Probability of suspension for nonuniform sediment

The probability of suspension for nonuniform sediment is an important parameter in mechanics of sediment transport, which is often used in the governing equations and boundary conditions of mathematical models. There were few theoretical research and experimental data on suspension probability, especially for nonuniform sediment. This article describes theoretical and experimental investigation on suspension probability for nonuniform sediment in turbulent flow. From the dynamic viewpoint, probability for sediment suspension was considered as one that the instantaneous lift force at the bottom is greater than the effective gravity of particles. Similarly, probability for sediment suspension is defined as one that the instantaneous upward velocity is greater than the settling velocity of particles. Assuming that the instantaneous longitudinal and vertical velocities near the bottom obey normal distribution, two probability expressions for any kth fraction of nonuniform suspended sediment are derived. An experimental method for the probabilities of sediment motion is proposed and used to flume experiments with uniform and nonuniform sediment. Then, the formulas for probability of sediment suspension are obtained with coefficients determined by the experimental data on uniform suspended load. The calculated values from both proposed formulas agree well with the experimental data on nonuniform suspended load, showing high accuracy of the formulas. It is found that the suspension probability based on dynamic viewpoint can be transformed into a function of suspension parameter. The probabilities for suspension from both viewpoints are functions of suspension parameter in the resistance square area, which reasonably reveals the physical mechanism of sediment suspension.