Overflow Concentration and Sedimentation in Hoppers

Sediment spillage from hopper overflow constitutes a source for sediment plumes and can also impact the turbidity of aquatic environments. The overflowing mixture is often different from the mixture pumped into the hopper (the inflow), because the mixture undergoes compositional transformation as a result of different timescales in the segregation of the various sediment fractions. The heavier constituents in a mixture will have had time to settle, and overflowing sediments are therefore primarily composed of the finer and lighter constituents, whose concentrations potentially exceed those at the inflow. The hopper constitutes a complex system despite its geometrical regularity; the complexities are largely from the settling processes in concentrated polydisperse mixtures. These settling processes can, however, be captured by employing available settling formulas applicable for multifractional sediment mixtures (i.e., polydispersions). Strictly speaking, these formulas have been validated for homogeneous and unenergetic mixtures only, but the hopper system fulfills these criteria reasonably well. A proper description of the compositional transformation during filling and subsequent overflow stages can be captured using a sediment budget approach, i.e., by using continuity equations for water and sediment phases. In this study, the compositional transformation and the bed height inside the hopper are obtained by solving these equations, considering monodisperse, bidisperse, and polydisperse mixtures, the former analytically. Although assumptions tied to the mathematical model are fulfilled best for hoppers rigged with a multiple-inflow system, the model accurately predicts measured concentrations in the final stage of overflow for single-inflow systems. The model can be used as a preprocessing tool for engineering plume models, providing source specifications for overflow spill and for the subsequent dumping of hopper loads.