dune bed in the main channel and a corresponding plane bed, washed out dunes or
antidunes in the contracted channel. However, Laursen's equation does not correctly
account for the increase in transport that will occur as the result of the bed planing out
(which decreases resistance to flow, increases the velocity and the transport of bed
material at the bridge). That is, Laursen's equation indicates a decrease in scour for this
case, whereas in reality, there would be an increase in scour depth. In addition, at flood
flows, a plane bedform will usually exist upstream and through the bridge waterway, and
the values of Manning's n will be equal.
4. W1 and W2 are not always easily defined. In some cases, it is acceptable to use the
topwidth of the main channel to define these widths. Whether topwidth or bottom width is
used, it is important to be consistent so that W1 and W2 refer to either bottom widths or
5. The average width of the bridge opening (W2) is normally taken as the bottom width, with
the width of the piers subtracted.
6. Laursen's equation will overestimate the depth of scour at the bridge if the bridge is
located at the upstream end of a natural contraction or if the contraction is the result of
the bridge abutments and piers. At this time, however, it is the best equation available.
7. In sand channel streams where the contraction scour hole is filled in on the falling stage,
the y0 depth may be approximated by y1. Sketches or surveys through the bridge can
help in determining the existing bed elevation.
8. Coarse sediments in the bed material which armor the bed may limit scour depths with
live-bed contraction scour. Where coarse sediments are present, it is recommended that
scour depths be calculated for live-bed scour conditions using the clear-water scour
equation (given in the next section) in addition to the live-bed equation, and that the
smaller calculated scour depth be used.
Clear-water Contraction Scour. The recommended clear-water contraction scour equation is
based on a development suggested by Laursen (1963). Its development is presented in
Chapter 3 as part of the development of the critical velocity equation. The equation is:
K u Q2
y2 = 2/3
y s = y 2 - y o = (average scour depth,m)
Average depth in the contracted section after contraction scour, m (ft)
Discharge through the bridge or on the set-back overbank area at the
bridge associated with the width W, m3/s (ft3/s)
Diameter of the smallest nontransportable particle in the bed material
(1.25 D50) in the contracted section, m (ft)
Median diameter of bed material, m (ft)
Bottom width of the contracted section less pier widths, m (ft)
Existing depth in the contracted section before scour, m (ft)
Coefficient derived in Chapter 3 as an extension of critical velocity