Variational RANS modelling of dike erosion due to overtopping flow using a bed-load decoupled approach

Earthen dike failure from overtopping poses a high risk to infrastructure and environment, leading to critical operational losses, especially under climate change-induced water scarcity scenarios. Accurate prediction of this phenomenon is essential for its prevention. Conventional depth-averaged models (e.g., Saint-Venant) are inadequate due to the strong flow vertical acceleration over the dike, which violates hydrostatic pressure assumptions. To address this, variational RANS modeling, which is proven effective for fixed-bed transient flow simulations, is applied here to simulating erosive flows for the first time. We use the Vertically-Averaged and Moments equations (VAM) model coupled with the Exner equation to compute bed-load transport and dike erosion. The model simplifies the process by decoupling bed deformation from VAM hydrodynamics and omitting geotechnical computations. This new approach was validated against an overtopping failure experiment, demonstrating good agreement with the experimental data.