Stability of stones on mild slopes

Abstract

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.