damages E($D/yr} to be estimated for a breakwater design, which is the same 

 as the "equivalent annual amount" that might be derived by discounted cash 

 flow analysis. An interactive FORTRAN computer program called "BWDAMAGE" has 

 been developed at WES. This program estimates E{$D/yr} given values of 

 foD{H, ) and S for Equation 14, e and <i> for an Extremal Type I cpd of 

 significant wave heights (Equation 19), representative armor repair unit 

 prices and the volume of the armor layer. This program is documented further 

 in Appendix D of this report. Its intended use is for comparison of alter- 

 native plans, and for this purpose the limited statistical confidence of the 

 applied formulae is acceptable. Substitution of a measured damage function 

 from model tests of a particular design would greatly improve the reliability 

 of the program's estimates. 



67. A number of refinements to the above scheme of analytical predic- 

 tion of rubble-mound breakwater damage are conceivable. The effects of wave 

 period and storm duration on stability have been recently investigated by a 

 number of specialists. The effects of wave period and storm duration were 

 incorporated directly into the stability formulae proposed for quarrystone 

 rubble-mound breakwaters by Van der Meer and Pilarczyk (1984) (Equations 5 

 through 8). The Joint effect of wave height and period on armor damage, in 

 the form of the surf parameter (Equation 4), and risk analysis in terms of a 

 probability distribution of wave steepness is discussed in Bruun (1985). The 

 DHI-Iribarren stability formula (Equation 3) directly incorporates the effect 

 of wave period as the corresponding wave length (Graveson, Jensen, and Soren- 

 sen 1980). This latter work also addresses the effect of storm duration by 

 focusing on the rate at which damage occurs for variations of the other sta- 

 bility related factors (W , H , T , cos 9 , etc.). The following relation of 

 damage was derived from the data of Graveson, Jensen, and Sorensen (I98O): 



where 



D = damage rate D/t , in percent armor displacement per hour 



K = the DHI-Iribarren stability coefficient 



= p gu H L /WA (u cos 9 - sin 9) from Equation 3 

 r° s p 



K is a function of wave height and period, so all three parameters (H , T , 



t) are also included in the_ DHI approach, since 



43 



