The aim of this research is to provide amathematical model that describes the physics in a levee when waves are overtopping a flood embankment. Ideally, this numerical simulation can replace empirical methods based on overtopping simulations and provide more insight into the physical process of an overtopping flow on a levee. This could prove to be useful for the design andmaintenance of flood barriers. Different interpretations of the stress tensor of pore water have each lead to distinct systems of partial differential equations. For each interpretation, the resulting system has been solved, using a finite element analysis in combination with a time-stepping method, in order to assess the validity of the imposed definitions. However, only one definition lead to a mathematical framework that yielded trustworthy results. In this finalmathematical framework, both the hydrostatic water pressure and the gravitational force have been disregarded, resulting in a system only consisting of variables such as soil particles displacements, pore water velocities and a distribution function »(t ). The distribution function »(t ) represents the fraction of the exerted wave stress on the surface carried by the pore water. By definition, the fraction can vary over time, which stands in contrast to state of the art models. The applicability of the results is limited, since the problem is simplified to a one-dimensional setting in which only normal stresses are exerted. The mathematical framework could theoretically be extended to multiple dimensions. However, it remains contestable whether it sufficiently simulates the physics in a levee. Further research is needed to show whether the extension holds when shear stresses are present and whether the same distribution function »(t ) can be applied to non-axial directions. In conclusion, this research is a proof of concept and serves as a stepping stone for more research. The used code can be found at https://github.com/HaveMersie/Overtoppingfailure

Large parts of the Netherlands are vulnerable to flooding. Due to the great impact that a flood would have for the Dutch society, The flood safety standards are very strict, which means that the required failure probability of flood defences is very low. To keep the flood risk within acceptable limits of the hinterland, flood embankments are assessed on whether the probability of failure matches the stringent norms using the methods and rules which are stated in the legal assessment instrument (WBI). Within the WBI the probability of failure of the flood embankment equals the sum of the probability of occurrence of individual failure mechanism. This thesis specifically focuses on the failure mechanism: sliding of the landside slope cover due to wave overtopping of clay flood embankments. Due to wave overtopping the relative permeable top layer of the clay embankment becomes saturated. This leads to a shallow subsurface flow parallel to the landside slope cover which is unfavourable for the geotechnical stability of the landside slope cover. The stability assessment of this mechanism is currently assessed with the Edelman & Joustra formula. This formula method is not based on a probabilistic or semi-probabilistic analysis and therefore does not give an failure probability. Instead it uses safety factors. Levee managers therefore believe that the outcome is overly conservative (Waterschappen, et al., 2021). This thesis addresses the question: How can the stability assessment of the Edelman & Joustra formula can be optimized for clay flood embankments in the Netherlands within the legal assessment instrument? To answer this question, new semi-probabilistic safety factors were derived based on a full probabilistic assessment of the Edelman and Joustra formula. The outcomes show that the current approach is not always as conservative as is often assumed. Application of the newly derived safety factor allows levee managers to be more flexible in how to account for the contribution of this failure mechanism to the total levee failure probability. The newly developed method therefore prevents unnecessary rejection and over-dimensioning of flood embankments, so the available resources for flood embankment improvements can be used better.

Wave overtopping is responsible for many dike failures, dike breaches and severe flooding. The erosion resistance of dikes to overtopping waves is determined by the strength of the grass cover. Therefore, a thorough understanding of the erosion resistance of grass covers is desired to enable a good and effective dike management. In the existing approach to assess the erosion resistance of grass covers, the erosion resistance is empirically quantified in terms of local hydraulic loads. However, despite the cyclical nature of overtopping waves, no insights into the dependence of the erosion resistance on successive loads are available. To improve the understanding of the resistance of grass covers to wave overtopping induced loads, understanding of the development of the mechanical behaviour of grass sods is essential. In this study the mechanical behaviour of grass covers under tensile loads have been examined by means of direct pull tests executed in the field. Especially the influence of repetitive wave loading and the conditions during testing were of interest. The results of this study show that the deformation of the grass cover due to tensile load is time dependent. The failure mode of the grass cover is influenced by the degree of saturation of the grass cover. The maximum strength and mechanical behaviour of the grass cover is influenced by accumulation of damage. The findings presented in this study provide a better understanding of the processes that influence the mechanical behaviour of the grass cover. Moreover, insights in the development of the process of damage accumulation are revealed. Based on the findings of this study, a method is proposed to determine the resistance of grass covers against repetitive loads by means of direct pull tests. In this method the resistance of grass covers against repetitive loads is described by an estimation of the fatigue limit. Relating the fatigue limit of a grass cover to hydraulic loads, enables an assessment of the erosion resistance of a grass cover at a specific location.

