Laursen's Live Bed Contraction Scour Equation

Laursen's equation for estimating live bed scour in a contracted section in a rectangular channel can be expressed in the following form:

y2/y1 = (W1/W2)k2
Where
y1, y2 = flow depths in the approach section and the contracted section.
W1, W2 = channel widths of the approach section and the contracted section
k2= experimental constant related to sediment transport

(Please note that this equation is a simplified form of Laursen's Equation for a contraction of a rectangular channel with a uniform bed-material.)

The ratio of q2/ q1 may be substituted for W1/ W2, and above equation may be written as:

y2/y1 = (q2/q1)k2
Where q1, q2 = unit discharges in the approach section and the contracted section

This is a comparative equation, equating the rates of sediment transport at the uncontracted and contracted sections. The equation applies to both clear-water and live-bed cases to the extent that the shear stresses in the two sections are considered equal. These cases are solved in ABSCOUR program by assuming that the critical velocity has been reached at the contracted section.

For the clear-water contraction scour, the program lets the user choose between Neill's equation and Laursen's equation. For the live-bed contraction scour, to account for the armoring effect by the coarse sediments, the program chooses the smaller scoured flow depth of the live-bed scour equation and the clear-water scour equation.

The contracted section, Section 2, is best represented for most cases as the downstream end of the bridge where the flow is still contracted. The upstream uncontracted approach section, Section 1, is typically considered to be about one bridge length or more upstream where the flow is uniform and not influenced by the bridge contraction.