A probabilistic/deterministic approach for the prediction of the sediment transport rate

• Bedload model and comparison with laboratory and literature data.
• Composite probability of detachment and of particle’s range.
• Deterministic expression for the average length of the particle jump.
• Simplicity of the approach and of the final expression.

In this paper we present a probabilistic/deterministic model for the evaluation of the sediment transport rate in a stream. Starting from Einstein’s theory, the approach was obtained by trying to overcome some of the intrinsic limitations. The approach is based on two distinct probability functions, one relevant to the detachment of grains and the second relevant to the length of particle jumps. The sediment transport rate is obtained by integrating the distribution of the ranges of the particle jumps multiplied by the average particle velocity. The relationship for the average ranges of particle jumps is an opportune combination of the Einstein and Yalin expressions. The final formulation was calibrated by means of a large number of experimental data and also by comparison with some of the most widely-used empirical formulas. The results show a better agreement between theory and experiments than do the other theories analyzed.