Dikes constructed of a sand core, clay cover and natural vegetation as (landside) slope protection are common flood defence structures in the Netherlands. The design parameters, such as the crest height of dikes, are determined through risk assessment to reduce the remaining probability of a failure mechanism, such as overflow. Little is known about the exact process leading to failure of the typical Dutch dikes in case the failure conditions actually occur. The most notable floods in the Netherlands have all been caused by dike breaching, where local damage in the dike lead to breach formation. This research describes the process of breach formation due to overflow and determines what design parameters affect the resistance of a dike against breaching. The proposed model (BRAM, a Breach Resistance Analysis Model) combines existing methods to determine the time-to-failure of the grass and clay cover with a newly developed process-oriented headcut erosion model. The model assesses the total time-to-failure of a dike through sequential failure of its components. The following process is simulated. Overflow over a dike causes a turbulent flow along the landside slope, resulting in local damage to the grass cover on either a prescribed weak spot or slope transition. The clay cover is subsequently eroded and the granular core material becomes exposed to the flow. A key assumption in the applied method lies in the fact that every newly exposed layer is less resistant to erosion than the layer above, resulting in slope steepening. Therefore, a near-vertical cliff, referred to as a headcut, is formed. When the overflowing water no longer follows the profile of the steep slope, a cascading flow, resembling a waterfall, forms a scour pit. The turbulent flow in this scour pit also erodes the core material of the dike, allowing horizontal erosion to undercut the slope. The undercutting of the slope causes the headcut to tumble over, moving the headcut and jet impact point to move towards the waterside slope, essentially restarting the scour process. This iterative process continues until the invert height of the dike is lowered to zero and the overflow rate is increased further. Model validation shows good agreement with test results on both large and small scale, as long as the assumptions regarding the structure of the dike hold (a dike profile consisting of a granular core under a clay layer and grass cover). When applied to three case studies, the BRAM-model predicts a similar total time-to-failure as the most advanced current model, posed by d’Eliso (2007). The predicted time-to-failure for the grass cover shows a significant difference. The BRAM-model predicts the grass cover to fail significantly faster than the model by d’Eliso (2007). This difference is offset by a longer predicted time-to-failure of the clay cover. Finally, the proposed model predicts a 50% slower headcut migration rate, as compared to the results by D’Eliso. This is a result of the more advanced description of the headcut erosion process. As the time-to-failure of the headcut migration phase is relatively short compared to the total breach formation process (between 10% and 25%), the total predicted time-to-failure is quite similar between both models. The main advantage of the BRAM-model is its suitability for design testing. The main weakness remains the unpredictable location of headcut initiation, which depends too strongly on spatial variation of the resistance of the dike to be predicted accurately, based on available data. Design parameters to increase the time-to-breaching have been identified. The most relevant were the steepness of the dike slope and thickness of the clay cover. Sensitivity analysis showed that the steepness and thickness of the clay cover, but also the porosity of the core material can be adapted to increase the time-to-failure of a dike. A breach-resistant dike may be designed for a limited overflow duration. Case studies showed three test dikes to sustain an overflow rate of 100 l/m/s for various hours by the grass and clay cover. As soon as the core material becomes exposed, the breach formation process accelerates significantly. The exact duration depends on the profile and construction material of the dike.

