2D Process-Based Morphodynamic Model for Flooding by Noncohesive Dyke Breach

Abstract

Inundation models based on the shallow water equations (SWE) have been shown to perform well for a wide variety of situations even at the limit of their theoretical applicability and, arguably, somewhat beyond. One of these situations is the catastrophic event of floods induced by dyke breach and consequent dyke erosion. The dyke collapse is often not sudden—as assumed by many flood simulations in which the dyke boundary is treated as a “dam-break.” The dyke erosion is a gradual and complex process that delays the onset of the flood, affecting the hydrograph of the flow. To simulate correct temporal passage of a flood, it is important to understand the rate at which these dykes collapse. In this paper, an overtopping flood event combined with dyke erosion is simulated. The model is built upon the two-dimensional (2D) shallow water equations together with sediment-flow interactions and incorporates a sediment transport equation. The model is solved using a second-order Godunov-type finite volume method that is accurate and robust. For breach formation, the lateral erosion collapse due to slope instabilities has a significant impact and must be considered, in this paper a simple mathematical approach in two dimensions is proposed to evaluate the stability of lateral bed slope. Several experimental tests are used for validating the morphodynamic model. It is verified that the simulated results agree well with measured data, and that the model predicts such flow phenomena effectively. The validated model is applied to predict a flood event caused by dyke breach with an initial trapezoidal shape due to flow overtopping. The predicted results for the flood event indicate that the 2D process-based morphodynamic model is capable of simulating the spatial and temporal changes of the flood event, including predicting the outflow hydrograph with good agreement, as well as the erosion of the dyke and subsequent deposition process.