Susceptibility of hydraulic structures to internal erosion: modeling of suffusion process

Internal erosion is a primary cause of hydraulic structure failure, manifesting as two key phenomena: piping erosion and suffusion. These processes differ in their geometrical and hydraulic boundary conditions, resulting in varying levels of failure risk. Piping erosion is the more hazardous and rapid process, often leading to immediate failure if not promptly addressed. In contrast, suffusion gradually alters the permeability of the medium, potentially culminating in failure after a prolonged period of development. In this study, we propose a model for suffusion based on Darcy’s law, Papamichos' erosion law, and Einstein's viscosity evolution relation. The model describes the temporal evolution of the average porosity in the porous medium, the concentration of eroded particles in the fluid, and the mass of particles eroded, while highlighting the impact of hydraulic and mechanical parameters, such as the erosion coefficient and maximum porosity, on this evolution. The numerical solution is obtained using the finite difference method, with the sample discretized into elementary layers. For discretization, an explicit off-centered scheme was adopted. The simulation results reveal that suffusion is strongly influenced by soil hydraulic and mechanical parameters, particularly the erosion coefficient (λ) and final porosity (Ømax).