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Discrete and continuum modelling of grain size segregation : application to bedload transport

  • Chassagne, Rémi
Publication Date
Nov 19, 2020
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Understanding particle size segregation is one of the great challenge in fluvial geomorphology. It is still notoriously difficult to predict sediment transport more accurately than within one order of magnitude. One of the main origin of this difficulty is particle size segregation, a granular process of particle sorting in the sediment bed. Size segregation is therefore a grain scale process impacting the morphological scale.This PhD presents a numerical study of size segregation as a granular process during bedload transport. A coupled fluid discrete element method (DEM) is used to study the infiltration of small particles in a large particle bed. This configuration, close to granular flows on erodible beds, is characterized by a particle velocity profile, a shear rate profile and an inertial number profile exponentially decreasing into the bed. It presents a particular segregation phenomenology with small particles infiltrating the bed as a travelling wave, the velocity being controlled by the inertial number at the bottom of the layer. The segregation velocity is observed dependent on the local small particle concentrations and on the size ratio. The segregation problem is also analyzed with an advection diffusion model. With advection and diffusion coefficients both proportional to the inertial number, the continuum model perfectly reproduces the dynamics observed in the DEM results.Very recently, a new segregation advection diffusion model has been derived based on particle scale forces, in particular a granular buoyancy force (or segregation force) and an inter-particle drag force. This provides new physically based parametrisations for the advection and diffusion coefficients. This new model is analysed in the bedload configuration, and reproduces qualitatively the DEM results. To improve the model, new dependencies on the inertial number and small particle concentration are proposed for the segregation and drag forces.Finally, the impact of size segregation on sediment transport is studied through the mobility of bidisperse already segregated particle beds. Large particles are placed above small ones, and it is observed that, in the same fluid and surface bed conditions, the transport rate is higher in the bidisperse configuration than in the monodisperse one. For the range of studied size ratio (r<4), it is showed that it is not a rugosity but a granular effect. This is analyzed within the framework of the mu(I) rheology and it is demonstrated that the buried small particles are more mobile than larger particles and play the role of a conveyor belt for the large particles at the surface. Based on rheological arguments, a simple predictive model for the additional transport in the bidisperse case is proposed, which reproduces quite well the DEM results for a large range of Shields numbers and for size ratios smaller than 4. The results of the model were used to identify four different transport regimes of bidisperse mixtures, depending on the mechanisms responsible for the mobility of the small particles.This work represents an important improvement in the understanding of size segregation during bedload transport and questions our understanding of bidisperse granular media, which have not been much studied. It also represents a first step in an upscaling process towards the morphological scale through continuum models.

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