Laursen-Copeland

Laursen (1968) developed a total-load sediment transport formula based on flume experiments initially and later expanded it to included data from Arkansas River. Copeland and Thomas. (1989) then generalized the equation for gravel transport. One important aspect of the Laursen-Copeland formula is that it is valid from silts to gravel.

1)	$\begin{array}{l}\displaystyle q_{tk}^{}=a\rho _{w}Uh\left(\frac{d_{k}}{h}\right)^{7/6}\left(\frac{\theta '_{b}}{\theta _{crk}}-1\right)^{n}f_{tk}^{LC}\left(\frac{u'_{}}{\omega _{sk}}\right)\end{array}$

where

$\begin{array}{l}{q_{tk}}^*\end{array}$ = sediment transport capacity [M//L/T]

$\begin{array}{l}a\end{array}$ = 0.01

$\begin{array}{l}θ'_{b}\end{array}$ = grain-related Shields number [-]

$\begin{array}{l}θ_{crk}\end{array}$ = critical Shields number [-]

$\begin{array}{l}U\end{array}$ = current velocity magnitude [L/T]

$\begin{array}{l}h\end{array}$ = water depth [L]

$\begin{array}{l}n\end{array}$ = empirical coefficient (default is 1.0) [-]

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

$\begin{array}{l}ω_{sk}\end{array}$ = sediment particle fall velocity [L/T]

$\begin{array}{l}d_{k}\end{array}$ = grain class diameter [L]

The transport function f_tk^LC(u_*/ω_sk) is approximated by the following regression equation:

2)

$\begin{array}{l}f_{tk}^{LC}\left(\frac{u_{*}}{\omega _{sk}}\right)=\begin{cases} 7.04\times 10^{15}\left(\frac{u_{*}}{\omega _{sk}}\right)^{22.99}\,\,\mathrm{for}\,\,\frac{u_{*}}{\omega _{sk}}\leq 0.225\\ 40\frac{u_{*}}{\omega _{sk}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mathrm{for}\,\,0.225< \frac{u_{*}}{\omega _{sk}}\leq 1.0\\ 40\left(\frac{u_{*}}{\omega _{sk}}\right)^{1.843}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\mathrm{for}\,\,1.0< \frac{u_{*}}{\omega _{sk}} \end{cases}\right.\end{array}$

Larson (1968) and Copeland (1989) used a critical Shields number of 0.039. In HEC-RAS 2D sediment the Shields number may be calculated with another method or be user-specified. In addition the coefficient a and exponent n may be modified by the user. However, it is recommended to calibrate the transport formulas using the transport scaling and mobility factors.