Distributions for wave overtopping parameters for stress strength analyses on flood embankments

A process based assessment of the probability of failure of a flood embankment, as well as an assessment of the consequences of failure of an embankment require insights into the stresses on the landside slope of an embankment. These assessments are hindered by the empirical nature of the wave overtopping parameters. Failure initiation is often linked to an allowable mean overtopping discharge which forms the input for the overtopping volumes distribution. The high level of uncertainty associated with predicting the mean overtopping discharge therefore leads to high levels of uncertainty in predicting wave overtopping volumes. The mean overtopping discharge is thereby not directly related to run-up parameters. This paper addresses these issues by presenting new distributions for the velocity, discharge, depth, volume, and shear stresses at the crest for those waves that overtop which have been derived from the wave run-up parameters. The proposed distributions are independent on the mean wave overtopping discharge and the large inaccuracies associated with predicting this. The proposed method has the added benefit of being able to express overtopping parameters in terms of each other. The paper also provides a method for determining the change in these random overtopping values along the landside slope, thereby facilitating a direct comparison between wave overtopping events and overflow events.