Environmental Engineering Reference
In-Depth Information
removing all of the diffused air from the base plate, a new
water level reading,
h
a
2
, is recorded.
where:
M
a
2
=
final mass of air in the burette,
9.8.4 Computation of Diffused Air Volume
The diffused air volume in the base plate,
V
fa
, is registered
on the water volume change indicator as though it were
water leaving the soil specimen. The measured water volume
changes from the soil specimen must therefore be corrected
for the volume of diffused air (i.e., diffused air volume must
be subtracted from the total water volume).
The diffused air pressure below the high-air-entry disk is
assumed to be at a pressure equal to the water pressure in
the base-plate compartment,
u
c
. The diffused air mass
M
fa
can be expressed as
u
a
2
=
¯
absolute final air pressure in the burette [i.e.,
¯
u
atm
+
u
ab
+
(h
a
2
−
d)ρ
w
g
],
h
a
2
=
final reading of the water level in the burette, and
V
a
2
=
final volume of air in the burette (i.e.,
h
a
2
A
).
When the initial and final burette readings are at atmo-
spheric pressure,
u
ab
=
0 in Eqs. 9.74 and 9.75. The differ-
ence between the initial and the final mass of air in the burette
(i.e.,
M
a
2
−
M
a
1
) is the amount of diffused air removed from
the base plate,
M
fa
. The gas law is used to compute the dif-
fused air volume
V
fa
under isothermal conditions:
ω
a
RT
K
¯
M
fa
=
u
fa
V
fa
(9.73)
u
a
2
V
a
2
−¯
¯
u
a
1
V
a
1
=¯
u
fa
V
fa
(9.76)
where:
The diffused air volume is
u
a
2
V
a
2
−¯
¯
u
a
1
V
a
1
M
fa
=
mass of diffused air,
V
fa
=
(9.77)
ω
a
=
molecular mass of diffused air,
u
fa
¯
R
=
universal (molar) gas constant,
It is also possible to compute the amount of diffused air
removed from the base plate,
M
fa
, by reading the initial
and final water levels in the burette at the same applied
air pressure (Fredlund, 1975c). For example, if the initial
burette reading was taken at atmospheric pressure, the air in
the Lucite cylinder should be depressurized to atmospheric
pressure conditions before the final reading is recorded. The
diffused air volume is computed as
T
K
=
absolute
temperature
(i.e.,
T
K
=
273
.
16
+
T
,
temperature,
◦
C),
where
T
=
u
fa
=
¯
absolute diffused air pressure in the base plate (i.e.,
¯
u
fa
=¯
u
atm
+
u
c
),
u
atm
=
¯
atmospheric pressure (i.e., 101.3 kPa),
u
c
=
water pressure in the base plate, and
V
fc
=
volume of diffused air in the base plate.
The diffused air volume in the base plate,
V
fa
, is computed
by applying the ideal gas law to the air volume measured
in the diffused air volume indicator. Let us consider the ini-
tial and final conditions in the diffused air volume indicator
shown in Fig. 9.20. The initial mass of air in the burette,
M
a
1
, can be computed from its absolute pressure
u
a
1
(V
a
2
−
¯
V
a
1
)
V
fa
=
(9.78)
u
fa
¯
The base plate is generally flushed once or twice a day.
Corrections to intermediate water volume change readings
can be made using a linear interpolation of diffused air flow
with respect to time. No temperature correction is necessary
provided the temperature of the diffused air volume indicator
and the base plate of the triaxial cell are the same.
The accuracy of the diffused air volume indicator has
been tested by diffusing air through a saturated high-air-
entry ceramic disk. An air pressure is applied to the top of
a saturated ceramic disk. The saturated disk is connected to
the water volume change indicator. A change in the water
volume reading with time indicates the accumulation of dif-
fused air below the high-air-entry disk. The ceramic disk
remains saturated since the air-entry value of the disk is not
exceeded.
The volume of diffused air can be measured either peri-
odically using the diffused air volume indicator or contin-
uously using the water volume change indicator. The two
results should be essentially the same if the diffused air vol-
ume indicator performs satisfactorily. Figure 9.21 compares
the volume of diffused air measured using the water vol-
ume change indicator and the diffused air volume indicator.
u
a
1
and
¯
its volume
V
a
1
:
ω
a
RT
K
¯
M
a
1
=
u
a
1
V
a
1
(9.74)
where:
M
a
1
=
initial mass of air in the burette,
u
a
1
=
¯
absolute initial air pressure in the burette [i.e.,
¯
u
atm
+
u
ab
+
(h
a
1
−
d)ρ
w
g
],
u
ab
=
gauge applied air pressure in the Lucite cylinder,
h
a
1
=
initial reading of the water level in the burette,
d
=
height difference between the burette and the exit
tube,
V
a
1
=
initial volume of air in the burette (i.e.,
h
a
1
A
),
and
A
=
cross-sectional area of the burette.
Similarly,
the final mass of air in the burette can be
expressed as
ω
a
RT
K
¯
M
a
2
=
u
a
2
V
a
2
(9.75)
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