Environmental Engineering Reference
In-Depth Information
the errors due to imperfect amplitude calibration (and not for cable resistance) and
that the C-S method overestimates
σ 0 by a constant rate [40, 41]: this error can
be compensated for if the probe constant is evaluated every time the measurement
setup changes (even when the probes are identically manufactured). On the other
hand, the probe constant in the series resistors model has to be determined only
once for identical probes, also regardless of the cable length.
Finally, it is worth mentioning that for highly conductive media, because of the
strong attenuation of the signal, it becomes difficult to measure simultaneously the
apparent dielectric permittivity and the electrical conductivity. In [44], it was shown
that for 0
75 S m 1 , a possible solution could be to insulate the
rod-probes with a high-dielectric coating.
4Sm 1
.
< σ 0 <
0
.
5.5.2
Innovative Calibration Strategies: The TLM and the ICM
Methods
It is apparent from (5.20) and (5.21) that, once K p is determined for the specific
used experimental setup,
σ 0 can be easily evaluated through a single TDR mea-
surement on the considered sample. Therefore, the crucial step of this measurement
method, and hence the related metrological performance, is strictly related to the
accurate evaluation of K p . Since the estimation of K p is associated to a preliminary
calibration, it goes without saying that the minimization of the systematic errors
contributions is strictly related to this procedure; consequently, the evaluation of K p
strongly influences the resulting accuracy in the estimation of
σ 0 .
Starting from these considerations, two alternative and innovative approaches for
an accurate and simple evaluation of K p were assessed [13]. Both these methods
require only a couple of preliminary measurements: one in air and the other in a
reference liquid material, such as water, at known temperature (thus avoiding the
otherwise necessary calibration with several reference samples of known conduc-
tivity, as required by the traditional C-S method).
The first proposed method allows accurately estimating K p through the suitable
combination of TDR measurements with a specific TLM of the measurement setup.
On the other hand, the second proposed method leads to the accurate estimation
of K p through two ICMs performed through an LCR meter. As will be detailed later,
the ICM method has the great advantage of being very rapid, without compromising
the final accuracy.
The proposed approaches were validated through repeated
σ 0 measurements: 1)
on reference electrolyte solutions; 2) on sand samples progressively moistened with
de-ionized water; and 3) on sand samples progressively moistened with salted water.
The obtained results are compared with those achieved through the traditional C-S
method.
Additionally, the performance comparison between C-S and ICM methods is
evaluated through a rigorous metrological analysis, which, in turn, provides the mea-
surement uncertainty in the final estimations of
σ 0 .
 
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