Environmental Engineering Reference
In-Depth Information
Finally, the last section of this chapter describes an enhanced TDR-based method
for measuring static electrical conductivity (
σ
0
), especially useful for granular ma-
terials, such as soil. In particular, two innovative approaches for simplifying and
'speeding-up' the time-consuming preliminary procedures that have to be carried
out for TDR-based estimation of
0
are presented. The first method relies on the
combination of the TDR measurements with a transmission-line modeling (TLM)
of the measurement cell; the second method simply relies on a couple of indepen-
dent capacitance measurements (ICM) performed through an LCR meter.
σ
5.2
Dielectric Models for the Estimation of Water Content
Basically, in BMR, the value of the volumetric water content,
, is inferred from per-
mittivity measurements
2
. In fact, the relative permittivity of water (approximately
80) is considerably higher than the typical relative permittivity of many granular ma-
terials of interest (e.g., soil); therefore, the presence of water changes considerably
the overall dielectric permittivity of the MUT.
Different methods can be adopted for deriving
θ
θ
from TDR measurements. The
simplest approach is based on the evaluation of
θ
from measurement of the apparent
dielectric constant (
ε
app
) of the considered material [10].
A simple approach for TDR-based soil moisture monitoring relies on the use of
empirical material-specific calibration curves that provide the functional relation-
ship
app
[10]. These curves must be determined through preliminary measure-
ments on samples moistened at pre-fixed known moisture levels (
θ
−
ε
θ
ref
): a known
volume of the considered material is moistened with fixed amounts of water and,
for each level of moisture, the corresponding
ε
app
is retrieved from measurement
of the apparent length. The points (
app
) are fitted through a polynomial, and
the obtained curve is used as reference for the successive measurements on samples
of the same material, with unknown moisture levels [10]. As aforementioned, this
approach is simple and adequately accurate.
Another widespread approach relies on the adoption of empirical models, which
fit empirical relationship to experimental data. These models have some shortcom-
ings (such as the limited possibility of extrapolation outside the moisture range of
the original set of experiments [14]); nevertheless, they are routinely used especially
for soil-like materials.
In particular, for soils, one of the most widely used relationship between
θ
,
ε
ref
ε
app
and
θ
is the Topp's equation [46, 63]:
2
3
ε
app
=
3
.
03
+
9
.
3
θ
+
146
θ
−
76
.
7
θ
.
(5.1)
2
Volumetric water content is expressed as θ
=
V
wat
/
V
tot
,where
V
wat
is the volume of water,
and
V
tot
is the total volume of the mixture. The corresponding gravimetric water content
can be calculated as
(
ρ
wat
/
ρ
b
)
θ ,whereρ
wat
is the density of water, and
ρ
b
is the bulk
density of the moist granular material.
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