Geotechnical Engineering

DHARM

20 GEOTECHNICAL ENGINEERING

=

()

()

Ge

e

+

1 +

.γw – γw

= γw

Ge

e

()

()

+

+

−

L

N

M

O

Q

1 1 P

∴ γ′ =

()

()

.

G

e w

−

+

1

1

γ ...(Eq. 2.30)

γd = W

V

s

But, w =

W

W

w

s

, as a fraction

(1 + w) =

()WW

W

ws

s

+

= W/Ws

whence Ws^ = W/(1 + w)

∴ γd =^

W

Vw()()11+ w

=

+

γ

(w as a fraction) ...(Eq. 2.31)

Gm =

γ

γw

GSe

e

=

+

+

(.)

()1 ...(Eq. 2.32)

Solving for e, e =

()

()

GG

GS

m

m

−

−

...(Eq. 2.33)

2.3.3 Unit-phase Diagram

The soil-phase diagram may also be shown with the volume of solids as unity ; in such a case,
it is referred to as the ‘Unit-phase Diagram’ (Fig. 2.5).

It is interesting to note that all the interrelationships of the various quantities enumer-
ated and derived earlier may conveniently be obtained by using the unit-phase diagram also.

Water

Solids

e

ae

S.e

1

Zero

S.e.gw

1.G.gw

Air

Volume Weight

Fig. 2.5 Unit-phase diagram

For example; Porosity,

n = volume of voids

total volume

= e/(1 + e)