Hydraulic Structures: Fourth Edition

(c) Scour depth under the bridge

If the contracted width (i.e. the bridge length, L) is less than the régime
width,W(equation (9.9)), the normal scour depth, DN, under the bridge is
given by

DNRs(W/L)0.61 (10.18)

whereRsis the régime scour depth (equation (9.10)).
The maximum scour depth in a single-span bridge (no piers) with a
straight approach (case 1) is about 25% more than the normal scour given
by equation (10.18), whereas in the case of a multispan structure with a
curved approach reach (case 2) it is 100% more than the normal scour.
If the constriction is predominant, the maximum scour depth is the
maximum of case 1 or case 2, or the value given by

DmaxRs(W/L)1.56. (10.19)

(d) Scour around bridge piers

Several formulae based on experimental results have been proposed to
predict the ‘maximum’ or ‘equilibrium’ scour depth (ys, below general bed
level) around bridge piers. In general, these assume the relationship

ys/b(y 0 /b,Fr,d/b) (10.20)

wherebis the pier width, y 0 is the upstream flow depth, dis the sediment
size, and Fris the flow Froude number.

CULVERTS, BRIDGES AND DIPS 439

Table 10.4 Values of KNandKA

Type of pier Conveyance ratio, 

0.9 0.8 0.7 0.6 0.5

KN KA■KN KA ■KN KA ■KN KA ■KN KA

Square nose and tails 0.91 0.96 0.87 1.02 0.86 1.02 0.87 1.00 0.89 0.97
Semicircular nose and
tails 0.94 0.99 0.92 1.13 0.95 1.20 1.03 1.26 1.11 1.31
90° triangular nose
and tails 0.95 0.94 0.92
Twin-cylinder piers
with or without
diaphragms 0.91 0.89 0.88
Lens-shaped nose and
tails 0.95 1.00 0.94 1.14 0.97 1.22