There is obvious difference of transport mechanism between the uniform and non uniform sediment, in this paper, the incipient motion of non-uniform sediment is theoretically studied, based on the method of probability theory combined with mechanics, the mean of sediment particle’s force arm and the expression for the probability of incipient motion with shelter-exposure effects to be considered are derived. There is a discontinuity point in Han’s fine sediment distribution function, based on the sediment motion mechanism and L-S integral property, author bears out that it does not influence the mean of force arm. Once the incipient probability is built, the incipient velocity can be determined. From the experiment for the incipient motion of non uniform sediment with colored sand conducted by Han, the coefficients in the computational formula are determined. Verifications with Han’s experiment data show that the theoretical formula is better than Han’s. The computed results fully reflect the characteristics of threshold motion of non-uniform sediment.Finally the formula of uniform sediment is established, as a special case.
