ERDC/CHL CHETN-III-70
July 2005
For comparison, the present Coastal Engineering Manual method given by Equation 4 estimates
runup to be Ru2% = 15.9 ft.
Calculate runup for 1:4 slope:
After checking that the 1:4 structure slope falls within the range of applicability for the plunging/
spilling wave runup equation, the nondimensional relative 2-percent runup is found from
Equation 13 as
1/ 2
0.7 ⎛ M
⎞
Ru 2%
= 4.4 ( tan α ) ⎜ F2 ⎟
(0.505) = 4.4 (0.25)0.7 (0.35)1/ 2 (0.505) = 0.50
⎝ ρgh ⎠
h
and the dimensional 2-percent runup is
Ru 2% = 0.50 h = 0.50 (20 ft) = 10.0 ft
The present Coastal Engineering Manual method given by Equation 4 estimates runup to be
Ru2% = 11.5 ft.
SUMMARY: This CHETN has described a new empirical formula for estimating the vertical runup
distance above the swl that will be exceeded by only 2 percent of the irregular wave runups on
rough, impermeable slopes. The formula is based on the same hypothesis used in an earlier analysis
of runup on smooth, impermeable slopes (Hughes 2003b, 2004b), i.e., the weight of water above swl
at maximum runup is proportional to the maximum depth-integrated wave momentum flux occurring
in a wave just before it reaches the toe of the impermeable plane slope.
The irregular wave runup data on rough/riprap slopes of Ahrens and Heimbaugh (1988) and van der
Meer and Stam (1992) were analyzed in terms of the nondimensional wave momentum flux
parameter. There was only slight difference in runup between waves that broke on the slope
(plunging and spilling breakers) and nonbreaking (surging and collapsing) waves. The laboratory
data were well represented by applying a constant reduction factor to the corresponding equation for
runup on smooth, impermeable slopes. The new formula (Equation 13) has reasonable predictive
capability for irregular wave runup on slopes in the range 1:2 to 1:4. An example calculation
illustrates application of the runup equation.
POINTS OF CONTACT: This CHETN is a product of the Coastal Inlet Structures work unit of
the Coastal Inlets Research Program (CIRP) being conducted at the U.S. Army Engineer Research
and Development Center, Coastal and Hydraulics Laboratory. Questions about this technical note
can be addressed to Dr. Steven A. Hughes (Voice: 601-634-2026, Fax: 601-634-3433, email:
Steven.A.Hughes@erdc.usace.army.mil). For information about the Coastal Inlets Research Program
(CIRP), please contact the CIRP Technical Leader, Dr. Nicholas C. Kraus at
Nicholas.C.Kraus@erdc.usace.army.mil. Beneficial reviews were provided by Dr. Jeff Melby,
Coastal and Hydraulics Laboratory; and Mr. John Ahrens, retired Coastal and Hydraulics Laboratory
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