increases are deducted. In fact, the relationship must increase in a discontin- 

 uous way. Small to moderate increases in armor unit weight should have little 

 or no effect on cost since the same equipment can be used to handle slightly 

 larger units. However, when armor unit weight exceeds some limit, larger con- 

 struction equipment is required and the cost jumps up. For the example in this 

 report, the cost of casting, stripping, handling, and placing individual units 

 (exclusive or material costs) was assumed constant. The relative cost of core 

 material, under layer stone, and armor are also important. A most important 

 factor affecting the result is the proportioning of total armor layer cost be- 

 tween the relative costs of labor and materials. 



Another factor related to armor unit size must be kept in mind when large 

 concrete armor units (740 tons) are being considered. As concrete units in- 

 crease in size their veZat-lve strength decreases and the possibility of breakage 

 increases. The weight of an armor unit increases with its volume or with the 

 cube of its length dimension. Its strength, if unreinf orced, increases only 

 with the square of its length dimension; hence, in the extreme, an armor unit 

 could break under its own weight. This factor must be taken into account when 

 an increase in armor unit weight is being considered. Conceivably, the no- 

 damage stability coefficient for large armor units could be a function of their 

 weight. 



Additionally, the results obtained in the analysis may not be uniformly 

 valid to all rubble-mound design problems. Economic analyses are highly 

 site-specific and thus no general analysis is ever totally valid for any real 

 project. The analysis presented should, however, illustrate a need to inves- 

 tigate several rubble-mound alternative structures for various levels of 

 design. 



II. ANALYSIS 



A typical cross section for the armored side of a hypothetical island in 

 the mouth of Delaware Bay is shown in Figure 1. Basically, it represents a 

 typical rubble-mound structure cross section with armor on only one side. 

 The leeward side is the interior of the island. The crest elevation was 

 established to preclude overtopping by a wave 18 feet (5.5 meters) high with 

 the wave period selected to result in maximum runup. (Details of the design 

 problem are given in Ch. 8 of the SPM.) The design significant wave height 

 used in Hudson's (1958, 1959)^'^ equation for armor unit weight was 18 feet. 



^HUDSON, R.Y., "Protective Cover Layers for Rubble-Mound Breakwaters, Studies 

 Completed Through March 1957," Miscellaneous Paper 2-276, U.S. Army Engineer 

 Waterways Experiment Station, Vicksburg, Miss., July 1958. 



^HUDSON, R.Y., "Laboratory Investigations of Rubble-Mound Breakwaters," Vvo- 

 oeedings of the American Society of Civil Engineers, Vol. 85, No. WW3, 1959. 



