Geotechnical Engineering

DHARM

70 GEOTECHNICAL ENGINEERING

Also from Eq. 3.47, if the shrinkage limit is already determined by the first approach,

G =^1

100

γ

γ

w

d

F − ws

HG

I

KJ

...(Eq. 3.53)

ws being in per cent.

Shrinkage Ratio (R)

‘Shrinkage ratio’ (R) is defined as the ratio of the volume change expressed as per cent of the

dry volume to the corresponding change in moisture content from the initial value to the shrink-

age limit:

R =

()VV

V

id

d

−

× 100/(wi – ws) ...(Eq. 3.54)

wi and ws being expressed as percentage.

(wi – ws) =

()VV

W

idw

d

−γ

× 100 from Fig. 3.20 (ii) and (iii).

Substituting in Eq. 3.54,

R =

W

V

G W

V

d

dw

d

w

m

d

γ d

γ

γ

==()dry = ...(Eq. 3.55)

Thus, the shrinkage ratio is also the mass specific gravity of the soil in the dry state.
The test data from shrinkage limit test can be substituted directly either in Eq. 3.54 or
in Eq. 3.55 to obtain the shrinkage ratio.

If the shrinkage limit and shrinkage ratio are obtained, the approximate value of G may
be got as follows:

G =

1

[( / ) 1 Rw− s/ 100 ]

...(Eq. 3.56)

ws being in per cent.

(Note: This relationship is easily derived by recasting Eq. 3.46 and recognising that R = γd/γw).

Volumetric Shrinkage (Vs)

The ‘Volumeter Shrinkage’ (or Volumetric change Vs) is defined as the decrease in the volume

of a soil mass, expressed as a percentage of the dry volume of the soil mass, when the water

content is reduced from an initial value to the shrinkage limit:

Vs =

()VV

V

i d

d

−

× 100 ...(Eq. 3.57)

Obviously, the numerator of Eq. 3.54 is Vs.

∴ R =

V

ww

s

()is−

or Vs = R(wi – ws) ...(Eq. 3.58)

Degree of Shrinkage (Sr)

‘Degree of Shrinkage’ (Sr) is expressed as the ratio of the difference between initial volume and

final volume of the soil sample to its initial volume.