Question

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?

Answer 1

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

Step-by-step 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