Background

Transported sediment is comprised of bed load, suspended load, and wash load. Van Rijn (1993) defines them as:

Suspended load: That part of the total sediment transport which is maintained in suspension by turbulence in the flowing water for considerable periods of time without contact with the streambed. It moves with practically the same velocity as that of the flowing water.

Bed load: The sediment in almost continuous contact with the bed, carried forward by rolling, sliding, or hopping.

Wash load: That part of the suspended load which is composed of particle sizes smaller than those found in appreciable quantities in the bed material. It is in near-permanent suspension and, therefore, is transported through the stream without deposition. The discharge of the wash load through a reach depends only on the rate with which these particles become available in the catchment area and not on the transport capacity of the flow.

Because wash load volume is purely a function of the upstream catchment and not the study reach, it is ignored in the sediment transport computations. However, a particle size considered wash load at one cross section in a reach, may become suspended load at a downstream section, and eventually may become bed load. Therefore, it is important to account for the wash load in a system-wide sediment analysis.

The initiation of motion of particles in the bed depends on the hydraulic characteristics in the near-bed region. Therefore, flow characteristics in that region are of primary importance. Since determining the actual velocity at the bed level is difficult, particularly with 1-D model results, shear stress has become the more prevalent, though not exclusive, way of determining the point of incipient motion. Shear stress at the bed is represented by the following:

1)	$\begin{array}{l}\displaystyle \tau _b =\gamma RS\end{array}$

Symbol	Description	Units
$\begin{array}{l}\tau _b\end{array}$	Bed shear stress
$\begin{array}{l}\gamma\end{array}$	Unit weight of water
$\begin{array}{l}R\end{array}$	Hydraulic radius
$\begin{array}{l}S\end{array}$	Energy slope

Another factor that plays an important role in the initiation and continued suspension of particles is the turbulent fluctuations at the bed level. A measure of the turbulent fluctuations near the bed can be represented by the current-related bed shear velocity:

$\begin{array}{l}\displaystyle \displaystyle u_* = \sqrt{\frac{\tau _b}{\rho}}\end{array}$

or

2)	$\begin{array}{l}\displaystyle u_* = \sqrt{gRS}\end{array}$

Where: $\begin{array}{l}u_*\end{array}$ = Current-related bed shear velocity

Additionally, the size, shape, roughness characteristics, and fall velocity of the representative particles in the stream have a significant influence on their ability to be set into motion, to remain suspended, and to be transported. The particle size is frequently represented by the median particle diameter (dm). For convenience, the shape is typically represented as a perfect sphere, but sometimes can be accounted for by a shape factor, and the roughness is a function of the particle size.

In general, a typical sediment transport equation for multiple grain size classes can be represented as follows:

3)	$\begin{array}{l}\displaystyle g_{si} =f(D,V,S,B,d,\rho , \rho _s , sf,d_i ,p_i ,T)\end{array}$

Symbol	Description	Units
$\begin{array}{l}g_{si}\end{array}$	Sediment transport rate of size class i
$\begin{array}{l}D\end{array}$	Depth of flow
$\begin{array}{l}V\end{array}$	Average channel velocity
$\begin{array}{l}S\end{array}$	Energy slope
$\begin{array}{l}B\end{array}$	Effective channel width
$\begin{array}{l}d\end{array}$	Representative particle diameter
$\begin{array}{l}\rho\end{array}$	Density of water
$\begin{array}{l}\rho _s\end{array}$	Density of sediment particles
$\begin{array}{l}sf\end{array}$	Particle shape factor
$\begin{array}{l}d_i\end{array}$	Geometric mean diameter of particles in size class i
$\begin{array}{l}p_i\end{array}$	Fraction of particle size class i in the bed
$\begin{array}{l}T\end{array}$	Temperature of water

Not all of the transport equations will use all of the above parameters. Typically one or more correction factors (not listed) are used to adapt the basic formulae to transport measurements. Refer to the respective references for more detail.