Geotechnical Engineering

DHARM

40 GEOTECHNICAL ENGINEERING

Assuming that the sand is in the densest state:

emin =

V

V

v

s

min

max

,

for which the corresponding value of density index is taken as unity.

It can be understood that the density index is a function of the void ratio:

ID = f(e) ...(Eq. 3.13)

This relation between e and ID may be expressed graphically as follows.

1

ID

O

Density index,

ID

emin e 0 emax

q

This fact that the

relationship is

linear may be

guessed easily

Void ratio, e

Fig. 3.6 Void ratio-density index relationship

It may be seen that:

tan θ =

1

()eemax− min

∴ cot θ = (emax – emin) ...(Eq. 3.14)

For any intermediate value e 0 ,

(emax – e 0 ) = ID. cot θ ...(Eq. 3.15)

∴ ID =

()

cot

eemax− 0

θ

Substituting for cot θ from Eq. 3.14

ID =

()

()

max

max min

ee

ee

−

−

(^0) ...(Eq. 3.8)
Obviously, if e 0 = emax, ID = 0,
and if e 0 = emin, ID = 1.
For vary dense gravelly sand ID sometimes comes out to be greater than unity. This
would only indicate that the natural packing does not permit itself to be repeated or simulated
in the laboratory.
Representative values of density index and typical range of unit weights are given in
Table 3.2.