Hydraulic Structures: Fourth Edition

The force on the wall is obtained by integrating the pressure variation.

The variation of the dynamic pressure component with respect to the

depth is assumed as parabolic with zero at H/2. Hence the force on the

wall per unit width due to breaking waves is

Fb

1

3

Hpb

1

2

 gHd

H

4



  4 πH  (^3) d . (15.18)
If the wall slopes at an angle to the vertical, then the dynamic pressure pb
must be multiplied by cos^2 .
Goda’s method (Goda, 1974, 2000) is used widely to calculate the
horizontal force on a vertical breakwater resting on a rubble mound or
foundation. The formulae cover both breaking and broken conditions of
waves but not aeration. The wall pressure distribution on the vertical wall
resting on rubble mound without overtopping is shown in Fig. 15.7. The
pressure is atmospheric at a vertical distance Rwhich is the run up, given as
R0.75 (1cos)Hd
whereHdis the design wave height. If the waves do not break before the
structureHd1.8Hsand for broken waves Hdis the highest of the random
waves at a distance 5Hsseaward of the structure. is the angle between
wave crests and the wall. Referring to Figure 15.7,
P 1 0.5 (1cos)(
1 
2 cos^2 ) gHd
P 3 
1 P 1

H



4

d



L

gH



6

640 COASTAL ENGINEERING

db Ds

5 Hs

P 3

Pa

ds

R

Sea bed

Fig. 15.7 Pressure distribution in Goda’s method