Clear-Water Scour at Abutments

Clear-water scour can be calculated with equation (1) or (2) for live-bed scour because clear-water scour equations potentially decrease scour at abutments due to the presence of coarser material. This decrease is unsubstantiated by field data.

1)	$\begin{array}{l}\displaystyle \displaystyle y_s = 4y_1 \left( \frac{K_1}{0.55} \right) K_2 Fr^{0.33}_1\end{array}$

Symbol	Description	Units
$\begin{array}{l}y_s\end{array}$	Scour depth	ft (m)
$\begin{array}{l}y_1\end{array}$	Depth of flow at the toe of the abutment on the overbank or in the main channel, taken at the cross section just upstream of the bridge.	ft (m)
$\begin{array}{l}K_1\end{array}$	Correction factor for abutment shape, Table 10-4
$\begin{array}{l}K_2\end{array}$	Correction factor for angle of attack ( $\begin{array}{l}\theta\end{array}$ ) of flow with abutment. $\begin{array}{l}\theta\end{array}$ = 90 when abutments are perpendicular to the flow, $\begin{array}{l}\theta\end{array}$ < 90 if embankment points downstream, and $\begin{array}{l}\theta\end{array}$ > 90 if embankment points upstream. _{$\begin{array}{l}K_2 = (\theta / 90) ^{0.13}\end{array}$}
$\begin{array}{l}Fr_1\end{array}$	Froude number based on velocity and depth adjacent and just upstream of the abutment toe

2)	$\begin{array}{l}\displaystyle \displaystyle y_s = 2.27 K_1 K_2 (L')^{0.43} y^{0.57}_a Fr^{0.61} + y_a\end{array}$

Symbol	Description	Units
$\begin{array}{l}y_s\end{array}$	Scour depth	ft (m)
$\begin{array}{l}K_1\end{array}$	Correction factor for abutment shape, Table 10-4
$\begin{array}{l}K_2\end{array}$	Correction factor for angle of attack ( $\begin{array}{l}\theta\end{array}$ ) of flow with abutment. $\begin{array}{l}\theta\end{array}$ = 90 when abutments are perpendicular to the flow, $\begin{array}{l}\theta\end{array}$ < 90 if embankment points downstream, and $\begin{array}{l}\theta\end{array}$ > 90 if embankment points upstream (Figure 10-1). $\begin{array}{l}K_2 = (\theta / 90)^{0.13}\end{array}$
$\begin{array}{l}L'\end{array}$	Length of abutment (embankment) projected normal to flow	ft (m)
$\begin{array}{l}y_a\end{array}$	Average depth of flow on the floodplain at the approach section	ft (m)
$\begin{array}{l}Fr\end{array}$	Froude number of the floodplain flow at the approach section, $\begin{array}{l}Fr= V_e / (gy_a)^{1/2}\end{array}$
$\begin{array}{l}V_e\end{array}$	Average velocity of the approach flow $\begin{array}{l}V_e = Q_e / A_e\end{array}$	ft/s
$\begin{array}{l}Q_e\end{array}$	Flow obstructed by the abutment and embankment at the approach section	cfs (m³/s)
$\begin{array}{l}A_e\end{array}$	Flow area of the approach section obstructed by the abutment and embankment	ft² (m²)