the Weibull distribution of incident wave steepness, relative crest freeboard, probability of overtopping waves and discharge are examined to determine the variation of individual overtopping volumes with respect to these key parameters. A key finding from the study is that no major differences in Weibull distribution shape parameter were observed for the tested impermeable and permeable sloped foreshores. Existing empirical formulae were also shown to predict reasonably well the Weibull distribution shape parameter, b, at sloping structures with both impermeable and permeable slopes.

ANALYSIS OF THE IMPACT PROCESS AT DIKES WITH CROWN WALLS AND PARAPETS

This paper is focused on the analysis of the impact process at dikes with crown walls and parapets under breaking and non-breaking waves. A small-scale laboratory campaign was performed at the Hydraulic Laboratory of Bologna. The experiments were aimed to analyze the vertical pressure distribution along the crown wall and the resulting wave forces, by varying geometrical and hydraulic parameters. The tested configurations included different off-shore slopes, dike crest widths, crown-wall heights, dike crest freeboards and the inclusion of the parapet. The measurements were combined with the image analysis of the run-up and of the wave impact process. A sub-set of the experiments was numerically reproduced, with the openFOAM modelling suite, to support and to extend the experimental results. The results confirmed the link between the air content, the shape and the magnitude of the pressures according to the breaker type, already observed for larger-scale experiments.

Refinement of integrated formula of wave overtopping and runup modeling

This study attempts to refine a model named the Integrated Formula of Wave Overtopping and Runup Modeling (IFORM) to improve the prediction performance of mean wave overtopping discharge for a broader range of installation conditions. The empirical formula describing the relation between overtopping discharge and maximum runup has been re-examined. A set of piecewise formulas is implemented in the IFORM by optimal reconstruction of coefficients depending on the magnitude of deficit in freeboard. The refined IFORM improves the tendency to underestimate the discharge in the range of relatively high freeboard conditions, while it retains the high performance of the original IFORM in the range where the crest freeboard is relatively low. The refined model's capability for overtopping prediction is validated by comparison with various existing experimental datasets for inclined/vertical seawalls installed at relatively shallow water depth or on land. The prediction accuracy is also examined by comparison with well-known overtopping formulas. Qualitative and quantitative comparisons validate that the current model is able to reproduce the experimental observations over a broad range of overtopping conditions and that the performance of the model proposed in the present study is as good as existing representative models.

Explicit Neural Network-derived formula for overtopping flow on mound breakwaters in depth-limited breaking wave conditions

Sea level rise due to climate change, as well as social pressure to decrease the visual impact of coastal structures, have led to reduced crest freeboards, and this increases the overtopping hazard. In previous studies, pedestrian safety during overtopping events was assessed considering the overtopping layer thickness (OLT) and the overtopping flow velocity (OFV). This study analyzed the statistics of OLT and OFV on mound breakwaters without crown walls during severe wave storms. Small-scale 2D physical tests were conducted on mound breakwaters with dimensionless crest freeboards between 0.29 and 1.77, testing three armor layers (single-layer Cubipod®, and double-layer cubes and rocks) in depth-limited breaking wave conditions and with two bottom slopes. Neural Networks were used to develop new estimators for the OLT and OFV exceeded by 2% of the incoming waves with a high coefficient of determination (0.866 ≤ R2 ≤ 0.876). The best number of significant figures in the empirical coefficients of the new estimators was determined according to their variability. The 1-parameter Exponential and Rayleigh distribution functions were proposed to estimate the extreme values of OLT and OFV with 0.803 ≤ R2 ≤ 0.812, respectively.

Wave overtopping of smooth impermeable seawalls under unidirectional bimodal sea conditions

Reduction of risks due to overtopping of coastal defences is an essential requirement for the design, management and adaptation of coastal structures. Extensive knowledge is available on the prediction of overtopping of smooth, sloping and vertical impermeable seawalls. The existing prediction methods provide less certain guidance for combined wind and swell conditions. This experimental study focuses on overtopping characteristics of coastal seawalls under random bimodal waves. Both unimodal and corresponding bimodal conditions were simulated under different slopes and crest freeboards. Proportions of swell in the bimodal sea were varied in each test. Mean wave overtopping discharges were calculated for non-breaking random waves over at least 1000 waves. EurOtop formulae agree closely with our measurements from the unimodal experiments whereas they underpredict the observed wave overtopping rates for bimodal conditions even when using the recommended Tm−1,0 period for such cases. A modification to the EurOtop formula is proposed on the basis of the experimental results, to better capture the overtopping discharge under bimodal conditions.

