Question

A soil engineer collects a sample of soil having a moist unit weight of a soil of 20 kN/m³, water content available is 10 % and the specific gravity of the solid is 2.50. what is the degree of saturation of the soil? (Assume unit weight of water = 9.81 kN/m³)

1. 250 %
2. 85 %
3. 74 %
4. 50 %

Answer 1

Correct Answer - Option 3 : 74 %

Concept:

1. Relationship between bulk unit weight, water content, specific gravity, and the void ratio is:

\(\gamma = \frac{{\left( {G \:+\: Se} \right)\:×\:{\gamma _w}}}{{1 + e}}\)

Where,

γ = Bulk unit weight, G = Specific gravity of soil solids 

S = Degree of saturation, e = void ratio, γw = unit weight of water

2. Relationship between the degree of saturation, water content, specific gravity, and the void ratio is:

S × e = w × G

w - Water Content,

Calculation:

Given,

w = 0.10, γ = 24.5 kN/m3

G = 2.5

Since Se = wG, so in place of S × e we can also put w × G

\(\gamma = \frac{{\left( {G \:+\: Se} \right)\:×\:{\gamma _w}}}{{1 + e}}= \frac{{\left( {G \:+\: wG} \right)\:×\:{\gamma _w}}}{{1 + e}}\)

\(20 = \frac{{\left( {2.5 + 0.10 × 2.5} \right) × 9.81}}{{1 + e}}\)

e = 0.34

As,  S × e = w × G

\(S = \frac{{0.1 × 2.5}}{{0.34}} × 100 = 73.5\% \)