Question

The volume of a soil sampler is 45 cm³. When the soil collected by it is poured into a graduated jar, the volume of water displaced by it is 20 cm³. The void ratio and porosity of the soil will be
1. 0.555 and 1.25
2. 1.25 and 0.555
3. 0.692 and 2.25
4. 2.25 and 0.692

Answer 1

Correct Answer - Option 2 : 1.25 and 0.555

Concept:

Void ratio (e):

Void ratio is usually defined as the ratio of the volume of voids to the total volume of soil solid.

Porosity (n):

Porosity is defined as the ratio of the volume of voids to the total volume of the soil.

The relationship between void ratio and porosity are as follows:

\(\rm{e=\frac{n}{1-n}\; and\; n=\frac{e}{1+e}}\)

Calculation:

Given, V = 45 cm³

Volume of water displaced = volume of solids

VS = 20 cm3

Volume of voids, VV = V – VS = 45 – 20 = 25 cm3

\(\therefore {\rm{e}} = {\rm{\;}}\frac{{{{\rm{v}}_{\rm{v}}}}}{{{{\rm{V}}_{\rm{s}}}}} = {\rm{\;\;}}\frac{{25}}{{20}} = 1.25\)

Relationship between Void ratio and Porosity:

\(n=\frac{e}{1+e}\)

\(n=\frac{1.25}{1+1.25}\) = 0.555