DHARM

38 GEOTECHNICAL ENGINEERING

Vs

Vv

Vs

Vv

Vs

Vv Voids

Voids

Voids

Solids Solids Solids

Loosest state

void ratio : emax

Intermediate state

void ratio : e 0

Densest condition

void ratio : emin

Fig. 3.5 Relative states of packing of a coarse-grained soil

The density index may be considered zero if the soil is in its loosest state and unity if it

is in the densest state. Consistent with this idea, the density index may be defined as follows:

ID =

()

()

max

max min

ee

ee

−

−

(^0) ...(Eq. 3.8)
where,
emax = maximum void ratio or void ratio in the loosest state.
emin = minimum void ratio or void ratio in the densest state.
e 0 = void ratio of the soil mass in the natural state or the condition under question.
emax and emin are referred to as the limiting void ratios of the soil.
Sometimes ID is expressed as a percentage also. Equation 3.8 may be recast in terms of
the dry unit weights as follows:
ID = 11 1 1
γγγγmin 0 min max
−
F
HG
I
KJ
−
F
HG
I
KJ
...(Eq. 3.9)

γ
γ
γγ
γγ
max min
0 max min
F 0
HG
I
KJ
−
−
F
HG
I
KJ
...(Eq. 3.10)
These forms are more convenient since the dry unit weights may be determined directly.
However, if it is desired to determine the void ratio in any state, the following relation-
ships may be used:
e =
G w
d
.γ
γ

• 1 ...(Eq. 3.11)

e =

VG

W

w

s

..γ

• 1 ...(Eq. 3.12)

A knowledge of the specific gravity of soil solids in necessary for this purpose. The deter-

mination of the volume of the soil sample may be a source of error in the case of clay soils;

however, this is not so in the case of granular soils, such as sands, for which alone the concept

of density index is applicable.

The maximum unit weight (or minimum void ratio) may be determined in the labora-

tory by compacting the soil in thin layers in a container of known volume and subsequently