Quantification of measurement errors, model and scale effects related to overtopping

Abstract

CLASH is concentrating on investigations of wave overtopping for different structures in prototype and in laboratory. The model investigations have focussed on wave overtopping and the comparison of overtopping results from small-scale model tests and prototype measurements. Possible differences in the results from small-scale tests and prototype were analysed with respect to measurement accuracy as well as model and scale effects. This report proposes a methodology to assess the aforementioned effects and to provide the uncertainties and correction factors for quantifying the various influences when performing model tests. First, the available literature on scale and model effects has been reviewed. It was found that scale effects especially for wave run-up and overtopping have been reported in the past. Manydikes up to 25% higher wave run-ups were observed. Wave overtopping for armour slopes in front of vertical walls in prototype was reported to be up to 10 times higher than in model tests but it is still not clear whether this is due solely to scale effects. Second, some theoretical considerations were performed to derive critical Weber and Reynolds numbers which should always be exceeded during model tests. It was found that for wave run-up and wave overtopping Weber numbers should not fall below Wecrit = 10 and that water depths should always be larger than 2 cm and wave periods longer than 0,35 s. This is usually the case in all models. Additionally, the overtopping related Reynolds numbers should be larger than 1·103 which is also the case for most of the model tests. Results for all field and model investigations have been plotted for the investigated sites using data from the field and two models of smaller scale. Results have shown that model tests performed for the vertical wall in Samphire Hoe and the steep Zeebrugge rubble mound breakwater do not deviate much from the prototype data points. However, for the flatter slope in Ostia differences between prototype and model have been observed in the order of up to one order of magnitude. A Monte-Carlo simulation was used to determine the variation which may occur when different measurement uncertainties and scale effects are considered. The results show a large dependency on the magnitude of the overtopping rate itself which was also evident from the observation of the model tests. Differences of a factor of about 5.0 for large overtopping rates and a factor of about 40.0 for low ones are observed. Finally, a new parameter map for scaling was proposed taking into consideration the aforementioned findings (Fig. 22). The map depends on whether or not the structure is ‘rough and sloping’ and eventually suggests a scaling predictor. The latter was then applied to the test cases of Zeebrugge and Ostia.