(y_{s} / y_{a}) = 2.27 K_{1} K_{2} (L^{'} / y_{a})^{0.43} Fr ^{0.61} + 1

[ SI Units (metric): y_{s}, y_{a} and L^{'} in m ] [ U.S. Customary Units: y_{s}, y_{a} and L^{'} in ft ] [ Fr = Froude number; g = gravitational acceleration ]

Reference:

Evaluating Scour at Bridges, FHWA Hydraulic Engineering Circular No. 18, Fifth Edition, 2012.

To determine the abutment scour depth y_{s}, the calculator requires the following information:

Average depth of flow on the floodplain y_{a}, in m (or ft).

Mean flow velocity directly upstream of the embankment v_{1}, in m/s (or fps).

Length of active flow obstructed by the embankment L^{'} , in m (or ft).

Angle of embankment with flow θ , in m (or ft).

Fig. 1 Abutment shapes.

Abutment shape (Fig. 1), to determine the shape coefficient K_{1}.

K_{1} = 0.7 for spill through.

K_{1} = 1.00 for vertical wall.

K_{1} = 0.82 for vertical wall with flared wingwalls.

Angle of embankment to the flow, to determine the coefficient K_{2} = (θ/90)^{0.13 }

θ < 90^{o} if embankment points downstream

θ > 90^{o} if embankment points upstream