GATE-2018 (24) :Wyllie – Time average equation

 

27) The mass and volume of a fully dried soil sample are 2200gm and 1100 cm³ respectively, If the specific gravity of the soil particles is 2.5 and water density is 1 gm/cm³, the void ratio of the soil is____________

 (Thanks to Chandrasekhar, ANU)

Solution:

 Given that the specific gravity ($G_{s}$) = 2.5

Water density ($\rho_{w}$)= 1 gm/cc

Mass of fully dried soil sample = 2200gm

Volume of fully dried soil sample = 1100cm³

 Then the density of the fully dried soil

 $density(\rho_{dried soil})=\frac{mass}{volume}$

$density(\rho_{dried soil})=\frac{2200}{1100}$

$density(\rho_{dried soil})=2 gm/cc$

 

We know that

$\rho_{dried soil}=\frac{G_{s}\rho_{w}}{1+e}$

 Substitute the given values in the above equation we get

$\rho_{dried soil}=\frac{G_{s}\rho_{w}}{1+e}$

$2=\frac{(2.5)(1)}{(1+e)}$

$(1+e)=\frac{(2.5)}{2}$

$1+e=1.25$

$e=1.25-1$

$e=0.25$