The total volume of the soil sample is 50 ml. Find the void ratio if the volume of solids is 30 ml. 

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DDA JE Civil 29 Mar 2023 Shift 3 Official Paper
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  1. 86.67%
  2. 56.67%
  3. 76.67%
  4. 66.67%

Answer (Detailed Solution Below)

Option 4 : 66.67%
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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 = 50 ml

Volume of water displaced = volume of solids

VS = 30 ml

Volume of voids, VV = V – VS = 50 – 30 = 20 ml

\(\therefore {\rm{e}} = {\rm{\;}}\frac{{{{\rm{v}}_{\rm{v}}}}}{{{{\rm{V}}_{\rm{s}}}}} = {\rm{\;\;}}\frac{{20}}{{30}} = 0.667\) = 66.67 %

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