example, a bridge with foundations in clay that is to be replaced in a few years. However, as
Briaud et al. (1999) point out the ultimate scour in cohesive material is as deep as in sand bed
material.
7.7.2 Comparison of Pier Scour Equations
Jones (1983) compared many of the more common equations. His comparison of these
equations is given in Figures 7.3 and 7.4. Some of the equations have velocity as a variable
(normally in the form of a Froude number). However, some equations, such as Laursen's, do
not include velocity. A Froude number of 0.3 was used (Fr = 0.3) in Figure 7.3 for purposes of
comparing commonly used scour equations. In Figure 7.4, the equations are compared with
some field data measurements. As can be seen from Figure 7.4 the CSU equation encloses
all the data points, but gives lower values of scour than the other equations. The CSU
equation includes the velocity of the flow just upstream of the pier by including the Froude
Number in the equation.
The equations illustrated in Figures 7.3 and 7.4 do not take into account the possibility that
larger sizes in the bed material could armor the scour hole. That is, the large sizes in the bed
material will at some depth of scour limit the scour depth. FHWA's HEC-18 scour depth
equation has a coefficient, which is applied to the CSU equation, that decreases the scour
depth when the bed material has large particles.
Mueller (1996) compared 22 scour equations using field data collected by the USGS
(Landers and Mueller 1996; Landers, Mueller, and Richardson 1999). He concluded that the
HEC-18 equation was good for design because it rarely under predicted measured scour
depth. However, it frequently over predicted the observed scour. The data contained 384
measurements of scour at 56 bridges. Figure 7.5 gives six of his 22 comparisons. The six
equations in Figure 7.5 are Shen's, Froehlich's, Laursen's, Melville and Sutherland's, HEC-
18, and Mueller's modified HEC-18 equation (HEC-18BM).
7.7.3 Colorado State University's Equation
The Colorado State University's Equation (Richardson et al. 1975) is as follows:
0.65
a
ys
Fr10.43
= 2.0 K 1 K 2
(7.6)
y1
y1
where:
ys
=
Scour depth, m (ft)
y1
=
Flow depth just upstream of the pier, m (ft)
K1
=
Correction for pier shape from Table 7.1 and Figure 7.6
K2
=
Correction for flow angle of attack of flow from Table 7.2 and Equation 7.8
a
=
Pier width, m (ft)
Froude number = V1 / (gy1) 0.5
Fr1
=
V1
=
Velocity upstream of pier, m/s (ft/s)
7.13
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