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Soil Mechanics and Foundation Engineering - Engineering

Q1:

A soil mass coated with a thin layer of paraffin weighs 460 g. When immersed, it displaces 299 cc of water. The weight of paraffin is 10 g. If specific gravity of solids is 2.5 and that of paraffin 0.9, the void ratio of soil, is

A 0.55

B 0.60

C 0.65

D 0.70

ANS:B - 0.60

Dry unit weight=(G*Unit weight of water)/(1+e),
(460+10)/(299)=(2.5*1)/(1*e),
e = .5923~ 0.6,
e = 60.

So, the correct option is "B" In that question, you should go for bulk density.

Then find dry density using bulk and dry density relationship then go for void ratio using a dry density.Specific gravity = Weight/(Volume*Density of water).
Volume of Paraffin = Weight/Sp. Gravity => 10/(0.9*1) = 11.11 cc.
Now, volume of soil = (Wt of soil with paraffin coating - Wt. of paraffin)/(Sp. Gravity of soil*Density of water).
Therefore, volume of soil (Vs) = (460-10)/(2.5*1) = 180 cc.
Volume of soil when immersed in water (V) = 299 - 11.11 = 287.89 cc.
V = Vv+Vs => Vv = V-Vs => Vv = 287.89 - 180 = 107.89 cc.
Hence, Void ratio (e) = Vv/Vs = 107.89/180 => e = 0.6. Parffin volume = 10/(0.9*1.0) = 11.11 cc (1.0 - density of water).
Vol.of Soil = (460-10) /(2.5*1.0) = 180 cc.
Vol.of Soil = 299 -11.11 = 287.89 cc.
Vol.of Voids = 287.89 - 180 = 107.89 cc.
Void Ratio = Vol.Voids / Vol os Soilds = 107.89/180 = 0.60.