Environmental Engineering Reference
In-Depth Information
The contribution of each compressibility component to
the overall compressibility of the air-water mixture is
illustrated in Fig. 15.8 for various degrees of saturation.
The case considered has an initial absolute air pressure
voids. The effect of air solubility on the compressibility of
an air-water mixture is shown in Fig. 15.9 for several ini-
tial absolute air pressures. The
B
a
and
B
w
parameters are
assumed to be equal to 0.8 and 0.9, respectively.
The figure shows that the effect of air solubility on the
compressibility of an air-water mixture is the same (i.e., on a
logarithmic scale) for any initial air pressures. However, the
effect of air dissolving in water does not result in a smooth
transition for the compressibility of an air-water mixture as
saturation is reached (i.e.,
S
= 100%). There is a discontinu-
ity at the point where there is no more free air to be dissolved
in the water. As a result, the second term in Eq. 15.13 must
be dropped, and the compressibility abruptly decreases to the
compressibility of water. If the free air does not have time
to be dissolved in the water, the term
hSB
a
/ u
a
in Eq. 15.13
must be set to zero. In this case, the compressibility of pore
fluid has a smooth transition back to saturation, as shown in
Fig. 15.9.
u
a
0
of 202.6 kPa (i.e., 2 atm).
15.3.3 Effects of Free Air on Compressibility
of Mixture
Figure 15.8 shows that the compressibility of an air-water
mixture is predominantly influenced by the compressibility
of the free air portion [i.e.,
(
1
−
S)B
a
/ u
a
]. When the soil
voids are filled with air (i.e.,
S
= 0.0), the compressibility
of the pore fluid is equal to the isothermal compressibility
of air (i.e., 4
.
94
10
−
3
kPa
−
1
at
u
a
= 202.6 kPa). At satu-
ration (i.e.,
S
= 100%), the soil voids are completely filled
with water, and pore fluid compressibility becomes equal
to that of water (i.e., 4
.
58
×
10
−
7
kPa
−
1
). The inclusion of
even 1% air in the pore fluid is sufficient to significantly
increase the pore fluid compressibility (see Fig. 15.8). The
compressibility of water is only significant when computing
the compressibility of a saturated soil.
×
15.3.5 Other Relations for Compressibility
of Air-Water Mixtures
The compressibility of air-water mixtures has been investi-
gated by numerous researchers. For example, an equation for
the compressibility of an air-water mixture has been proposed
that neglects the compressibility of the water and assumes
zero matric suction (Bishop and Eldin, 1950; Skempton and
Bishop, 1954). Therefore, the compressibility of the air is
considered as representative of the compressibility of the
pore fluid. The proposed equation is suitable for conditions
where the air phase constitutes a significant portion of the
pore fluid. These proposed equations can be obtained by
ignoring the first term in Eq. 15.13. Also, the
B
a
15.3.4 Effect of Dissolved Air on Compressibility
of Mixture
The solution of air in water gives the effect that the soil
is compressible. The compressibility due to the solution of
air in water (i.e.,
hSB
a
/ u
a
) is approximately two orders of
magnitude greater than the compressibility of water (i.e.,
SC
w
B
w
). Air dissolving in water significantly affects the
compressibility of an air-water mixture when the free air
volume becomes less than about 20% of the volume of
and
B
w
Compressibility of
water,
C
w
4.5 x 10
−
7
(kPa
−
1
)
=
0
100
Compressibility
of air-water
mixtures,
C
aw
Compressibility
of water
portion
20
80
Compressibility due
to dissolving of
air in water
40
60
Compressibility
of free-air
portion
T
=
20
°
C
u
ao
=
202.6 kPa
60
40
h
0.02
=
B
a
1.0
B
w
= 1.0
=
80
20
100
0
10
−
8
10
−
7
10
−
6
10
−
5
10
−
4
10
−
3
10
−
2
10
−
1
Compressibility (C), kPa
−
1
Compressibility of air,
C
a
=
4.94 x 10
−
3
(kPa
−
1
)
Figure 15.8
Components of compressibility of air-water mixture.
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