Environmental Engineering Reference
In-Depth Information
(in which
S
11
,
MEAS
(
is derived from the TD/FD combined approach), it is possible
to retrieve the unknown value of moisture content. To carry out this minimization
procedure, all the parameters in (5.13), with the exception of
f
)
, should be known.
For this purpose, the sand porosity was preliminarily assessed through the so-
called water saturation method
5
.
As for the complex permittivity of water, its frequency-dependent behavior was
obtained through a Debye model; in turn, the dependence of the Debye parameters
on temperature was taken into account through empirical expressions reported in
the literature [35]. Static electrical conductivity was measured through the well-
known Castiglione-Shouse method [8], which allows the estimation of
θ
σ
0
from TDR
measurements (in particular, the same probe was used).
Finally, the two remaining unknowns (namely,
ε
sp
and
α
) were estimated as fol-
lows: two measurements were performed, on dry sand (
θ
=
0)andonsandmoist-
ened at a known
were extracted
through a preliminary minimization routine (which was performed over
θ
value (namely, 25%); successively,
ε
sp
and
α
ε
sp
and
α
,
and considering
θ
as a known value). On a side note, it is worth mentioning that the
value of
ε
sp
might also be directly measured through the TDR technique using, for
example, the procedure reported in [54].
5.4.2.2
Preliminary Validation of the TSC Procedure
The proposed TSC procedure was preliminarily tested on bi-distilled water and
ethanol. To this end, the three TDR measurements on the short circuits were used
to derive the error network parameters, according to (5.16)-(5.18). Successively, the
error correction procedure, based on (5.19), was applied to
S
11
,
MEAS
(
measured
at section B for the two liquids. Fig. 5.6(a) shows, for the case of bi-distilled wa-
ter, a comparison among the absolute values of the
S
11
f
)
(
)
at section B, obtained
through the TD/FD combined approach [11]; the corrected
S
11
at section A; and
the theoretical
S
11
behavior obtained through TL modeling of the rods immersed
in water (characterized through its Debye model). Similarly, Fig. 5.6(b) shows the
comparison for the case of ethanol.
In the TL modeling, for the probe rods, an effective length of 152 mm (including
the fringing effect at the rods distal end) was always considered.
The analyzed frequency band was limited to 500 MHz, because the three-rod
probe configuration and dimensions do not allow accurate and repeatable measure-
ments above such frequency. The figures clearly show the effect of the adopted
calibration and of the error correction procedures, yielding corrected reflection co-
efficients curves that are in close agreement with the ones expected from theory.
f
5
A known volume of water (
v
w
) was added to a known volume of dry sand (
v
s
); the volume
of the sand included the pores. After the sand was saturated with water, the total volume of
the mixture (
v
mix
) was measured. Eventually, the volume fraction of the pores was obtained
as
(
v
w
+
v
s
)
−
v
mix
, from which the sand porosity could be easily derived.
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