This thesis investigates the hydraulic stability of single-layer Cubipod armour on gentle impermeable slopes, a combination outside standard breakwater design guidelines and relevant to the reconstruction of the IJmuiden Southern Breakwater. The study is based on 22 physical model tests in the TU Delft wave flume, on 1:2 and 1:3 slopes, with two underlayer thicknesses, a double-layer configuration, a single-layer cube reference, and five armour units carrying custom-built embedded rocking sensors.

The gentler 1:3 slope was less stable than the 1:2 slope. The design stability numbers are Nsd = 1.98 on the 1:2 slope and 1.81 on the 1:3 slope, both governed by the initiation of damage. Doubling the underlayer thickness gave no improvement, placement porosity proved critical, and rocking-induced fatigue is not expected to limit the design. ... Read more

This thesis investigates local and global scour processes around four-legged jacket (4LJ) foundations
for offshore wind turbines under current-only conditions using the 3D CFD Large Eddy Simulation (LES) model TUDflow3D. Jacket foundations, while increasingly deployed in deeper offshore environments, remain less studied than monopiles on local scour and scale effects and introduce new scour patterns like global scour. The research addresses this gap by evaluating the predictive performance of TUDflow3D against laboratory experiments, extending simulations to field scale, and assessing the applicability of monopile-based empirical scour relations to jacket configurations.

Laboratory-scale numerical simulations replicate the experimental study of Welzel et al. (2023) for both clear-water and live-bed regimes, validating the model for a 4LJ foundation. Model performance is assessed through morphodynamic comparison and time-averaged observation of the hydrodynamics, supplemented by a sensitivity analysis on numerical parameters: morphological acceleration factor, relaxation factors, numerical domain and grid resolution.

The validated model is then scaled to field conditions using a mobility similarity approach, enabling
investigation of scale effects on scour magnitude, spatial extent, and equilibrium timescales.
After the scaling up, both models are analyzed in order to enhance the knowledge that is known until now from 4LJ foundations.

For local scour, the spatial extent of scour was determined by adapting a formulation for monopiles and quantified throughout the entire scour evolution, revealing a consistent footprint over time. Scaling to field conditions demonstrated that the upstream–downstream scour pattern persists, but with reduced magnitudes in local scour depth due to scale effects, observed by the reduction of time-averaged bed shear stresses around the legs. This reduction in magnitude was approximately 30%–35% when compared in terms of dimensionless scour for both regimes and for both upstream and downstream piles. Timescale analysis showed that scour equilibrium occurs later at locations farther from the piles. When scaling, it was also found that scour on clear-water regimes
require months while live-bed regimes is in the order of magnitude of days to reach local scour equilibrium.

For global scour, live-bed conditions produced a footprint extending up to twice the jacket footprint
radius with rapid initial development, while clear-water conditions yielded slower, more confined scour. The order of magnitude for the global scour is variable depending on the location, but it reached values around 0.9 - 1 D on the center of the jacket and downstream of it.

Finally, empirical monopile scour formulas were evaluated, showing that they still provide reasonable order-of-magnitude estimates for upstream piles and capturing scale effects, as well it was proved that the scaling up from laboratory scale to field scale developed for monopiles can be useful also for 4LJ foundations.

The study demonstrates that CFD LES modeling is a robust and flexible tool for detailed, process based scour prediction around complex foundation geometries. Beyond validation, its ability to simulate field-scale morphodynamics and provide high-resolution temporal and spatial data makes it a valuable complement to laboratory testing, ... Read more

Riparian forests in front of levees can dampen incoming waves and reduce erosion, thereby decreasing the risk of flooding. This makes them a sustainable addition to stand-alone dikes, potentially decreasing the overall costs for future dike reinforcement measures. However, there are currently no guidelines for the design, monitoring, and maintenance of dike-forest combinations as significant uncertainties remain. For instance, most studies on the effectiveness of forests in attenuating waves focus on mild wave climates or rely on scaled tests using simplified tree mimics. As a result, prototype-scale studies on wave damping by forests under extreme conditions—essential for design and assessment purposes—are lacking.

This thesis investigated wave damping by riparian forests, with a specific focus on pollard willow trees, which are commonly found along the riverbanks in the Netherlands and other parts of Europe. The primary aim was to reduce the uncertainties associated with the application of forest-dike combinations. The foundation and source of innovation for this thesis is the data from real-scale flume tests, conducted on a 40-m-long live pollard willow forest, subjected to significant wave heights up to 1.5 metres. The analysis of these tests revealed several important areas for further investigation. First, the vertical frontal-surface area (Av) distribution of leafless trees should be measured in detail, as leaves were found to minimally affect wave damping. Second, flume studies at various scaled often form the basis of calibration and validation of analytical, numerical and empirical wave-vegetation models, however, the extent to which small-scale tests accurately represent wave-vegetation interaction at real scale remains unknown. The data from the real-scale tests made it possible to design scaled tests (with 3D-printed tree mimics) and compare the results between both scales. Lastly, during real-scale tests, the live tree branches were observed to sway by nearly 180 degrees under the highest water levels and wave conditions, highlighting the importance of and need for further research into branch flexibility.

Numerical models of vegetation largely underestimate the vegetation surface by assuming that vegetation consists of only stems and a single branch order and by neglecting tapering of branches. In Chapter 2, we investigate methods to obtain accurate Av distributions over the height of live willow trees. One method used a combination of manual measurements and tree allometry relations to create tree models (resulting in a detailed representation of Av). This method was compared to the results of a relatively more practical method: Terrestrial Laser Scanning. The findings showed a large variation of (calibrated) bulk drag coefficients between measuring methods and highlight the importance of reliable frontal-surface area estimations and consequently for reliable wave attenuation predictions.

Until now, no prior studies have compared real-scale and scaled tests with woody vegetation. We therefore conducted scaled tests with complex 3D-printed willow tree mimics to explore scale effects in scaled tests with vegetation (Chapter 3). The maximum measured wave damping (30%) was shown to be roughly 1.5 times higher than the real-scale tests (20%) for water levels just above the knot of the trees. The amount of wave height damping decreased for larger water levels, following the same trend as that of the real-scale tests. The largest effects were attributed to increased viscous damping (due to smaller branch Reynolds numbers), and non-exact flexibility scaling. These notable deviations illustrate that real-scale tests, though expensive, may still be needed to validate the results of scaled tests for woody vegetation. Alternatively, accounting for these discrepancies can increase the reliability of scaled tests for wave damping studies on woody vegetation and reduce the need for more expensive real-scale tests.

