Geotechnical Engineering

DHARM

INDEX PROPERTIES AND CLASSIFICATION TESTS 85

∴ ws =

γw

170 wG

1 100 1

170

1

271

100

...

−

F

HG

I

KJ

=−F

HG

I

KJ

= 21.9%

∴ Shrinkage limit of the clay = 21.9%.

Example 3.20: A saturated soil sample has a volume of 23 cm^3 at liquid limit. The shrinkage

limit and liquid limit are 18% and 45%, respectively. The specific gravity of solids is 2.73.

Determine the minimum volume which can be attained by the soil.

The minimum volume which can be attained by the soil occurs at the shrinkage limit.

The phase diagrams of the soil at shrinkage limit and at liquid limit are shown in Fig. 3.24:

Water

V = 23 cmL^3

Solids

0.45 Wi

Water

Solids

Vs W=Wsd

0.18 Ws

W=Wsd

Vm

Vs

(a) At liquid limit (b) At shrinkage limit

Fig. 3.24 Phase diagrams (Example 3.20)

At liquid limit,

Volume of water = 45 Ws cm^3 , if Ws is the weight of solids in N.

Volume of solids =

W

G

s W

w

s

γ

=

×

− =

981 10

1000

.^3981.^ Ws cm

3

Total volume =

1000

981.

Ws + 45 Ws = 23

whence Ws = 0.2818 N

At shrinkage limit,

the volume, Vm = Vs + 0.18 Ws

=

0 2818

0 0273

18 0 2818

.

.

FHG +×. IKJ cm 3

= 15.4 cm^3.

Example 3.21: An oven-dry soil sample of volume 225 cm^3 weighs 3.90 N. If the grain specific

gravity is 2.72, determine the void-ratio and shrinkage limit. What will be the water content

which will fully saturate the sample and also cause an increase in volume equal to 8% of the

original dry volume?

Dry unit weight of the oven-dry sample =

39

225

.

N/cm^3 = 17.33 kN/m^3

But γd =

G

e

. w
()

γ

1 +