Numerical simulation of breach growth in sand-clay dikes

Abstract

In the Netherlands mathematical models have been applied to represent the breach growth in sand dikes (Bres model (Visser 1998) and Breach model (Steetzel and De Vroeg 1998)). They were also applied to clay dikes in order to adapt and extend them. However these models contain empirical parameters and assumptions that restrict their application especially for clay dikes. This report presents the alternative of applying numerical models, which solve the unsteady flow and sediment equations, to the simulation of breach growth in sand-clay dikes. The breach development is a three dimensional phenomena with strong interaction between flow and sediment. Concerning hydrodynamic aspects the numerical model should be able to represent mixed flows (supercritical and subcritical flows) as well as transitions of flows (hydraulic jumps). A numerical model has been developed which solves the full Navier-Stokes equations (3D model). The model can be reduced to compute the 2DH shallow water equations by adopting the number of vertical layers equal to one. Further a morphological module has been incorporated to the 1D version of the model. Therefore two numerical models are developed, a 3D-2DH hydrodynamic model and a 1D morphological model. This study illustrates the ability of the numerical model developed (3D/2DH and 1D) to simulate the particular flow conditions during the breaching of dikes and explore the possibility of incorporating a morphological module in order to reduce empiricism and extend its application to more general situations. The 3D/2DH numerical models are applied to simulate the flow patters for a determined time and geometry of the breach for the dike of the Zwin experiment, 1994. Furthermore the development of the first stages of the breach growth, vertical erosion, is illustrated by applying the 1D morphological numerical model. The numerical model appears as a useful tool to represent the hydrodynamics of breach growth in dikes. However studies are required to verify the 3D/2DH models to accurate represent flow transition in a contraction specially under supercritical flows. The model could be combined with physical experiments in order to calibrate the parameters. The number of experimental tests would be reduced and more general situations simulated. This research is considered as a first step towards the numerical morphological model of the breaching process. Further research should be conducted regarding the interaction between flow and sediment in cohesive material and in sand-clay dikes. It is proposed that the 3D/2DH model be applied firstly in combination with experimental tests for the study of the hydrodynamic and morphological processes in sand-clay dikes. The model could be after that reduced to 1D model in which relations could be applied based on the 3D/2DH model applications and experimental tests.