94 



increasing relative crest height, hjh, and increasing relative freeboard, 

 RJH mo , until the crest height reaches the upper limit of wave runup. 



Energy dissipation 



The ability of low and submerged rubble structures to dissipate wave 

 energy has long been appreciated, but only in recent years has it been possible 

 to quantify this property. There is not a lot of specific information available 

 on the wave energy dissipating characteristics of rubble structures, even 

 though this is regarded as one of the major advantages over other structure 

 types (Ahrens and Cox 1990). The primary reason for this is that energy 

 dissipation cannot be directly measured, but must be inferred from 

 measurements of wave transmission and wave reflection. The basic 

 conservation of energy for rubble structures can be written as: 



K 2 t + JC? + dissipation = 1.0 ( 45 > 



Ahrens used the prediction equations for transmission and reflection 

 coefficients in the energy conservation relation given by Equation 45 to 

 determine energy dissipation characteristics for given breakwater 

 configurations. Figure 55 was developed by Ahrens (1987) to illustrate the 

 distribution of wave energy in the vicinity of a reef breakwater. Generally, 

 the greatest energy dissipation was observed for short period waves on 

 structures with crest heights high enough to be non-overtopped. The lowest 

 energy dissipation of about 30 percent occurred for reefs with a relative crest 

 height less than 0.7 Qijh < 0.7). For submerged reefs, energy dissipation 

 increases with increasing steepness H mo IL and with increasing relative reef 

 width A/hL . Structures with crests near the still-water level will dissipate 

 between 35 and 70 percent of incident wave energy, with dissipation being 

 strongly dependent on relative reef width. For structures with moderate to 

 heavy overtopping (0 < RJH^ < 1 .0), energy dissipation is strongly 

 dependent on relative reef width, but not on wave steepness. 



Detailing Structure Cross Section 



Coastal structures must be designed to satisfy a number of sometimes 

 conflicting design criteria, including structural stability, functional 

 performance, environmental impact, life-cycle costs, and other constraints 

 which add challenge to the designer's task {Shore Protection Manual 1984). 

 The requirement to satisfy a number of different design criteria often results in 

 the designer performing a number of iterative analyses to assure that the 

 selected cross-section provides the desired functional performance and 

 structural stability at the least cost over the design life of the project. 

 Optimization of rubble-mound breakwaters is discussed in Chapter 5. 



Chapter 4 Structural Design Guidance 



