trvmk section situated in relatively deep water with no overtopping of 

 the structure, for nonbreaking waves approaching the breakwater with an 

 angle of incidence, 3, of 90°, for random placement of stone armor 

 units, and for various values of H/A, d/A, a, and D. The term on the 

 left side of the equality sign, which was derived using a combination of 

 the dynamic and dimensional analysis methods, was designated the stability 

 number, Ng. It was found that, for the selected test conditions, 



Nj = (K cot a)l/3 (6-4a) 



from which 



^a "^ ~~r~', \T (6-4b) 



" K(73/7^-l)3cota 



and, K = F(A,P^,D). Tests in which 3 = 90° and both partially breaking 

 waves and waves breaking directly onto the breakwater slope are used 

 should show in accordance with equation (6-3b) , that 



K = f(^^,|,A,Pt, d). (6-5) 



Information obtained from the generalized tests is used primarily for 

 purposes of preliminary design. In the final design of a proposed struc- 

 ture where the geometry of the structure section is planned according to 

 local conditions and the purpose of the structure, scale model studies 

 are often necessary to ensure that the structure will provide the desired 

 protection at a minimum of cost. 



b. Vertical-Wall (Impervious) Breakwaters and Jetties . When vertical- 

 wall, gravity-type breakwaters or jetties are situated in depths of water 

 (relative to the wave dimensions) such that the waves do not break on the 

 face of the structure, when the height of the structure is such that all 

 but minor overtopping is prevented, and when the angle of wave approach 

 3 is 90°, the pressure intensity as a function of elevation (in the ver- 

 tical plane of the structure face) can then be calculated by using either 

 the equations of Sainflou (Sainflou, 1928; Hudson, 1953) (first order of 

 approximation) or of Miche (Miche, 1944a; Karael, 1968a) (second order of 

 approximation) for the "clapotis" (a French term that refers to the phe- 

 nomenon in which a series of progressive waves is reflected by a vertical 

 surface perpendicular to the advancing waves and produces standing waves 

 seaward of the structure). Sainflou's equations give conservative results 

 and his pressure curve, modified to simplify calculations, is considered 

 adequate for design in most instances. However, if the geometry of the 

 breakwater is more complex (e.g., with the upper part of the seaward face 

 sloping, as suggested by Van de Kreeke and Paape (1964) and Lundgren (1962) 

 to reduce the effects of wave forces on the stability of the structure), 

 the angle of wave attack is less than 90°, or if there is considerable 

 overtopping, model tests are necessary for an accurate determination of 

 the wave forces on the structure. Such models are designed and operated 

 by Froude's law. 



320 



