This study treats a detached homogenous low-crested structure (HLCS) made of Cubipod concrete elements placed seaward of a vertical wall (forming a basin in between) to reduce overtopping. Assessing the complex hydrodynamics and effects of changing the geometry of such a system in relation to overtopping reduction is challenging. The numerical model OpenFOAM was applied to this end. Forchheimer coefficients for wave transmission and the flow through the HLCS were calibrated and validated using existing physical modeling data (α = 500 and β = 1.0, with varying porosity based on the Cubipod shape), while the effect of the basin and vertical seawall was determined fully numerically. The crest freeboard (R_c), crest width (B), and basin length (L_B) were the main geometrical parameters that influenced the performance of the HLCS in reducing overtopping. An exponential decay was observed in the overtopping discharge when the values of these geometrical parameters increased. As L_B increased, this decay was primarily due to the dissipation of the broken-wave bores. The largest gradient in the predicted overtopping discharge was noted at R_c/H_s,i ≈ 0, B/H_s,i ≈ 4.5, and L_B/L_p ≈ 1.2, where H_s,i is the incident significant wave height and L_p is the peak wavelength in the basin.

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Vegetation in front of levees, dikes and seawalls can decrease wave energy and therefore contribute to the safety against flooding. However, wave damping predictions by vegetation are still inaccurate due to measurement and modelling uncertainties. Many studies focused on finding reliable predictive tools using scaled flume tests with vegetation mimics. Scaling down vegetation can however lead to discrepancies with realistic scales, known as scale errors. In this work scaled tests were conducted on 3D-printed elastic replicas of willow trees and compared with real-scale experiments. We identified differences in measured wave dissipation between the scaled hydraulic model (1:10) and its real-scale prototype with 5m high live willow trees under storm conditions (1:1). The maximum measured wave damping (30%) was roughly 1.5 times higher than the real-scale experiments (20%). Following the same trend of the real-scale experiments, this amount of wave height damping declined for larger water levels. Largest effects are argued to be due to increased viscous damping (smaller branch Reynolds numbers) and non-exact flexibility scaling. These significant deviations illustrate that full-scale experiments, although expensive, are still needed to validate the results of scaled experiments for woody vegetation. Alternatively, accounting for these discrepancies can make scaled experiments more reliable and expensive real-scale experiments less needed for wave damping studies on woody vegetation.

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Initial damage, caused by previous wave loading or other events, might affect the hydraulic stability of pattern-placed revetments. Three common types of damage are considered in this study. The effect of this assumed initial damage on the hydraulic stability and failure probability of revetments is quantified using a FEM model. This model is developed using data from large-scale flume and field experiments. Using results from the FEM model, surrogate models are created to predict the effect of each type of initial damage on the hydraulic stability and failure probability. Through the use of these surrogate models, it is demonstrated that S-shaped deformation caused by filter migration around the wave impact zone has the largest effect on the hydraulic stability decreasing up to 30%, and failure probability per year increasing up to 10,000 times. When the granular filling between the joints of the columns is washed-out, the stability decreases up to 29% and the failure probability increases up to 700 times. A missing column has a limited effect on the hydraulic stability and failure probability when there is no other (structural) damage. However, if it originates from underlying damage, it might be an initial sign of total failure of the revetment. This study demonstrates the effectiveness of finite element modeling for studying (damaged) revetments, which can be used to complement flume experiments. The results can be used to prioritize maintenance efforts in risk-based maintenance of pattern-placed revetments.

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Physical model tests have been performed to study static stability of rock-armoured mild slopes. Current stability design formulae for steeper rock-armoured slopes focus on plunging and surging waves. Slopes of 1:6 and milder usually have more spilling breakers which decreases the load. Also, on mild slopes displaced rocks more often remain present in the wave attack zone, which increases the strength. These aspects lead to an overdesigned structure when existing formulae for steep rock-armoured slopes are used. The present wave flume tests were used to understand the processes and develop a design formula for rock-armoured mild slopes with an impermeable core. These tests were performed for statically stable rock-armoured slopes of 1:6 to 1:10. The tests confirmed that not all existing damage parameters are able to accurately describe the static stability on milder slopes. For mild slopes it is more accurate to describe the damage based on the eroded depth rather than on the eroded area or number of moved stones. In this study, a design formula and guidelines are provided for practicing engineers that design or evaluate the stability of mild rock-armoured slopes.

