After the failure of several large breakwaters in late 1970’s and early 1980’s where the role of rocking and breakage of armour became apparent, the importance of understanding this rocking phenomenon is given a great emphasis. Single layer randomly placed armour units are widely used in breakwater designs as they are more economical due to the less volume requirement. But these single layer units have a much more “brittle” behaviour and strength of the units becomes a critical factor. As the stresses developed after the impact is difficult to measure directly in the scale models, currently percentage rocking is used as a design criterion. But a clear relationship between this quantity and breakage has not been identified. Even though the single layer armour unit types are widely used the knowledge on the rocking behaviour of this type of units are limited. Therefore, to get a better insight into the rocking behaviour of single layer armour units a previously proposed technique of instrumented unit with embedded sensor was adopted. This technique was found to be promising in detecting the rocking motion in standalone mode. However, one issue of that technique was relatively lower sampling frequency. Because of that, enough data could not be captured to resolve the rocking motion in time very accurately. Therefore, in this report the measurements with standalone IMU sensor embedded in 3D printed model armour unit has been developed further. Firstly , different techniques were adopted to get the optimum sampling frequency and sampling frequency was increased from 25 Hz to 100 Hz. This report includes further details on the processing method and obtained results after performing the 2D physical model testings. It is the first time that stand alone rocking motions are reported for single layer armour units. By increasing the sampling frequency from25 Hz to 100 Hz, rocking events can now be resolved in time by 5-10 measurements points. Gyroscope data and accelerometer data were combined to separate the linear acceleration from raw accelerometer data. Upward and downward rotational motions were distinguished, and impact velocities were calculated based on both accelerometer and gyroscope. By analyzing the data it was observed that the angle of rotation during the rocking event is small and usually unit returns to its original position after a full rotation.

The purpose of this MSc thesis is to do an experimental study into the spatial and temporal variation of rocking armour units. Armour units on a breakwater slope under wave loading can sometimes start to move back and forth, this phenomenon is known as rocking. Rocking can lead to significant impacts between armour units, which can result in breakage. This is especially important for single layer armour units, like the Xbloc. The development of the smart Xbloc makes it possible to measure accelerations and angular velocity with a stand alone sensors at a sampling frequency of around 100 Hz. The current literature does not provide the spatial distribution of the number of impacts and the impact velocities due to rocking. Furthermore, only limited knowledge is available on the distribution in time. The research aim of this thesis is: Determining the spatial and temporal distribution of the number of moving armour units, the number of impacts and the impact velocity of rocking armour units. To achieve this aim a physical scale model was set up and model tests have been performed with 10 smart Xbloc units to measure rocking. The collected data, analysis and results provide a unique look into the behaviour of single layer armour units. The results can be used to validate rocking models and provide valuable statistical information on the number of impacts and the impact velocities.

The design of offshore and coastal hydraulic structures is very much dependent on the hydraulic boundary conditions, such as significant wave height, mean wave period and wave direction, among other parameters. A proper design value of these parameters is required during the design process, based on the corresponding safety philosophy and the lifetime of the structure. In this context, an extreme event is characterised by a combination of unfavourable parameters. However, the interdependencies between the parameters are not always accounted for in the design process, despite the fact that some parameters are clearly related. This potentially leads to an overly conservative or optimistic design. To complicate matters further, a given sea state might consist of a combination of wind wave and swell systems, sometimes coming from different directions and with different spectral shapes. Different combinations of crossing wave systems might lead to the same total significant wave height, mean wave period and mean wave direction. Only analysing the total wave parameters might oversimplify the situation in the presence of combined wave systems. In this thesis a methodology has been developed to establish extreme offshore wave conditions given the presence of these combined wave systems. A time series that partitions the total wave into a wind wave- and swell component is used as input for the analysis. The location of interest being off the coast of southern Brazil, where combined sea states are observed regularly. The main objective is to compute design values for all wave parameters of interest. With these design values a number of extreme offshore sea states are described in terms of a single total wave system and equivalent combinations of two wave systems. The former resulting in a single-peaked wave spectrum and the latter in an equivalent double-peaked wave spectrum. The extreme offshore sea states are transformed to the nearshore and compared. The single-peaked and equivalent double-peaked wave spectra may result in very similar values for the wave energy nearshore, albeit with different spectral shapes and directions. For the investigated directional combination, this means that the more elaborate approach with two wave systems potentially affects the design of coastal infrastructure if it is sensitive to spectral shape and direction, although the uncertainty of the result is not quantified. Equivalent wave systems could be compared for other directional combinations in future research to investigate if the more elaborate approach results in a more cost-effective design of coastal infrastructure. The quality of the multivariate vine copula model, used to compute the set of design values for the wave parameters of interest, is assessed in multiple ways. It is recommended not to pick a single set of design values at a point of high joint probability density. Instead it is suggested to use conditionalised samples from the vine copula model to determine the most unfavourable combination of load parameters, which has to be evaluated case-by-case.

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.