Geotechnical Engineering

DHARM

INDEX PROPERTIES AND CLASSIFICATION TESTS 79

Dry unit weight, γd =

γ

(1 + )w 0.0573

=

+

23.34

() 1 kN/m

3

= 22.075 kN/m^3

Grain specific gravity, G = 2.72

γd =

G

e

. w
()

γ

1 + or 22.075 =

2.72 9.81

(1 + )

×

e

whence, the void-ratio, e ≈ 0.21

Degree of saturation, S = wG/e =

0.0573 2.72

0.21

×

= 74.2%.

Example 3.10: A soil sample consists of particles ranging in size from 0.6 mm to 0.02 mm. The
average specific gravity of the particles is 2.66. Determine the time of settlement of the coars-
est and finest of these particles through a depth of 1 metre. Assume the viscosity of water as
0.001 N-sec/m^2 and the unit weight as 9.8 kN/m^3.

By Stokes’ law (Eq. 3.19),

v = (1/180). (γw/μw) (G – 1)D^2

where v = terminal velocity in cm/sec,

γw = unit weight of water in kN/m^3 ,

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

G = grain specific gravity, and

D = size of particle in mm.

∴ v =

1

180

×9.80

0.001

(2.66 – 1)D^2 ≈ 90 D^2

For the coarsest particle, D = 0.6 mm

v = 90 × (0.6)^2 cm/sec. = 32.4 cm/sec.

t = h/v = 100.0/32.4 sec. = 3.086 sec.

For the finest particle, D = 0.02 mm.

v = 90(0.02)^2 cm/sec. = 0.036 cm/sec.

t = h/v = 100.000

0.036

sec. = 2777.78 sec. = 46 min. 17.78 sec.

This time of settlement of the coarsest and finest particles through one metre are nearly

4 sec. and 46 min. 18 sec. respectively.

Example 3.11: In a pipette analysis, 0.5 N of dry soil (fine fraction) of specific gravity 2.72 were

mixed in water to form half a litre of uniform suspension. A pipette of 10 ml capacity was used

to obtain a sample from a depth of 10 cm after 10 minutes from the start of sedimenation. The

weight of solids in the pipette sample was 0.0032 N. Assuming the unit weight of water and

viscosity of water at the temperature of the test as 9.8 kN/m^3 and 0.001 N-sec/m^2 respectively,

determine the largest size of the particles remaining at the sampling depth and percentage of

particles finer than this size in the fine soil fraction taken. If the percentage of fine fraction in