Phenomenological interpretation of internal erosion in granular soils from a discrete fluid-solid numerical model

Abstract

Internal erosion in granular soils may involve different steps: the detachment of solid particles from the granular skeleton under the action of water seepage; the transport of the detached particles carried with the water flow in the pore space; and eventually, for some erosion processes, such as suffusion, the possible reattachment of some transported particles to the solid skeleton of the soil, acting as a filter. The first part of this paper is devoted to the description and interpretation of the first step about the particle detachment. The analysis is mainly based on direct numerical simulations performed with a fully coupled discrete element-lattice Boltzmann method. Dynamics of the solid granular phase is represented thanks to the discrete element method in which each solid particle is explicitly described, whereas dynamics of the interstitial water flow is solved with the lattice Boltzmann method. Interactions between the solid phase and the fluid phase are handled at the particle scale avoiding the introduction in the model of some phenomenological constituents to deal with fluid-solid interactions. Numerical modellings of hole erosion can be interpreted similarly to laboratory hole erosion tests where the erosion rate is linearly related to the hydraulic shear stress. Further investigations from the numerical results suggest that the erosion rate for hole erosion in granular soil, can also be interpreted as a function of the water flow power according to a power law. The latter interpretation is applied to experimental data from suffusion tests on a cohesionless soil and glass bead mixtures. Here again, if change of erosion rate due to filtration is discarded, erosion rate is correctly described by the water seepage power according to a power law. Finally, a simple phenomenological model is suggested to describe the whole suffusion process, based on the previous results, to describe the particle detachment, and completed to take also into account the transport and filtration phases. Predictions of this model are compared with experimental results from suffusion tests on glass bead mixtures