engineer named Cavanilles Iribarren. Iribarren (1938) presented the first 

 widely used empirical formula for estimating a stable armor unit weight, given 

 incident wave height, seaward slope of the structure, density of the sea wa- 

 ter, and certain characteristics of the armor material. He assumed that 

 stones on the outer slope were subject to gravity and wave forces, the latter 

 of which included buoyant, impact, and friction components. The Iribarren 

 formula was intended to predict the minimum weight stone which would remain in 

 place when subject to waves of a given height. This height, defined in scale 

 model tests as the level of "incipient damage," indicated that over the entire 

 slope no more than 1-5 percent of the stones was displaced (d'Angremond 1975). 

 The Iribarren formula is coming back into use in its original and in modified 

 forms and will be discussed again later in this report. 



13. During and after World War II, the approach of Iribarren was con- 

 tinued by Robert Hudson, a Corps investigator at the Waterways Experiment Sta- 

 tion (WES) in Vicksburg, Mississippi. Hudson performed a great number of 

 scale model tests on a variety of rubble-mound breakwater configurations. He 

 also published a paper (Hudson 1958) which presented an armor unit weight pre- 

 diction formula with many of the same features and assumptions as those of 

 Iribarren. This formula is still in almost universal use by coastal engineers 

 because of its relative simplicity and the many experimental and prototype 

 tests of its reliability. The Hudson formula is 



W = "^ 



A^K^ cot 9 ^^^ 



d 



where 



W = weight of armor unit at the level of incipient damage* 



p = mass density of the armor material 



g = acceleration of gravity 



H = incident wave height 



A=(p-p)/p 

 ^^r ^w w 



p = mass density of the water 



w ■' 



K, = an empirical stability coefficient 

 e = the angle from horizontal of the seaward slope of the structure 



* For convenience, symbols and abbreviations are listed in the Notation 

 (Appendix E) . 



11 



