NOTES ON DETERMINATION OF STABLE UNDERWATER BREAKWATER SLOPES 



BY 

 Kenneth Kaplan, Engineering Division 



The method of determining undervrater stone sizes and stable slopes 

 proposed by Iribarren and Nogales (1) contains certain inherent weaknessesj 

 first, the Airy wave relationships commonly used for waves moving up a 

 gradually sloping beach are considered to apply at points over a breakwater 

 slope. Second, it is assumed that waves will break in a depth of water 

 equal to their breaking wave height. Third, and perhaps most important, 

 the cause of stone removal both above and below the water surface is con- 

 sidered the same 6 That this last does not hold may be seen by referring 

 to the force diagram from which the basic Iribarren equation is derived (2), 

 in Tidiich an intermittent "flow-no fluid" is considered to be the basic 

 cause of stone removal above still water levelo 



It would seem that a more realistic approach would be one in T\4iich 

 use is made of the currents caused by wave actiono To this end, the re- 

 lationship derived by Blanchet (3) dealing with the destruction of stone 

 masses by currents may be applied. That is ' 



- v^/<,^2g^ /^ :^s/r?Cct-ao) 



(1) 



in which v is tlae critical current velocity for stone mound disintegration; 

 K is a complex non-dimensional coefficient, but one which should 



be fairly constant for stones of the same form; 

 B is a characteristic dimension of the stone; 

 y^ndll ^^® the specific gravities of the stone and fluid of immersion 

 ■* '^ respectively; 



(X is the angle the mound makes with the horizontal; and 

 a^ is the angle of repose of the constituent stones. 



The weight of each stone may be written as 



- I^^Hz%^D^ (2) 



in which 60 is the xinit weight of fre sh water . From this 



The maximum current due to wave action which would exist at depths 

 below still water in the absence of the breakwater is given by 



, ^^ r , cosh Z7rrc^-Z)yi 7 



20 



