Soil at a borrow area has a total unit weight of 120-PCF and a water content of 15 percent.  The soil from the borrow area will be used as structural fill and compacted to an average dry unit weight of 110-PCF.  The soil shrinkage is most nearly: 

Solution:  

At the borrow area, the dry unit weight is determined from the equation:

Dry unit weight =    Total Unit Weight / (1 + water content)

 Dry Unit Weight = 120 / (1 + 0.15) = 104-PCF  

The shrinkage factor is the ratio of the volume of compacted material to the volume of borrows material (based on dry unit weight), or:  

Shrinkage factor = 104-PCF / 110-PCF = 0.945  

Convert the shrinkage factor to a percentage:  

Percent shrinkage = (110 - 104) / 110 = 0.055 = 5.5%