Additionally, scaled tests with flexible conical shapes were conducted to study the effects of flexibility on wave damping in greater detail (Chapter 4). The first-mode cone deflection was determined at ~0.7 times the length of the cone to avoid higher-order modes in the measurements. The findings showed that cone deflections greater than 5 degrees had a large spread in force reduction and resulted in a significant decrease in measured forces of up to 50% compared to their rigid counterparts. This work demonstrated that the effective length principle, which has already been successfully applied to grassy vegetation such as salt marshes and seagrass, is a promising dimensionless parameter for predicting force reduction in conical shapes--and could potentially be extended to tree canopies.

Lastly, the experimental data was used as input for analytical wave damping models, which allowed us to discuss the opportunities for riparian forest-dike solutions in the Netherlands (Chapter 5). The outcome of our probabilistic study suggested that pollard forests in front of existing dikes offered the greatest benefit in mitigating failure caused by the erosion of grass on the outer-slope of the dike due to wave impact. We also discussed that the height of the trunk, which determines the location of the knot—where the frontal surface area, and consequently wave damping, are greatest—can serve as a key design parameter for forest-dike systems.

The thesis offers an overview of key parameters and their associated uncertainties, contributing to the ongoing integration of (riparian) forests into dike design and assessment methodologies. ... Read more

Geotextiles are widely used in civil engineering, particularly in hydraulic engineering where they serve as filters and protect sand and clay from erosion. Their primary function is to prevent the washout of fine materials from the subsoil. Geotextiles are permeable fabrics and are usually made from plastics like polypropylene and polyethylene. However, due to environmental concerns surrounding synthetic geotextiles, there is a growing interest in moving away from plastics towards natural fibers. To facilitate this transition, understanding the engineering properties of these materials is essential. This study focuses on sandtightness, aiming to make applications more feasible.

Geotextiles can reduce the total thickness of a granular filter and thereby the costs. Because a geotextile can replace multiple granular filter layers, less material is required, which also results in lower emissions. Filters can be distinguished into two categories: geometrically open and geometrically closed filters. Sand particles cannot pass through a geometrically closed filter. The sandtightness is independent of the magnitude of the hydraulic load. Open filters prevent the erosion of the base material up to a certain hydraulic load. Open geotextile filters are not common used in hydraulic engineering.

Previous research has primarily focused on synthetic geotextiles, developing formulas to predict critical filter velocities based on their properties ((Van Der Knaap et al., 1986) and ( (Klein Breteler, 1988)). In contrast to these synthetic-focused studies, a study by Lemmens in 1996 on natural geotextiles, such as jute cloth, revealed a critical hydraulic gradient of 0.26, suggesting jute's potential as an alternative to synthetic materials. Despite these findings, stability criteria for natural geotextiles remain undefined, and newly developed geotextiles from natural materials have not yet been tested.
To address this gap, experiments were conducted in a flume set-up at the Fluid Mechanics Laboratory at TU Delft, using both woven and non-woven geotextiles made from natural materials such as jute, hemp, and wool. In the flow flume, a steady current was applied to a one meter long stretch of rock, closed at the top, with a geotextile-covered sand bed beneath it, allowing hydraulic gradients up to i = 1 to be exerted. This set-up enabled the determination of the critical load.

A total of 19 tests were conducted with 11 different configurations, involving variations with 7 different types of geotextile (4 woven jute geotextiles and 3 non-woven geotextiles made of hemp, jute, and wool). During all test steps of the 19 tests in the flow flume, measurements of water levels, pressures, and discharge were taken. Two endoscopes were installed at different locations in the filter layer, with holes drilled into two stones to secure the endoscopes. This allowed the camera to be positioned at the top of a pore, providing a view of the geotextile and detecting passing sand grains.

To determine the critical test step where the movement of base material begins, an innovative method of analyzing the erosion state was employed using endoscope images. These endoscopes are capable of detecting sand grains, allowing for the observation of erosion dynamics. In 4 of the 19 tests, the eroded sand was also suctioned after each test step to gain insight into the amount sediment transport. This indicates that even before the critical threshold level, there are small amounts of erosion immediately after increasing the hydraulic load. If the critical threshold level has not yet been reached, this erosion will return to zero during the rest of the test step. When determining the critical test step, two values were used for the critical load: a non-erosion criterion (Ho, 2007) and a criterion of 0.2 gr/s/m² (Klein Breteler, 1988), as used in previous studies to determine the start of movement. The non-erosion criterion is qualitative, whereas the Klein Breteler criterion is quantitative. It was found that these criteria are not equivalent, with a factor of 2 to 3 difference in the critical filter velocity.

This study concluded that the critical load for sediment transport is primarily determined by the filter velocity for open natural geotextiles. This contradicts previous studies that suggest a critical hydraulic gradient for open natural geotextiles. The critical filter velocity is influenced by the geotextile's characteristics, including thickness, opening size, and water permeability. Notably, the structure of the geotextile itself significantly affects the critical filter velocity. In this study, two woven jute geotextiles (J4: 422 gr/m² and O90 = 516.1 μm, J5: 518 gr/m² and O90 = 819.0 μm) with different structures were tested. The difference in opening size between the two geotextiles is approximately a factor of 1.5. However, the geotextile with much larger openings had a 1.75 times greater critical filter velocity with a start of movement criterion of 0.2 gr/s/m². Additionally, while the grading and size of the filter layer's grains influenced the critical hydraulic gradient, they had little to no effect on the critical filter velocity, emphasizing the significance of geotextile properties in determining their performance and stability under hydraulic load.

Ultimately, based on the tests, it can be concluded that the newly developed non-wovens could be a good alternative to synthetic geotextiles when considering sandtightness under parallel flow. All three non-wovens are reasonably stable at a hydraulic gradient of i ≈ 1, which is the maximum gradient that could be applied in our test set-up.

