A more quantifiable means to estimate the amount of stone required for an 

 overlay is given by the coverage fraction, C.F., where 



C.F. = rr~, (9) 



w r 



(w/w r ) 1 /3 



where C is the overlay stone weight per square meter of embankment surface. 

 McCartney and Ahrens (1976) found that the coverage fraction of 100-percent 

 coverage varied by stone shape when C.F. = 0.42 (typical for a relatively 

 blocky quarrystone) and C.F. = 0.55 (typical for rounded boulders). The mini- 

 mum W50 weight for the overlay stone should be computed using equation (5). 

 A wide gradation in the overlay stone is not recommended since each stone is 

 exposed to wave action and receives little support or shelter from adjacent 

 stones. The prototype-scale overlay tests (discussed by McCartney and Ahrens) 

 used an overlay with the following maximum, minimum, and average overlay 

 weights: 



Wmax =3.1 W 50 



Wmin = 0.4 W 50 (10) 



W = 0.87 W 50 



where W50 is the median weight of the overlay gradation; an overlay gradation 

 wider than denoted above is not recommended . 



*************** EXAMPLE PROBLEM 5*************** 



This example reviews concepts discussed throughout the text, introduces a 

 few new ideas, and develops several possible alternate designs to present ad- 

 vantages and disadvantages of each design. 



GIVEN : A low bluff composed of bank-run gravel is eroding due to wave attack. 

 Behind the bluff is a large industrial park and further erosion cannot be 

 permitted. A riprap revetment is to be built with a design freshwater depth 

 at the toe of 1.83 meters (6.0 feet); no overtopping should be permitted, 

 however, the consequences of overtopping would not be life threatening. The 

 offshore slope is 1 on 100; the design deepwater, unrefracted, significant 

 wave height is 1.52 meters and the design wave period is 5.0 seconds. There 

 is no wave refraction between deep water and the structure site. The unit 

 weight of the armor and filter stone is 2,644 kilograms per cubic meter and 

 the EM-size gradation should be assumed for the armor stone. 



FIND : Consider slopes of 1 on 1.5, 1 on 2, 1 on 3, and 1 on 5. For each slope, 

 compute the zero-damage median riprap armor weight, the minimum armor layer 

 thickness, the minimum Wss for the filter layer, and the elevation above 

 the design water level to which the riprap must extend to prevent overtopping. 

 Compare the advantages and disadvantages of the various slopes. 



As a second part of this example, assume there is existing riprap pro- 

 tecting the bluff but the stone is too small for the design wave conditions. 

 Compute the weight of overlay stone required to upgrade the existing riprap 



24 



