Bed-load transport rate based on the entrainment probabilities of sediment grains by rolling and lifting

A function for the bed-load sediment transport rate is derived. This function is obtained by using the entrainment probabilities of the rolling and lifted sediment grains, and by introducing two travel lengths, respectively. The predictions from the new bed-load function agree well with experimental results over the entire experimental range and show significant improvement over the commonly used formula for the bed-load transport rate. The new function shows that, in terms of contributing to the bed-load transport rate, the total entrainment probability of the sediment grains is a weighted summation of those for the lifted and rolling grains, rather than a simple addition of the two. The function is also used to predict the total entrainment probability, saltation length, and the bed layer thickness at a high bed-load transport rate. These predictions all agree well with the experimental results. It is found that, on average, the travel length for the rolling sand grains is about an order of magnitude less than that of the lifted grains.