Applications 
Since the equations for above surface and sub-surface stone weights are 
not entirely compatible, the determination of sub-surface weights as outlined 
above should be restricted to depths below a wave height from the surface; 
slopes for above surface stones being carried down to that level. 
The crest height of a breakwater should be at least one and one-half 
wave heights above design water level. 
Sample Problem 
A breakwater is to be founded in sea water, in a depth at one place, 
of 70 feet below MHW. Inspection of the quarry indicates that the maximum 
average stone weight available will be 10 tons with a specific gravity of 
2,05. To utilize the quarry to the fullest extent, three stone classes are 
to be used with average weights of 10 tons for class A stone, 5 tons for class 
B stone, and 500 pounds (quarry run) for class C stone. The wave attack for 
design at the structure's position was determined to have a height of 15 feet 
and a length of 450 feet, and to approach from such a direction that the 
refraction coefficient at that position is K,s l. 
From reference 6 when d/L = 70/450 = 0.1553, d/Lp = 0.1167 
and H/H',) = 0.922 
wimeneieres ll Oo TO & 600 feet 
and Eee SE: 56 ikea 3 0S ( aL 
5 555) = 16227 feet. 
Above surface stone weights and slopes - From Plates 3a and 6 stable 
slopes for various stone weights may be fixed in the following manner. 
-W 
Slope W/K' (Fig. 3a) K' ("ig. 6) Pounds Tons 
Lon 3 B05 NO? 0.038 19,000 9.5 
Jon 2) 1/25) x.1106 0.022 27,500 13.75 
The last column shows stone weights stable on slopes of 1 on 3 and 1 on 2 
respectively under this particular wave attack. 
For this problem since the class A stone averages 10 tons, the slope of 
1 on 3 will be chosen for the cap rock. 
Sub-surface stone weights and slopes - The calculation sheet following 
summarizes the steps necessary for the determination of H, and H' of equation 
(6). These values are olotted on Figure 1. The cap rock and attendent 
slopes are carried down to a depth of one wave height (15 feet) and the class B 
14 
