Weirs are constructed inside rivers to manage the water level. On the one hand they need to be designed sufficiently strong to prevent failure or destruction, while on the other hand they need to be economically feasible. If a structure is designed too strong, unnecessary costs are made and the structure becomes too expensive.

One of the potential failure mechanisms for weirs is erosion of the soil downstream of the weir. Bed protections consisting of rock and concrete are placed to prevent this erosion. Numerical modelling can give additional insight in the design of such a bed protection. This thesis aims to improve the design of bed protections downstream of underflow weirs through numerical modelling. This is done through two research objectives, being 1) proposing a numerical modelling strategy to create a design method for riprap bed protections downstream of underflow weirs, and 2) preserving a small computation time compared to full scale 3D models, as this is ideal for a future application in engineering.

A new approach is formulated by using the stability parameter of Steenstra (2014), ψRS, as basis. This parameter is based on multiple flow situations, except the underflow gate. For this reason the underflow gate is investigated in the current research. The output of the created OpenFOAM models can be applied to this parameter, leading to ψ-curves that can be compared with measured damage.

The first research objective is obtained by the application of three different turbulence mixing length approaches, of which two approaches created interesting results. The first approach is the Bakhmetev approach, leading to a conservative design outcome with a gradual decreasing stability pattern. The second is the Shear Stress Relation (SSR), leading to a promising result with better defined instability regions that compare with measured bed damage. From the desire to work conservatively, the results reveal that in the design phase of a bed protection downstream of a weir, the application of the Bakhmetev approach for the mixing length is recommended over the SSR approach.

Extended physical testing containing three aspects is needed to strengthen the promising findings of the SSR. These aspects are 1) a damage stone count including a sieve distribution, 2) a setup with varying gate heights and stone dimensions, and 3) varying water levels and discharges per different gate height and stone size. In addition a preliminary 2D numerical model study is advised, which allows to investigate the areas of interest for PIV flow measurements.

The second research objective is achieved by the application of a 2D RANS model and the simplification of the water level through a rigid lid. This simplification still leads to workable results, with computation time that are in the range of two to eight hours, operating on ten cores in one computer. This makes the approach attractive for engineering applications and for future applications in renovation tasks for weirs in the Meuse.

The design of hydraulic structures like breakwaters and crest walls is often based on empirical formulations, physical models test, numerical models and a fair amount of expert judgement. Each technique has its own pros and cons. The main limitation of the empirical formulas is that often they have to be applied outside their range of validity. Physical modelling also has its own shortcomings. When breaking waves hit the structure, the location of the maximum pressures is still not well known due to the high spatial variability. By using an array with low spatial resolution, the forces estimated in the physical ume will usually underestimate to some extent the actual forces experienced by the wall (Ramachandran et al., 2013). In the last decades, numerical modelling has become an attractive alternative in simulating wave-structure interactions. Nevertheless, estimating loads on crest walls in the numerical ume is still at its early stages. On that account, the present work validates the prediction of wave induced forces on the front face of crest walls on top of rubble mound breakwaters in CoastalFOAM. A scale model of the Holyhead breakwater, located in Wales, is used. The key validation topics are the reproduction of wave-structure interaction when heavily breaking waves reached the wall, the evaluation of the ventilated boundary condition implemented by Jacobsen et al. (2018), the porous ow inside the armour layer formed by Tetrapods units and whether the simplication of not using a turbulence model, as done by Jensen et al. (2014) and Jacobsen et al. (2018), is also valid under heavily breaking waves. Four validation cases were used to test the capabilities of the numerical ume. The results conrm that it is possible to accurately reproduce the wave conditions and the wave induced forces from a physical modelling campaign. Overall, the CoastalFOAM model is able to capture the shape and the order of magnitude of the force events. A calibrated model predicts the highest wave induced forces (forces with an exceedance probability of 0.4% and 0.1%) with errors lower than 20%. Moreover, the results indicate that for practical applications it is not essential to include a turbulence model in the numerical ume to obtain reliable forces on the front face of crest walls for dierent wave conditions. Another outcome of this study is that the implementation of the ventilated boundary condition is required in the interface between water surface and structural elements to mimic accordingly the air-water mixture when the structure is subjected to a heavy wave attack. Nonetheless, there is still room for improvement in this area, where a better understanding of this boundary condition and of the air entrapment during wave-structure interaction needs further research. Despite the large computational time required by the numerical ume when large wave trains must be simulated, a CFD model during design stages of breakwaters and crest walls provides higher spatial and temporal resolution of the wave induced pressures exerted on the wall than a physical test. Therefore, a better picture of the forces and pressure distribution in the front face can be obtained.

