Question

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 

Answer 1

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