84 



With a lower crest the wave overtops the structure and the rundown will be 

 much smaller, which increases stability. An example of a low-crested 

 breakwater is shown in Figure 48. 



The stability of a low-crested breakwater with the crest above the still- 

 water level is first established as being a non-overtopped structure (Van der 

 Meer 1990). Stability formulae such as Hudson's formula or Van der Meer's 

 formulae can be used to determine the required stone diameter of the non- 

 overtopped breakwater. Required stone diameter for an overtopped 

 breakwater can then be determined by multiplying the stone diameter for a 

 non-overtopped breakwater by a reduction factor to account for the increase in 

 stability. After analysis of several data sets, Van der Meer (1991) describes 

 the increase in stability as a function of dimensionless freeboard R* in the 

 form of the following reduction factor: 



Reduction factor for D^q, r = 1/(1.25 - 4.8 Rp (28) 



for < /£ < 0.052 



where R* = dimensionless freeboard, R c /H s (s J2ir) 05 (29) 



R c = crest freeboard, level of crest relative to still water 



s = fictitious wave steepness, 2irH s /gT 2 (30) 



T = peak wave period 



Equation 28 describes the stability of a statically stable low-crested breakwater 

 with the crest above still-water level in comparison with a non-overtopped 

 structure. Figure 49 shows Equation 28 for various wave steepnesses. The 

 reduction factor for the required stone diameter can be read off the graph or 

 computed using Equation 28. It can be seen in Figure 49 that an average 

 reduction of 0.8 in diameter is obtained for a structure with the crest height at 

 the still-water level. The required mass is a factor (0.8) 3 = 0.51 of that 

 required for a non-overtopped structure. 



Dynamically stable reef-type breakwaters 



A reef breakwater is a low-crested rubble-mound breakwater without the 

 traditional multi-layer cross section (Figure 50). This type of breakwater is 

 little more than a homogeneous pile of stones with individual stone weights 

 similar to those used in the armor and first underlayer of conventional 

 breakwaters (Ahrens 1989). Because of their high porosity and low crest, reef 

 breakwaters are stable to wave attack and, at the same time, if they are high 

 enough, can dissipate wave energy effectively. Since they have no core, they 

 cannot fail catastrophically and therefore a logical strategy is to allow them to 

 adjust and deform to some equilibrium condition (Ahrens 1989). The equilib- 

 rium crest height, along with corresponding transmission, are the main design 

 parameters. Tolerable crest height reductions and maintenance requirements 

 should be defined by the designer. 



Chapter 4 Structural Design Guidance 



