Air Flow through Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 454

saturation) to establish an air permeability functional rela-
tionship k a (u a −

u w ) or k a (S) . The air permeability func-
tion also applies to the air coefficient of transmission D a
since the two coefficients are related by the gravitational
constant, g .
Experimental verifications have been performed for Fick's
law and Darcy's law and some results are presented in
Fig. 9.3 (Blight, 1971). A series of permeability tests were
performed by establishing steady-state air flows through dry
soils. The soils were assumed to have a rigid structure with
no measurable volume change during the tests. The air flow
measurements were referenced to the air-filled pore space
(Blight, 1971). The mass rate of air flow must be multiplied
by the air porosity, n a , as shown in Fig. 9.3a, when using
the bulk soil as the reference state.
The applicability of Fick's law to air flow is demonstrated
in Fig. 9.3b. The mass flow rate J a is almost linearly pro-
portional to the pore-air pressure gradient (∂u a /∂y) , with
D a being the coefficient of proportionality corresponding to
a small change in the pore-air pressure gradient. It should be
noted that the air pressure gradients used in the above exper-
iment were relatively high. The magnitudes of D a and k a
vary with the volume-mass properties of an unsaturated soil.

9.3.1 Coefficient of Permeability with Respect
to Air Flow
Several relationships have been proposed between the air
coefficient of permeability and the volume-mass properties
of a soil. The coefficient of transmission D a can either be
computed in accordance with Eq. 9.18 or measured directly
in experiments. The coefficient of permeability for the air
phase, k a , is a function of the fluid (i.e., air) and soil volume-
mass properties. The fluid properties are generally consid-
ered to be constant during the flow process. Therefore, the
air coefficient of permeability can be expressed as a function
of the volume-mass properties of the soil. The volumetric
percentage of air in the pores largely controls the flow rate
of air through a soil. The air coefficient of permeability
increases as soil suction increases (or the degree of satu-
ration decreases), giving rise to the terminology of an air
permeability function.

9.3.2 Relationship between Air Coefficient
of Permeability and Degree of Saturation
The air coefficient of permeability of an unsaturated soil is
strongly influenced by the degree of saturation of the soil.
The air coefficient of permeability approaches its maximum
value when the water degree of saturation is low. The air
coefficient of permeability decreases as the water degree of
saturation increases until the suction reaches the air-entry
value of the soil. The air-entry value is the point where air
starts to enter the largest pores of the soil. Air flow takes
the form of air diffusion through the soil-water when soil
suction is below the air-entry value of the soil. At this point,
the air coefficient of permeability is extremely small.

Figure 9.3 Verifications of Fick's and Darcy's laws for flow of
air through dry porous medium: (a) mass of air flow versus air
pressure gradient (Fick's law); (b) flow rate of air versus pressure
gradient (Darcy's law) (after Blight, 1971).

The prediction of the air coefficient of permeability based
on the pore-size distribution and the SWCC has also been pro-
posed for the air phase. The relative air coefficient permeabil-
ity function k ra is essentially the inverse of the relative water
coefficient-of-permeability function k r w , as shown in Fig. 9.4.
The data are for Hygiene sandstone, and the respective air