# A soil has a bulk density of 20 kN/m3 and water content of 25%. The dry density of the soil would be:

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A soil has a bulk density of 20 kN/m3 and water content of 25%. The dry density of the soil would be:
1. 26.7 kN/m3
2. 18.0 kN/m3
3. 16.0 kN/m3
4. 15.0 kN/m3

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Correct Answer - Option 3 : 16.0 kN/m3

Concept

Bulk unit weight of soil (γ):

It is defined as the ratio of the total weight of soil to the total volume of soil mass

${{\rm{γ }}} = \frac{{\rm{W}}}{{\rm{V}}}$

Dry unit weight of soil (γd):

It is defined as the ratio of the total dry weight of soil to the total volume of soil mass

${{\rm{γ }}_{\rm{d}}} = \frac{{\rm{W_S}}}{{\rm{V}}}$

Water content (W):

Water content also called as moisture content is defined as the ratio of weight of water to the weight of soil solids in the soil mass

${\rm{W}} = \frac{{{{\rm{W}}_{\rm{w}}}}}{{{{\rm{W}}_{\rm{s}}}}} × 100$${\rm{W}} = \frac{{{{\rm{W}}_{\rm{w}}}}}{{{{\rm{W}}_{\rm{s}}}}} × 100$

For dy soils, W = 0

For moist soils it is around, W = 60 %

For a Saturated soils, W > 0

The relation between γ, γd, and W is

${{\rm{γ }}_{\rm{d}}} = \frac{{\rm{γ }}}{{1 + {\rm{W}}}}$

Calculation:

Given,

γ = 20 kN/m3

W = 25 % = 0.25

${{\rm{γ }}_{\rm{d}}} = \frac{{\rm{γ }}}{{1 + {\rm{W}}}}$

${{\rm{γ }}_{\rm{d}}} = \frac{{\rm{20 }}}{{1 + {\rm{0.25}}}}$

γd = 16 kN/m3