WAVE RUN-UP 643
and adequate drainage must be provided behind the wall to reduce slope
failure and undermining.
When a wave breaks on a structure such as a sea wall or breakwater,
some of its energy is dissipated in turbulence and the rest is used to run up
on the wall, gaining potential energy. The height of the run-up determines
whether there will be overtopping. The slope, , of the face of an imper-
meable wall to the horizontal to ensure breaking of the wave is given by
Iribarren and Nogales (1949) as
tan
1/2. (15.19)
Slopes steeper than given by the above expression cause surging and
reflection; for flatter slopes, the waves break on the slope. HIis the inci-
dent wave height.
For surging waves on steep slopes, the run-up Ruis
Ru/HI(π/2)1/2. (15.20)Laboratory studies show that for surging waves Ru/HIis no greater than
about 3.
For small slopes, the run-up Ruof the breaking wave is the vertical
height above the still-water level and is related to the wave height in non-
dimensional form as
Ru/H 0 1.016 tan(H 0 /L 0 )^ 0.5. (15.21)The subscript ‘0’ denotes the deep-water conditions. With L 0 gT^2 /2π, the
above equation may be expressed as
Ru/H 0 0.405 tan(H 0 /gT^2 )^ 0.5. (15.22)TheShore Protection Manual(US Army, 1984) presents charts for the
estimation of the wave run-up of regular waves on rubble-mound break-
waters and riprap slopes. Ruis reduced by the porosity and roughness of
the wall but materials used under permeable conditions are exposed to
uplift pressures due to the receding wave. Equation (15.21) for an impervi-
ous surface can be modified for a porous surface, as
Ru/H 0 1.016 tan(H 0 /L 0 )^ 0.5r (15.23)wherer1 is an empirically determined factor (Table 15.1).
Equation (15.23) gives the mean run-up for regular waves; this,
however, will vary from wave to wave under the action of irregular waves.
The run-ups due to irregular waves on coastal structures with smooth
slope have been determined from model studies for two measures of wave
HI
2 g8
T