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The presence of marine pollutants such as marine plastics has increased significantly over the last decades and poses a major environmental problem, in both the coastal and offshore area. Marine pollutants are transported, mixed and diffused in the ocean, which means the understanding and modelling of marine transport is key for mitigation purposes (Moulton et al., 2022). Additional to large scale and planetary currents that play a major role in marine transport, free surface waves, internal gravity waves in density stratified fluids and the Coriolis force due to the rotation of the Earth are also fundamental drivers of transport that need to be accounted for. The fundamental fluid mechanics processes associated with these are often not resolved in large-scale models, but are instead included in a parametrised form. However, some fundamental processes associated with wave-induced currents (e.g., Stokes drift) in rotating, density-stratified fluids with a free surface remain unclear and untested. In addition, parametrisation for different environments, forcings and time scales must be developed and tested before being implemented into models for them to reliably predict transport, accumulation and storage of marine pollutants. For this purpose, the Delta Transport Processes Laboratory (DTPLab) is being developed at TUDelft Hydraulic Engineering Laboratory. This laboratory pioneers the combined experimental study of surface waves, density stratification and Coriolis forces in a single laboratory. The DTPLab was designed with a multi- users and purposes vision, with interchangeable facilities and state-of-the-art measurement devices. This paper presents the DTPLab facilities (under construction) and equipment that make this laboratory unique in the world, and describes, as an example of what is feasible, a novel experiment that will be performed in this lab.</jats:p>@en

Single layer randomly placed armour units are used in many rubble mound breakwaters around the world. For these armour layers first extraction of units starts at high loads and can then progress quickly. Before the first extraction of a unit, typically no quantitative description of damage can be given. But additional to extraction, breakage of armour units due to rocking could be a major damage mechanism. This paper treat novel embedded Rocking Sensors. The technique is used to obtain the first measurements of rocking-impact velocities of single-layer units. They are also the first tests where the instrumented units can naturally move with the compacting layer during storm build-up. Physical model tests were performed on an armour layer with XBloc units. With 8 to 10 instrumented units per test run, in total 640 single measurements of the rocking motion of a unit during a 1200 wave test run were obtained, for three water levels and five wave heights. From the Rocking Sensors the number of impacts and rotational impact velocities were obtained. From an image analysis the along-slope settlement of the units during the tests was quantified. The rotational motion expressed by was found to be most convenient to express the motion. It can be seen that the units in the armour layer rock much more often than visually observed. Settlement seems to be a continuous progress, with most units rocking intermittently. Highest impact velocities are seen to occur around the water line, and in the uprush phase of the waves. A maximum impact velocity for all tests of 0.34 m/s (model scale) was measured. A preliminary design expression for rocking impact velocities of single layer units (Xblocs) is given. The paper shows that novel measurement techniques like the Rocking Sensors and vision techniques can and should be used to quantify damage mechanisms to rubble mound single-layer armour, additional to counting the extracted number of intact units.@en

Overtopping plumes from wave impact is relevant to coastal defence for overtopping analysis of sea walls, levees, and gates. Improved insight into this phenomenon will further enhance the prediction of wave overtopping and its induced hazard, e.g., erosion, saltwater ingress, and a hindrance to traffic. A series of small-scale experiments have been carried out in the WaterLab at TU Delft to characterize the droplets formed by wave impacts. Focused waves were generated by the piston-type wavemaker to control the wave breaking point on the wall, which allowed the creation of different types of wave impact. Impacts were investigated respectively: non-breaking, flip-through, and air pocket. After the wave impact, all the stages of the plume formation were filmed using a high-speed camera at a frame rate of 500fps. In this study, the spray sheet breakup and droplet formation are investigated. A simple approach to estimate the maximum spray height is proposed, which can be used for the splash type overtopping in the future.@en

