The HEC No. 18 publication recommends using a modified version of Laursen's (1960) live-bed scour equation:

1) \displaystyle y_2 = y_1 \left[ \frac{Q_2}{Q_1} \right] ^{6/7} \left[ \frac{W_1}{W_2} \right] ^{K_1}
2) y_s = y_2 - y_0
SymbolDescriptionUnits

y_s

Average depth of contraction scourfeet (meters)

y_2

Average depth after scour in the contracted section. This is taken as the section inside the bridge at the upstream end in HEC-RAS (section BU)feet (meters)

y_1

Average depth in the main channel or floodplain at the approach sectionfeet (meters)

y_0

Average depth in the main channel or floodplain at the contracted section before scourfeet (meters)

Q_1

Flow in the main channel or floodplain at the approach section, which is transporting sedimentcfs (m3/s)

Q_2

Flow in the main channel or floodplain at the contracted section, which is transporting sedimentcfs (m3/s)

W_1

Bottom width in the main channel or floodplain at the approach section. This is approximated as the top width of the active flow area in HEC-RAS.feet (meters)

W_2

Bottom width of the main channel or floodplain at the contracted section less pier widths. This is approximated as the top width of the active flow area.feet (meters)

k_1

Exponent for mode of bed material transport.


V /ω*

k1

Mode of Bed Material Transport

< 0.50

0.59

Mostly contact bed material discharge

0.50 to 2.0

0.64

Some suspended bed material discharge

> 2.0

0.69

Mostly suspended bed material discharge

V^* = (g y1 S1)1/2 , shear velocity in the main channel or floodplain at the approach section, ft/s (m/s).
\omega = Fall velocity of bed material based on D50, ft/s (m/s).
g = Acceleration of gravity, ft/s2 (m/s2).
S_1 = Slope of the energy grade line at the approach section, ft/ft (m/m).