Toe Scour Mixing Method

The HEC-RAS sediment transport follows Einstein(1950), HEC-6, and most sediment transport models by apportioning transport across available grain classes in proportion to the gradation of the bed.
Where: T_c is Total transport capacity, n is the number of grain size classes, B_j is the percentage of the active layer composed of material in grain size class "j", and T_j is the Transport potential computed for the material in grain class "j". Partitioning capacity based on the gradation of the active layer is a classic assumption based Einstein's (1950), who proposed sediment discharge of a size class is proportional to the fractional abundance of that size class in the bed

This approach generally works when couple with an "active layer" bed model that tracks the gradation of a surface layer separately. Without an active layer, transport functions compute huge masses for small particles, removing these materials from deep within the bed, much deeper than physically possible.

The toe scour method does not have an active layer. Therefore, transport methods have unrestricted access to all the fine materials in the bank. Apart from the standard uncertainty of the transport functions, this is the primary reason that the cohesionless method overpredicts transport, it can numerically wick fine materials deep in the bank, while the coarser materials remain.

The HEC-RAS/BSTEM development team experimented with three mixing methods to mitigate this numerical artifact:

Cumulative: Applies the same assumption as the bed, apportioning capacity by the prevalence in the bank layer. However, since the bank layer has no active layer and does not update, this provides an unlimited supply of finer material and usually over-predicts scour.

Maximum Prevalence (default): This method apportions capacity according to the relative proportion of the bank gradation. However, it only erodes the most prevalent grain class. This assumes that the dominant grain class moderates scour. This method is more appropriate if trace fines and low percentage fine sands cause the other methods to over-predict scour and was designed for framework supported materials.

Maximum Capacity: This method was designed for matrix supported materials. It assumes that the prevalent fine material, the one with the largest product of transport potential and prevalence, controls the scour distance. So the scour distance associated with the largest capacity grain class is applied, assuming that the other particles are larger clasts that will fall into the channel when released from the scoured fine matrix.