3. Influence of Surface Roughness. 
Armor units placed on the surface of a smooth structure will increase the 
amount of energy loss in a wave encountering the structure, thereby reducing 
the amount of wave reflection. The suggested prediction equation for a revet-— 
ment with one layer or armor rock with representative diameter, d, is 
los 
H- 
a = exp ee coté - 0.5 (=) | (18) 
for use with equation (16), where L is the wavelength at the toe of the struc- 
ture. This equation was developed from the data in Table 1. 
Figure 6 illustrates the joint influence of a relative armor roughness 
parameter, Va/L coté, and a relative breaking height parameter, H;/Hp, on the 
reflection coefficient reduction factor, a. An examination of equation (18) 
and Figure 6 indicates that if all other factors remain fixed, the reflection 
coefficient will decrease as the ratio of the stone size to wavelength, d/L, 
increases, as the cot® increases (the slope becomes flatter), or as the ratio 
of the incident wave height to the breaking wave height, (H;/H,), increases. 
Figure 7 shows a comparison between predicted reflection coefficients using 
equations (18) and (16) versus observed reflection coefficients for monochro- 
matic and irregular waves on a 1 on 2.5 slope armored with one layer of stone 
with d/dg = 0.15. The correlation coefficient is 0.98 for monochromatic waves 
and 0.94 for irregular waves. 
The ratio of armor stone diameter to incident wave height, d/H;, on the 
average has little influence on the reflection coefficient for one layer of 
armor, so this parameter is not included in equation (18). Some deviation 
from equation (18) occurs where stone size is much larger than wave height and 
resulting predictions are conservative. For example, where the stone size-to- 
wave height ratio is greater than 2.0, equations (16) and (18) overpredict 
reflection coefficients by an average of 6 percent. 
1.0 —————=) 
0.9 
0.8 
0.7 
[o) 
Ww 
—_+- ——__ + ——_,___] 
0.001 0.01 0.1 1.0 
J a/c cot @ 
Figure 6. Joint effect on one layer of armor and Hy /Hy, on the 
reflection coefficient reduction factor, a. 
18 
