ekS - Instytut Agrofizyki im. Bohdana DobrzaÅskiego PAN w Lublinie ...
ekS - Instytut Agrofizyki im. Bohdana DobrzaÅskiego PAN w Lublinie ...
ekS - Instytut Agrofizyki im. Bohdana DobrzaÅskiego PAN w Lublinie ...
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ε α = ∑V<br />
α<br />
iε<br />
i<br />
(29)<br />
i<br />
where V i is the volumetric concentration of i-th phase and ε i is the dielectric<br />
constant of this phase.<br />
The four-phase model proposed by de Loor [25,26] and used by Dirksen and<br />
Dasberg [27] and Dobson and Ulaby [28] is:<br />
( ε − ε ) + 2θ<br />
( ε − ε ) + 2θ<br />
( ε − ε )<br />
3ε<br />
s + 2θ<br />
w w s bw bw s a a s<br />
ε =<br />
(30)<br />
⎛ ε s<br />
⎞ ⎛ ε s<br />
⎞ ⎛ ε s<br />
⎞<br />
3 + θ w<br />
⎜ −1<br />
⎟ + θbw<br />
⎜ −1<br />
⎟ + θ a<br />
⎜ −1<br />
⎟<br />
⎝ ε w ⎠ ⎝ ε bw ⎠ ⎝ ε a ⎠<br />
where the indexes s, w, bw and a refer to solid phase, water, bound water and air,<br />
respectively. This model describes heterogeneous mixture where foreign granules<br />
with dielectric constant ε i are <strong>im</strong>bedded in a homogeneous and isotropic dielectric<br />
with dielectric constant ε. The <strong>im</strong>bedded foreign granules in Eq. (30) represent<br />
free water, bound water and air. The host medium is the solid phase.<br />
The empirical models ε (θ ) and ε (θ,ρ), where ρ is the soil bulk density, form<br />
the formula of the appropriate regression curves [58,59,78,90]. The formula (31)<br />
presented below and discussed in Skierucha [78] will be used in this paper as the<br />
reference:<br />
( 0,573<br />
+ 0,582ρ<br />
+ (7,755 0,792ρ)<br />
θ ) 2<br />
ε = +<br />
(31)<br />
where ρ [g/cm 3 ] is the soil bulk density.<br />
The verification of the discussed 3-phase and 4-phase models is presented in<br />
the following sections.<br />
5.1. Material and methods<br />
Sixteen mineral soils of different texture, volumetric water content and bulk<br />
and particle density were investigated (Table 6).<br />
The following variables were measured: dielectric constant, ε, bulk density, ρ,<br />
particle density, ρ s , and grav<strong>im</strong>etrically determined volumetric water content, θ.<br />
Dielectric constant, ε, was determined using TDR (LOM/m from Easy Test, Ltd.<br />
[29]). The remaining variables were measured with the application of standard<br />
methods.<br />
The solid phase dielectric constant, ε s , was calculated from the formula<br />
(derived from the formula (27)):<br />
35