*************** EXAMPLE PROBLEM 1*************** 



GIVEN : An earth embankment (to be protected from wave attack) located on a 

 freshwater lake has a slope of 1 on 3, i.e., cot 6 = 3.0; the design wave 

 height at the toe of the embankment is 1.52 meters (5.0 feet). The unit 

 weight of the stone to be used in the armor and filter layers is 2,644 

 kilograms per cubic meter (165 pounds per cubic foot) . 



FIND ; The zero-damage median riprap weight, the minimum armor layer thick- 

 ness, and the minimum Wgs for the filter layer stone. 



SOLUTION : Solving equation (5) gives 



N sz = 1.45(3.0) 1/6 = 1.74 



Next, using equation (4) 

 H 



N c 



W 5 oy/3 /«r _ 

 w r / 



and solving for W50, gives 



W50 = 2,644(1.52) = 397 kii g rams (875 pounds) 



(1.74) 3 / 2,644 n \ 3 

 \l,000 / 



The minimum armor layer thickness given by equation (2) is 



/ 397 V /3 

 r min ~ 2 -° 1 2 644 / = 1 '° 6 meters ^ 3 ' 49 feet ^ 



To compute Wgs for the filter stone, first use equation (1) to compute 

 W 15 for the riprap, i.e., 



W 15 (riprap) = 0.4 x 397 = 159 kilograms (350 pounds) 



Since the riprap and filter stone have the same unit weight, equation (3) 

 can be written as 



D 15 (riprap) = |" w 15 (riprap)" ] /3 _ |~ 159 " l^ 

 D 85 (filter) [ W 85 (filter) J |_W 85 (filter)) 



3 



< 4.0 



which gives a minimum Wg5 (filter) of 2.48 kilograms (5.5 pounds). If the 

 riprap had a gradation narrower than the EM gradation, the minimum Wqs 

 (filter) would have had to have been greater than 2.48 kilograms, since W15 

 (riprap) would have been greater than 159 kilograms. 

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