Air Flow through Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 457

computed by taking the properties of the pore fluid into
consideration. Bear (1972) called intrinsic permeability the
“medium's permeability” and described it as “an average (or
macroscopic) medium property that measures the ability of
the porous medium to transmit fluid through it.”
Two primary fluid properties that influence the hydraulic
conductivity k are commonly measured in the laboratory
(Fredlund and Rahardjo, 1993a). The fluid properties are
(1) density of the fluid, ρ (kg m − 3 ) , and (2) dynamic vis-
cosity of the fluid, υ (Pasorkgm − 1 s − 1 ). The mathemat-
ical relationship between intrinsic permeability K( m 2 ) and
hydraulic conductivity k( ms − 1 ) can be written as follows:

an exit pressure p 2 where p 1 > p 2 . The test is performed
under isothermal conditions at 20 ◦ C. The air flow rate can
be written in accordance with Darcy's law:

K
υ a

p 1 − p 2

Q a = A (9.25)

L

where:

volumetric flow rate, m 3 s − 1 , Q a =

υ a = dynamic viscosity of air, and

K = intrinsic permeability of the porous medium.

Similarly, the water flow rate (m 3 s − 1 ) can be written

ρg
υ

γ
υ K

k = K = (9.24)

using Darcy's law:

K
υ w

p 1 − p 2

where:

Q w = A (9.26)

L

gravitational acceleration, m s − 2 , g =

where:

density, kg/m 3 , and

ρ =

unit weight of the medium, N m − 3 . γ =

Q w = volumetric flow rate and

υ w = dynamic viscosity of water.

The pore fluid properties can be “scaled” to the properties
of water at standard conditions (Parker et al., 1987). Using
the properties of water at 20 ◦ C a hydraulic conductivity of
10 − 5 m/s measured using water will give an intrinsic per-
meability of approximately 10 − 12 m 2 . The density of water
was taken to be 1000 kg/m 3 and the dynamic viscosity υ
was taken to be 1 cP (where 1 cP

It is possible to compare the flow volumes of air and water
since the intrinsic permeability is a constant. The air volume
flow rate would be 56.4 times more than the water volume
flow rate using dynamic viscosities corresponding to 20 ◦ C:

10 − 3 Pa s

1mPas).
Intrinsic permeability can be used to convert flow prop-
erties used in one discipline (e.g., geotechnical engineering)
to flow properties used in another discipline (e.g., petroleum
and soil science disciplines). The concept of intrinsic per-
meability also has an important role to play in unsaturated
soil mechanics. For example, the measurement of saturated
water coefficient of permeability can be used to calculate
a value for air coefficient of permeability for a dry soil
at the same void ratio. Or vice versa, air flow measure-
ments in the laboratory or field on a dry soil can be used to
compute saturated coefficient of permeability. Saturated soil-
water coefficient-of-permeability measurements can also be
used in conjunction with a SWCC to estimate the air per-
meability function for an unsaturated soil. The properties of
the pore fluid can provide an estimate of the relative ease
with which air and water can flow through a soil.
The viscosity of water and air are dependent upon tem-
perature as mentioned in Chapter 2 (Tuma, 1976). Dynamic
viscosity is presented in centipoises , where 1 cP

= =

Q a
Q w =

υ w
υ a =

1 . 009
0 . 0179 =

56 . 4 (9.27)

The ratio of air coefficient of permeability k a to water coef-
ficient of permeability k w must take into consideration the
relative densities of air and water. The ratio of the air coeffi-
cient of permeability to water coefficient of permeability cor-
responding to 20 ◦ C and standard pressure (i.e., 101.3 kPa) is

k a
k w =

ρ a
υ a

υ w
ρ w =

1 . 196
0 . 0179

1 . 009
998 . 2 =

1
14 . 8

(9.28)

Equation 9.28 shows that the air coefficient of permeabil-
ity is 14.8 times less than the water coefficient of permeabil-
ity. The information from Eqs. 9.27 and 9.28 may at first
seem to be contradictory. Perhaps that is the reason why it
is possible to encounter seemingly contradictory statements
regarding the ease of air and water flow through soils in the
literature.
The ratios of mass flow rates of air and water, dM a / dt
and dM w / dt , respectively, can be written as follows:

=
10 − 3 kg m − 1 s − 1 .At20 ◦ C, the viscosity of water is 1.009 cP
whereas the viscosity of air is only 0.0179 centipoise; a
viscosity ratio of 56.37. The density of water changes with
temperature and typical values were shown in Chapter 2
(McCutcheon et al., 1993).
Let us consider air flow and water flow through a hori-
zontal tube, porous medium with a cross-sectional area A
and length L under an applied entrance pressure p 1 and

dM a / dt
dM w / dt =

ρ a Q a
ρ w Q w =

ρ a υ w
ρ w υ a =

1
14 . 8

(9.29)

A comparison of the air mass flow rate and the water
mass flow rate shows that the mass flow rate of water will
be 14.8 times more than the mass flow rate of air. However,
more air (by volume) will flow through a porous medium