Correct Answer - Option 3 : 0.5
Concept:
From a fundamental relationship, the density of soil is given by:
\({{\rm{\gamma }}_{{\rm{bulk}}}} = \frac{{\left( {{\rm{G}} + S × e} \right) × {\gamma _w}}}{{1 + e}} = \frac{{\left( {{\rm{G}} + w × G} \right) × {\gamma _w}}}{{1 + e}} = \frac{{\left( {1 + {\rm{w}}} \right) × G × {\gamma _w}}}{{1 + e}}\)
Where
\(\gamma\) = Density of soil, \(\gamma_w\) = Density of water, G = Specific gravity of soil, S = Degree of saturation, w = Water content, and e = void ratio
For the dry density of soil: Degree of saturation (S) = 0
The dry density of soil(\(\gamma_d\)) is given by
\({{\rm{\gamma }}_{\rm{d}}} = \frac{{\left( {\rm{G}} \right) × {\gamma _w}}}{{1 + e}}\)
Calculation:
Given data
The specific gravity of solids = 3
The mass-specific gravity = 2
The dry density of soil(\(\gamma_d\)) is given by
\({{\rm{\gamma }}_{\rm{d}}} = \frac{{\left( {\rm{G}} \right) × {\gamma _w}}}{{1 + e}}\)
\({\gamma_d \over \gamma_w} = {G \over 1+e}\)
\(G_m = {G \over 1+e}\)
Where Gm = Mass specific gravity
\(2 = \frac{{\left( {\rm{3}} \right)}}{{1 + e}}\)
\({{1 + e}} = 1.5\)
e = 0.5
The void ratio is 0.5.