ECOncrete®‘s Coastalock is an ecologically designed armour unit, providing an alternative and/or a complement to traditional armour layers with ecologically enhanced armouring that provides shoreline stabilization, while also creating well-defined local ecosystems that mimic natural rock pools. The 2D physical model tests performed at TU Delft focused on the stability, reflection and overtopping of a slope with regularly placed single layer Coastalock armour. The 2V:3H slope had an impermeable core, no wave breaking on the foreshore and no rock toe. The stability was seen to double, with stability number Ns (Ns= Hs/ΔDn50) increasing from roughly 2 to 4 and above, by increasing the porosity between the blocks from spacing the units from 0percent to 25percent. So less concrete use led to more stability. The mean overtopping discharge could be characterized by a roughness factor of gamma_f = 0.610 (for 25percent spacing). A key goal of the Coastalock development is to demonstrate that with the use of innovative eco-engineered armour unit design it is now possible to add ecological considerations into the design process to promote biodiversity and provide ecosystem services, achieving both structural and ecological goals.@en

When constructing land reclamations, often sand is placed on top of the coarse rock of the bund surrounding the reclamation. The use of a geometrically open filter between the interface of sand and rock could be cost effective. It is expected that even a geometrically open filter with sand on top of gravel might be stable due to the arching mechanism. For such a “reversed” open filter the actual stability is unknown. Hence this study focusses on the stability of a reversed geometrically open filter under cyclic loading. This paper mainly describes the development of the test setup. First the numerical model OpenFOAM was used to extract the gradients from a representative case study. Next a test setup was developed to generate these low-magnitude loads at full-scale. Various sand-filter combinations were tested, with a range of ratios of the diameters of the gravel filter (D15F) and the sandy base layer (D85B) and sand with a unimodal distribution. They were tested for both parallel (i//) and perpendicular (iꞱ) gradients. The order of magnitude of the occurring gradients obtained with the numerical model for the case-study were a parallel gradient of i//,2% ≈ 1%, decreasing to 0 going downward, and a rather constant perpendicular gradient of iꞱ,2% = 0.2-0.3 for the lowest 4 m of the reversed granular filter. The critical perpendicular gradients were estimated at iꞱc ≈ 0.2 to 0.1 for filter ratios of D85F/D15B = 7.5 to 9.5. The critical parallel gradients were measured at i//c ≈ 2% down to 1%, but might be influenced by simultaneously occurring perpendicular gradients. Even though for the test case no stable situation could be proven with respect to the perpendicular gradient, realistic situations with stable reversed open filters seem possible.@en

With the capacity to reduce wave energy and trap sediment, Scirpus mariqueter has become an important native species of annual grass for ecology restoration at the Yangtze Estuary in eastern China. Due to seasonal variances of biophysical characteristics, S. mariqueter usually bends and breaks in winter, resulting in flattened stems that may reduce its wave attenuation capacity. To investigate the effects of vegetation flattening on wave attenuation, a set of flume experiments were conducted for flattened and standing vegetation under different wave conditions. The model vegetation was designed to represent the wilted S. mariqueter collected in winter with dynamic similarity. Results showed that the wave damping coefficient for flattened vegetation (β_F) was 33.6%-72.4% of that for standing vegetation (β_S) with the same vegetation length. Both β_F and β_S increased with wave height but decreased with water depth. A wave attenuation indicator (WAI) was defined to generate empirical formulas for β_S and β_F as well as their ratio β_F/β_S. The empirical formulas were then applied to modify the existing standing vegetation-based wave attenuation model for flattened vegetation and performed successfully. Understanding the wave attenuation characteristics of flattened vegetation is essential for the management of ecological restoration and coastal protection.

