CHARTS AND TABLES FOR DETERMINING SURFACE STONE SIZES 
FOR RUBBLE MOUND STRUCTURES IN WAVE ACTION 
by 
W. H. Vesper and Kenneth Kaplan, Engineering Division 
Beach Erosion Board 
INTRODUS TION 
Data pertinent to the design and construction of rubble mound structures 
for resisting wave action have been compiled and are presented here in 
limited tabular and graphical form. 
The methods of calculation for stone sizes and related slopes are based 
upon translations of the works of Ramon Iribarren Cavanilles and Casto Nogales 
y Olano. These translations appeared in the Beach Erosion Board Bulletin, 
Volume 3, No. 1, January 199 and Volume 5, No. 1, January 1951. 
The equation used to calculate the stone sizes is the dimensionally 
homogeneous form of Iribarren's formula developed by Robert Y. Hudson, 
M. ASGE and presented in Transaction of the American Society of Civil Engineers, 
Volume 116, 1951. 
Terms and Symbols 
oe «ss Breakwater slope angle with the horizontal 
M  « Effective coefficient of friction, rock on rock (= 1.09) 
da = Depth of water at the breakwater's position 
se 
u 
Wave height at the breakwater's position in the absence of the 
breakwater 
Hypothetical wave height with orbital velocity the same as 
exists at depth d with a surface wave height of H, 
= 
tt 
H, = Deep water wave height associated with H 
H' g = Deep water wave height associated with H, if refraction effects 
are ignored. 
Wave height over points on the breakwater slope showing the 
steepening effect of the breakwater 
a 
+33) 
fk 
K = An empirical dimensional coefficient in Iribarren's original 
equation (1) 
K! = An empirical dimensionless coefficient in Hudson's modified 
equation (2) 
10 
