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Soil Mechanics and Foundation Engineering - Engineering

Q1:

A moist soil sample weighing 108 g has a volume of 60 cc. If water content is 25% and value of G = 2.52, the void ratio is

A 0.55

B 0.65

C 0.75

D 0.80

ANS:C - 0.75

G = 2.52.
w = .25.
W = 108g.
V = 60cc.
Y = W/V = 108/60 = 1.8.
Yd = Y/(1+w) = 1.8/(1+0.25) = 1.44.
Yd = GYw/(1+e).
=> 1.44 = (2.52*1)/(1+e),
=>1+e = 1.75,
=>e = 0.75. M=108g,
V=60cc,
W=0.25,
G=2.52,

Y = M/V*9.81.
= 1.8*9.81 = 17.67.

Yd = Y/1+w = 17.66/ 1+0.25 =14.13,
e=2.52*9.81/14.13-1 =0.75. W=108g , v= 60cc, w = 25% G= 2.52.
Yd = GYw/(1+e).
Yd = Y/(1+w).

Y = w/v = 108/60= 1.8g/cc.
Yd = 1.8/(1+0.25).
= 1.44g/cc.

Yd = GYw/(1+e).
1.44 = 2.52*1/(1+e).
1+e = 2.52/1.44.
1+e = 1.75.
e=0.75. Ybulk = (G + se)Yw/1+e.
Se = wG.
Ybulk = (G+wG)Yw/1+e.
Ybulk = 108/60=1.8.
1.8 = (2.52+(.25*2.52))/1+e.
e = .75. First find,
W/g= 108/60 =1.8g/cc.

Dry density (yd)= bulk density ÷(1+w) = 1.8÷(1+.25)= 1.44g/cc.

Then to find void ratio..
Yd = {(G*Yw)/(1+e)} = { 1.44=(2.52*1)÷(1+e) }
1+e =1.75= 0.75 Ans.