This experimental research is focused on fail mechanisms in non-cohesive soil beneath the jet with a Jet Erosion Test(JET). A vertical plain jet impinges fluid to a sand bed, which causes zero shear stress beneath the jet averaged over time. Many erosion theories would say that no pick-up happen at that point.

E_c=u/(√(H⁄d) √(ΔgD50 ))

Large range of erosion parameter was done in this research with video recordings to the activities beneath the jet. Tests varies with those parameters outflow velocities, stand off distances(SOD) and grain sizes. Comparisons are made to Rajaratnam, who has executed similar JET with varies erosion parameter too. The cavity depths and hill heights correspond well as function of the erosion parameter. Cavity widths have deviations for values above 4.0, which might cause by different grain properties or by the limitation of flume width. Secondary flow limits the width growth over time.

Weak deflected jet showed only surface erosion by micro turbulence at the soil bed till erosion parameter 1.0. One smooth bed was formed between two hill tops. Static bed did not exceed the concerning sand during and after start.
Increasing further the erosion parameter (1.0-5.0), soil deformation was also seen with ejection beneath the jet. Bearing capacity by Prandtl's theory was insufficient and failed the soil bed. Consequence, the inner cavity exceeds the internal friction angle of sand with dynamic erosion.
Erosion parameter larger than 5.0 had a wider cavity. Grains in soil translate and rotate in the start phase by insufficient bearing capacity. Vortices sweep around the jet with chaotic particle transport in the inner cavity.

Theories of Van Rijn, Meyer Peter Müller and Van Rhee underpredict for JET. The pick-ups rates are in all cases lower, which are based on the shear stress on bed. The impinging jet has different flow field and failure mechanism, which can be better related to the jet momentum.

A growing risk of flooding in coastal areas and the corresponding development of legislation drive continuous development in the field of hydraulic engineering. Failure due to
wave overtopping is not fully understood from a physical point of view. Existing knowledge gaps, processes that are not yet explained by physics or not even discovered, are
explained by empirical relations. The fact that knowledge on the relevant processes for overtopping load and soil resistance is fragmented and limited, causes limited application of it in practice.
To improve the understanding of failure caused by overtopping, a model that computes the soil stresses (soil stress is related to failure) in a dike cover, during overtopping load, is developed. It is possible that this model approach leads to additional knowledge on wave overtopping, e.g. new failure mechanisms or shift in normative mechanisms.

It is shown that overtopping has a large variety of appearances and so does failure due to overtopping. Literature study shows the large number of processes and characteristics, all with variable magnitude, that is relevant in the wave load and the soil strength during wave overtopping. Main wave load processes are shear stress (gradients), turbulence and impact. The considered soil strength process is the ratio between the stress (relative to the strength), for which the Young’s Modulus, Poisson’s ratio, soil weight, hydraulic conductivity and the subsoil stiffness are shown to be the main soil characteristics.

The developed model, a numerical 2D model with the model domain oriented parallel to the flow direction, computes the stress distribution and development in a loaded soil. For this case it is focused on dike land side slopes loaded by overtopping waves in particular, that is on dealing with clay, saturated conditions, fast varying load and a sloped surface. Stress equations in the model are derived, based on equilibrium of forces (horizontal and vertical) and motionless soil. The model is able to indicate initiation of failure for failure mechanisms that are associated with soil stresses, e.g. lifting of soil and head cut erosion. Soil in the model is loaded by normal and shear stress. The latter is, deviant from conventional methods, modelled as a shear stress gradient.

Test runs for verification and validation show that the model gives good results for cases with constant loads. Comparison of load cases with non-continuous overtopping wave loads shows both similarities and differences in the resulting soil stress. The most outstanding difference is the magnitude of the stress at depth. The differences indicate
starting points for further research.
Model employment demonstrates the future possibilities. A single wave load, computed by the model itself, is modelled. This run gives, at first view, plausible results.

