The deposition is assumed to occur only over the hydraulically wet portion of cells. Hence, the area-averaged deposition rate may be written as

where

$//<![CDATA[ \begin{array}{l}r_{A}^{HF}\end{array} //]]>$: fraction of horizontal area corresponding to hydraulic flow [-]

$//<![CDATA[ \begin{array}{l}D_{tk}^{HF}\end{array} //]]>$: hydraulic flow deposition rate [M/L²/T]

The formulation for the hydraulic flow deposition rate depends on whether the sediments are cohesive or noncohesive.

Noncohesive Sediments

The concentrated flow erosion and deposition formulation by Wu et al. (2007) and others is given by

where

$//<![CDATA[ \begin{array}{l}\alpha_{tk}\end{array} //]]>$: adaptation coefficient [-]

$//<![CDATA[ \begin{array}{l}\omega_{sk}\end{array} //]]>$: sediment settling velocity [L/T]

$//<![CDATA[ \begin{array}{l}C_{tk}^* = q_{tk}^* / (hU)\end{array} //]]>$ : sediment concentration potential [M/L³]

$//<![CDATA[ \begin{array}{l}q_{tk}^*\end{array} //]]>$: sediment transport potential [M/L/T]

$//<![CDATA[ \begin{array}{l}h\end{array} //]]>$: water depth [L]

$//<![CDATA[ \begin{array}{l}U\end{array} //]]>$: depth-averaged current velocity [L/T]

Cohesive Sediments

The sediment deposition rate for cohesive sediments is given by (Krone 1962; Partheniades 1962; Mehta and Partheniades 1975)

where

$//<![CDATA[ \begin{array}{l}D_{tk}^{HF}\end{array} //]]>$: total-load deposition rate [M/L²/T]

$//<![CDATA[ \begin{array}{l}P_D\end{array} //]]>$: probability of deposition [-]

$//<![CDATA[ \begin{array}{l}\omega_{sf}\end{array} //]]>$: floc settling velocity [L/T]

$//<![CDATA[ \begin{array}{l}C_{tk}\end{array} //]]>$ : total-load mass concentration [-]

The grain class settling velocity may be equal to the dispersed particle settling velocity or a floc settling velocity depending on the sediment concentration. The probability for deposition by Krone (1962) and Partheniades (1962) is given by

where

$//<![CDATA[ \begin{array}{l}\tau_b\end{array} //]]>$: bed shear stress [M/L/T²]

$//<![CDATA[ \begin{array}{l}\tau_{crD}\end{array} //]]>$: critical shear stress for deposition [M/L/T²]

In HEC-RAS 1D sediment the critical shear stress for deposition is set to the critical shear stress for erosion (i.e. mutually exclusive erosion and deposition model). Although the mutually exclusive erosion and deposition model has been successful in many laboratory and field studies (e.g. Dahl et al. 2018) the approach has several issues. Sanford and Halka (1993) found that the mutually exclusive model fails to reproduce field measurements in Chesapeake Bay, USA. Sanford and Halka also presented a summary of field observations with similar behavior. Winterwerp (2003) found that the laboratory experiments of Krone (1962) can be reproduced using a continuous deposition model (i.e. P_D = 1) and a stochastic erosion model. Even if a minimum shear for settling is considered physically reasonable for free settling cohesive particles, it is not reasonable for flocs which can have settling velocities as high as noncohesive particles. In addition, erosion without deposition represents an equilibrium concentration that is infinite, which is not physically reasonable. The critical shear for deposition could be made a function of the fall velocity, but formulations for this do not exist. Winterwerp and van Kesteren (2004) concluded that the probability of deposition in fact does not exist and that for engineering applications the continuous deposition model should be utilized. In fact, many newer sediment studies have shown that cohesive sediment erosion and deposition occur simultaneously. For these reasons, HEC-RAS 2D the probability of deposition is set to 1 representing a continuous deposition model. This also simplifies the model calibration because there is no need to specify and calibrate a critical shear stress for deposition.