Numerical simulation of wave overtopping above perforated caisson breakwaters

A two-dimensional numerical model was used to study the wave overtopping performance above perforated caisson breakwaters under regular waves. The turbulent flow was simulated by solving the Reynolds Averaged Navier–Stokes (RANS) equations and the k–ε turbulence model equations. In the numerical wave flume, the free surface was tracked by the Volume of Fluid (VOF) method, and a relaxation zone was added to avoid the unwanted re-reflection from the inflow boundary. Based on the ideal gas equation at a constant temperature, the pressure change caused by the compressed air inside the wave chamber was incorporated into the numerical model for accurately simulating the wave motion inside the wave chamber. The numerical results of the free surface elevations inside and outside the wave chamber, the wave overtopping discharges and the reflection coefficients of perforated caisson breakwaters were in good agreement with the experimental data. This means that the numerical model is valid in estimating wave action and overtopping on complicated coastal structures with perforated thin walls. The distributions of flow velocity and turbulence kinetic energy (TKE) around the perforated caissons were clarified, which gave a better understanding of the wave overtopping mechanism above the perforated caisson breakwaters. Numerical results showed that the wave energy transferred by the overtopping flows is much smaller than that dissipated by the perforated caisson breakwater. When the relative freeboard (the ratio of the crest freeboard to the incident wave height) of the perforated caisson breakwater was larger than 0.58, the existence of the overtopping flow has no significant influence on the reflection coefficient. Besides, avoiding the air compression inside the wave chamber can effectively reduce the overtopping discharge. Increasing the caisson porosity or the wave chamber width can also reduce the overtopping discharge above the perforated caisson breakwaters.

Random wave overtopping of vertical seawalls on coral reefs

Reliable estimations of overtopping rates are necessary for the design of vertical seawalls. Although many studies have been carried out to address this, few have paid attention to vertical seawalls built on coral reefs. In this study, a physical model was constructed with an idealized coral reef topography and vertical seawalls located on the middle or inner reef flat. A steep fore-reef slope in combination with a shallow and horizontal reef flat led to significant changes in wave heights, periods, spectra, and shapes across the reef. State-of-the-art overtopping formulas were tested against the experimental data, but none of them produced satisfying results. The reasons for the inapplicability of these formulas in this regard were discussed, which highlighted the necessity of distinguishing the significant influence of coral reefs on incident waves reaching engineered structures from structures fronted by relatively deep water and foreshores. A new formula for estimation of overtopping rates of vertical seawalls on coral reefs under non-impulsive conditions was derived. This formula is a function of the relative wave height at the seawall toe and the relative crest freeboard, whereas the spectral period is not incorporated. The performance of the new formula was investigated using various combinations of dimensional and dimensionless parameters.

Hydrodynamic performance investigation on an upper and lower water exchange device

Water exchange is an important way to guarantee its good quality between surface and bottom seawater, and it plays a significant role in water environment and ecology as well as fish farming systems. The conceptual experiment (Yin et al., 2018) was extended to present an Upper and Lower Water Exchange Device for strengthening the vertical water exchange performance, and a 3-D CFD mathematical model combining with Reynolds-Averaged Navier-Stokes equations, standard k-ε equations and VOF technique was developed to investigate its hydrodynamic performance and the vertical water exchange capacity for regular waves. The extrapolated relative error and the grid convergence index were used to estimate the discretization error. A series of experiments were conducted to measure the wave surface and water velocity histories, the experimental data were used to validate the mathematical results, and they agreed well with each other. It was found that the inside water motion is determined mainly by the wave overtopping and water entrainment. Generally, the net flow rate decreases at first and then increases with increasing wave steepness. In addition, the ratio of crest freeboard height to incident wave height plays a significant role in water exchange performance. A small ratio leads to an upward movement of the inside water, whereas a high value contributes to a downward net flow to some extent. Finally, a simple formula on the net flow rate was deduced with the dimensional analysis method and the least squares method, and it was validated well with the related data.

Flooding of Piazza San Marco (Venice): Physical Model Tests to Evaluate the Overtopping Discharge

