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A stochastic fraction bedload transport rate model for nonuniform sediment

Based on a method of combining stochastic processes with mechanics, a new bedload formula for the arbitrary ith size fraction of nonuniform sediment is theoretically developed by using a stochastic model of sediment exchange and the probabilistic distribution of fractional bedload transport rates. The relations, proposed recently by Yang, for the probability of fractional incipient motion and for the average velocity of particle motion are introduced to bedload formula. Plenty of experimental data for the bedload transport rate of uniform sediment are used to determine parameters. The theoretical bedload formula for any fraction of nonuniform sediment possesses several advantages, including a clear physical concept, a strict mathematical derivation, and a self-adaptability to uniform sediment. The formula is verified with experimental data expressing the transport of nonuniform sediment under full motion in laboratory flume. The result shows that the experimental observations agree well with the predicted fractional bedload transport rates.