Geotechnical Engineering

DHARM

440 GEOTECHNICAL ENGINEERING

(b) Bulk density, γ =

18 5 100

1000 1000

.( )×^3

×

= 18.5 kN/m^3

(c) Dry density, γd =

γ

()(.)1

1850

+ 1 01058

=

w +

= 16.73 kN/m^3

γd =

G

e

γw

()1+

Assuming a value of 2.65 for grain specific gravity,

16.73 =

265 10

1

.

()

× ,

+e since γw^ ≈ 10 kN/m

3

(1 + e) =

265 10

16 73

.

.

×

= 1.584

(d) Void ratio, e = 0.584

Also, wG = S.e

S =

wG

e

=01058 2 65×

0 584

..

.

= 0.48

(e) Degree of saturation, S = 48%

If air is fully expelled, the solid is fully saturated at that water content.

∴ wG = e = 2.65 × 0.1058 = 0.28

New dry density =

265 10

1028

.

(.)

×

+

= 20.7 kN/m^3

New volume =

(.)

(.)

1028

1 0 584

1000

+

+

× = 808 cm^3

Example 12.3: The soil in a borrow pit has a void ratio of 0.90. A fill-in-place volume of 20,000
m^3 is to be constructed with an in-place dry density of 18.84 kN/m^3. If the owner of borrow area
is to be compensated at Rs. 1.50 per cubic metre of excavation, determine the cost of compen-
sation. (S.V.U.—B.E., (R.R.)—Nov., 1975)
In-place dry density = 18.84 kN/m^3
Assuming grain specific gravity as 2.70 and taking γw as 9.81 kN/m^3 ,

18.84 =

270 981

1

..

()

×

+ei

(1 + ei) =

270 981

18 84

..

.

×

= 1.406

ei = 0.406 (in-plane Void ratio)

Void-ratio of the soil in the borrow-pit,

eb = 0.90

In-place volume of the fill, Vi = 20,000 m^3