Recommendations for future research include testing with coarser sand, longer test durations, and synthetic counterparts for comparative analysis. Suggested improvements to the test set-up involve detailed height measurements of the sand bed and filter layer, and using high-resolution cameras for better sediment tracking. This sediment tracking by an endoscope can be improved by using a fixed pore for the endoscope for all tests. This can ensure that the pore volume is consistent across all tests and the size of the geotextile section captured in the image is also consistent. There is potential to use endoscope images for quantitative analysis of sediment transport. Further, the study emphasizes examining different flow conditions (perpendicular, and non-stationary) to enhance geotextile designs, particularly in dynamic environments like coastal revetments. ... Read more

Armoured slopes are commonly used in coastal structures to dissipate wave energy and protect adjacent infrastructure. To limit the height of these slopes in an efficient manner, regularly a concrete crest wall is placed at the upper part of the slope. Understanding the loads on these crest walls is essential for the design of coastal protection works. Conducting scaled physical model tests is a well established approach to confirm and optimise the design of coastal structures, albeit time consuming, scattered, and costly. This study aims to investigate the use of compact, focused wave signals in comparison to the common practice of using wave signals typically comprising a thousand waves in physical model tests. The physical model tests conducted in this study revealed that a compact wave signal was able to reproduce the extreme hydraulic response recorded during the simulation of a thousand irregular waves. This was observed in terms of sliding failure and extreme pressures exerted at the front vertical wall of the model crest wall. Results showed that the shape of the pressure signals, pressure distributions and integrated forces are reasonably well reproduced during focused waves. This suggests that this approach is promising for reproducing extreme responses at crest walls using focused waves; thus, resulting in reduced testing times. However, findings so far cannot support the use of this approach as a standalone tool for this application. ... Read more

The expanding offshore wind industry is facing challenges with excessive movement of the power cables that connect offshore turbines to the grid. The casings that surround the exposed parts of cables near structures, known as cable protection systems (CPS), show damage before the end of their expected service life, requiring costly repair and maintenance. A potential solution is to stabilise the CPS by placing one or more rock-filled mesh bag (rock bag) on top of it. There are multiple rock bag manufacturers and distributors. The bags are made of polyester netting that is relatively flexible. The sizes considered for this study are 4 and 8 ton (4000 and 8000 kg), but smaller and larger sizes are available. Currently, little is known about the behaviour and stability of these rock bags in offshore environments. The goal of this study is to expand the knowledge through empirical model testing.
480 experiments were conducted in a flume in the hydraulic engineering laboratory of Delft University of Technology. Two set-ups were used, one with a flat rough bed, to test two or three rock bags side by side and grouped formations of bags. The other is a realistic halved model of a monopile, scour protection and CPS. Regular wave, irregular wave and combined wave-current conditions have been tested.
Analysis of before and after top images of the tests is used to establish a failure criterion. In this way, a stability limit applicable for irregular wave fields is found. The effects of grouping and near monopile flow amplification are quantified.
... Read more

The surge in demand for inland vessel goods transportation has necessitated the operation of larger vessels with increased drafts. These larger vessels generate significant induced loads from their more powerful bow thrusters during berthing and mooring. These loads can lead to scour, which ultimately results in instability of the quay wall. To counteract this, stone gradings are penetrated with colloidal concrete as bottom protection. However, prior studies indicate that the flow velocity profile perpendicular to a quay wall decreases more rapidly than guidelines suggest, implying a potential reduction in the extent of colloidal concrete application. This is relevant for the Netherlands, where a multitude of hydraulic structures, including an estimated 130 locks, are in need of renovation or replacement. \\

\noindent This study seeks to comprehend the impact of bow thruster-induced loads directly perpendicular to the quay wall, on stone displacement near a quay wall and this study compares the outcomes of this field measurement with existing guidelines and scale modelling. The research question is therefore: ''\textit{How can results from a full-scale test improve the design and performance of loose-rock bottom protection against bow thruster-induced loads for quay walls accommodating inland vessels?}''\\

\noindent In order to answer this question a full-scale field measurement is conducted with the largest inland vessel in Europe. During this field measurement, free flow tests were performed and bottom velocity, pressure fluctuations and stone displacement were determined. \\

\noindent The applied bow thruster power and under keel clearance are marked as two important parameters for stone displacement. For the impact of this applied bow thruster power and under keel clearance, a variety of scenarios is examined. After each scenario a survey is done to look at individual stone displacement. Velocity measurements are taken to get more information about the flow velocities. The velocities were measured relatively far away from the bottom, resulting in low velocities. The actual bottom velocity is determined by validating and using the findings of the scale modelling performed by \textcites{Deltares}.\\

\noindent Free flow tests are performed to directly measure the outflow velocity and compare it with existing guidelines. From these tests, it is concluded that the existing guidelines for outflow velocity result in an overestimation of the required $d_{n50}$, with a measured loss coefficient of 0.65 as opposed to the proposed 0.90. Even with the reduced loss factor for the outflow velocity, the bottom velocity calculated with the Dutch method guideline is higher compared to the actual bottom velocities, demonstrating again, as already indicated in prior studies, that the guidelines are too conservative. \\

\noindent The turbulence intensity values play a significant role in validating the findings derived from scale modelling conducted by Deltares. The measured turbulent intensity values show similarities with the earlier findings, indicating a turbulent environment and validation of the Deltares scale modelling. \\

\noindent Based on pressure measurements, it is estimated that at the onset of movement, the pressure differences of the turbulent eddies are in the order of 50 to 90\% of the critical force to cause stone movement. \\

\noindent The in this study developed parameter R = $\frac{V_0}{UKC} \cdot t \cdot \frac{1}{k_{sl}} \cdot C_R $ shows that an increase in applied bow thruster power, a decrease in under keel clearance, an increase in duration and in slope lead to a linear relation with the normalised cross-section area of the near-quay erosion hole. \\

\noindent In addition, the full-scale field measurement showed that the stone displacement predominantly occurs within the first two and a half meters of the bottom protection, suggesting a possible reduction in the width of the colloidal concrete application. For a fictive quay wall the suggested reduction is compared with the design following the original guidelines. The suggested reduction alternative could save 75\% of the amount of colloidal concrete and CO$_2$ emissions. ... Read more

Coastal areas face increasing threat from erosion. The use of coastal protection structures is imperative to counter this. Concrete “armouring” is widely used due to durability and cost-effectiveness. Conventional methods of “armouring” result in habitat degradation and loss of biodiversity. ECOncrete developed Coastalock, an armour unit designed to provide coastal protection but also to create marine habitats.

Initial tests conducted on impermeable slopes in deep water conditions revealed, that tightly placed units experienced pressure gradients across the top layer, leading to failure. The aim of this study is to investigate the hydraulic performance of Coastalock, both with and without modification, within permeable breakwater structures. The study examines the influence of toe berms on different surfaces, assessing the armour layer’s susceptibility to sliding.

The research aims to bridge existing knowledge gaps regarding Coastalock behavior under varying wave conditions through literature review and physical model tests conducted in the 2D wave flume at TU Delft.

