Investigation of granular behavior in bedload transport using an Eulerian-Lagrangian model

Etude du comportement granulaire en transport par charriage basée sur un modèle Eulérien-Lagrangien Turbulent bedload transport represents the main contribution to the riverbed morphological evolution, and associates the non-trivial collective granular behavior with a turbulent fluid flow. Therefore, its description is both a scientific challenge and a societal issue. The present numerical approach focuses on the granular phase characterization, and considers idealized steady uniform bedload transport, with monodisperse spherical beads and a unidirectional fluid flow. This simplified configuration allows to study the underlying physical mechanisms.A minimal coupled numerical model is proposed, associating a three dimensional discrete element method with a one-dimensional volume-averaged fluid momentum balance resolution. The model is compared with classical experimental results of dimensionless sediment transport rate as a function of the Shields number. The comparison is extended to granular depth profiles of solid volume fraction, solid velocity and sediment transport rate density in quasi-2D bedload transport configurations. Parameter sensitivity analysis evidenced the importance of the fluid-particle phase coupling, and showed a robust agreement of the model with the experiments. The validated model is further used to analyze the granular depth structure in bedload transport. Varying the channel inclination angle and the specific density, it is shown that the classical Shields number and dimensionless sediment transport rate formulations do not take appropriately into account the effects of these two parameters. Analyzing the solid depth profiles and the continuous two-phase flow equations, the neglected fluid flow inside the granular bed is identified as the missing contribution. Its importance is enhanced near the transition to debris flow. A rescaling of the Shields number is proposed and is shown to make all the data collapse onto a master curve when considering the dimensionless sediment transport rate as a function of the modified Shields number. Lastly, the bedload transport granular rheology is characterized by computing locally the stress tensor as a function of the depth. The lowermost part is shown to follow a creeping regime and exhibits signature of non-local effects. The dense granular flow on the top of it, is well described by the mu(I) rheology and is observed to persist up to unexpectedly high inertial numbers. It is characterized by the co-existence of frictional and collisional contributions. The transition from dense to dilute granular flow is controlled by the Shields number, the slope and the specific density. Saltation is observed in the uppermost granular layer. These findings improve the understanding of bedload transport granular mechanisms and challenge the existing granular rheologies.