FHWA HEC-18 Equation
The FHWA HEC-18 equation (Richardson and Davis 2001) to predict local scour depths at a
pier, based on the CSU equation, is recommended for both live-bed and clear-water scour.
The equation predicts maximum pier scour depths. The equation is:
= 2.0 K 1 K 2 K 3 K 4 K 5
Scour depth, m (ft)
Flow depth just upstream of the pier, m (ft)
Correction for pier shape from Table 7.1 and Figure 7.6
Correction for flow angle of attack of flow from Table 7.2 and Equation 7.8
Correction factor for bed condition from Table 7.3
Correction factor for armoring by bed material size from Equation 7.9
Correction factor for pier width from Equation 7.13 or 7.14
Length of pier, m (ft)
Froude Number directly upstream of the pier = V1/(gy1)1/2
Mean velocity of flow directly upstream of the pier, m/s (ft/s)
For round nose piers aligned with the flow the depth of scour has the following limits.
ys ≤ 2.4 times the pier width (a) for Fr ≤ 0.8
ys ≤ 3.0 times the pier width (a) for Fr > 0.8
The correction factor for angle of attack of the flow K2 given in Table 7.2 can be calculated
using the following equation:
K 2 = Cosθ + Sinθ
If L/a is larger than 12, use L/a = 12 as a maximum in Equation 7.8 and Table 7.2.