H r / H, b 6 a 2 \ 



c '-^- f ( m '-T'h'h-^) (72) 



where H r is the reflected wave height, and 6 the effective pore length. 

 For any particular breakwater configuration, m, b/h, and 6/h are con- 

 stant. Then, the reflection coefficient, C r , can be displayed as a function 

 of the square of the ratio of wave frequency, a, to the natural frequency 

 of the system, w, for constant values of incident wave steepness, H-/L. 

 Hence, the reflection is a function of the breakwater geometry, the wave 

 steepness, and the dimensionless wave frequency. a 2 /u) 2 can be redefined 

 as o 2 h/g by considering the linear deepwater wave theory equivalent 



7 , 2irg 

 a z = kg = (73) 



L 



Richey and Sollitt (1969a, 1969b) conducted a laboratory investigation to 

 study a number of breakwater geometries as potential solutions for floating 

 bridge problems • or other applications desiring wave energy dissipation. It 

 was evident that the optimum breakwater design is one which attains a minimum 

 reflection coefficient at the peak energy frequency and maintains small values 

 of C over the frequency range of the incident wave spectrum. This will 

 yield a minimum energy level in the reflected wave spectrum. The natural 

 frequency of the breakwater can be adjusted to cause C to resonate at any 

 desired frequency by changing the width of the breakwater, b. With this in 

 mind, Richey and Sollitt suggested that the other breakwater parameters be 

 fixed according to combined engineering and economic considerations, which 

 allows the breakwater width to be chosen to attain the desired resonant fre- 

 quency. For the porous-walled breakwaters investigated, the most effective 

 absolute porosities appeared to be in the range of 0.2 to 0.3. The pore 

 diameters should remain less than one-half the average design wave height with 

 the pore length about 1.3 times the pore diameter. The breakwater depth, h, 

 should be at least one-eighth wavelength at the resonant frequency. For the 

 breakwater in Figure 125, the effect of varying breakwater width (other param- 

 eters remaining constant) on the reflection coefficient, C , is shown in 

 Figure 126. Figure 127 shows the effect of varying initial wave steepness 

 on the reflection coefficient with a constant width breakwater for the same 

 breakwater configuration. Figure 128 presents the effects of various wave 

 steepnesses when the breakwater is altered slightly by omitting the bottom 

 (a free vertical exchange between the sea and the chamber). 



In a sample application of the design procedures, the principles were 

 applied to an assumed site just north of the Lake Washington Floating Bridge, 

 State of Washington, using only waves generated from northerly winds. A 

 windspeed of 15 miles per hour is considered common in this region, so for 

 design purposes, the associated waves are characterized as having significant 

 heights of 1.0 foot and periods of 2.0 seconds. For maximum energy dissipa- 

 tion within the breakwater, the minimum reflection coefficient should be near 

 the frequency of the maximum wave energy. This value depends on several vari- 

 ables, but generally lies near a 2 /u 2 =1.2. A representative value of the 

 breakwater chamber width, b, was found to be about 6 feet. Although the 

 theory was developed for deepwater wave properties, its extension to include 

 intermediate and shallow-water waves should be straightforward by using the 

 pressure response functions appropriate for the wave climate at the particular 

 site of interest. 



187 



