online_contraction_scour_live_bed:  Contraction scour under live bed conditions
using modified Laursen 1960 equation

Modified Laursen formula

ys / y1 = ( Q2 / Q1 ) 0.86 (W1 / [W2) k1  -  ( yo / y1 )

[ yo, y1, Q and W in any consistent set of units ]
[ S1 in m/m or ft/ft ]
[ T in °C or °F ]
[ D50 in mm or ft ]


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

DESCRIPTION:      [Sample Input]     [Main Page]

To determine contraction scour depth under live bed conditions ys, the calculator requires the following information:

  • Mean flow depth below the bridge, before scour yo, in m (or ft).

  • Mean flow depth upstream of the bridge y1, in m (or ft).

  • Discharge upstream of the bridge (only in the main channel) Q1 in m3/s, or (or cfs).

  • Discharge in the contracted section Q2 in m3/s, or (or cfs).

  • Bottom width in the section upstream of the bridge W1, in m (or ft).

  • Bottom width in the contracted section, excluding piers W2, in m (or ft).

  • Energy slope in the main channel upstream S1, in m/m (or ft/ft).

  • Median diameter of the bed material D50, in mm (or ft).

  • Water temperature θ , in oC (or oF).

1. To determine K1, first calculate the shear velocity in the upstream section V*, and the fall velocity of bed material ω.

    1.1. The shear velocity V* is calculated using the formula V* = (gy1S1)1/2

    1.2. The fall velocity ω is determined using the graph in Figure 1.

curva omega

Figure 1.  Fall velocity of bed material.

    1.3. Finally, with V* and ω, K1 can be defined using Table 1.

Table 1.  Exponent K1
V* / ω Mode of bed material transport K1
< 0.5
Mostly contact bed material discharge
0.5 - 2.0
Some suspended bed material discharge
> 2.0
Mostly suspended bed material discharge

2. The contraction scour depth ys can then be calculated using the following equation:

  ys           Q2              W1             yo
_____  =  (____) 0.86   (____) k1  -  ____
  y1           Q1              W2             y1

    yo = Given

    y1 = Given

    Q1 = Given

    Q2 = Given

    W1 = Given

    W2 = Given

    k1 = Calculated in step 1.

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