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

18) In a soil sample, specific gravity of soil particles is 2.5 and the void ratio is 0.5. the density of the soil sample when it is fully saturated with water is _____kg/m³ (Assume that the density of the water is 1000 kg/m^3,   and no volume change of the soil sample with saturation)

(Thanks to Chandrasekhar, ANU)

 

Solution:

  Given that the  specific density = $\frac{(G_{s}+e)\rho_{w}}{1+e}$

 Specific gravity  $ G_{s}$= 2.5

Void ratio (e) = 0.5

Density of the water= 1000 kg/m³

  specific density = $\frac{(G_{s}+e)\rho_{w}}{1+e}$

     = $\frac{(G_{s}+e)\rho_{w}}{1+e}$

    = $\frac{(2.5+0.5)1000}{1+0.5}$

   = $\frac{3000}{1.5}$

   = 2000 kg/m³