Wave run-up on rubble breakwaters: spectral effects

Seven sets of data for wave run-up on a rubble mound breakwater were combined and re-analysed, with full-scale, large-scale and small-scale model test results being taken into account. The dimensionless wave run-up value Ru_2%/H_m0 was considered, where Ru_2% is the wave run-up height exceeded by 2% of the wave run-up events and H_m0 is the significant wave height. The wave run-up data sets were compared and a clear influence of the spectral shape, characterised by the spectral width parameter ε, on wave run-up was noticed: high values of ε correspond to high values of Ru_2%/H_m0 and vice versa. Differences in wave run-up results between the various data sets could be explained by a difference in spectral width observed within these data sets. A multi-regression formula was fitted to all wave run-up data. The formula is valid for permeable rubble mound breakwaters covered with either grooved cubes or rip-rap with a slope steeper than 1 : 2, surging waves and a JONSWAP-type wave spectrum.