The current model gives a reasonable representation of soil stress development. Further development is recommended to make the model useful for dike assessment and design. To do so, the model should be improved by probabilistic parameter definition, addition of soil stress damping and considering the impulsive nature and turbulent oscillations of wave load. Furthermore, it can be extended by the comparison between soil stress and strength, addition of spatial variability of the soil, enabling computations of non-planar parts of the slope and enabling the connection with other hydrodynamical models.

In the Netherlands flood protection is immensely important for the safety of the nation. The shocking outcome of the 1953 flooding proves this point. In modern days, the development of socioeconomic and climate change factors casts doubt on the effectiveness of conventional approaches to flood risk management. Consequently, this project explored new approaches to flood risk management.
An analysis of climate change effects led to estimation of future loading conditions. Subsequently, a detailed hydrodynamic analysis was conducted. It highlighted the significant levels of uncertainty that climate change introduces into loading conditions. Also, it confirmed the team’s perception, that the Westkapelle case region requires additional safety measures to guarantee an acceptable level of safety in the future. But how to guarantee the acceptable level of safety in the most efficient way? The team adopted the concept of robustness to find an answer. In a keynote publication Mens (2015) describes robustness in the following way: "Robust flood risk systems have some degree of resistance and some degree of resilience: the system can withstand some floods (no response), and for other (larger) floods impacts are limited and the system can recover quickly from the flood impact (response and recovery)." The team set out to include robustness as an integral part of the design process to handle uncertainties. The project shall be seen as an explorative study how this can be done, revolving around Westkapelle as a case study that proves the methodology’s feasibility. Robustness and uncertainty were included on multiple levels throughout the design process. Firstly, the range of uncertainties was quantified. Secondly, the effect, that single parameters have on the magnitude of uncertainties, was assessed. Thirdly, the system’s capacity was analysed to find the required overtopping reduction for guaranteeing sufficient safety. Fourthly, constructive measures were assessed on their robustness potential and satisfaction of stakeholder needs via a Multi Criteria Analysis (MCA). The MCA was then employed to select the type of constructive and non constructive measures to achieve the required levels of overtopping and safety. With the information on uncertainties, the measures were combined to form a robust design, consisting of living breakwater, dike heightening, surface protection and two policy measures. Probabilistic analysis was also done to see the sensitivity of the failure probability to sea level rise in different loading and design scenarios. A thorough comparison between the conventional design, that has been applied to the project location, and the robust design followed. The robust design came out on top. Robustness was found to be an effective tool in countering uncertainties. Where conventional design methodologies are lacking flexibility and precision, the robust design methodology makes use of the system and its resilience to find an optimal solution. Its applicability may not be limited to flood risk management only but stretch out to other civil engineering disciplines.

This research focuses on the development and feasibility of an online grain size estimator for a trailing suction hopper dredger (TSHD), based on the mass balance within a hopper, and using hopper settling models. The idea of the grain size estimator is to use existing hopper settling models iteratively for a certain time window with ‘online’ sensor input and different soil inputs. The resulting loading graphs are compared to the measured loading graphs, after which the most probable soil type is indicated.

This research is a continuation of the research of Strooker (2017) where not only the mass balance within a hopper, but also different occurring processes were taken into account. The grain size estimator developed for this research, is solely based on the mass balance within a hopper, and is focused on selecting a suitable
hopper settling model, simulating a great amount of trips of various projects and interpreting the results.

The research shows that the Modified Camp model performed well in validating the hopper settling model and was therefore chosen to be implemented into the grain size estimator. After determining the limitations
of the estimator, two projects and two vessels were used to simulate 1500+ trips in total with the available sensor data. The results are presented visually in different ways and compared to the measured soil model
of the considered project. It is concluded that at one project (Liverpool), there are multiple areas where the results of the grain size estimator clearly matched the soil model. The second project (Kaohsiung) showed less conclusive results. It seems that the results of both the first part of each trip as well as the whole trip,
produces results where the areas of soil are best distinguishable. The time window for where the soil type is determined also affects the accuracy and reliability. Longer time windows mean less accuracy, but a more reliable result. The accuracy was found to be only changing slightly between time windows of 30-600 seconds, but the reliability of the model is difficult to quantify.