Earth embankment failures are most often caused by overtopping. This type of event is expected to become more frequent in the near future due to climate change. When overtopped, the earthen dike suffers from erosion caused by high velocity flows. Eventually, a breach is created that first deepens and then widens as the flow continues to enter the protected area. The dynamic of the breach opening plays an important role in the way a given area is flooded after a dike failure. This type of event is usually simulated using the shallow-water equations combined with the Exner equation and a bank failure operator to reproduce the progressive erosion of the embankment and the growth of the breached area. The parameters of the bank failure operator are in general tuned to better reproduce the effects of apparent cohesion that causes the dike material to hold almost vertically in the breached area. However, such a bank failure operator is a simplification that overlooks the precise effects of pore pressure on soil shear strength. The evolution of the degree of saturation is classically neglected, the past hydrological history is not considered in the initial strength of a given embankment. In addition, embankments do not usually consist entirely of non-cohesive uniform material, and the shear resistance of the soil depends not only on the angle of friction but also on cohesion. Complex behaviors can be observed in the geomaterials, such as softening of the shear strength, which cannot be accounted for with a simplified bank failure operator. In this work, we present a model that attempts to encompass a variety of complex phenomena occurring throughout a dike failure event. The main idea lies in the combination of a coupled surface-subsurface flow solver with a large displacement geomechanical model. The coupled surface-subsurface flows solver, part of the Watlab environment (https://sites.uclouvain.be/hydraulics-group/watlab/index.html), provides information on the evolution of the saturation degree in the dike, water depths and velocities during a dike overtopping event. The surface flow is evaluated using the shallow-water equations, while the 2D Richards equation is simultaneously solved for the flow through the dike. The key novelty in this work is the combination of this latter solver with a geomechanical solver to better simulate the breaching process. The Particle Finite Element Method (PFEM) is employed to reproduce the large displacements that can occur during an earthen dike failure. Complex constitutive laws can be employed and the saturation degree variation in time is accounted for. Several numerical tests were conducted to demonstrate the validity of the proposed framework. The effects of initial saturation degree and physical parameters on the dike failure process are studied, highlighting their importance in the evaluation of dike resistance to overtopping flows.
Delpierre et al. (Wed,) studied this question.