Hydraulic Structures: Fourth Edition

RUBBLE-MOUND BREAKWATERS 651

armour units displaced in the zone of wave attack. Damage is permissible
if the intermediate layers and the core of the rubble-mound breakwater
are not exposed to wave attack. Also, a structure designed to resist waves
of moderate severity may suffer damage without complete destruction.
There must be a trade-off between the initial cost of a damage-free break-
water for most severe waves and the maintenance cost of the breakwater
designed on the basis of permissible damage. The Shore Protection
Manual(US Army, 1984) gives the ratio of wave height causing per cent
damage to the wave height responsible for 0–5% damage. The wave run-
up on smooth slopes is given by equations (15.23) to (15.28). The reduc-
tion factors due to the porosity and roughness for some units are given in
Table 15.1 (Bruun, 1972).

(b) Van der Meer formulae

Van der Meer (1987) presents formulae for the stability of rock armour
from results of model tests with random waves taking into account the
effects of a number of variables not included in the Hudson equation
(15.32). The formulae are:

(i) for breakers with Irribarren number 2.5 on smooth slopes and
2.0 on rough slopes

6.2P0.18

0.2

^ 0.5; (15.36)

(ii) for breakers with 2.5 on smooth slopes and 2.0 on rough slopes

1.0P^ 0.13

0.2

co t 
P. (15.37)

is the Irribarren numbertan/(H/L 0 )0.5whereis the slope of the

structure and His the wave height at the structure. ∆is ( (^) s )/ ,Nis the
number of waves in design wave conditions, Sis the damage number
defined as Ad/D^250 ,Pis the notional permeability factor and D 50 is the
nominal diameter of the rocks. Adis the cross-sectional area of erosion.
Van der Meer (1987) relates the mean mass of the rocks M 50 to the
sizeD 50 as
D 50 
1/3

. (15.38)

The recommended values of the design damage number Sequivalent to
the number of stones of size D 50 from a D 50 width of the structure are
given in Table 15.5.

M 50



(^) s

S



N

Hs



∆D 50

S



N

Hs



∆D 50