Logarithmic Law for Transport Capacity of Nonuniform Sediment

Abstract

Sediment transport capacity is one of the key parameters in river sediment dynamics. New formulas for fractional and total transport capacity for nonuniform sediment were established and are presented in this paper, based on energy equilibrium and the fact that flow resistance decreases as sediment concentration increases. As this study shows, the transport capacities for a single fraction and total sediment are logarithmic functions of the sediment transport parameter (STP). The proposed formulas based on logarithmic law have many advantages: (1) the critical velocity for suspension of nonuniform sediment is innately embodied with simple form in the logarithmic formulas; (2) the interaction between different size particles was considered in settling velocity for any fraction of nonuniform sediment and the mean settling velocity for nonuniform sediment is equal to the geometric average of settling velocities for a sediment fraction; and (3) the formulas have the same form for fractional and total transport capacity and self-adaptability to uniform sediment. The logarithmic law was verified against laboratory and field data, and was found to perform better than power law. The derived critical velocity for suspension with interaction between nonuniform particles taken into account in the fractional and total critical velocity for suspension was also tested by using laboratory data, and it performs quite well for a wide range of particle diameters despite its simple form. The logarithmic law appropriately depicts the whole suspension process from initiation to transport and thus provides insight into the suspended motion of nonuniform sediment.