soil is excavated from a borrow to construct an embankment with a net volume of 50,000 cy. this is performed by compacting 12-in layers of the soil to a dry weight of 110 pcf at a moisture content of 18%. the unit weight of soil in the borrow is 120 pcf with a water content ratio of 15.4%. what is the volume of the required soil excavated in the borrow pit?

52,891.735 cy

Explanation:

Data provided in the question:

Net volume of the soil excavated = 50,000 cy = 50,000 × 27 ft³

Dry weight of the soil = 110 pcf

Moisture content = 18%

Unit weight of soil at borrow site, γ = 120 pcf

Water content ratio, w = 15.4% = 0.154

Thus,

Weight of sold required = Dry weight × Net volume of the soil excavated

= 110 × 50,000 × 27

= 148,500 kips

Dry density of soil at borrow site =

=

= 103.986 pcf

Therefore,

The volume of soil required = weight ÷ Density

=  [ 148,500 × 10³ ] ÷ 103.986

= 1428076.857 cft

or

=  1428076.857 ÷ 27 cy

= 52,891.735 cy