Structure from motion photogrammetry enabled the creation of 3D models of the armour layer after wave attack, facilitating the tracking of armour layer deformation of selected test series. The research includes measurements of overtopping discharge and reflection coefficient.

The findings shed light on failure mechanisms observed in Coastalock armour layers on permeable core slopes, attributed to built-up pressures exceeding self-weight and interlocking capabilities during wave run-down. 'Breathing' involves upward movement perpendicular to the slope during wave run-down and downward movement during wave run-up. Friction and partial interlocking contribute to the formation of a bulge in the armour layer, growing in size and magnitude, leading to extraction.

Observing increased 'breathing' and extraction thresholds with larger inter-unit void sizes, was confirmed for permeable cores. No stability increase compared to impermeable core was found, attributed to reduced maximum run-down levels. A lowering of overtopping and reflection was found for the permeable core.

The protrusions implementation necessitated a new configuration, termed the 'Protrusion Optimized' configuration, with an orientation change from cavity upwards to downwards at SWL. 10% protrusions reduced the stability number threshold for 'breathing', while 22.5% protrusions prevented filter layer migration and reached up 𝑁𝑠=4.2 without 'breathing' or extraction. A stability increase was found in 𝑠0𝑝=0.02 conditions, attributed to the ‘reservoir effect’. Incorporating protrusions and transitioning to the 'Protrusion Optimized' configuration increased reflection due to increased surface area and reduced permeability.

Changing the orientation location towards the midpoint between SWL and the bottom row or facing all units upwards resulted in increased stability in terms of ‘breathing’ and extraction, as well as a downslope shift of the damage location. Upwards-oriented units led to smoother slopes and higher reflection coefficients, both attributed to the water retaining properties of the cavity.

The presence of toe berms, showed no significant impact on damage progression or the location. Downslope movement well below the threshold indicative of near extraction was observed.

Recommendations for advancing 22.5% protrusions are proposed, advocating a Ns=2.6 for surging waves in deep water conditions. This design offers notable overtopping reduction, orientation flexibility, and reduced concrete usage and project duration.
... Read more

The dissertation focussed on the kind of closure methods used, in the past and at present, to repair breached dikes and to close tidal channels by simple means. By simple means one must think about the application by (mainly) manual labour of local materials and small-scale tools and equipment. The closure of tidal channels is also required in reclamation schemes and to construct dams between islands or from an island to the mainland.
This research was in the first place aimed at Dutch closure methods as practised in the Netherlands, Germany (Schleswig Holstein) and Ghana/Bangladesh (20th century). But it was also considered useful to check the closure methods used in other countries than the ones just mentioned.
Typical topics addressed have been hydraulic features, materials and equipment applied, the importance of manual labour in these closures and their output.
Related topics addressed in this dissertation are the development in time of closure methods and the reasons why sometimes closures failed.
Though flood embankments and sea defences as part of reclamation works have been constructed from the 11th/12th century onward, limited technical information about their construction as well as possible subsequent repairs after breaching, could only be traced for six projects carried out during a period of more than 400 years (1263 – 1675).
More information could be traced about the methods and constructions used in general but not for specific projects.
The closure methods used during the period 1200 – 1700, nearly always started by dumping a horizontal sill of clay clods up to the level of Low tide. Subsequently, the gap was narrowed by dumping clay clods, and the actual closure was, finally, effected by lowering constructions made up of sink-fascines (fascines imprisoning a gravel core or clay clods) and clay clods.. Alternatively, a cofferdam could be constructed across the flow gap.
In case of low tidal ranges, a row of sheet piles or piles, closely placed to each other, was driven across the gap. Sometimes, ships were ballasted and sunk on top of the sill.
At the end of the 17th century floating fascine mattresses were introduced in closure works. They were ballasted and immersed in the breach or tidal channel and functioned as bed protection of the easily erodible soil. Moreover, the aforementioned sill could now be constructed by stacking fascine mattresses on top of each other, again up to the level of Low tide. Subsequently, the closure was performed gradually in a horizontal direction by constructing a bund in sections, comprising fascines, clay clods, stones and wattle work.
From the end of the 19th century up to the middle of the 20th century jetties were constructed across the gap to be closed. A narrow gauge railway track on the jetty enabled the dumping of clay clods or stones in the gap from side tip wagons. Until the Second World war the side tip wagons were loaded by hand and in most cases pushed by manual labour.
During past centuries in many cases simple means were not adequate to close dike breaches and, consequently, the flooded polders could not be reclaimed and had to be given back to the sea.
In the period 1969 – 1985 Dutch closure techniques based on the principles described above were introduced for tidal closures in Ghana and Bangladesh. This required the adaptation of the said closure techniques to locally available construction materials, equipment and skills. Also here, a significant input of manual labour was part of the closure operation.
Closure techniques applied in China, East-Pakistan (which, later became independent as Bangladesh), England and Japan were also studied. It was surprizing to learn that the sink-fascine (having in each country another name, other dimensions and composition) had a major role in closure projects in China and East-Pakistan and, to a lesser extent, in Japan. Moreover, the application of ropes and hawsers (as in the Dutch fascine constructions) turned out to be of vital importance. In China and Japan the closures were required to repair dike breaches along non-tidal rivers. In East-Pakistan and England the closures studied were in the tidal zone.
Finally, a tidal closure performed in Bangladesh (at the Nalian River) by manual labour and simple means in the year 2020, has been studied.
The 75 case histories presented in this dissertation reflect the art of river and tidal closures by simple means over a period of nearly 760 years (1263 – 2020) in six countries. In most cases the area of the tidal basin which could be closed by simple means was less than 2 km2 while the tidal volumes were less than 2 million m3. Production rates in tidal closures varied between 0.26 and 0.62 m3 of fill placed per manhour.
But most of the simple means described can be considered as history. There are, however, countries where cheap manual labour is abundantly available and tidal closures could still be constructed by simple means. Such closures by simple means have been described for the year 1969 (Ghana) and the period 1979 – 2020 (Bangladesh).
The insights from this dissertation will therefore also be useful for future closures constructed by using simple means.
... Read more

In this study loading characteristics of rubble mound breakwater crown walls are investigated. This is done using a 2D physical model, testing for overall stability (through sliding) and temporal & spatial distributions of pressure along the face and base of the crown wall. A variety of wave conditions and geometries is used, with special attention for the influence of foundation level on the loading characteristics. This study shows the importance of this parameter and its link to the time lag between the maximum horizontal force and maximum vertical force in a wave impact. Using a new analysis method based on the factor of safety, this time lag is quantified and a reduction factor for the vertical forces is introduced. ... Read more

