Question

The value of porosity of a soil sample in which the total volume of soil grains is equal to twice the total volume of voids would be
1. 30%
2. 40%
3. 50%
4. 60%

Answer 1

Correct Answer - Option 3 : 50%

Concept:

Porosity:

Porosity of a soil sample is defined by the ratio of the volume of voids to the total volume of the soil. In simpler words, porosity expresses the percentage voids of total volume of a certain soil sample.

\({\rm{Porosity}},{\rm{\;n}} = {\rm{\;}}\frac{{{{\rm{V}}_{{\rm{voids}}}}}}{{{{\rm{V}}_{{\rm{total}}}}}} = \frac{{{{\rm{V}}_{{\rm{voids}}}}}}{{{{\rm{V}}_{{\rm{voids}}}}{\rm{\;}} + {\rm{\;}}{{\rm{V}}_{{\rm{solids}}}}}}\)

Where,

V_voids is the volume of the voids.

V _total is the total volume of soil sample which is the sum of volume of voids and volume solid soil grains V_solids .

Calculation:

Given,

Total Volume of soil Grain = V

Total Volume V = 2 × Volume of Voids (V_v)

\({\rm{Porosity}},{\rm{\;n}} = {\rm{\;}}\frac{{{{\rm{V}}_{{\rm{voids}}}}}}{{{{\rm{V}}_{{\rm{total}}}}}}\) = V_v/2V_v

∴ Porosity (η) = 1/2 = 50% 

Void ratio (e):

 \({\rm{e = }}\frac{{{{\rm{V}}_{\rm{v}}}}}{{{{\rm{V}}_{\rm{s}}}}}{\rm{;e}} > 0\)

Void ratio is defined as the ratio of the volume of voids to the volume of solids.

There is no upper limit of the void ratio in soil suspension.

The void ratio of fine-grained soil is generally higher than that of coarse-grained soil.