Question

The unit weight of a soil sample is 20 kN/m³ and the water content is 18%. The dry density of the soil sample is:
1. 21.18 kN/m3
2. 16.94 kN/m3
3. 11.12 kN/m3
4. 11.89 kN/m3

Answer 1

Correct Answer - Option 2 : 16.94 kN/m3

Concept:

Bulk Unit weight (γb): 

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

\({γ _b} = \frac{W}{V} = \frac{{{W_s} + {W_w}}}{{{V_s} + {V_w} + {V_a}}}\)

Water Content (w):​

Water content or moisture content of a soil mass is defined as the ratio of the weight of water to the weight of solids (dry weight) of the soil mass.

\({\rm{w = }}\frac{{{{\rm{W}}_{\rm{w}}}}}{{{{\rm{W}}_{\rm{s}}}}};{\rm{w}} \ge 0\)

It is denoted by the w and is commonly expressed as a percentage. The minimum value for water content is 0. There is no upper limit for water content.

Dry Unit Weight (γ­d):-​

Dry unit weight is defined as the weight of soil solids per unit volume of soil. It is denoted by the letter symbol γd it has the unit of kN/m3.

\({{\rm{γ }}_{\rm{d}}}{\rm{ = }}\frac{{{{\rm{W}}_{\rm{s}}}}}{{\rm{V}}}{\rm{ = }}\frac{{{{\rm{W}}_{\rm{d}}}}}{{\rm{V}}}\)

It is used as a measure of the denseness of soil. A high value of dry unit weight indicates that more solids are packed in a unit volume of soil hence a more compact soil.

Specific gravity of solids (G):-​

The specific gravity of solids is defined as the ratio of the unit weight of solids to the unit weight of water. It is denoted by the letter G and is a unitless quantity.

\({\rm{G = }}\frac{{{{\rm{γ }}_{\rm{s}}}}}{{{{\rm{γ }}_{\rm{w}}}}}\)

Explanation:

\({γ_d} = \frac{γ}{{1 + w}} = \frac{{20}}{{1 + 0.18}} = 16.94\; kN/{m^3}\)