Geotechnical Engineering

DHARM

INDEX PROPERTIES AND CLASSIFICATION TESTS 49

Assuming G = 2.67, on an average,

v =

1

180

×()( )9.792 2.67−^1

0.001

. D^2 = 90.85D^2
∴ v ~− 91 D^2 ...(Eq. 3.20)

where D is in mm and v is in cm/sec.

Using the approximate version of Stoke’s law, one can determine the time required for
a particle of a specified diameter to settle through a particular depth; e.g., a particle of 0.06
mm diameter settles through 10 cm in about 1/2 minute, while one of 0.002 mm diameter
settles in about 7 hours 38 minutes.

From Eq. 3.19,

v =

1

180

.γ

μ

w

w

(G – 1). D^2

∴ D =^180

1

..

()

μ

γ

w

w

v

G−

If the particle falls through H cm in t minutes

v = H/60t cm/sec.

∴ D =

180

160

μ

γ

w

w

H

Gt

.

().−

=

3

1

μ

γ

w

wG

H

()− t

×

∴ D = K Ht/ ...(Eq. 3.21)

where K =

3

1

μ

γ

w

w()G−

...(Eq. 3.22)

Here,

G = grain specific gravity of the soil particles,

γw = unit weight of water in kN/m^3 at the particular

μw = viscosity of water in N-sec/m^2 temperature.

H = fall in cm, and t = time in min.

The factor K can be tabulated or gaphically represented for different values of tempera-

ture and grain specific gravity.

Stokes’ Law is considered valid for particle diameters ranging from 0.2 to 0.0002 mm.

For particle sizes greater than 0.2 mm, turbulent motion is set up and for particle sizes

smaller than 0.002 mm, Brownian motion is set up. In both these cases Stokes’ law is not valid.

The general procedure for sedimentation analysis, which may be performed either with

the aid of a pipette or a hydrometer is as follows:

An appropriate quantity of an oven-dried soil sample, finer than 75–μ size, is mixed

with a known volume (V) of distilled water in jar. The sample is pretreated with an oxidising

agent and an acid to remove organic matter and calcium compounds. Addition of hydrogen

peroxide an heating would remove organic matter. Treatment with 0.2 N hydrochloric acid