Finite volume method for coupled surface-subsurface flows with geotechnical stability evaluation

Delpierre, Nathan [UCL - SST/IMMC/GCE - Civil and environmental engineering] Rattez, Hadrien [UCL - SST/IMMC/GCE - Civil and environmental engineering] Soares Frazao, Sandra [UCL - SST/IMMC/GCE - Civil and environmental engineering]

Purpose: 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 usually neglects the effect of 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. In the case of severe droughts preceding rainfalls, as observed during the summer 2022, desiccation cracks can appear and lead to preferential paths for the water to infiltrate the soil during subsequent rainfalls dangerously increasing the internal pore pressure. Methods: Here we present a combined approach in which the flow through the embankment is solved using the Richards equation that is coupled to the system of shallow-water equations for the flow over the embankment. At the same time, the mechanical stability of the embankment is evaluated using the shear-strength reduction method. The groundwater flow is simulated by solving the 2D Richards equation on an unstructured triangular mesh with an implicit finite volume scheme, based on a direct gradient evaluation. The shallow-water equations are solved on a one-dimensional mesh using an explicit scheme with Roe’s formulation for the fluxes. Finally, the shear strength reduction method is used on the same mesh as the one describing the groundwater flow considering the variation of pore pressure and saturation degree in space and time. Results: Several tests were performed to demonstrate the ability of the proposed coupled solver to evaluate the influence of surface and subsurface flows on the mechanical stability of the embankment. In particular, the effects of initial soil’s saturation degree and pore pressure fluctuation have been studied. The results point out that the initial saturation degree of the soil or the saturated hydraulic conductivity are of great importance on the time needed to reach failure while to dike is submitted to an overtopping flow. Conclusions: A surface-subsurface flows solver coupled to the shear-strength reduction method is presented. This model allows to study the effects of pore pressure variation and overtopping flows on the stability of earthen embankment. This method can provide crucial information on the time needed to reach the full failure of the dike, a key-factor for the floods process assessment.