Worldwide, rubble mound breakwaters are designed and built to shelter and protect coastal areas from overtopping and flooding, especially harbours and shorelines. Rubble mound breakwaters are essential to preserve desired hydraulic conditions within the hinterland, avoiding damage to inhabited or industrial areas. This research focuses on the wave overtopping of rubble mound breakwaters as failure mechanism. To assess the wave overtopping engineers can adopt multiple methods. These methods can be ordered in increasing degree of accuracy and costs: empirical methods, neural networks, numerical models and physical laboratory experiments. The preliminary design phase is a highly iterative process. Using physical laboratory experiments within this phase is an expensive choice, therefore empirical methods are often preferred. Nevertheless, this research revealed that empirical methods, e.g. the so called EurOtop 2018, show significant shortcomings in assessing average overtopping quantities over rubble mound breakwaters, even more when the geometrical complexity of the structure increases (presence of protruding wave wall). This thesis re-calibrated the roughness coefficient proposed by the original EurOtop 2018 approach, referred to as the updated EurOtop 2018 method. Numerical models are proposed as a possible solution between empirical methods (which can be carried out quickly given their low complexity) and physical laboratory experiments (which need more time but are characterised by high accuracy). They have been increasingly used and accepted in the past decades. Following this trend, the Joint Industry Project (JIP) CoastalFOAM was launched with the objective to develop and validate a numerical model (OpenFOAM, waves2Foam, OceanWaves3D and JIP additions; referred to as CoastalFOAM) capable of accurately modelling the wave-structure interaction of rubble mound breakwaters. This research aims to calibrate and evaluate the CoastalFOAM model to assess small to large wave overtopping of rubble mound breakwaters with protruding or non-protruding wave wall, considering 500 waves. The evaluation of CoastalFOAM shows that this numerical model can be used, instead of empirical methods (e.g. updated EurOtop 2018), to assess the average overtopping discharges. CoastalFOAM showed excellent agreement with measurements for large and medium overtopping cases, while resulting less accurate for small overtopping cases. The analysis revealed, however, that the average overtopping discharge as a quantity is not capable of identifying the magnitude of large overtopping events (without modelling all 500 waves). This can be considered critical in determining whether the structure is safe enough in terms of Serviceability Limit State (SLS) or Ultimate Limit State (ULS). Consequently, this thesis proposes a new methodology to assess the maximum overtopping volume within a storm, applying the concept of wave focusing and using the NewWave theory. The input variables for the NewWave profile are extracted from the spectral properties at the toe of the breakwater. A first order wave maker is used to generate the NewWave profile, making the methodology sensitive for the degree of non-linearity of the considered wave conditions. This NewWave methodology offers improved accuracy to assess the maximum overtopping volumes when compared to the EurOtop 2018 approach. Furthermore, this research proposes to apply the inverse EurOtop 2018 technique to assess the average overtopping discharge using the NewWave maximum overtopping volume. However, the accuracy of this methodology is lower than that obtained with the updated EurOtop 2018 guidelines. This study shows that CoastalFOAM can be used, instead of the current empirical methods, to assess the average overtopping discharge within the design cycle of rubble mound breakwaters. However, according to what has emerged, CoastalFOAM shows to be less accurate in calculating small overtopping discharges as opposed to medium and large. On the other hand, when considering the maximum overtopping volume as design criterion the proposed NewWave methodology showed to be the most efficient and accurate.