Towards a Universal Theory of Multi-Grain Size Sediment Transport Using the Transport Length and Erosion-Deposition Model Framework

International audience; Due to flow variability and sediment heterogeneity, different modes of transport are observed, either successively or simultaneously, in natural rivers. All these modes contribute to the total sediment transport and thus should be considered in the context of fluvial sediment transport and morphodynamic modeling. However, a universal sediment transport law from bed load to suspended load applicable to the full range of hydraulic conditions and to sediment mixtures is lacking despite numerous published transport capacity laws. Similarly, morphodynamic fluvial models typically assume transport-limited conditions that can not capture under-capacity conditions occurring potentially for a certain range of grain sizes and flow conditions. Thus, we aim at building a self-consistent theory by gathering widely accepted concepts of sediment transport in the framework of erosion-deposition models using a disequilibrium transport length. First, we develop a new transport length model that takes into account the different transport modes as a physical continuum. Second, we combine this continuous model of transport length with the erosion-deposition model that we adapt to account for multi-grain sizes. All these steps use existing, tested elementary ingredients that do not require further calibration parameters. Predicted transport lengths range over several orders of magnitude and, for the same hydraulic conditions, the transport length increases with finer grain sizes. Modeled stream capacities obtained at saturation are in agreement with flume observations for both single-grain and multi-grain approaches with at least 70% of the experimental data predicted within a factor 10. The main result is, to our knowledge, the first Multi-Grain Size Sediment Transport model encompassing the diversity of transport modes in non-stationary regimes and predicting how stream capacities scale with bed shear stress. We illustrate how this universal theory of sediment transport can be used to better understand the relationship between grain sizes and transport distances. And we develop long-term transport laws that include the effects of water discharge variability and sediment heterogeneity on fluvial morphodynamic instabilities and deposit stratigraphy, e.g., armor layer and downstream fining.