The stability of stones on mild slopes under wave attack

Abstract

The static stability of stones on mild slopes under wave attack is investigated by this research. First it was checked whether there are any numerical models that could be used to describe the stability of mild slopes. As such, there is no existing model at this moment that can accurately model the stability of mild slopes. To model this correctly, the model has to be able to model plunging and spilling waves, include bed sediment transport and to model the velocity and acceleration due to a breaking wave over multiple layers in depth. The existing models do comply mostly with one of these specifications. To get accurate results, the stability should be modelled with all of the specifications and not one model complied with this. Therefore, it was decided to investigate the stability of stones on mild slopes under wave attack with physical modelling tests at the research institute Deltares. The physical tests were executed with a constant slope angle of tan α = 1:10 and a constant nominal median stone diameter. The wave steepness (that determines the type of breaking for a constant slope angle), the significant wave height, the number of waves and the layer thickness are varied in between the tests to determine the influences of each parameter on the stability. Of each test an erosion profile is made by photogrammetry from which the profile-related damage parameters can be determined. In the bed strips with coloured stones are laid down to follow the transport of the stones. According to these erosion profiles three damage parameters were determined. The damage level, S, as used by Van der Meer (1988), the erosion depth, de, and the damage depth, E3. The damage depth, E3, is used to describe the damage for mild slopes. The range of the damage depth for start of damage to failure is from 0.5 to 2.3. These values are only applicable for a layer thickness of 2.5dn50 and a slope angle of tan α = 1:10. The development of the damage depth is investigated for multiple parameters. The breaker type gives a change in development of the damage depth. For a wave condition with plunging breakers the damage depth development is higher per increasing wave height than for a wave condition that includes both plunging and spilling breakers. For the transition zone from plunging to spilling breakers the damage depth increase is very small if the wave height increases. The damage depth is influenced by the number of waves, because after about 11,000 waves the development of the damage depth is still linearly increasing with the number of waves. The damage depth was not stabilized towards a maximum value after this number of waves. It can be concluded that the transport of the stones is mainly all below the still water level. This also followed from the damage zones. These indicated that the total area of the damage is in between the -2Hs and SWL. The maximum area location is around -0.8Hs w.r.t. the SWL. The transport is mostly upslope, which is attributed to the mechanism whereby wave forces are strong in upslope direction. The location where the most stones are picked up depend on the breaker type, the wave height and the layer thickness. Plunging breakers cause damage more downslope than spilling breakers. Plunging breakers cause more local damage and have a much smaller runup than the spilling breakers. Per increasing wave height, the location of damage is shifted more downslope due to the increase in breaker depth.