This study investigates the capacity of an open inverted filter to stabilize the interface between the sand fill and core fill in a rubble mound breakwater. The strength of this filter relies on the arching mechanism of the base material, which is directly influenced by factors such as stability ratio and effective stresses. These forces arise from porous flow, and its quantification involves both parallel and perpendicular hydraulic gradients.
A full-scale physical model, with a 760 mm open inverted filter, is employed to determine the critical hydraulic gradients required to initiate erosion. The model consists of three compartments, with the central compartment containing the open inverted filter. The two side compartments are filled with water, with one of them featuring a plunger mechanism to induce flow. Pressure sensors and water level gauges are used to measure the hydraulic gradients. In addition to the physical model, a numerical model is developed to gain insights into the flow dynamics within the system.
The tests reveal that an increase in effective stress results in higher critical parallel and perpendicular gradients. Furthermore, the addition of fines at 5% or 10% seems to enhance the critical parallel and perpendicular gradients. A negative correlation was found between SR and 𝑖⊥,𝑐𝑟𝑖𝑡, the results were fitted to a hyperbolic function. The findings further indicate that, even after erosion occurs, a stable interface can be reestablished. Therefore, designing solely for the single largest wave is not imperative.
... Read more

Over the past centuries, the Dutch rivers have been extensively engineered with the construction of hydraulic training works. A changing climate and increasing demands of river functionalities require innovations to the system to ensure its resilience. Exploring potential applications of Xstream elements might contribute to the development of sustainable river management strategies. The 33 cm high concrete three-dimensional cross is the little version of the Xbloc, a widely used breakwater element for coastal protection. Random arrangement of Xstream elements creates 60% porous spaces and the ability to build slopes at a 45∘ angle. Alterations to the riverbed morphology induced in the near-field of homogeneous Xstream hydraulic structures are assessed in the present study. A physical scale model featuring a movable bed of lightweight sediment was employed to simulate a river section. Minimising any compromises on Froude scaling, this material was used to properly scale the Shields parameter, striving dynamic similarity between the model and reality. Bed load transport processes are reasonably well represented by this material, providing well matched equilibrium scour depths and good qualitative comparisons of the influence of structural variations on these processes. Multiple setups differing in material and geometry were tested in a 12 m long and 2.6 m wide sediment recirculating flume. The primary comparisons of this study include:
• the flexible groyne head in the model against field data;
• two abutments with a 1:2.5 slope, varying in material between stone and Xstream elements;
• two abutments made of Xstream elements, differing in slope between 1:1 and 1:2.5.
Water levels were gauged and flow velocities were measured with acoustic Doppler velocimeters during the experiments. High-resolution bed elevation data was collected by means of a laser scanner. Generally, results of the model show an overestimation of bedform dimensions. This is attributed to the concessions necessitated by the limitations of the test facilities due to the low length scale factor. The effect of contraction was exaggerated in the model as the structure width to flow width ratio was 3 times greater and the influence of any upstream river training works was neglected. The flexible groyne head blocked 43% of the cross sectional flow area in the model. Furthermore, due to the laminar flow behaviour, the water encountered increased resistance within the structure. The deepest scour is found along the leading edge of the structures. This can be explained by the intricate flow patterns created by the primary vortex entering the flow acceleration. Inspired by the longitudinal training wall as built in the river Waal, a less porous stone abutment was constructed to compare the effect of porosity and roughness of Xstream elements on local sediment displacement under high water conditions. The increase in water level in front of the Xstream abutment was half that of the stone abutment and streamwise velocities in the main flow were 5% lower. These findings indicate better dissipation of energy by the Xstream abutment. Nevertheless, the relative turbulence level was 17% higher close to the Xstream abutment due to the higher roughness, resulting in equivalent peak velocities in both experiments. Along the Xstream abutment, however, the scour depth was twice as large. Taking into account the live-bed conditions, where sediment is supplied from upstream causing the scour depth to fluctuate around its equilibrium, a significant difference of at least 20% remained. The principle of a falling apron, a mechanism where individual units at the toe of a structure tumble down, covering one slope of the scour hole and thereby increasing the roughness, could be the reason for this. The erratic shaped Xstream elements enhance complex turbulence patterns very locally. Due to the absence of a supporting filter construction or a bed protection layer, the Xstream abutment was undermined, leading to individual elements decaying at the base of the structure. The interlocking ability of Xstream seems to be stronger when the structure is built with a steeper slope. This insight can be taken into account in the design of Xstream hydraulic structures. The substantial discrepancy in density between the Xstream model units and the angular polystyrene particles must be considered as the geotechnical properties may differ from the real world. The present study has shown the kinetic energy absorbing capacity of Xstream. Turbulence levels increase due to higher roughness. Exposing a uniform structure of Xstream elements to high water conditions might lead to instability which alters both positive and negative effects. Future research must give valuable insight into how the design of Xstream structures could look like for a durable implementation in the Dutch river system. ... Read more

Groynes in the Lower Elbe estuary in Germany are subject to attack from overflowing long-period primary ship-induced waves. Damage can occur on the crest and lee side of the structure due to the high turbulent overflowing flow velocities. An actual design tool for groynes exposed to overflowing primary ship waves is not yet present. Therefore, experimental research based on physical modelling is performed to establish a relationship between the damages and corresponding overflowing primary ship waves. This can be used as a design tool for groynes exposed to these types of wave attack. ... Read more

Mangroves can provide coastal protection by attenuating waves, currents, and trapping sediment (Menéndez et al., 2020; Bao, 2011). The effect of mangroves on the hydrodynamics depends on their size, location, density, distribution and morphology of the vegetation (Mendez and Losada, 2004). Mangrove loss during storm events will therefore impact the coastal protection. The soil-root interaction and influences of soil properties in the resistance of a mangrove tree against failure is neglected in most studies of flood protection by mangroves, due to a lack in understading.

This thesis improves the understanding of the soil-root interaction by deriving the schematization for multiple failure mechanisms in comparison with field observations. Firstly, the wind and wave forces are modelled to determine the different loads in the forest. Secondly, a novel schematization was developed of different failure mechanisms considering the soil properties and root system. All results are developed for a case study of a fringe forest in Demak, existing of Avicennia marina rooted in a silty, saturated soil. To be able to determine the difference between the seaward and landward edge of the forest, the width of the forest is increased to 500 meter. Also, due to a lack of information on the mechanical strength of Avicennia m., the mechanical properties of Rhizophora m. are used, which will overestimate the resistance due to the higher wood density of Rhizophora m. (Manguriu et al., 2013).

