Computing breakwater stability using SWASH

Abstract

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.