Wave run-up on a rough, permeable slope of a rubble mound breakwater

Abstract

Although a lot is known nowadays about the run-up on smooth and impermeable slopes as well as the run-up on slopes covered with a rock armour layer, the physical properties of the armour layer of a rubble mound breakwater are not incorporated in the relations describing the run-up on a breakwater’s slope. The roughness of a slope and its permeability, which can be described by a characteristic diameter of the armour unit and the porosity of the layer, are not used in the description of the run-up. This report is an attempt to get insight into the influence that the roughness and the permeability of a slope have on the run-up on this slope. In order to achieve this goal, non-dimensional parameters are derived describing the roughness of a slope and its permeability. Firstly, the framework of the design of a breakwater is given in order to place the run-up on a rough, permeable slope. The run-up itself is dealt with separately. Experiments were performed in order to obtain data that can be used to quantify the influence of the roughness of the slope and its permeability. The experiments were performed leaving the permeability of the whole structure out of consideration. To achieve a difference in porosity of the armour layer, rock armour units were used as well as tetrapod armour units. Two approaches of data analysis are applied on the data obtained from these experiments. This first approach describes the run-up on a rough, permeable slope by a combination of a roughness parameter, a permeability parameter and the breaker parameter. The roughness parameter and the permeability parameter are derived by forming non-dimensional parameters that describe roughness and permeability. The run-up, usually made non-dimensional using the wave height (H) is made non-dimensional here using the nominal diameter. This gave better results in combination with the derived parameters describing the roughness and the permeability of a slope. The second approach describes the run-up on a rough, permeable slope by using the relative run-up Ru/H and a newly derived non-dimensional parameter resembling the Iribarren parameter, but incorporating the influence of the permeability of the armour layer. When the relative run-up is put against the Iribarren parameter and is put against the newly derived non-dimensional parameter, the appearing scatter is less in the latter case. In both approaches, two relations describing the run-up on a rough permeable slope are derived. One for breaking waves and one for non-breaking waves. For the second approach, the found relations have a significant resemblance with the known formulae for run-up on a slope covered with rock armour units, derived by van der Meer and Stam. When the relations derived following the both approaches are compared, the relations derived by the second approach are the relations that give the best feeling with the physical processes as they occur. The relation for non-breaking waves, derived using the first approach, is applied on data obtained from physical model tests on a breakwater covered with tetrapod armour units. The calculated nondimensional run-up is compared with the measured non-dimensional run-up. The results show that the permeability of the whole structure can not be neglected, especially in the case of non-breaking waves.