Environmental Engineering Reference
In-Depth Information
where
n
m
is the number of monolayers of water molecules of thickness
δ
bounded
to the soil particles;
S
e
is the soil specific area; and
ρ
b
=
ρ
(
1
−
φ
)
is the soil bulk
s
density,
ρ
s
being the soil dry density [19]. For complex media, such as soil,
α
≈
0
.
5;
nevertheless, in general,
is a fitting parameter [43].
A further enhancement of these models can be achieved by taking into account
the frequency-dependence of the permittivity for each of the soil constituents [68].
In fact, when dealing with complex materials or when a high percentage of water is
present in the medium, the dielectric mixing model should also consider the depen-
dence of the dielectric characteristics on frequency and the effect of
α
0
[27]. Taking
into account the frequency dependence of permittivity is usually accomplished with
the so-called inverse modeling, which may be developed either directly in time do-
main [32] or in frequency domain [9, 33].
Dielectric mixing models have proved to be suitable in many practical applica-
tions and their perspectives for further use seem to be very promising, not only for
soil-like materials, but for a variety of materials (e.g., materials for construction
[14]).
σ
5.3
Evaluation of Moisture Content Directly from TDR
In this section, the estimation of moisture content from TDR-measurement of the
apparent dielectric constant is addressed. In particular, the adoption of
cal-
ibration curves is described in detail, and the strategies for deriving accurate and
reliable curves are discussed.
As aforementioned, for a given material, the
ε
app
−
θ
calibration curve can be
assessed as follows. Samples of the considered material are moistened at prefixed
values of moisture (
ε
−
θ
app
θ
ref
), and the corresponding apparent dielectric constant (
ε
app
)
is measured through the TDR method. The (
ε
app
,
θ
ref
) points are fitted through, thus
obtaining a regression curve.
In this way, in successive moisture content measurements on the same type of
material, it is enough to measure
ε
app
, and the corresponding moisture level is simply
retrieved from the calibration curve, with a certain confidence level. However, it
must be pointed out that calibration curves are specific for each kind of material;
hence, different curves must be derived for different materials (also, for example,
for different types of soil).
As a matter of fact, different procedures are used for the extrapolation of empir-
ical calibration curves, which, as a result, are not readily comparable. In fact, the
individuation of an optimal calibration curve for each of the materials under inves-
tigation is a key point to improve the accuracy of results. Despite the deep interest
surrounding TDR, neither an assessment of standard measurement procedures, nor
the corresponding metrological characterization has been thoroughly investigated.
To fill this gap, the strategies for obtaining accurate calibration curves were
specifically investigated. Furthermore, the metrological performance of the method
was assessed through a statistical analysis on the results obtained through the two
TDR instruments considered in this topic (namely, the HL1500 and the TDR80E04).
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