benefits foregone will be higher. Even though structure first costs are low, 

 the total average annual project cost may still be relatively high since annual 

 costs for repair and maintenance will be high. An optimum design wave height 

 between the preceding extremes will result in a structure that minimizes average 

 annual project costs. This design level can only be found by investigating a 

 range of design wave heights and assessing the costs and benefits associated 

 with each. 



The effect of the preceding observations on concrete armor unit costs of 

 optiniizing the design level is to give projects designed for larger waves an 

 economic advantage. Designs for larger waves will have fewer armor units with 

 only relatively small additional costs incurred for designing a larger struc- 

 ture, i.e., the curve labeled "First Cost" in Figure 3 will be relatively flat. 

 If the added costs are sufficiently small, they will be more than offset by 

 decreased maintenance and repair costs and increased project benefits. The 

 effect, therefore, is to shift the minimum of the total cost curve in Figure 3 

 to the right toward higher design wave heights. 



III. SUMMARY AND CONCLUSIONS 



The design of rubble-mound structures with concrete armor units should con- 

 sider optimizing the design by investigating a range of possible design wave 

 heights and the costs associated with each. This will result in a design which 

 balances first costs against average annual maintenance and repair costs to 

 obtain a least-cost structure. The relatively small change in overall structure 

 first cost associated with a significant change in the recommended stability 

 coefficient for dolosse armor suggest that it may be more economical to design 

 using fewer larger armor units since a part of the cost of concrete armor is 

 proportional to the number of units required. As the stability coefficient for 

 an armor unit is increased, the amount of concrete and other materials required 

 to armor a given area of the structure decreases; however, the number of units 

 needed to cover the given area increases. Any savings in construction materials 

 accrued by using smaller armor units are thus offset by increased labor costs 

 needed to form, reinforce, strip, and place a greater number of units. This 

 observation suggests that the minimum point on the total annual costs curve will 

 be shifted toward the right to favor higher optimum design wave heights. 



The effects of increasing armor unit size on their relative strength must 

 be considered, particularly if large units are being considered. 



It is recommended that designers of rubble-mound structures work closely 

 with cost estimators to ensure that an optimum level of design is achieved. 

 This can only be obtained if a range of design wave heights and corresponding 

 structure designs is evaluated. 



13 



