Coupled surface and subsurface flows for earthen embankments using finite-volume methods

The majority of breaching of earthen embankments is triggered by overtopping flows or waves. These phenomena are usually simulated using the shallow-water equations complemented by the Exner equation to reproduce the progressive erosion of the embankment and the growth of the breached area. Such an approach neglects the degree of water saturation in the embankment as well as the flow through the embankment that can alter the stability of this structure by reducing the soil’s mechanical strength. This is enhanced in case of severe droughts, as observed during the summer 2022, when desiccation cracks were observed in several embankments, leading to preferential paths for the water to infiltrate the soil during subsequent rainfalls. In this paper, we present a combined approach in which the degree of saturation and the flow through the embankment are solved using the Richards equation that is coupled to the system of shallow-water equations for the flow over the embankment. The groundwater flow is simulated by solving the 2D Richards’s equation on an unstructured triangular mesh with an implicit finite volume scheme, based on a direct gradient evaluation. The shallow-water equations are solved in one dimension on a structured mesh using an explicit scheme with Roe’s formulation for the fluxes. Several tests were performed to demonstrate the capacity of the proposed Richards’s solver to reproduce transient groundwater flows and compared to results from the literature obtained with different numerical approaches. In the same way, the shallow-water’s equation solver was validated by comparison with previous experimental results from the literature. Then, by coupling both models using a source term, a mass-conservative coupled model was obtained. It became possible to simulate the evolution of the pore water content inside a dike subjected to overtopping for different initial conditions. Further work will focus on the interaction of dike’s related flows with erosion and mechanical failure processes, and on the validation of the model by comparisons with experimental data that will be obtained with medium-scale tests