SOME OBSERVATIONS ON THE ECONOMICS OF "OVERDESIGNING" 

 RUBBLE-MOUND STRUCTURES WITH CONCRETE ARMOR 



hy 

 J. Richard Weggel 



I . INTRODUCTION 



Development of the design problem presented in Chapter 8 of the Shore 

 Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering 

 Research Center, 1977)-^ provided an opportunity to calculate the relative cost 

 of a revetment -breakwater on the seaward side of a hypothetical manmade island 

 armored with concrete armor units built at various slopes with various concrete 

 unit weights. One type of armor unit evaluated was the dolos. The recommended 

 stability coefficient ^K^) for dolosse was 13.6 when the initial calculations 

 were made. The stability coefficient was subsequently raised to 25.0 based on 

 the results of hydraulic model tests. This change led to a comparison of cost 

 figures for the dolosse revetment-breakwater designed using ¥jq = 25.0 with 

 one designed using K^ = 13.6. A recalculation of the cost of the dolos- 

 armored structure using the new, nearly doubled, stability coefficient, gave 

 some interesting observations regarding the consequences of overdesigning, and 

 are presented in this report . 



This report deals primarily with the first cost of a strvrture, not its 

 average annual cost which is the sum of its first cost amortized over the struc- 

 ture's economic life and the average annual cost of repairing the structure 

 following events that exceed design conditions; however, the results of the 

 first-cost analysis have interesting implications regarding minimization of the 

 risk of damage to the structure resulting from waves greater than the design 

 wave. 



The cost figures used in this analysis were based roughly on 1972 costs 

 and, because of the academic, illustrative nature of the original problem, were 

 only approximately based on real costs associated with the rehabilitation of 

 the Humbolt jetties at Eureka, California, in 1970-72. Consequently, the cost 

 figures should not be assumed valid today or even to have been valid in the 

 1970-72 time frame. What is important to the conclusions presented is the 

 relative change in cost arising from a substantive change in stability coeffi- 

 cient. Other important economic and physical design factors, some of which 

 may be peculiar to dolosse and others generally applicable, are not considered 

 here. For example, structures requiring larger dolosse may need to be designed 

 using lower stability coefficients in order to preclude motion that could break 

 the units; i.e., there may be a scale effect. This factor might be perculiar 

 to dolosse because of their fragility compared to other, stouter units. Another 

 factor not considered is the influence of increasing the armor unit size on 

 construction equipment requirements. Increasing armor unit size beyond a cer- 

 tain point will require increasing the capacity of handling and transporting 

 equipment such as cranes, trucks, barges, etc. Consequently, the cost of cast- 

 ing, stripping, handling, and placing individual concrete armor units is not 

 independent of armor unit size but increases with size even after material cost 



^U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore 

 Protection Manual, 3d ed.. Vols. I, II, and III, Stock No. 008-022-00113-1, 

 U.S. Government Printing Office, Washington, D.C., 1977, 1,262 pp. 



