The filter criterion given by equation (3) is somewhat more conservative (i.e., 

 requires larger stone in the filter layer) than the criteria accepted by 

 Thomsen, Wohlt, and Harrison (1972) and given in the SPM, EM 1110-2-2300, and 

 ETL 1110-2-222 (U.S. Army Corps of Engineers, 1978), but it appears necessary 

 based on the riprap stability tests conducted by Ahrens (1975) . 



If the armor stone is large, it may be necessary to have a second under- 

 layer of stone beneath the first underlayer. The stone-size relationship 

 between the first and second underlayers is also given by equation (3) . The 

 thickness of the underlayers should be at least three median stone diameters 

 (i.e., 3D 50 ) and not less than 0.23 meter (9 inches) (see ETL 1110-2-222). 

 Sometimes it is economical to replace the smallest size underlayer with a 

 geotextile fabric; however, because of unsatisfactory experience, Corps policy 

 currently does not permit the use of geotextile fabrics beneath riprap on 

 embankment dams and navigation channels. 



3. Zero-Damage Stability . 



The usual method to evaluate riprap stability is by use of Hudson's (1959) 

 stability number, N s . The stability number is defined by the equation 



N c = 



1/3 . 



(4) 



' ; 50 



where H is the local wave height and w w is the unit weight of water (1,000 

 and 1,026 kilograms per cubic meter or 62.4 and 64 pounds per cubic foot for 

 freshwater and for seawater, respectively) . Normally, the wave height used in 

 equation (4) would be the height at the toe of the structure; however, in some 

 situations, particularly on deep reservoirs, where there is no clearly defined 

 toe for the structure, the deepwater wave height may be used in equation (4). 

 The use of the significant wave height in equation (4) is discussed in sub- 

 section 5. 



When the stability number is used to define the zero-damage stability con- 

 dition, the symbol N sz is used, and the corresponding wave height is the 

 local zero-damage wave height, H z . For zero-damage stability, the relation 

 between the stability number and the slope of the embankment to be protected 

 is 



N sz = 1.45(cot 6) /6 (5) 



where 9 is the angle between the embankment face and the horizontal . Equa- 

 tion (5) is intended for use with armor stone placed by dumping and is con- 

 sidered to be conservative enough to account for wave period effects (Ahrens 

 and McCarthy, 1975), for both breaking and nonbreaking wave conditions, and 

 for naturally occurring irregular wave conditions (discussed in the next two 

 subsections) . 