This paper aims at evaluating the wave overtopping discharge over the pavement of “Piazza S. Marco” (Venice) in order to select the best option to mitigate the risk of flooding of the Piazza and to protect the monuments and historic buildings, e.g., the “Basilica S. Marco”. In fact, the MO.S.E. (MOdulo Sperimentale Elettromeccanico) system is designed to keep the water level below a certain value, for the safety of the lagoon, but it does not guarantee the defence of the Piazza, where flooding is still possible, being its pavement locally much lower than the maximum expected water level. To completely defend the Piazza, specific additional works are planned to prevent the back-flow through the natural drainage system (now the primary pathway) or by filtration or by overtopping. This paper investigates on the overtopping mechanism, under conditions compatible with a fully operational MO.S.E. system, through 2-D experiments. The pavement of the Piazza is gently sloping towards the masonry quay which, in some parts is formed by 5 descending steps, and in some other parts, is just a vertical wall. Close to the “Marciana” Library, a critical part is present, with a slightly lower crest freeboard. In total, three cross-sections were examined in the 36 m long wave flume of the Padova University. The test programme includes 10 irregular wave attacks and three different water levels. The test results differ considerably from the results of the available formulas, since the investigated cross-sections by far exceed their range of applicability. The presence of the steps affects only the reflection coefficient rather than the overtopping discharges. In general, if the waves incident to the Piazza are higher than 40 cm, which is a possible scenario, some other adaptation works must be considered, such as the pavement rise, temporary barriers or the reduction of the waves impacting the quay through, for instance, floating breakwaters.

Numerical Simulation of Wave Overtopping on Breakwater with an Armor Layer of Accropode Using SWASH Model

In this paper, a new method for predicting wave overtopping discharges of Accropode armored breakwaters using the non-hydrostatic wave model Simulating WAves till SHore (SWASH) is presented. The apparent friction coefficient concept is proposed to allow the bottom shear stress term calculated in the momentum equation to reasonably represent the effect of comprehensive energy dissipation caused by the roughness and seepage during the wave overtopping process. A large number of wave overtopping cases are simulated with a calibrated SWASH model to determine the values of equivalent roughness coefficients so that the apparent friction coefficients can be estimated to achieve the conditions with good agreement between numerical overtopping discharges and those from the EurOtop neural network model. The relative crest freeboard and the wave steepness are found to be the two main factors affecting the equivalent roughness coefficient. A derived empirical formula for the estimation of an equivalent roughness coefficient is presented. The simulated overtopping discharges by the SWASH model using the values of the equivalent roughness coefficient estimated from the empirical formula are compared with the physical model test results. It is found that the mean error rate from the present model predictions is 0.24, which is slightly better than the mean error rate of 0.26 from the EurOtop neural network model.

Oblique Wave Attack on Rubble Mound Breakwater Crest Walls of Finite Length

Rubble mound breakwaters usually present a crest wall to increase the crest freeboards without a large increase of the consumption of material. Methods in the literature to design crest walls are based on estimates of the wave loads. These methods are focused on the maximum loading that attacks a single position of the crest wall. In practice, crest walls have a finite length. Since the maximum loading does not occur at the same instant over the entire length of the crest wall for oblique waves, these methods overestimate the loading in the situation of oblique waves. Wave loads under oblique wave attack have been measured in physical model tests. A method to account for the effect of the finite length of crest walls has been developed, and design guidelines have been derived. The results of this study in combination with the existing methods in the literature to estimate the wave forces enable a more advanced design of crest walls.

Influence of Mild Bottom Slopes on the Overtopping Flow over Mound Breakwaters under Depth-Limited Breaking Wave Conditions

The crest elevation of mound breakwaters is usually designed considering a tolerable mean wave overtopping discharge. However, pedestrian safety, characterized by the overtopping layer thickness (OLT) and the overtopping flow velocity (OFV), is becoming more relevant due to the reduction of the crest freeboards of coastal structures. Studies in the literature focusing on OLT and OFV do not consider the bottom slope effect, even if it has a remarkable impact on mound breakwater design under depth-limited breaking wave conditions. Therefore, this research focuses on the influence of the bottom slope on OLT and OFV exceeded by 2% of incoming waves, hc,2% and uc,2%. A total of 235 2D physical tests were conducted on conventional mound breakwaters with a single-layer Cubipod® and double-layer rock and cube armors with 2% and 4% bottom slopes. Neural networks were used to determine the optimum point to estimate wave characteristics for hc,2% and uc,2% calculation; that point was located at a distance from the model toe of three times the water depth at the toe (hs) of the structure. The influence of the bottom slope is studied using trained neural networks with fixed wave conditions in the wave generation zone; hc,2% slightly decreases and uc,2% increases as the gradient of the bottom slope increases.

Overtopping layer thickness and overtopping flow velocity on mound breakwaters

Mound breakwater design is evolving owing to rising sea levels caused by climate change and social concern regarding the visual impact of coastal structures. The crest freeboard of coastal structures tends to decrease while overtopping hazard increases over time. Pedestrian safety when facing overtopping events on coastal structures has been assessed considering the overtopping layer thickness (OLT) and overtopping flow velocity (OFV). This paper proposes a new method to estimate the OLT and OFV on mound breakwater crests during extreme overtopping events, based on 123 2D small-scale physical tests of conventional low-crested mound breakwaters with a single-layer Cubipod® and double-layer rock and cube armors. The new method to estimate OLT exceeded by 2% of incoming waves is based on formulas given in literature for dikes, but adapted and calibrated for mound breakwaters. The formula to estimate the OFV exceeded by 2% of incoming waves is based on the correlation between the statistics of the OLT and OFV, considering an empirical coefficient calibrated for each type of armor layer. Exponential and Rayleigh distribution functions are proposed for estimating the OLT and OFV with exceedance probabilities under 2%. Although the statistics of OLT and OFV depend on similar variables, contrary to intuition, specific OLT and OFV corresponding to the same overtopping event appear to be independent.

