Geotechnical Engineering

DHARM

86 GEOTECHNICAL ENGINEERING

∴ 17.33 =

272 10

1

.

()

×

+e

∴ e ≈ 0.57

∴ Void-ratio = 0.57

Shrinkage limit, ws = e/G = 0.57/2.72 = 21%

The conditions at shrinkage limit and final wet state are shown in Fig. 3.25:

Water

Solids

Vs W=Wsd

0.21 Wd

Vm

Water

Solids

Vs W=Wsd

Vw

(a) At shrinkage limit (b) Final wet state

Fig. 3.25 Phase-diagrams of soil (Example 3.21)

Vs =

W

G

d =^390

0 0272

.

.

= 143.38 cm^3

Volume in the final wet state, V = (225 + 0.08 × 225) = 243 cm^3

Volume of water in the final wet state, Vw = (243 – 143.38) cm^3 = 99.62 cm^3

Weight of water in the final wet state = 0.9962 N

Water content in the final wet state =

0 9962

390

.

.

= 25.5%.

Example 3.22: The plastic limit and liquid limit of a soil are 33% and 45% respectively. The
percentage volume change from the liquid limit to the dry state is 36% of the dry volume.
Similarly, the percentage volume change from the plastic limit to the dry state is 24% of the
dry volume. Determine the shrinkage limit and shrinkage ratio.

The data are incorporated in Fig. 3.26 for making things clear:

Say, Vd is the dry volume.

PB = 0.24 Vd

LC = 0.36 Vd

LD = 0.12 Vd

PD = 12%

From the triangles LPD and LSC, which are similar,

PD/SC = LD/LC

12 012

SC 036

=.

.

V

V

d

d

= 1/3

∴ SC = 36%

∴ Shrinkage limit, ws = wL – (SC) = (45 – 36) = 9%