A sampler with a volume of 50 cm³ is filled with a soil sample. When soil is poured into a graduated cylinder, if displaces 30 cm³ of water, n porosity and void ratio of soil respectively are

Concept:

Void ratio (e): This is defined as the ratio of the volume of voids (V_v) in the sample to the volume of soil solids (V_s). 

$e=\frac{V_v}{V_s}$

Porosity (n): This is defined as the ratio of the volume of voids (V_v) in the sample to the total volume of the soil (V), expressed in percentage.

$n=\frac{V_v}{V}$

$n\mathrm{\%}=\frac{V_v}{V}\times 100$

Calculation:

Given

Total volume of soil sample (V) = 50 cm³

The soil sample displaces 30 cm³ of water which means the volume of soil solids is 30 cm³.

Volume of soil solids (V_s) = 30 cm³

Volume of voids (V_v) = 50 - 30 = 20 cm³

Porosity (n) = $\frac{V_v}{V}=\frac{20}{50}=0.4$

$Voidratio(e)=\frac{V_v}{V_s}=\frac{20}{30}=0.666$

Void ratio (e) = 0.666 ≈ 0.67

Hence option (3) is correct.