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

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

Development of Wave Overtopping Formulas for Inclined Seawalls using GMDH Algorithm

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

QUANTIFYING BEACH AND DUNE RESILIENCE USING THE COASTAL RESILIENCE INDEX

US Army Corps of Engineers Coastal Storm Risk Management (CSRM) projects have reduced coastal vulnerability and helped communities anticipate and mitigate toward improved resilience. This study proposes the Coastal Resilience Index (CRI) to quantify storm damage reduction benefits due to beach restoration projects in the context of resilience. The CRI considers metrics of the beach and dune system and disturbance factors such as storm surge and waves, using five non-dimensional factors: Protective Elevation (PE), Volume Density (VD), Protective Width (PW), Crest Freeboard (CF) and wave run-up (WR). The CRI is the summation of these five non-dimensional factors. This study developed a geographic information systems (GIS) based tool to automatically extract morphologic features from historic profiles and profiles extracted from LiDAR data to quantify beach resilience over time.

PHYSICAL MODEL TESTS OF WAVE OVERTOPPING AND FORCES ON BREAKWATER CROWN WALLS

This paper describes new physical model tests aiming at measuring both wave overtopping and wave induced forces on rubble mound breakwater crown walls. The physical model and the equipment used for the measurements are described in detail. For the completed tests, a detailed analysis is reported, by evaluating the properties of the incoming waves at the toe of the breakwater and some statistical parameters to describe the wave induced forces and pressures on the crown wall. Careful analysis is also carried out to evaluate how the distribution of the pressures changes with time. It is found that the upper part of the wall is subjected to the first large quasi-impulsive action of the wave; the lower part of the wall is afterwards flooded and a quasi-hydrostatic pressure develops along the height of the wave wall. As far as the pressures on the base of the crown wall are concerned, they develop after a quite large time lag after the maximum of the horizontal force. First attempts to correlate the maximum horizontal force with some explanatory variables such as the ratio of the crest freeboard and of the significant wave height of the incoming waves indicate a promising correlation, also in agreement with the existing literature on the topic. The overtopping rate are also measured and compared with empirical formulas. The correlation between the wave induced forces and the average overtopping discharge on the breakwater is also investigated.

THE INFLUENCE OF A CROWN WALL ON WAVE OVERTOPPING OVER RUBBLE MOUND STRUCTURES

The crest of a breakwater is often equipped with a crown wall with multiple functions such as a border of the pedestrian walkway, support of the rubble mound or concrete armour units, and reduction of the wave overtopping over the structure in storm conditions. However, the knowledge on how a crown wall influences the overtopping discharge is yet still limited. EurOtop (2016) advises to take the maximum of the crest freeboard Rc and the armour freeboard Ac in case a crown wall is present, and to use the average between Ac and Rc when no crown wall is present. This advice is based on expert judgement rather than on experimental research. The goal of the present work is to carry out experimental research and confirm or update the advice on overtopping over a crown wall for rubble mound structures.

Reliability analysis and optimum maintenance of coastal flood defences using probabilistic deterioration modelling

This paper presents a method for time-dependent reliability analysis, future performance predictions and optimum maintenance strategy of coastal flood defences such as earth sea dykes subjected to changing operation conditions. The reliability analysis takes into account both the changes of hydraulic variables such as water level and wave height due to climate change and the deterioration of structural capacities such as crest freeboard loss and soil seepage length degradation over time. A probabilistic time-dependent semi-Markov process is adopted for estimating the transition probabilities on the basis of available field data through routine inspections and expert judgements. Limit state equations are established for evaluating time-dependent probability of failures associated with wave overtopping through the flood defence crest and piping in the underlying water conductive soils. A multi-objective optimisation method is then employed to find optimum solution space for asset inspection and maintenance by minimising both costs for inspection and annual risk of structural failures. The results for a typical earth sea dyke at Thames Estuary show that the probability of failures associated with wave overtopping and soil piping will increase significantly over time, thus appropriate maintenance strategy is required to reduce the risk caused by changing operating conditions.

Hydraulic Stability of the Armor Layer of Overtopped Breakwaters

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