The in situ moist unit weight of a soil is 17.3 kN/m3 and the moisture content is 16%. The specific gravity of soil solids is 2.72. This soil is to be excavated and transported to a construction site for use in a compacted fill. If the specification calls for the soil to be compacted to a minimum dry unit weight of 18.1 kN/m3 at the same moisture content of 16%, how many cubic meters of soil from the excavation site are needed to produce 2000 m3 of compacted fill?

Explanation:

Given that,

Moist content w = 16%

The in situ moist unit weight of the soil : γ(in situ) = 17.3 kN/m³

Specific gravity of the soil

G(s) = 2.72

Minimum dry unit weight of the soil

γd(compacted) = 18.1 kN/m³

Moist content is same as above

w = 16%

Question

how many cubic meters of soil from the excavation site are needed to produce 2000 m³ of compacted fill?

Let determine the in situ dry unit weight γd(in-situ) using the relation

γd(in-situ) = γ(in-situ) / [1 + (w/100)]

γd(in-situ) = 17.3/ [1 + (18/100)]

γd(in-situ) = 17.3 / ( 1 + 0.18)

γd(in-situ) = 17.3 / 1.18

γd(in-situ) = 14.66 kN/m³

To determine the Volume of the soil to be excavated (Vex)

Let the Volume to be excavated = V

We can use the relation

V=V(fill) × γd(compacted) / γd(in situ)

Given that, V(fill) = 2000m³

V(fill) is the volume of the compacted fill

Therefore,

V=V(fill) × γd(compacted) / γd(in situ)

Vex = 2000 × 18.1 / 14.66

Vex = 2469.13 m³

So, the excavated volume of the soil is 2469.13 m³

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