Analytical model for bed load transport in steep channels by the probabilistic approach of incipient motions

Document Type : Research Paper


Assistant Professor, Department of Water and Science Engineering, College of Agriculture, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.


Estimation of Bed load transport in steep channels and mountain rivers, is important due to the complexity probabilistic processes of sediment transport and drawback of research in steep slopes. Most of bed load equations are developed for mild slope channels. Bed load transport in steep channels in additions to the effects of random properties of turbulent flow, and random distribution of grains in bed, also is affected by the steep slope. The probability of incipient motion in these channels is different form mild slope channels, and the conditional entrainment probability of them is less addressed. Therefore, in this study, a probabilistic based approach is used to develop the probability equations of the triple incipient motion thresholds of rolling, sliding and saltation on steep slopes and a probabilistic analytical model for estimating the bed load in steep slope rivers is presented based on the normal probability distribution of velocity fluctuations. Verification of the model results based on 564 experiments in slopes of one up to 20 percent, declares that the motion probability is a weighted summation of rolling, sliding and saltation probabilities. Comparing the bed load estimation in model with observed values indicates that the model with R2=0.92 and RMSE=3.52, have accurate estimation in steep slopes. The comparisons with six bed load equations in previous studies its superiority is confirmed. The main contribution of the study developed an analytical model for bed load transport in steep slopes that can used for bed load estimation in Mountain Rivers.


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