The results show that the drag forces were largely influenced by the tree architecture (such as vegetation width and height), forest density and inundation of the tree. Larger wind and wave forces, and therefore a larger moment occured if the width of the vegetation increased. If the height of the tree increases, a smaller part of the canopy is submerged. This leads to a decreased area that is exposed to waves and therefore a declined wave force. A higher tree does enlarge the area subjected to wind forces, resulting in an increased total moment. Overall, the 2.8-meter tree analysed in this thesis experienced the largest horizontal forces and moment at the seaward edge of the forest due to the relatively large water depth at this location. Furthermore, the maximum horizontal force and moment shift to the landward edge for larger trees due to the increase of wind contribution. To investigate the stability under these loads, the different failure mechanisms need to be inspected.

The failure mechanisms of root breakage and slippage are not important because of the high safety factors and no observations in the field. The failure mechanism trunk breakage also showed a high safety factor, contradictiory to field observations pulling willow trees. The model results and field observations showed that a combination of upwind soil uplift and bending of roots was found most likely to occur. For this failure mechanism, the roots are schematized as beams with a spring-support on the leeward side of the trunk. The roots are exposed to the weight of the overlying soil and the overturning moment. The model showed that an increase in the participation angle α or root diameter, or increase in root length results in larger stresses in the windward roots. The amount of uplift enlarges when the root diameter or root length increases or the participation angle decreases. The modulus of subgrade reaction and modulus of elasticity influence the distribution of the overturning moment over the leeward and windward roots. The largest difference between the moment inside the leeward and windward roots is found with a high modulus of elasticity or high modulus of subgrade reaction. This difference is in agreement with the contrasting reaction between soil types as stated in literature (Dupuy et al., 2007).

The results show the dependence of the different failure mechanisms on soil and root properties, but also on the forest architecture. This research shows that the incorporation of mangrove stability in wave attenuation models cannot be neglected. Using an effective stress approach, instead of a total stress approach as in this thesis, would provide extra information, such as soil behaviour in time during loading. It is therefore recommended to measure pore pressures under static or cyclic loading, resulting in the progression of the effective stress over time. The inclusion of more accurate soil descriptions would enable reducing uncertainty in nature-based solutions and enables to describe the soil-root reaction to loading over time. ... Read more

On the east coast of Romania, at Eforie, coastal erosion manifests. To strengthen the coastal area a large coastal protection project was setup involving beach nourishment combined with the construction of breakwaters. The breakwaters are designed with the well-known modified Van der Meer formulas. To ensure confidence in the breakwaters stability the designs were tested during a 3D physical model test. The designs were stable, however the measured damage to the breakwater was larger than was expected. Investigating the physical model test resulted in three important aspects, that need to be investigated. First, a broad list of configurations, that could responsible for the damage, could be identified. Secondly, excessive wave breaking on the foreshore during the model test resulted in a shift in wave energy from higher to lower frequency waves. These low frequency waves, or so-called infragravity waves became increasingly dominant near the coast. Their effect on the stability of the structure is however unknown. Thirdly, the incoming waves were very oblique and on a shallow foreshore, resulting in a different failure mechanism than is incorporated in the modified Van der Meer formulas. A new stability method has to be formulated to investigate breakwater stability for this physical model test. Due to the broad list of configurations and the possible influence of infragravity waves, real scale or physical model tests are not feasible and a numerical model needs to be used. A reliable and widely applicable method to link breakwater stability to a numerical model has however not yet been composed. Therefore, the goal of this thesis is to propose a method that can link breakwater stability to a numerical model and to assess whether the identified configurations resulted in the damage along the statically stable rubble mound breakwater, measured during the Eforie physical model test.

First, an investigation is performed on the physical model test set-up and observations, resulting in a final list of 5 configurations, that are investigated in this research: The applied offshore transitional slope (1), the assumption of uni-directional waves (2), the slope of the lower foreshore (3), the depth-contour lines inducing wave focusing (4) and the very oblique wave angle on a shallow foreshore (5). Secondly, a method is proposed linking breakwater stability to a velocity signal from the numerical model SWASH. An equation is formulated, based on the theory of Izbash (1935), with a slope factor included, and scaled with the theory of Shields (1936). It requires a velocity signal, that can be obtained from SWASH, to calculate a stone size required for stability.

Thirdly, a numerical model is set up in SWASH, with grid dimensions 3m x 2m, resembling the physical model test. The breakwater is modelled as an impermeable core with a permeable porosity layer placed on top. The thickness of the porosity layer is based on the thickness of the outer armour layer of the original breakwater. The numerical model is validated by comparing the wave characteristics, at several locations along the breakwater, to wave data available from the physical model test. The numerical model shows accurate resemblance of the wave characteristics. Since the wave velocity is linked to the wave height, it is assumed that the wave velocity on the breakwater is also correctly modelled. The model is therefore found valid for the modelling study. In the numerical model along the still waterline measurement points are indicated that provide the velocity and waterlevel signal during a simulation. In the numerical model two layers in the vertical are assumed and tested to be sufficient. The velocity of the top layer resembles the velocity that flows just over the stones. Therefore from the velocity signal of the top layer the governing u_0.2% along the waterline at the breakwater is obtained and from the waterlevel signal the wave spectrum is derived. In the study simulations are performed in which the configurations are tested one by one, and all simulations are assessed on two parameters: the u_0.2% and the wave spectral transformation along the breakwater. The results from the different simulations are compared relatively to identify the relative effect the configurations have on the velocity and wave characteristics.

The results of this research show that breakwater stability can be predicted reasonably well from a velocity signal obtained from SWASH. The velocity signal, obtained from SWASH, results in reliable stone sizes. The configurations could be investigated with the proposed method and the results provide reliable and useful insights. In addition, the proposed method is able to identify the effect of infragravity wave energy on the stability of a breakwater. The method is also tested by calculating the relative obliqueness factors for different incoming wave angles, which shows promising results. It is important to reproduce the breakwater porosity well in the numerical model as it can significantly influence the velocity signal. A decrease/increase of the porosity thickness with 30% or 0.6m can result in an increase/reduction of 20-26% in velocity respectively.

