Question

The void ratio of a clay sample is 0.5 and the degree of saturation is 70%. What is the bulk unit weight of the soil ? (Assume G = 2.7)
1. 10.46 kN/m³
2. 14.32 kN/m3
3. 17.77 kN/m3
4. 19.95 kN/m3

Answer 1

Correct Answer - Option 4 : 19.95 kN/m3

Concept:

The dry unit weight of soil, γd is given by

\({γ _d} = \;\frac{{G{γ _w}}}{{1 + e}}\)

bulk unit weight of soil, γb

\({γ _b} = \;\frac{{\left( {G\; + \;Se} \right)\;{γ _w}}}{{1\; + \;e}}\)

The relationship between the degree of saturation, water content, specific gravity, and the void ratio is:

s × e = w × G

Calculation:

Given,

G = 2.7, Degree of Saturation (S) = 70% = 0.7

Void ratio (e) = 0.5

We know, S × e = w × G

→ 0.7 × 0.5 = w × 2.7

→ w = 0.129

\(γ_b = \frac{{\left( {G + eS} \right){γ _w}}}{{1 + e}}\)

\(γ_b = \frac{{\left( {2.7 + 0.5 \times 0.7} \right)× {9.81}}}{{1 + 0.5}}\)

γ_b = 19.947 kN/m³