Soulsby-van Rijn

Soulsby (1997) proposed the following equation for the total load sediment transport rate

1)	$\begin{array}{l}q_{bk}^{*}=\begin{cases} 0.005Uh\left(\frac{U-U_{crk}}{\sqrt{R_{k}gd_{k}}}\right)^{2.4}\left(\frac{d_{k}}{h}\right)^{1.2}\,\,\,\,\,\mathrm{for}\,\,U>U_{crk}\,\,\\ 0\,\,\,\,\,\,\,\text{otherwise}\,\, \end{cases}\right.\end{array}$

2)	$\begin{array}{l}q_{sk}^{}=\begin{cases} 0.012Uh\left(\frac{U-U_{crk}}{\sqrt{R_{k}gd_{k}}}\right)^{2.4}\left(\frac{d_{k}}{h}\right)d_{k}^{-0.6}\,\,\,\,\mathrm{for}\,\,U>U_{crk}\\ 0\,\,\,\,\,\,\text{otherwise}\,\, \end{cases}\right.\end{array}$

where

$\begin{array}{l}{q_{bk}}^*\end{array}$ = fractional bed-load sediment transport potential [L²/T]

$\begin{array}{l}{q_{sk}}^*\end{array}$ = fractional suspended-load sediment transport potential [L²/T]

$\begin{array}{l}R_{k}\end{array}$ = ρ_sk/ρ_w − 1 = submerged specific gravity of a particle [-]

$\begin{array}{l}ρ_{sk}\end{array}$ = sediment density [M/L³]

$\begin{array}{l}ρ_{w}\end{array}$ = water density [M/L³]

$\begin{array}{l}U\end{array}$ = effective depth-averaged current velocity [m/s]

$\begin{array}{l}U_{crk}\end{array}$ = critical depth-averaged velocity for incipient motion [m/s]

The Soulsby-van Rijn formula was developed by calibrating the above equations to the van Rijn (1993) sediment transport model. The formulas were originally proposed for well-sorted sediments. The formulas have been modified here for nonuniform sediments by replacing the median grain size with the grain class diameter and multiplying the critical depth-averaged current velocity with a hiding and exposure correction factor. Here the Wu et al. (2000) hiding and exposure correction factor is utilized but in principle others may also be used. van Rijn (1984a,b; 2007a,b) computed the critical depth-averaged current velocity using the van Rijn formula.