A new statistical model for threshold friction velocity of sand particle motion

A theoretical formulation of threshold friction velocity of sand particles is established by considering the equilibrium of moment forces acting on an irregular particle following Bagnold's scheme. Owing to the statistical nature of the microstructure of soil surface, of the particle shape and of positions in the bed, the threshold friction velocity is random. Based on the probability theory of multi-dimension random variable, the probability of the threshold friction velocity, its mean value and standard deviation are calculated. The mean value and standard deviation are fitted as functions of sand particle's diameter. A formula of ‘wet’ threshold friction velocity is also given.