Until now, an extensive design method for mild slopes has not been available. The aim of this thesis is to understand the stability of rock on mild slopes under wave attack for impermeable cores in order to optimize designs. Physical model tests have been executed to study this stability for a 1:8 slope. Mossinkoff (2019) executed physical model tests for a 1:10 slope and a re-analysis of these tests is included in this thesis as well. Damage caused by entrained rocks is quantified by damage parameters using stereophotogrammetry and coloured rocks in strips. In this study, the influence of several hydraulic and structural parameters on damage parameters has been investigated for mild slopes. A positive correlation has been found between the significant wave height and the damage parameters. Besides this, based on the analysis it can be concluded that the wave steepness and damage parameters are negatively correlated. An increase in layer thickness of the rocks does not seem to increase the stability of rock on mild slopes. However, the slope angle does have an effect on the stability as a milder slope is associated with less damage. Another conclusion is that more damage continues to be observed even after 15 000 waves. Based on the results of the physical model tests, a design formula is developed for mild slopes to be able to increase efficiency in designs of coastal structures for these mild slopes. This study also provides evidence that rocks on mild slopes have different characteristics of damage and damage development compared to steep slopes. The largest share of entrained rocks transport in upward direction and rocks on mild slopes seem to be more mobile compared to steep slopes. This suggested that it might be more efficient to study the moment when the filter layer or the core becomes visible instead of the static stability of rock within the armour layer itself.

The static stability of stones on mild slopes under wave attack is investigated in this research. The first part of the research is focused on reproducing the physical scale model tests regarding profile change of Kramer (2016) numerically with the model XBeach-G. The erosion profiles modelled with the bed-load transport formulas of Nielsen (2006) and Van Rijn (2007) in XBeach-G do not match the erosion profiles of the profile change experiments of Kramer (2016). The bed-load transport formulas of Nielsen (2006) and Van Rijn (2007) are not able to model the sediment transport in XBeach-G accurately. Furthermore, XBeach-G cannot determine the velocity and acceleration near the bed, because the model solves the flow due to currents and waves for a single layer. Therefore, it can be concluded that XBeach-G should not be used to describe static stability of stones on mild slopes under wave attack. For the application of dynamically stable structures (which is not investigated in this research), XBeach-G functions satisfactorily (Postma, 2016). For further research, a model that solves the hydrodynamics for multiple layers should be applied. In this way, the hydrodynamics near the bed can be used to describe the static stability of stones.

The aim of the second part of the research is to develop a design method that describes the static stability of stones on mild slopes under wave attack. The basis of this design method is the initiation of motion of a stone and the hydrodynamic forces that initiate this movement. The hydrodynamic forces and corresponding mobility parameters are determined with the velocity and the acceleration near the bottom. Using Bubble Image Velocimetry (BIV), the velocity and the acceleration are derived from the videos of the BIV experiments of Kramer (2016) with regular waves breaking on a slope. It is found from the results of the BIV analysis that the effective, adapted Shields parameter θ’McCall can be used to describe movements of stones on mild slopes under wave attack. This mobility parameter has been determined with the bed shear stress of McCall (2015), which added an inertia term to include the influence of accelerations. For initiation of motion of stones, it appears that the stability parameter θcr could be a value of 0.024 (in case no slope correction factor has been applied). To substantiate a design method that describes the static stability of stones on mild slopes under wave attack, the value of 0.024 could be used to define a threshold for initiation of motion of stones. More experiments need to be executed to optimize this value of the stability parameter. Moreover, a statistical value for the stability parameter could be used (like θcr,1%) to describe the static stability of stones by means of a certain number of stones that are allowed to move for a certain number of waves.