The five discussed configurations provide partial explanations to (in)directly induce the higher breakwater damage in the physical model test. Both the applied offshore transitional slope (1) as the assumption of uni-directional waves (2) result in a slight underestimation of the breakwater stability and therefore a somewhat conservative design along the entire length of the breakwater. The combined effect resulted in a reduction of 0-6% around the head of the breakwater, h/Hs = 2.5-4.8, and a reduction of 16-24% near the shore, h/Hs = 1.1-1.8. Especially near the shore the breakwater is conservatively designed, due to the fact that both the transitional slope as the assumption of unidirectional waves increases the infragravity wave energy in the system. It is found that incoming waves break around h/Hs = 1.7 after which the infragravity waves induce a temporary increase in waterlevel, around h/Hs = 1.1-1.8. This allows the depth-limited short waves to become bigger resulting in higher velocities and more damage on the breakwater. This affects the breakwater stability closer to shore and needs to be taken into account when designing a breakwater in these conditions. The lower foreshore (3) induces the generation of infragravity waves, which affect the velocity closer to shore as described above. The depth-contour lines (4) result in a wave focusing effect increasing the velocity around h/Hs = 1.1-1.8 with 8-11%. Based on the results of this thesis the very oblique wave angle on a shallow foreshore (5) does not induce higher velocities and breakwater instability. It is however assumed that the effect of a breaking plunging wave, inducing acceleration and pressure difference effects on the stones on a slope, is not sufficiently into account, due to the grid dimensions used in the model. As other plausible causes of the increased damage are disproven, it seems likely that the different oblique wave breaking process that is not modelled in detail leads to the increased damage. ... Read more

To estimate wave attenuation by mangrove forests, trees are often schematized as uniform cylinders (over the height) representing a tree’s stem. However, trees have more complex geometrical features that influence the interaction between waves and tree structures. Recent studies have shown that the frontal surface area distribution over the height Av(z) is a crucial parameter for estimating wave attenuation by vegetation (Kalloe et al., 2022; van Wesenbeeck et al., 2022) because it can account for complex geometrical features. This study aims to model the complex geometry of the Avicennia marina mangrove species. The research question then becomes:

How to construct geometrical tree models of Avicennia marina vegetation and how to obtain the projected frontal surface area distribution over the height, Av(z)?

In this study, manual measurements were performed to obtain tree structure parameters. Both canopy and root measurements were conducted for Avicennia marina vegetation with varying characteristics (age and density). Two saplings (approximately 1.5 years old) with variable canopy densities and two young trees (around five years old) with varying canopy densities were measured. We stored canopy measurements in a so-called tree data structure consisting of nodes (representing the branches) that contain information about the individual branches, such as branch orders, -lengths and -diameters and edges, which are links that establish direct relations from one branch to another. After that, we developed a search tree algorithm to loop through all tree data, compute parameters of interest and store the results in assigned data arrays. Parameters of interest to obtain after the data analysis were branch dimensions and diameter ratios of branches (between various branch classes). This information was necessary to create a blueprint for constructing geometrical tree models.
Tree modelling started with the construction of a root (pneumatophore) model. Additionally, the frontal surface area of these roots was computed and displayed as a function of the height. In addition to the root model, we constructed two canopy models. The first model is based on relations between branches and can be called deterministic or dependent (canopy model 1). The second canopy model (canopy model 2) generates branch dimensions based on the normal distribution of branch diameters and is, therefore, more probabilistic with branches independent of each other. Both canopy models construct branches based on information travelling from preceding branches. The models account for the proper placement of branches within 3D space by rotations and translations. The algorithm computes and outputs the projected frontal surface area over the height of a system of branches for a given direction (XZ-plane projection or YZ-plane projection). We validated the two canopy/tree models against validation measurements. Three trees were divided into seven vegetation layers, and branches were registered that intersected with the layers. As a result, estimation could be made on the frontal surface area per layer.

This study found that the frontal surface areas due to roots and canopies are significant and are well represented by the parameter Av(z). The contribution of the roots and canopy cannot be neglected in modelling wave dissipation by vegetation. The contribution of smaller branches to the total Av is significant, proving that considering only the tree stem is an underestimation. Moreover, the research shows that it is possible to develop a geometrical tree model based on a set of measurements and design rules that follow from observations, at least for the considered tree species. We could extrapolate and interpolate our results to generate tree models for a wide range of tree ages. Additionally, it is possible to create a forest by generating multiple trees.

Both tree models (1 and 2) showed little differences in Av(z) during the model validation process. Moreover, the validation measurements led, in general, to an overestimation of the total frontal surface area. Consequently, model validation was inconclusive regarding both tree models. However, we found that constructing tree models according to tree/canopy model 1 is preferred because it resembles an L-system more and is more practically applicable in computer models. We can improve future tree models by collecting more measurements regarding branch structures and root distribution as a function of tree age. This will result in increased model reliability. ... Read more

The water authority ”Hunze en Aa’s” initiated a demonstration project adjacent to the Dollard where non traditional dike reinforcement strategies could be developed. For this project Sweco designed a sea dike with an outer slope more gentle than traditional. This dike is called the ”Wide Green Dike” (WGD) and has an outer slope of 1:7. This dike is designed for 10 l/s/m overtopping with hydraulic boundary conditions provided by HYDRA-NL. This report examines whether 10 l/s/m of overtopping leads to failure of the WGD. In this context failure means erosion of the inner dike slope. Whether failure occurs is based upon the cumulative overload method (Steendam et al., 2015).

The WGD is rebuilt in a computational model called SWASH, which is a general-purpose numerical tool for simulating non-hydrostatic, free-surface, rotational flows and transport phenomena in one, two or three dimensions. The flow velocities on the rebuilt dike for the overtopping design condition are analysed. In this study SWASH is used to analyse 2D wave interactions from nearshore along a shallow foreshore towards and over a sea dike.

The simulation using the locally generated waves results in no overtopping. The overtopping criterion is normative for the crest height and no overtopping indicates that it is likely that the design of the dike can be optimized. But before any decisive conclusion can be made more research into the wave cli-mate in the Dollard is needed.

