Geotechnical Engineering

DHARM

18 GEOTECHNICAL ENGINEERING

A number of useful relationships may be derived based on the foregoing definitions and
the soil-phase diagram.

2.3.1 Relationships Involving Porosity, Void Ratio, Degree of Saturation,

Water Content, Percent Air Voids and Air Content

n = V

V

v, as a fraction

=

VV

V

V

V

W

GV

ss s

w

− =− =− 11

γ

∴ n =^1 −

W

GV

d

γw

...(Eq. 2.17)

This may provide a practical approach to the determination of n.

e =

V

V

v

s

=

()VV

V

V

V

VG

W

s

ss

w

s

−

=−= 11 −

γ

∴ e =

VG

W

w

d

..γ − 1

...(Eq. 2.18)

This may provide a practical approach to the determination of e.

n = V

V

v e = V

V

v

s

1/n = V/Vv =

VV

V

V

V

V

V

e e

e

sv

v

s

v

v

v

+ =+=+= 11 / () 1 +

∴ n =

e

()1+e

...(Eq. 2.19)

e = n/(1 – n), by algebraic manipulation ...(Eq. 2.20)
These interrelationships between n and e facilitate computation of one if the other is
known.

Q^ ac =

V

V

a

v

and n =

V

V

v

∴ nac =

V

V

a = n

a

or na = n.ac ...(Eq. 2.20)

By definition,

w = Ww/Ws, as fraction ; S = Vw/Vv, as fraction ; e = Vv/Vs

S.e = Vw/Vs

w = Ww/Ws =

V

V

V

VG

ws

ss

ws

sw

.

.

.

..

γ

γ

γ

γ

= = Vw/VsG = S.e/G

∴ w.G = S.e ...(Eq. 2.21)
(Note. This is valid even if both w and S are expressed as percentages). For saturated condition,
S = 1.