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Randomly placed breakwater armour units under wave loading can sometimes start rocking, which can lead to breakage of armour units. This failure mechanism can especially become important for single layer randomly placed armour units for which full displacement of units will only happen at higher stability numbers compared to older types of units, and where unit breakage can more easily lead to progressive damage to the armour layer. However, unlike older types of units, hardly any quantitative information is available on the impact velocities, and the number of impacts is mostly assessed using somewhat subjective visual observations. In design the observed number of rocking units is limited to the amount of visually observed rocking units. Hence a good quantification of impact velocities could lead to a more optimal design. This paper describes the further development of embedded rocking sensors to measure the motions of individual smart armour units. Multiple smart rocking sensors have been applied in a physical model of a breakwater and measurements were collected to determine the number of impacts and impact velocity of the armour units. The results have been compared to visual observations and the first results will be presented. It is concluded that the new technique can be used to obtain much more information on rocking, including impact velocities, and that more rocking occurs than is observed visually.@en

We present an experimental study on the gas flow field development over a plunging breaking wave prior to impact on a vertical wall. The variability of wave impact pressure over repeated measurements is well known (Bagnold, 1939). The formation of instabilities on the wave crest are postulated to be the main source of impact pressure variability (Dias and Ghidaglia, 2018). However, the mechanism that results in wave impact pressure variability and the influence of the gas phase in particular are relatively unknown. The velocity field of the gas phase is measured with particle image velocimetry, while simultaneously the local free surface is determined with a stereo-planar laser-induced fluorescence technique. The bulk velocity between the wave crest tip and the impact wall deviates from the mass conservation estimate based on the velocity profile between the wave crest and the impact wall. This is caused by a significant increase of the local gas velocity near the wave crest tip. The non-uniformities in the seeding concentration accumulate near the wave crest tip and reduce the accuracy of the velocity measurements. However, the bulk velocity estimate is significantly improved with a fit of the velocity profile that is based on a potential flow over a bluff body. Additionally, the development of vortex is observed and quantified for two typical measurements with either a disturbance on the wave crest or a smooth wave crest. The circulation development is comparable to the formation and separation of a vortex ring, which results in a saturated vortex that separates from the wave crest (Gharib et al., 1998). Furthermore, the impact location of the wave tip is altered by the formation of secondary vortices. The secondary vortex enhances the lift locally and alters the trajectory of the wave crest tip, which may result in additional variability of the wave impact pressure.@en

Wooden fences are nature-based supporting structures to restore mangroves in the Mekong Delta. The hydraulic functioning of wooden fences was studied in previous studies. However, the role of bathymetry in the dissipation and damping of waves by wooden fences has not been studied yet. Thus, in this study, a numerical approach is used to find the effect of the position of fences and the foreshore bathymetry, including two particular slopes of 1/200 and 1/500, on wave damping due to wooden fences. The results show that the bottom slope significantly influences the dissipation of incoming waves, the so-called pre-dissipation, before damping by the wooden fences. Differences in pre-dissipation occur between fence locations along the cross-shore slopes. The higher pre-dissipation takes place for wooden fences closer to the land, as the depth-limited wave height at the fence reduces. The efficiency in wave damping of wooden fences is also increasing as the freeboard is becoming larger for the fence located closer landward.

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The last years, capacity of vegetation to reduce wave impact is receiving considerable attention. To predict wave attenuation processes within vegetation fields reliable estimates of vegetation parameters are needed. This proves to be difficult for woody vegetation as it consists of complex branch structures, characterized by varying branch densities, diameters and angles. State of the art physical and numerical models effectively use a single value for the diameter, b _v and density, N of vegetation, which is unrepresentative for complex vegetation, such as trees. Trees can be better described by the projected frontal-surface area, A _v. Hence, this work compares methods to quantify the A _v in space for a pollard willow forest, and determines suitability of these methods for predicting wave attenuation using a spectral wave model (SWAN). We use data from manual measurements and Terrestrial Laser Scans (TLS), to estimate the vertical distribution of A _v; and data from large-scale flume experiments performed on a willow forest to verify model sensitivity to A _v inferences. As a baseline for comparison, tree models that describe the structure of the trees in various degrees of complexity are compiled. The most realistic tree model is used to quantify potential errors in TLS and basic manual measurements of N and b _v. An initial comparison shows that the TLS data underestimates A _v, which indicates that conducting manual measurements is more suitable to quantify a homogeneous forest. We found that the TLS suffers from shadowing effects (i.e., blockage of laser beams) and we recommend to apply a correction factor to improve its measurements. Furthermore, we identified the impact that the different methods to determine A _v have on the estimation of wave attenuation using SWAN; in addition we verified the model results with data from large-scale flume experiments performed on the willow forest. The modeled sensitivity tests indicate large differences in wave attenuation and, consequently, a wide range (0.94–1.70) of bulk drag coefficients, (Formula presented.), for the various methods applied. This shows the variation of outcome between measuring methods and highlights the importance of stating the selected method for reliable frontal-surface area estimations, and consequently for reliable wave attenuation predictions.

