Computing Pier Scour With The Froehlich Equation

A local pier scour equation developed by Dr. David Froehlich (Froehlich, 1991) has been added to the HEC-RAS software as an alternative to the CSU equation. This equation has been shown to compare well against observed data (FHWA, 1996). The equation is:

1)	$\begin{array}{l}\displaystyle \displaystyle y_s = 0.32 \Phi (a')^{0.62} y^{0.47}_1 Fr^{0.22}_1 D^{-0.09}_{50} + a\end{array}$

Symbol	Description	Units
$\begin{array}{l}\Phi\end{array}$	Correction factor for pier nose shape: 1.3 for square nose piers; 1.0 for rounded nose piers; and 0.7 for sharp nose (triangular) piers.
$\begin{array}{l}a'\end{array}$	Projected pier width with respect to the direction of the flow	ft (m)

Note

This form of Froehlich's equation is use to predict maximum pier scour for design purposes. The addition of one pier width (+ a) is placed in the equation as a factor of safety. If the equation is to be used in an analysis mode (i.e. for predicting the scour of a particular event), Froehlich suggests dropping the addition of the pier width (+ a). The HEC-RAS program always includes the addition of the pier width (+ a) when computing pier scour. The pier scour from this equation is limited to a maximum in the same manner as the CSU equation. Maximum scour $\begin{array}{l}y_s\end{array}$ ≤ 2.4 times the pier width (a) for $\begin{array}{l}Fr_1\end{array}$ ≤ 0.8, and $\begin{array}{l}y_s\end{array}$ ≤ 3.0 times the pier width (a) for $\begin{array}{l}Fr_1\end{array}$ > 0.8.