height (Allsop et al., 1985). The average run-up Rsreached by significant
wave of height Hsis
2.11 0.09p. (15.24)
The average run-up R 2 for waves whose height is exceeded by 2% of the
incoming waves is
3.39 0.21p (15.25)
wherepis the Irribarren number defined as tan/(Hs/Lp)0.5in which Lpis
the deep water wavelength corresponding to the peak period (see worked
example).
Over rough slopes the values of run-up are obtained by multiplying
the values determined for smooth slopes (equations (15.24) and (15.25))
by correction factors ras given in Table 15.1. For slopes with tetropods as
armour units the equation for run-up due to Allsop et al.(1985) is
1.32(1 exp( 0.31p)) (15.26)
1.83(1 exp (0.31p)). (15.27)
Coastal Engineering Manual (US Army, 2002) expresses run-up R 2 for
smooth slopes as
H
R 2
s
1.5p for 0.5p2.0
3.0 for 2 p 3 4 (15.28)
R 2
Hs
Rs
Hs
R 2
Hs
Rs
Hs
Table 15.1 Factor rfor various armour units
Armour unit r
Smooth, impervious 1.0
Concrete slabs 0.9
Concrete block 0.85–0.9
Grass on clay 0.85–0.9
One layer of quarrystone (impervious) 0.8
Rubble stone placed at random 0.5–0.8
Two or more layers of rockfill 0.5
Tetrapods 0.5
Those values may be considerably exceeded if tan(H 0 /L 0 )^ 0.52 (slope of cover layer).
644 COASTAL ENGINEERING
