Hydraulic Structures: Fourth Edition

WAVE RUN-UP 641

The coefficients
1 ,
2 and
3 are

 1 0.60.5

sinh

4 p

(4

D

p

s

D

/L

s/L)



2

2 min

1

3

(1 ds/db)(Hd/ds)^2 , 2ds/Hd

 3  1 (ds/Db)[1 1/cosh(2(Ds/L)]

Dsis the water depth measured from SWL to the seabed, dsis the depth
from SWL to the top of the rubble mound, dbis the water depth at break-
ing which is assumed at a distance of 5 Hsin front of the vertical wall, min
(a,b) is the smaller of the two values aandb.
Goda (1974, 2000) also presents formulae for uplift pressures on the
wall placed into the foundation. Wave forces exerted on vertical walls
resting on caissons are extensively treated in Coastal Engineering Manual
(US Army, 2002).
Sea walls and other coastal structures are susceptible to wave and
current induced erosion. At sloping front structures, scour undermines the
toe leading to their failure. The local scour can be reduced by reducing
wave reflection, achieved by decreasing the front slope of the structure,
making it permeable, increasing the roughness of the face or introducing a
horizontal berm. The extent of the scour is also controlled by placing large
stones in the affected areas or by other toe protection measures (Hoff-
mans and Verheij (1994)).

15.4 Wave run-up

Sea walls, many of which are sloping with berms, provide an almost imper-
vious surface over which wave uprush and backrush occur. As the severity
of the waves increases, the protection of the seaward face of the wall
changes from turf to heavy stone or concrete construction. Some examples
of sea walls are shown in Fig. 15.8: they are (a) stepped, (b) smooth sloping
and (c) vertical. The sea wall shown in Fig. 15.8(d) is similar in construc-
tion to a rubble-mound breakwater, with the cover layer consisting of
armour units designed to withstand large wave forces. A gently sloping
wall reduces reflection and thus erosion at the toe of the wall. Modern
designs frequently incorporate a curved section at the top of the sea wall
to deflect the waves downwards (Fig. 15.8(e)). Sea walls are expensive to
construct and to maintain. Their design must prevent undue overtopping
(see Section 15.5); the toe of the wall must be protected against erosion