Environmental Engineering Reference
In-Depth Information
100
80
Water
60
Air
40
20
Hygiene sandstone
0
0.1
1
10
100
Relative permeability (
k
rw
and
k
ra
), %
Figure 9.4
Relative permeability of water and air as function of degree of saturation during
drainage (modified from Brooks and Corey, 1964).
and water coefficients of permeability are plotted relative to
completely dry and wet conditions. In other words, the rela-
tive air coefficient of permeability is presented as a ratio of the
air permeability corresponding to the completely dry condi-
tion. Similarly, the relative water coefficient of permeability
is plotted relative to the water permeability corresponding to
the water-saturated conditions.
The following equations were used by Brooks and Corey
(1964) to describe the
k
a
(S
e
)
function:
The data also show that at under low applied soil suctions
the soil becomes saturated and the air coefficient of perme-
ability tends to a small value (i.e., diffusivity of air through
the water in the soil).
9.3.3 Relationship between Air Coefficient
of Permeability and Matric Suction
Equation 9.20 can also be expressed in terms of matric suc-
tion (
u
a
−
u
w
). The functional form for the air coefficient
of permeability takes on an inverse form of the equation
suggested by Brooks and Corey (1964) for the water per-
meability function:
k
a
=
0
.
0
for
u
a
−
u
w
≤
(u
a
−
u
w
)
b
(9.19)
S
e
)
2
(
1
S
(
2
+
λ)/λ
e
k
a
=
k
d
(
1
−
−
)
for
u
a
−
u
w
>(u
a
−
u
w
)
b
(9.20)
k
a
=
0
.
0f r
u
a
−
u
w
≤
(u
a
−
u
w
)
b
(9.22)
where:
1
λ
2
1
2
+
λ
(u
a
−
(u
a
−
u
w
)
b
u
a
−
u
w
)
b
k
a
=
k
d
−
−
k
d
=
coefficient of permeability with respect to the air
phase for a soil at a degree of saturation of zero.
u
w
u
a
−
u
w
for
u
a
−
u
w
>(u
a
−
u
w
)
b
(9.23)
The air coefficient of permeability
k
a
corresponding to
various degrees of saturation can be computed using Eq.
9.20. The relative coefficient of permeability of air perme-
ability,
k
ra
(%), can be written as follows:
Figure 9.2 illustrates the agreement between measured
data and the theoretical air coefficient-of-permeability func-
tion described using Eq. 9.23.
Several studies have been undertaken to measure the air
permeability of compacted soils. The coefficient of perme-
abilitywith respect to air,
k
a
, decreases as the degree of satura-
tion of the soil increases (Ladd, 1960; Olson, 1963; Langfelder
et al., 1968; Barden and Pavlakis, 1971). Figure 9.6 presents
air and water coefficients of permeability for a soil compacted
at different water contents or matric suction values by Barden
and Pavlakis (1971). The air and water coefficients of perme-
ability
k
a
and
k
w
were measured on the same soil specimen
k
a
×
100
k
d
k
ra
=
(9.21)
A comparison between the computed relative air perme-
ability for several soils with measured experimental data is
shown in Fig. 9.5. The data from each of the soils show that
the air coefficient of permeability increases with respect to
the applied soil suction until a maximum value is obtained.
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