Equilibrium bed-concentration of nonuniform sediment

Knowledge of the equilibrium bed-concentration is vital to mathematical modeling of the river-bed deformation associated with suspended load but previous investigations only dealt with the reference concentration of uniform sediment because of difficulties in observation of the bed-concentration. This work is a first attempt to develop a theoretical formula for the equilibrium bed-concentration of any fraction of nonuniform sediment defined at the bed-surface. The formula is based on a stochastic-mechanistic model for the exchange of nonuniform sediment near the bed, and described as a function of incipient motion probability, non-ceasing probability, pickup probability, and the ratio of the average single-step continuous motion time to static time. Comparison of bed-concentration calculated from the proposed formula with the measured data showed satisfactory agreement, indicating the present formula can be used for solving the differential equation goverming the motion of suspended load.