The void ratios at the densest, loosest, and natural states of a sand deposit are 0.2, 0.6, and 0.4, respectively. The relative density of the deposit is:

Concept:

Relative density: 

• Relative density is the measure of the compactness of cohesion-less soil.

• Relative density represents whether the soil is closest to its densest state or loosest state.

• It is defined as the ratio of the difference between the voids ratio of the soil in its loosest state and its natural state to the difference between the voids ratio in the loosest and densest state.

\({I_D} = \frac{{{e_{max}} - {e_{natural}}}}{{{e_{max}} - {e_{min}}}}\)

The relationship between the Relative Density and Void ratio of the soil sample is depicted in the graph below:

∴ Relative density varies inversely to the void ratio.

Classification of soil as per relative density as follows:

Calculation:

emax = 0.6, emin = 0.2, and natural void ratio (e) = 0.4

\({{\rm{I}}_{\rm{d}}} = \frac{{0.6 - 0.4}}{{0.6 - 0.2}} = \frac{{0.2}}{{0.4}} = 0.5\)

Expressing it in percentage = 0.5 × 100 = 50%