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A function for the bed-load sediment transport rate is derived. This isachieved from the first principle by using the entrainment probabilities of thesediment grains by rolling and lifting, and by introducing two travel lengths,respectively, for the first time. The predictions from the new bed-loadfunction agree well with the experimental results over the entire experimentalrange and show significant improvement over the commonly used formula forbed-load transport rate. The new function shows that, in terms of contributingto the bed-load transport rate, the total entrainment probability of thesediment grains is a weighted summation of those by the lifted and rollinggrains, rather than a simple addition of the two. The function has also beenused to predict the total entrainment probability, saltation length and the bedlayer thickness at high bed-load transport rate. These predictions all agreewell with the experimental results. It is found that, on average, the travellength for the rolling sand grains is about one order of magnitude less thanthat for the lifted ones.

Bed-Load Transport Rate Based on the Entrainment Probabilities of Sediment Grains by Rolling and Lifting