Overtopping failure in levees

Abstract

The aim of this research is to provide amathematical model that describes the physics in a levee when waves are overtopping a flood embankment. Ideally, this numerical simulation can replace empirical methods based on overtopping simulations and provide more insight into the physical process of an overtopping flow on a levee. This could prove to be useful for the design andmaintenance of flood barriers. Different interpretations of the stress tensor of pore water have each lead to distinct systems of partial differential equations. For each interpretation, the resulting system has been solved, using a finite element analysis in combination with a time-stepping method, in order to assess the validity of the imposed definitions. However, only one definition lead to a mathematical framework that yielded trustworthy results. In this finalmathematical framework, both the hydrostatic water pressure and the gravitational force have been disregarded, resulting in a system only consisting of variables such as soil particles displacements, pore water velocities and a distribution function »(t ). The distribution function »(t ) represents the fraction of the exerted wave stress on the surface carried by the pore water. By definition, the fraction can vary over time, which stands in contrast to state of the art models. The applicability of the results is limited, since the problem is simplified to a one-dimensional setting in which only normal stresses are exerted. The mathematical framework could theoretically be extended to multiple dimensions. However, it remains contestable whether it sufficiently simulates the physics in a levee. Further research is needed to show whether the extension holds when shear stresses are present and whether the same distribution function »(t ) can be applied to non-axial directions. In conclusion, this research is a proof of concept and serves as a stepping stone for more research. The used code can be found at https://github.com/HaveMersie/Overtoppingfailure