In this study, the wave-induced distribution of 13 microplastic (MP) samples of different size, shape, and density was investigated in a wave flume with a sandy mobile beach bed profile. The particle parameter were chosen based on an occurrence probability investigated from the field. MP abundances were analyzed in cross-shore and vertical direction of the test area after over 40,000 regular waves. It was found, that MP particles accumulated in more shallow waters with increasing size and density. Particles with high density (ρs>1.25 g/cm3) have been partly confined into deeper layers of the sloping beach during the formation of the bed profile. Particles with a density lower than that of water used in the experiments floated constantly in the surf zone or deposited on the beach caused by wave run-up. A correlation was found between the settling velocity of the MP particles and the flow velocity at the accumulation point and a power function equation developed. The obtained results were critically discussed with findings from the field and further laboratory studies.

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Wave overtopping—i.e., excess of water over the crest of a coastal protection infrastructure due to wave run-up—of a smooth slope can be reduced by introducing slope roughness. A stepped revetment ideally constitutes a slope with uniform roughness and can reduce overtopping volumes of breaking waves up to 60% compared to a smooth slope. The effectiveness of the overtopping reduction decreases with increasing Iribarren number. However, to date a unique approach applicable for a wide range of boundary conditions is still missing. The present paper: (i) critically reviews and analyzes previous findings; (ii) contributes new results from extensive model tests addressing present knowledge gaps; and (iii) proposes a novel empirical formulation for robust prediction of wave overtopping of stepped revetments for breaking and non-breaking waves. The developed approach contrasts a critical assessment based on parameter ranges disclosed beforehand between a smooth slope on the one hand and a plain vertical wall on the other. The derived roughness reduction coefficient is developed and adjusted for a direct incorporation into the present design guidelines. Underlying uncertainties due to scatter of the results are addressed and quantified. Scale effects are highlighted.

Stepped revetments are multi-functional coastal structures o ering protection against flooding. Despite the fact that these structures have been implemented for more than 60 years, comprehensive design guidance is lacking. Previous research studied overtopping of stepped revetments with slopes ranging between 1:1 to 1:4. To address the knowledge gap of predicting overtopping of stepped revetments with gentler slopes, this paper presents results of physical model tests for a 1:6 sloped stepped revetment with step heights of 0.05 m. The tests were conducted in a 110 m long, 2.2 m wide and 2.0 m deep wave flume. A fit through the overtopping results is compared with the reference curve for a smooth slope of EurOtop (2016), which allows the determination of the influence factor for roughness ( gamma_f ) of the stepped revetment. A value of gamma_f = 0.74 (r^2 of 0.94) is proposed to be used in combination with the overtopping prediction formula of EurOtop (2016) for slopes under breaking wave conditions. The results of the study indicate a high slope dependency for gamma_f .

The wave overtopping discharge at coastal defense structures is directly linked to the freeboard height. By means of physical modelling, experiments on wave overtopping volumes at sloped coastal structures are customarily determined for constant water levels and static wave steepness conditions (e.g., specific wave spectrum). These experiments are the basis for the formulation of empirically derived and widely acknowledged wave overtopping estimations for practical design purposes. By analysis and laboratory reproduction of typical features from exemplarily regarded real storm surge time series in German coastal waters, the role of non-stationary water level and wave steepness were analyzed and adjusted in experiments. The robustness of wave overtopping estimation formulae (i.e., the capabilities and limitations of such a static projection of dynamic boundary conditions) are outlined. Therefore, the classic static approach is contrasted with data stemming from tests in which both water level and wave steepness were dynamically altered in representative arrangements. The analysis reveals that mean overtopping discharges for simple sloping structures in an almost deep water environment could be robustly estimated for dynamic water level changes by means of the present design formulae. In contrast, the role of dynamic changes of the wave steepness led to a substantial discrepancy of overtopping volumes by a factor of two. This finding opens new discussion on methodology and criteria design of coastal protection infrastructure under dynamic exposure to storm surges and in lieu of alterations stemming from projected sea level rise.