Nevertheless, this is a workable statement in terms of an objective which is 

 adaptable to more than one means of determining structural dimensions. 



10. The functional performance criterion determines the incremental 

 economic benefits of a breakwater design since it defines the structure's 

 level of effectiveness as a wave barrier. It also affects the cost since a 

 certain additional increment of investment may be necessary to achieve a given 

 level of effectiveness. This level of effectiveness can usually be stated in 

 terms of a maximum transmitted wave condition during a given extreme event. 

 The probability of exceedance for this event can in turn be related to 

 property damage and other economic losses. Probability of exceedance is 

 usually stated in terms of any single year, but it can also be stated in terms 

 of all or some portion of the life of the project. A workable statement of a 

 functional performance criterion might be that "10 percent of transmitted 

 waves in any storm will exceed 1 m with less than 5 percent probability per 

 year." This statement assumes that "10 percent of transmitted waves" can be 

 related to some level of unacceptable property damage or operational 

 disruption inside the breakwater. An even more general statement might be 

 that "navigational delays and property damages from transmitted waves shall 

 occur with less than 5 percent probability per year." 



11. Criteria of both types need to be defined for each section of the 

 breakwater where either the environment (water depth, wave exposure, or other 

 factors) or the required level of protection significantly differs. These 

 sections can essentially be treated independently until a point when economy 

 of breakwater materials, related constructibility constraints, and the transi- 

 tion requirements become apparent. Usually the breakwater head, any elbows, 

 and one particular section of trunk will take precedence over other sections. 

 Head and trunk designs do not as yet lend themselves to reliable analytical 

 methods and typically require much subjective Judgment and extensive physical 

 modeling. Most remarks in the rest of this paper will refer to the critical 

 trunk section, with the understanding that other less critical trunk sections 

 may have different design criteria. 



The Hudson Formula 



12. Investigations into the stability of rubble-mound coastal struc- 

 tures were performed in the decade before the second World War by a Spanish 



10 



