Hydraulic Structures: Fourth Edition

WAVE FORCES ON COASTAL STRUCTURES 637

If the depth in the vicinity of the wall is such that the waves break before
or at the wall, it will be exposed to large impact pressures owing to the
compression of a trapped cushion of air between the advancing wave and
the wall. If water near the wall is deep enough, a standing wave or clapotis
is established adjacent to the structure and the force exerted on the wall is
given by the pressure distribution due to the clapotis.
Sainflou’s analysis is used to estimate the pressures developed in the
presence of the clapotis (Morris, 1963). It is for fully reflected standing
wave and cannot be applied when wave breaking or overtopping occurs.
According to this theory, the horizontal plane of the oscillations of the
standing wave is raised by an amount h 0 above the still-water level:

h 0  cotanh (15.7)

whereHandLare, respectively, the height and wavelength of the incident
wave and dis the undisturbed water depth (Fig. 15.5). The clapotis has
oscillations with a maximum height of 2H. From the linear theory, the
velocity potential, , for the standing wave of height 2His

 coskxcost

and

 coskxsint.

Hccosh[k(yd)]



sinh(kd)

∂



∂t

Hccosh[k(yd)]



sinh(kd)

2 πd



L

πH^2



L

Fig. 15.5 Pressure distribution on vertical wall