we obtain 



The component N, normal to the theoretical plane E F, of the weight P 

 of the submerged stone, is N = Pg » cos a, a being the angle of the 

 dike face with the horizont-alo 



The resistance to downward displacement, R, arising from the 

 friction of the stone, or more accurately stated, from the friction of 

 each of the stones which constitute the first layer on the stones which 

 constitute the surface E F of the second layer has the value 



f being the coefficient of friction of the rock-fill. If independently 

 of the size of the stones we approximate the natural slope of the rock- 

 fill by a slope of 4.5°, we have 



f= tan 4-5''=/ 



One has, consequently. 



/P=/= cos a- Kz^S 



The component of Pg parallel to the slope of the rock-fill, D, 

 is the force which tends to cause downward displacement of each of the 

 stones of the first layer and has the value D = P sin a. 



Considering the case of strict equilibrium or of waves of limited 

 height, to insure no downward displacement of a first layer stone as 

 a consequence of the diminution of its friction over those of the 

 second layer by the action of the forces P, we must have 



D = f? 



or 



^ sin a =■ Ps cos a- H2 '^S 



If we represent some linear dimension of the stone by y, and the 

 density of the material of which it is composed by d, then the weight 

 of the subnerged stone will be given by: 



in vfhich K-j is a coefficient which depends upon the form of the stone. 

 Analogously we have 



Then, substituting, we have: 



^3y^Cof-0 sin a = K3y^(d-i)cosa- /T^AV Ay^ 



