Geotechnical Engineering

DHARM

INDEX PROPERTIES AND CLASSIFICATION TESTS 53

Weight of water per unit volume of suspension = γw 1 −

F

HG

I

KJ

W

VG..γw

= γw – W

VG.

Initial weight of a unit volume of suspension = W

V

W

w VG

+−F

HG

I

KJ

γ

Initial unit weight, γi = γw +

()G.

G

W

V

− 1
...(Eq. 3.29)
Let us consider a level XX, at a depth z from the surface and let t be the elapsed time
from the start (Fig. 3.11).
Size D of the particles which have fallen from the surface through the depth z in time t
may be got from Eqs. 3.21 and 3.22, by substituting z from H. Above the level XX, no particle of
size greater than D will be present. In an elemental depth dz at this depth z, the suspension
may be considered uniform, since, initially it was uniform, and all particles of the same size
have settled through the same depth in the given time. In this element, particles of the size
smaller than D exist. Let the percentage of weight of these particles to the original weight of
the soil particles in the suspension by N.
Wt of solids per unit volume of the suspension at depth z = (N/100). (W/V)
By similar reasoning as for Eq. 3.29, the unit weight of the suspension, γs, at depth z and
at time t, is given by:

γz = γw +

()G ..

G

NW

V

− 1

100

...(Eq. 3.30)

∴ N =

100

1

G

()G−. (γz – γw).

V

W

...(Eq. 3.31)

Hence, if γz is obtained by a hydrometer, N can be got, thus getting a point on the grain-

size distribution curve.

In pipette analysis, the sampling depth is kept fixed; however, in the hydrometer analy-

sis, the sampling depth (known as the effective depth) goes on increasing with time since the

particles are allowed to settle. It is, therefore, necessary to calibrate the hydrometer with

respect to the sedimenation jar, with a view to determining the value of the effective depth for

any particular reading of the hydrometer. If the same hydrometer and the same sedimentation

jar are used for a number of tests, one calibration chart will serve the purpose for all the tests.

z

X

X

x

dz

Soil

suspension

Fig. 3.11 Suspension jar