Sediment Continuity

The HEC-RAS sediment routing routines solve the sediment continuity equation also known as the Exner equation:

$\begin{array}{l}\displaystyle \left(1-\lambda_p\right)B \frac{\delta n}{\delta t} = -\frac {\delta Q_s}{\delta x}\end{array}$

where:

B = channel width

η = channel elevation

λ_p= active layer porosity

t = time

x = distance

Q_s = transported sediment load

Like most continuity equations, the Exner equation simply states that the difference between sediment entering and leaving a control volume must be stored or removed from storage. The unique feature of the Exner equation is that sediment storage is stored in the bed in a multi-phase mixture with water, requiring porosity to translate mass change into volume change. The Exner equation translates the difference between inflowing and outflowing loads into bed change, eroding or depositing sediment.

HEC-RAS solves the sediment continuity equation by computing a sediment transport capacity for control volume (Q_s-out) associated with each cross section, comparing it to the sediment supply (Q_s-in) entering the control volume from the upstream control volume or local sources (e.g. lateral sediment loads). If capacity is greater than supply, HEC-RAS satisfies the deficit by eroding bed sediments. If supply exceeds capacity, HEC-RAS deposits the sediment surplus.