ERDC/CHL CHETN-III-70
July 2005
Estimating Irregular Wave Runup
on Rough, Impermeable Slopes
by Steven A. Hughes
provides a new formula for estimation of irregular wave runup on rough, impermeable slopes. The
runup guidance is based on the wave momentum flux parameter described in CHETN-III-67
(Hughes 2003a). Sample calculations illustrate application of the formula.
BACKGROUND: Estimates of maximum wave runup on rough, impermeable sloping structures
(riprap revetments) are necessary to determine whether overtopping will occur for a specified wave
condition and water level. Design formulas were originally developed based on theory and small-
scale laboratory experiments using regular waves. As laboratories acquired the capability to generate
more realistic irregular waves, improved wave runup formulas were proposed based on wave
parameters representative of the irregular wave train. However, unlike regular waves that result in a
single value of maximum wave runup, irregular waves produce a runup distribution. Thus, it was
necessary for the runup formulas to determine a representative parameter of the wave runup
distribution. Presently, the most common irregular wave runup parameter is Ru2%. This parameter is
defined as the vertical distance between the still-water level (swl) and the elevation exceeded by
2 percent of the runup values in the distribution. In other words, for every 100 waves running up a
slope, two waves would have a runup elevation exceeding the level estimated by Ru2%.
Irregular wave runup design guidance for rough, impermeable slopes given in the Coastal
Engineering Manual is based on runup measurements acquired during irregular wave rock armor
stability experiments conducted at Delft Hydraulics and reported by van der Meer and Stam (1992).
The guidance is presented as two empirical formulas with each formula valid over a specific range of
Iribarren numbers. The formulas in the Coastal Engineering Manual for the 2-percent runup
elevation are as follows:
Ru 2% ⎧0.96 ξom
for 1.0 < ξom < 1.5
⎪
=⎨
(1)
H mo ⎪1.17 (ξom )0.46
for 1.5 < ξom
⎩
with the Iribarren number defined as:
tan α
ξom =
(2)
H mo
Lom
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