It is important to decompose the signals when performing physical model experiments. In this paper, a nonlinear decomposition method is extended with the effects of a sloping bed. The approach is validated based on synthetic signals and numerical simulations. Verification with linear synthetic signals shows that the effect on the wave height is limited for intermediate water depth, but increases for shallow water depth with an error of up to 4%. Moreover, when not accounted for a sloping bed the wave height at the first wave gauge is overestimated in shallow water and underestimated in deep water. The results from the numerical simulations show that a shoaling coefficient for the bound waves based on the water depth ratio with a power 1 is reasonably accurate for the sub-harmonics but not valid for the higher harmonics. In addition, it is recommended to verify this assumption for a large range of test conditions. When applying both the method without and with the effects of a sloping bed on physical model experiments, the average differences are 1 % with a maximum up to 4 % in terms of the wave height.

When performing physical or numerical experiments in a wave flume, it is important to distinguish between the incident and reflected wave components. Recently wave separation methods including nonlinear effects were presented which can be applied for a large range of conditions and reduces the error in the wave separation. However, these nonlinear methods also result in a complex system of equations and require more wave gauges. In this work, physical model experiments with a high spatial resolution of wave gauges were carried out to validate different wave separation methods. All tests were analysed with a Linear method, the nonlinear method described in Eldrup and Lykke Andersen (2019) (ELA method) and a Modified ELA method. In this Modified ELA method, the model complexity depends only on the condition number of the phase difference matrix making the accuracy less dependent on wave gauge positions and noise. The results show that both Nonlinear methods are always preferred over the Linear method. A detailed analysis of the number of wave gauges shows that for the same distance between first and last gauge, 6 to 8 wave gauges are required for a converged solution independently of the wave gauge position. In an ideal situation – with an ideal number of wave gauges and ideal spacing between them – the ELA and Modified ELA methods should give nearly identical results. However, for the non-ideal conditions encountered in practice, the Modified ELA is shown to be more robust.

Physical model tests on the stability of rock armoured slopes have been performed to demonstrate the importance of water level variations during a storm, due to a tide or a storm surge. For the stability of rock armoured slopes also the importance of the sequence of storms at various water levels has been studied. The test results indicate that a smooth sinusoidal water level variation leads to an increase in damage compared to the same wave conditions at a constant water level. Furthermore, a stepwise approach of the sinusoidal water level elevation leads to other results than the approach with a continuous water level variation, whereas the continuous water level variation resembles the peak of a storm or the tidal water level variation better than a stepwise approach. If storms with different water levels attack the armour layer, the damage is generally smaller than if all storms attack the armour layer at the same water level. Furthermore, the results have been discussed based on earlier analyses where the statistics of rock armoured slopes have been addressed and the importance of the length effect has been illustrated using a method to apply results from physical model tests to real structures.