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For the design of vertical hydraulic structures pulsating wave forces need to be calculated. The total wave force is a result of every wave component (long waves and short waves) within a wave field. The common formulae are derived for regular or unimodal narrow sea states and use one characteristic wave height and period. Broad-banded spectra like bimodal sea states are present at many locations. Moreover, new hydraulic structures like Panamax or post-Panamax locks do have a large vertical surface exposed to pulsating wave loads. Swell components within the wave spectrum are disproportionally contributing to the total wave force compared to short waves. This depth effect for broad-banded or bimodal wave spectra is not considered by the traditional wave formulae which could result in significant underestimations of wave forces on hydraulic structures. This paper aims to determine the wave loads of irregular non-breaking wave fields under any wave spectrum: narrow banded, broad-banded, or bimodal. Spectral linear wave theory (LWT) is used to transform any wave spectrum to a wave force spectrum. The wave force or wave pressure at any level can directly be evaluated from the wave force spectrum or wave pressure spectrum for any shape of the wave spectrum considered within this research. Spectral LWT is compared to the outcome of wave flume experiments with bimodal seas and other wave force formulae, like the Goda formula and quasi-regular LWT and the NewWave theory. This paper gives a description and evaluation of the spectral LWT applied for bimodal wave spectra and a comparison of the accuracy and validity of other wave force formulae. The peak forces and peak pressures distribution obtained by spectral wave theory compare well to the measurements. It appears that the use of a spectral LWT to obtain characteristic extreme forces improves the accuracy of the extreme load more than the use of a second order wave model with a quasi-regular assumption (i.e. where the spectral shape is not considered). For the typical conditions that occur at hydraulic structures (horizontal bed, intermediate to deep water, non-breaking, and uni- and bimodal seas) the often-used Goda formula can both under of overestimate the peak loads. Goda is well applicable for conditions with (breaking) waves narrow wave spectra and values of kph <0.5.@en

Worldwide, communities are facing increasing flood risk, due to more frequent and intense hazards and rising exposure through more people living along coastlines and in flood plains. Nature-based Solutions (NbS), such as mangroves, and riparian forests, offer huge potential for adaptation and risk reduction. The capacity of trees and forests to attenuate waves and mitigate storm damages receives massive attention, especially after extreme storm events. However, application of forests in flood mitigation strategies remains limited to date, due to lack of real-scale measurements on the performance under extreme conditions. Experiments executed in a large-scale flume with a willow forest to dissipate waves show that trees are hardly damaged and strongly reduce wave and run-up heights, even when maximum wave heights are up to 2.5 m. It was observed for the first time that the surface area of the tree canopy is most relevant for wave attenuation and that the very flexible leaves limitedly add to effectiveness. Overall, the study shows that forests can play a significant role in reducing wave heights and run-up under extreme conditions. Currently, this potential is hardly used but may offer future benefits in achieving more adaptive levee designs.

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This paper presents a novel design method to predict fatigue of flood gates due to dynamic wave loading. The accumulation of fatigue damage is predicted probabilistically over the entire lifetime of the structure rather than with a set of normative events. Load events are defined using a joint probability distribution of historical wind and water level data. The random phase-amplitude model is employed to obtain realisations of the wave state for every combination of environmental conditions. Linear wave theory and pressure-impulse theory are used to predict both quasi-steady and highly dynamic wave pressures. The stress response of the structure is predicted with a hybrid semi-analytical and finite element model. By applying a mode matching technique the fluid-structure interaction is solved in a computationally efficient manner. This facilitates the large number of simulations required for a comprehensive fatigue analysis without making concessions in the physical modelling. The fatigue damage is then evaluated with the linear Palmgren-Miner method by applying a rainflow algorithm. A Monte Carlo analysis is performed to estimate the expected fatigue lifetime of the structure. The modular structure of the model routine allows for easy adaptation to other situations where fatigue due to hydrodynamic loading is of interest. The design method is applied to a case study of a flood gate with an overhang inspired by the situation at the Afsluitdijk. Non-fundamental modes are taken into account without simplification of the fluid-structure interaction process and found to be governing for the fatigue damage for the studied case. Moreover, the interference of vibrations due to consecutive wave impacts is shown to have a significant influence on the outcome of the fatigue assessment. For the case study, the design method leads to a 10-20% reduction of the governing fatigue damage compared to a method commonly used in practice. At specific locations on the flood gate fatigue damage is found to be underestimated by current design methods. The presented design method is therefore found to be a significant improvement.@en

