Computing Transport Capacity

The right-hand side of the continuity equation, the sediment gradient across the control volume, compares the sediment inflow with the sediment outflow. Sediment inflow is simply the sediment entering the control volume from the upstream control volume(s) and any local sources (lateral sediment inflows). Computing the sediment leaving the control volume is more difficult, a measure of the sediment mass the water can move, which is a complex function of the hydrodynamics and sediment properties. Sediment transport capacity is a measure of the control volume competence to pass sediment, computing the maximum sediment it can transport by grain class.

Grain Classes

HEC-RAS divides the sediment material into multiple grain classes. Default grain classes sub-divide the range of transportable material, (0.002 mm to 2048 mm) into 20 grain classes or bins, each including adjacent, non-overlapping fractions of the grain size spectrum. Default grain classes follow a standard log base 2 scale where the upper bound of each class is twice its lower bound, the upper bound of the smaller, adjacent class. The gain class represents all particles they contain with a single, representative grain size. HEC-RAS uses the geometric mean of the grain class to represent the grain size for each bin. Grain boundaries (and labels) are editable.

Computing the Transport Potential

Sediment transport potential is the transportable mass of a particular grain class in response to cross channel hydraulic parameters. HEC-RAS computes transport potential for each grain class with one of the sediment transport equations available in the program.

The sediment transport equations are empirical equations or algorithms that translate hydrodynamics into transport. However, most of these equations were developed for a single representative grain size.

To apply these equations to sediment mixtures, with multiple discrete grain classes, HEC-RAS computes transport potential, allying the transport function independently to each grain class present in the system, as if it were the only grain class in the system. Later transport potential is prorated by the prevalence of the grain class, to compute the transport capacity (see discussion below), which is the transport used in the Exner equation. But first HEC-RAS applies the transport function to each available grain class independently, computing a transport potential for each.

HEC-RAS includes eight 1D sediment transport potential functions. The three 2D (Wu, van Rijn, and Soulsby-van Rijn) functions are not available in 1D yet. Since sediment transport is sensitive to so many variables, transport potentials computed by the different equations can vary by orders of magnitude, depending on how the material and hydrodynamics compare to the parameters over which the transport function was developed. As much as possible, select a transport function developed for similar gradations and hydraulic parameters as the project reach. Appendix E in this document include the actual equations and algorithms. This section includes brief, qualitative notes on the use, applicability, and sensitivity of each equation.

Most sediment transport functions are based either on shear stress or stream power. They usually use an excess-shear or excess-power form, which compare the actual shear or power to a threshold. HEC-RAS does not compute any transport for that grain class if it is below the threshold (i.e. the grain class is not "competent"). The stream power equations use two different versions of stream power, the product of velocity and slope (VS) and the product of velocity and shear stress (tV). The six shear stress or stream power equations are:

Table: Transport functions based on excess shear stress and stream power.

*Engulend-Hansen is not an excess form of the stream power equation, but just a function of stream power.

Partitioning Capacity by Particle Size Distribution in the Bed

The transport capacity for each grain class is the transport potential multiplied by the percentage of that grain class in the bed. Therefore, the total transport capacity is:

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 (Vanoni, 1975).

Modeling Note – Partition Gradations for Empty Sediment Control Volumes

As long as the sediment control volume has bed sediment, it can partition the transport potential into capacity. However, if the active layer thickness = 0, either because it is a concrete channel with no starting sediment thickness (Initial Max Depth = 0) or because it scoured through the entire erodible depth, the bed partitioning assumption will run into trouble. If the active layer has no sediment, the fraction of each grain class is zero (_j=0 in the previous equation). Therefore, regardless of the computed potential, this approach will compute no transport capacity over a fixed bed. If the model computes no transport capacity, it will deposit all of the sediment in one time step, and erode in the next, causing oscillating errors and decreasing transport in half, because it only transports every other time step.

To offset this numerical artifact, recent versions of HEC-RAS uses the initial bed gradation to partition potential into capacity if the control volume has no bed sediment. This is also why HEC-RAS requires bed gradations for concrete channels. It uses the gradation to compute capacity.

Capacity Sensitivity to Movable Bed Limits

The first consideration when selecting movable bed limits should be which portion of the cross section the river will deposit or erode.  The movable bed limits delineate which cross-section, station-elevation points can move vertically.

However, placing the movable bed limits can also affect the total sediment transport capacity. Most transport equations compute transport capacity per unit width. HEC-RAS converts this transport-per-unit-width to total transport by multiplying the unit rate by the distance between the movable bed limits. Therefore, though there are complicating feedbacks between cross section shape, channel bank placement, and movable bed limits, movable bed limits that are farther apart, often generate more transport capacity.