As the scenario using the locally generated waves resulted in no overtopping, a new scenario is created. This scenario has other wave boundary conditions, such that there is overtopping. This simulation results in 57 l/s/m overtopping but without any initiation of damage on the lee side according to the cumulative overload method. This result would indicate that exceeding an average overtopping of 10 l/s/m might not necessary lead to failure for a dike with a more gentle, compared to standard, outer slope. The same simulation shows that the current relation for the flow on the lee side is likely not sufficient to describe the full flow pattern. According to literature the flow velocity on the lee side of a dike increases and stabilizes. However, SWASH simulation results show after the initial increase also a decrease in flow velocity. The current relations for the flow velocity on the lee side only include the first initial increase but do not include the observed decrease in flow velocity. The kinematic shock theory equation, shows good agreement with the decrease in velocity. The results show that the tipping point (change from flow velocity increase to decrease) is located at 97% of the predicted final flow velocity (Van Gent equation). It seems that a combination of the Van Gent equation and kinematic shock equation can represent the flow velocity along the lee side of a dike.
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With the advance of urbanisation in coastal regions comes an increase in armoured shorelines and the destruction of coastal marine habitats. To combat this, ECOncrete Tech Ltd has developed a new eco-friendly armour unit, the CoastaLock. With its ecological advantages proven, its hydraulic performance is still largely unknown. This thesis aims to do the first exploratory research into the stability, reflection and overtopping performance of this CoastaLock armour unit, through a literature study and physical model tests. Data is gathered during physical model tests on a deep-water impermeable slope with different wave steepnesses, armour unit spacings, underlayer thicknesses and block orientations.

The mechanism of breathing is witnessed in tests with CoastaLock armour units. This mechanism shows the armour layer repeatedly getting lifted up from the slope and placed back on it as a result of pressure differences over the top layer during maximum wave run down. This mechanism causes movement of granular material in the underlayer, with large under deformations as a result. This thesis, therefore, advocates for listing the breathing mechanism as a failure mechanism.
The CoastaLock armour units show stability numbers of approximately 2 when tested at armour spacings below 10%, and stability numbers larger than 4 when tested at armour spacings larger than 10% for a wave steepness of 3.5%. Wave steepness is shown to be of a minor influence too, with the influence of underlayer thickness and unit orientation being negligible.
The reflection coefficient is shown to be mainly dependent on wave steepness, and minorly on armour spacing. Reflection coefficients of approximately 0.8 to 0.5 are measured for wave steepnesses between 1.5% and 4.5%.
Overtopping is shown not to play a role in situations with armour spacings lower than 10%, as the layer fails before overtopping can become an issue. For the more stable spacings, those larger than 10%, the overtopping discharge is quantified and the roughness factor is shown to vary from 0.732 for 10% spacing to 0.61 for 25% spacing. Factors other than the spacing are of a minor to negligible influence.

The CoastaLock armour units show promising results for situations with a short leakage length and large armour spacings, i.e. situations where the pressure differences over the top layer are small. However, this research is the first exploratory research into these armour units and should therefore be interpreted as no more than an indication of the behaviour of CoastaLock. It is recommended to expand the research into these units, both on the units in different situations as on the failure mechanisms of the units and the solutions thereto. ... Read more

Witteveen+Bos as part of construction consortium Nautilus, has prepared the design of a sea defence system in Middelkerke. The very shallow water conditions (h/Hm0 = 0.3) and complex geometry of the structure, i.e. a high berm and stepped revetment, caused uncertainties in the usage of the empirical equations from the EurOtop Manual (2018) for wave overtopping discharges. Therefore, small-scale experiments have been performed to asses the overtopping discharges.
Physical model experiments can be used to determine wave overtopping discharges, but can be expensive and time consuming. Recent studies show promising results for the use of SWASH as tool to predict overtopping discharges for relative simple geometries, but SWASH is suspected to be less accurate for more complex cross-sections. Two methods (SWASH, EurOtop) are used to predict wave overtopping discharges for the new boulevard Middelkerke and the results are compared with measurements from small-scale experiments conducted in Ghent. The goal is to asses the feasibility of using both methods for this complex structure with stepped revetment in shallow water conditions.

The EurOtop Manual (2018) uses influence factors to account for roughness at the slope and the presence of a berm in the structure. To use the empirical formula to determine the average overtopping discharge for this specific complex cross-section, a berm influence factor was added to the equation
for shallow water conditions developed by Altomare et al. (2016). Recent studies of Schoonees et al. (2021) found that the influence of the roughness of a stepped revetment on overtopping discharge mainly depends on: a characteristic step height, relative overtopping discharge and the wave period at the toe of the structure. Using their research as guideline, a roughness influence factor of γf =
0.75-0.9 was estimated for the stepped revetment for this case study. Although not validated for this specific configuration, using the (adjusted) equation resulted in very comparable average overtopping discharges compared to the physical experiments in Ghent.

In this case study, the usability of SWASH to predict the average wave overtopping discharges has been evaluated. First, the SWASH model was calibrated based on the incident wave conditions at the toe of the structure (Hm0, Tm-1,0) with the data the physical experiment in Ghent. This were the target wave conditions of this study since they are generally used to determine the average wave overtopping discharges (e.g. EurOtop) and to exclude the wave-structure interactions. Thereafter, the structure was added to the bathymetry with a smooth slope and local friction was added to represent the stepped revetment, as resolving the small steps would require an overly fine grid.

SWASH was able to reproduce the target incident wave conditions of the physical experiment very well (Hm0<3%,Tm-1,0<5%). However, when the structure was added to the bathymetry, larger differences were seen for the wave conditions at the toe compared to the physical experiment, for which no explicit explanation was found. Contrarily, Hm0 and Tm-1,0 include the full wave field, primary waves and infragravity waves, and the limited number of overtopping waves made it difficult to asses the influence of the difference in wave spectrum on the overtopping discharges.
The overtopping reduction due the added roughness/friction compared to a smooth slope reference test, was eventually related to a Nikuradse roughness height for the stepped revetment. A Nikuradse roughness of 1-1.5 times the characteristic step height of the stepped revetment, resulted in very similar average overtopping discharges compared to measurements from the Ghent experiment.

Both the EurOtop Manual (2018) and SWASH were able to reproduce the average wave overtopping discharges from physical experiments, but the results need a wide confidence band since the number of overtopping waves were limited and discharges small (q < 1 l/s/m). Each method has their own benefits and limitations. The EurOtop Manual (2018) is easy to use, but the validity of the empirical equations are uncertain for more complex geometries. SWASH gives more detailed information than only an average q: spatially and temporarily varying surface elevations and velocities along the domain, by which direct attack on the slope and structures (extreme values of u and F) can be calculated. SWASH could also be used as a ’numerical laboratory’ to further parameterize the influence of roughness on wave overtopping for a wide range of boundary conditions and structural configurations.
... Read more