Wave overtopping is typically measured in the field using overtopping tanks. In this paper, an alternative system is developed that uses two laser scanners. The system also measures wave run-up, as well as run-up depths and velocities, both during perpendicular and oblique waves on a dike in the field. The paper considers the first calibration tests with the system in the field, with perpendicular and oblique waves generated by the wave run-up simulator on a grass dike slope. Furthermore, simulations are performed with the numerical wave model SWASH, to gain more insight in the potential performance of the system during actual oblique wave attack during a storm. The run-up is determined from the measured elevation and reflection intensity, which agrees well with the visually observed run-up. Run-up depths and front velocities can be determined accurately as well. The (virtual) wave overtopping discharge can be calculated from the data, which agrees well with the most commonly used overtopping equations for perpendicularly incident waves. Finally, from the simulated run-up data of obliquely incident waves, it is concluded that an estimate can be obtained of the incident wave period and wave angle of incidence at the toe of the structure.@en

Mangrove forests, that often act as natural coastal defences, enormously suffered due to ongoing climate change and human disturbances. Thus, it is necessary to have a countermeasure to mitigate the loss of mangroves. Wooden fences are becoming a viable nature-based solution to protect vulnerable replanted mangrove forests. However, the wooden fence's hydraulic characteristics are not yet fully understood due to the complication of branches arrangement. In the present study, a small-scale wave flume modelling of wave damping by a wooden fence was constructed using the inner branches as an inhomogeneous arrangement tested in earlier flow-resistance experiments. The physical model results indicate that the wooden fence is highly effective on wave transmission and that the effectiveness in wave reduction depends on the relative fence thickness, B/Hi. To understand the scale effect on wave transmission further, the numerical model SWASH was used with the laboratory wave data. By applying the prior experiments' drag coefficient on steady flow, the uncalibrated numerical model gave a good agreement with the wave model results, with a root-mean-square error for the total transmitted wave heights of 4.7%. After validation, potential scale effects for small scale tests were determined from scaling simulations at both full scales and the applied 1:5 model scale. These simulations were performed for a fence porosity of 0.81, and different fence thicknesses to understand scale effects between model- and full-scale. Both wave reflection and transmission at model-scale are about 5% higher than full-scale results due to the increased drag coefficient and viscous effects. The effects of fence thickness and porosity were the same in large and small scale, and much larger than the error due to scale effects. Hence testing fence efficiency at physical small scale is regarded as a useful tool, together with numerical modelling.@en

This paper establishes a computationally efficient model to predict flood gate vibrations due to wave impacts including fluid–structure interaction. In contrast to earlier models, composite fluid domains are included to represent the situation of a flood gate in a dewatering sluice with the presence of an overhang that causes the confined-wave impacts. The dynamic response of the gate-fluid system is derived in the frequency domain using a substructuring mode matching technique, in which the gate vibrations are first expressed in terms of in-vacuo modes while the liquid motion is described as a superposition of linear potentials. Pressure impulse theory is employed to predict the impulsive wave impact loads, which are superposed on the quasi-steady wave loads. The computational efficiency of the developed model allows for a large number of simulations. This makes it possible for the first time to perform probabilistic evaluations for this type of problems without doing concessions on the accuracy of the physical modelling of the involved fluid–structure interaction processes. This is demonstrated by application of the developed models within a probabilistic framework resulting in the explicit quantification of the failure probability of flood gates subjected to wave impacts.@en