increasing the steepness of the slope and thus diminishing the volume 

 of the dikeo 



From what has been said it is apparent that one must not forget 

 the importance of the density of natural or artificial stones in the 

 design of rock-fill dikes » 



With respect to the zone to which the formula is applied one 

 needs only to remember that, since the trochoid transforms itself into 

 a cycloid at the breaking of the wave, the elevation of its average 

 levels over that of the sea in repose, is 



^ _ _A_ 



ttAK ~ 4 



•Riis means that as the wave breaks, 3A of its total height A is above 

 the still water level » In order to avoid overtopping or the slight 

 spray which forms on this type of dike, it is desirable to raise the 

 dike to elevalion +As or better + 5 A A, so as to extend by the height 

 of the wave the slope formed by stones of weight P determined by the 

 formula = 



If we admit, as a hypothesis more unfavorable than reality, that 

 below the level - I/4. A the differences of pressure between the 

 anterior and posterior faces of the stones of the first layer (or 

 the pressures which tend to separate them from those of the second) 

 are proportional to the greatest pressures exerted by the surge at 

 each point, we arrive at the conclusion that in this constantly sub- 

 merged zone, the formula also can be applied by substituting A' for 

 '^^''/^/^LK " Here r^ is the horizontal semi -axis of the 



orbital ellipse corresponding to each depth, determined by applying 

 the trochoidal tiieory, and K = coth tt// q 



L 



This generalization of the formula, indicated in Figure 7, 

 supposes a certain margin of securityo It is also probable that the 

 coefficients K a 15 and 19, previously determined, introduce some 

 margin of safety^ chiefly the second because of the undertow caused 

 by the superstructure of the Artha dike. However it is not logical 

 to apply strict results, obtained by means of the application of 

 theoretical formulas to sea conditions when it is the general rule 

 to employ ample factors of safety for land conditions » 



In any case I shall be very grateful to my colleagues, who may 

 know of concrete practical cases in detail, if the y will have the 

 kindness to send them to me in order to compute the coefficients, 

 thereby establishing them mth more assurance o 



I believe that enough useful points have been derived from the 

 discussion of the simple formula obtained and of the fundamentals 

 that have served to determine it, therefore I close here the ex- 

 position which involuntarily has become too long and tedious » 



15 



