A depth-integrated morphodynamical model for river flows with a wide range of Shields parameters

Fast geomorphic transients may involve complex scenarios of sediment transport, occurring as bed-load (i.e. saltating, sliding and rolling) in the region close to the bottom, or as suspended load in the upper region of the flow. These two modalities of sediment transport may even coexist or alternate each-other during the same event, owing to the variability of the shear stress. The modeling of similar processes is therefore a really challenging task, for which usual representation of the flow as a mixture may result unsatisfactorily. In the present paper, we propose a two-phase depth-averaged model which is able to deal with both bed-load and suspended sediment transport. The mathematical model is derived from the expression of mass and momentum conservation equations, separately for liquid and sediment phase. The equations for the solid phase are written separately for bed-load and suspended load region. The bed-load layer thickness is assumed variable with the actual shear stress, while the solid concentration is described by the differential equations. The entrainment/deposition of sediment from the bed towards the bed-load layer is evaluated by a formula based on a modified van Rijn mobility parameter, while for the suspended sediment a first-order kinetic law is considered. The behavior of the resulting model under uniform conditions of flow complies with some of the proposed empirical formulations for bed-load thickness, average particle velocity and solid discharge. A numerical method based on a finite-volume approach is employed for the simulation of experiments in which both bed load and sediment transport are present. Even without any detailed calibration, simulated and experimental results show reasonable agreement.