The usual parameter in coastal research (see eq. 3) is "volume concen- 

 tration" defined as 



a' = Volume of solids/total volume . (8) 



The void ratio is related to the volume concentration by 



e = (1 - a')/a' . (9) 



In terms of the volume concentration, the unit weight of sand is 



Y = a'G Yu . (10) 



The few times that the unit weight of sand has been considered in 

 longshore transport predictions, it has been assumed that the sand is 

 all quartz (G = 2.65) and that a' = 0.60. This value of a' is appar- 

 ently derived from Chamberlain (1960) where a' = 0.60 is reported for 

 fine sand collected from the beach face, after compaction. However, 

 a', can vary significantly. For example, Chamberlain reported data 

 equivalent to a' = 0.53 for sand at the head of a submarine canyon and 

 as low as 0.27 for micaceous sand lower in the canyon (taken from 

 Shepherd, 1963). 



Theoretically, for sands consisting of perfect spheres of the same 

 size, a' ranges from 0.52 to 0.74, going from loosest to most dense 

 (42 percent increase). The following Table shows the actual data (when 

 converted to a' values) reported in Sowers and Sowers (1970, p. 30). 



Table. Ranges of volume concentration, a', and unit 



weights of sand, y (from Sowers and Sowers, 1970) 



Sand a max a min ^max ^min 



(lb/ft 3 ) (lb/ft 3 ) 



Uniform 0.67 0.54 110 89 



sub angular 



Well-graded 0.74 0.59 122 97 



sub angular 



Since G and a' have been assumed to be 2.65 and 0.60 when 

 calculated, .this is equivalent to saying that all sand is assumed to 

 have a unit weight, from equation (10), of 99.2 pounds per cubic foot. 



Using the "relative density" as defined by Sowers and Sowers (1970. 

 p. 31) and the Table, a sand having the assumed a 1 = 0.60 would be 



