This vfill not be the current velocity "which exists when the breakwater is in 

 place^ but if we propose that a measure of this current is the v' of 

 equation (A). 3 we nay call 



Substituting equations (3) and (5) in equation (1) and collecting the 

 coefficients ?ives 



.W.-...-^ f^=^/4^/VV^] 



(6) 



from which we may find the stable slope for stone of weight W under wave 

 attack of height H and period T at a depth of approximately z (better at 

 a depth, z - H '^'' '"'''"''' '^ '~%'.'"1) , in which the constant K (or K/ ) must be 



empirically determined. However if the above developnent is substantially 

 correct, K should reriHin fairly constant for any one tjrpe of stone* 



In tte report by Iribarren and Nogales (1) a table of stable slopes 

 is given for the brealovater at Argel measured after wave attach had 

 "shaken down" the slope So : Though the upper face of this breakwater consists 

 of artificial blocks, below the depth of 11 meters the armor stone is 

 natural quarry stone. The maximum wave attack immediately before the 

 structure is given as 6c4-5 meters in height with a period of 13e75 seconds* 

 The breakwater itself is founded in a depth of 35 meters. At the depth of 

 11 meters the stone weight is 4 metric tons and the slope is 1 on 1,5» The 

 value of "a" may be found ''from equation (4) (d - 2 =21 Meters) by use of 

 tables of hyperbolic functions (5)» Solving equation (6) for K (assuming 

 ^0 = ^5') s tentative value of K = 1»15 is established^ 



In an attempt to verify this value the results of model studies per- 

 formed in 1948 at the Waterways Experiment Station (A) were used. In these 

 tests prototype waves with a height of 15 feet and a length of 270 feet 

 were directed at a breakwater founded in a depth of 60 feet. The tests 

 were continued until the breakwater slopes attained stability. Two depths, 

 10 feet and 25 feet were chosen at random at i/itiich the average stone weights 

 were 10 tons and 1 ton respectively. Stable slopes were then calculated 

 and compared with those found in the model tests» At the 10-foot depth the 

 calculated slope was 1 on l<,4-6 and at the 25-foot depth the calculated 

 slope was Ion lo52. The actual slope at both these depths was 1 on 1,5» 



Though these values indicate substantial agreement with the preceding 

 theory, further studies are necessary specifically to determine the value- 

 or range of values - of Ko In addition prototype data of existing structures 

 should be analyzed to verify model conclusions. 



21 



