A model for the fluvial transport of different size and density classes

A numerical model is developed for the transport of mixed natural sediment and plastic particles, accounting for multiple size classes and material densities. The conceptual model drawn from a classico Hirano layered description. It includes a transport layer, an active layer and a substratum. In the transport layer mass conservation consists on fraction-wise Exner equations, including pickup and deposition rates, convective and diffusive transport in the transport layer, and local accumulation for each size and density class. Convective fluxes are the product of particle activity for each size and density classes (the conservative variables) and particle bulk velocity. The latter computed using a modified Luque and van Beek formulation, adapted to account for different sizes and particle densities. Thresholds for incipient motion are taken as calibration coefficients. A flux limiter is implemented to avoid over-saturation of the transport layer and to ensure positivity of particle activity. The pickup function is derived from probabilistic descriptions of sediment entrainment (taking into account density) and deposition rates are functions of actual particle activity and sedimentation velocity. The dynamics of the active layer is determined by empirical availability functions by size. The volume of the active layer is kept constant and scaling with the initial d90 of the mixture. Instantaneous mixing is assumed. As a consequence, during deposition the composition of the active is transferred to the substratum. During erosion, the composition of the substratum is incorporated in the active layer.

The model is calibrated with laboratory experiments conducted under steady and overfeeding flow conditions. Two flumes were employed. A 5.2 m long, 25 cm wide, and 35 cm deep flume was used to conduct flat-bed experiments in two scenarios: (i) homogeneous bed composed of plastic granules, and (ii) gravel or sand bed mixed with plastic granules, which were manually seeded at clastic bed surface for different covering percentage. A 12 m long, 40 cm wide channel was used to conduct gravel-sand sediment sorting experiments, leading to surface coarsening, and overfeeding experiments. Calibration consisted in finding best fits to threshold values of grain velocities, ensuring the observed equal mobility characteristics of poorly sediments with the same density. After calibration, the simulations reproduce the observed grave-sand sheet propagation in the overfeeding experiments. Simulations of the tests of different density classes indicate that coarse, low-density particles exhibit higher mobility than equally sized quartz particles, while the mobility of fine, low-density particles is comparable to that of natural sand of similar size. The model provides a consistent and conservative framework for representing the coupled transport and sorting of sediment–plastic mixtures in open-channel flows.

 

Acknowledgement: This works was supported by the Portuguese Foundation for Science and Technology (FCT) through project Project DT4Rivers COMPETE2030‐FEDER‐00760800 and European Union through Interreg Atlantic 2021-2017 project TRAP – EAPA_0122/2024