# Soil Erosion:Channel Sediment Transport Formulation

The present version of GSSHA employs the unit stream power method of Yang’s (1973) for routing sand-size total-load in stream channels. Unit stream power is defined as the product of the average flow velocity, U, and the channel slope So. The rate of work done per unit weight of water in transporting sediment is assumed directly related to the rate of work available per unit weight of water. Thus, the total sediment concentration or total bed-material load must be directly related to the unit stream power. The following relation gives the basic concept of Yang’s (1973) method:

(112)

where: Cs is the total concentration of sand-size sediment particles in motion, USo is unit stream power (L/T), U* is the shear velocity (L/T), ν = kinematic viscosity of the sediment-water mixture (L/T2), w = fall velocity of the sediment (L/T), d = particle diameter (L). With some mathematical and statistical manipulations with Buckingham’s π theorem, Yang (1973) derived an energy-based equation to estimate the total sand-size sediment concentration in the channel.

Only particles sizes larger than a user specified value for sand are transported in this manner. Smaller particles are assumed to be suspended, and not bedload, and are transported with the advection dispersion equation. The bed is assumed to be mobile, and the banks fixed. The bed can agrade or degrade to a user-specified maximum allowable depth(Figure 14).

In the channels size particles smaller than the user specified value of sand are assumed to be in suspension, and are transported as wash load. This treatment implies that the flow is turbulent, and the travel time to the outlet of the catchment is short compared to the settling time, such that particles do not settle in the channel network. This assumption, combined with no bank erosion, results in the channels being neither a source nor sink of fines. Routing of suspended fines is a natural extension of the explicit diffusive-wave channel routing method. Suspended fine sediments are routed as concentrations. The concentration changes as a function of gradients in both concentration and velocity.

Figure 14 – Channel bed erosion

## GSSHA User's Manual

10 Soil Erosion
10.1     Overland Erosion Formulation
10.2     Channel Sediment Transport Formulation
10.3     Sediment in Lake
10.4     Applicability of the Sediment Routing Methods
10.5     Simulations with Soil Erosion