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process of measurement is non-destructive, portable systems are available and the
method gives ability to automatize and multiplex probes (Baker and Allmaras [7],
Malicki and Skierucha [59], Topp et al. [90]). The bulk apparent dielectric
permittivity, ε b , of the soil is calculated on the base of the propagation velocity of
electromagnetic (EM) waves along the probe forming a waveguide consisting of
two or more parallel metal rods fully inserted into the analyzed soil. The dielectric
permittivity of water is much higher than the other soil constituents because of the
unique dipole nature of water molecules. Therefore having the soil dielectric
permittivity from the TDR measurements it is possible to determine indirectly the
amount of water in the soil.
The dielectric permittivity, ε, of soil as well as other dielectric materials or
mixtures with molecules forming permanent dipoles, like water molecule, are
subjected to orientation polarization (Chełkowski [14]) in the imposed EM field.
The permanent dipoles need finite time, called relaxation time, τ, to keep up with
the alternating EM field. When the frequency the field increases, the molecule
with the permanent dipole response lags in phase. Therefore the permittivity of
such dielectric material is a complex value (Litwin [50], von Hippel [96]):
σ
ε ε '( ω) i ⎛
ε"
( ω) dc ⎞
= −
⎜ + = ε '( ω)( 1 tanδ
)
ωε
⎟ + i
(36)
⎝
0 ⎠
where: i = −1
, σ dc is the electrical conductivity of the sample at low frequency,
−12
ε0 = 8.85⋅10
[Fm
-1 ] is a dielectric permittivity of free space. Its real part, ε '(ω),
is in-phase with the imposed EM field, while the imaginary part,
ε" ( ω) + σ dc / ωε0
, is out-of-phase. The loss tangent, tanδ, describing the overall
loss of energy in the dielectric material is defined as:
σ dc
ε"
( ω)
+
ωε 0
tanδ
= (37)
ε '
( ω)
This energy loss is associated with the out-of-phase components of soil complex
ε" ω attributed to dipole reorientation at high frequency
dielectric permittivity; ( )
of the applied EM field, while σ dc /ωε 0 to ionic conduction at low frequency of
the EM field.
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