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