A soil sample is taken from a borrow pit in Bellingham, Washington and has a natural void ratio of 1.27. The soil will be used for a highway project wherein a total of 150,000 m^3 of soil is needed in its compacted state. Its compacted void ratio will be 0.49. How much volume must be excavated from the borrow pit to meet the project requirements?

the volume of soil that must be excavated from the borrow pit to meet the project requirements is 228,523.48 m³

Explanation:

First we determine the volume of solid required for compacted state using the relation;

V_t = V_v + V_s

V_t is the total volume need in its compacted state( 150,000 m³)

V_s is the volume of solid required for compacted state

V_v is the volume of voids in the compacted state( 0.49V_s)

so we substitute

150,000 = 0.49V_s + V_s

150,000 = 1.49V_s

V_s = 100,671.14 m³

Now we determine the volume of voids ( V_v)  for natural material using the expression;

e = V_v / V_ s

given that e = 1.27

we substitute

1.27 = V_v /  100671.14

V_v = 127,852.34 m³

Now the total volume to be excavated from the barrow pit in Bellingham will be determined using the relation;

V_t = V_v + V_s

we substitute our values

V_t = 127,852.34 m³ + 100671.14 m³

V_t = 228,523.48 m³

Therefore, the volume of soil that must be excavated from the borrow pit to meet the project requirements is 228,523.48 m³