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1
Frequency Dependence of Permittivity of Free and Bound Water
in Soils for Different Textures
P. P. Bobrov
1, 2
, V. L. Mironov
2
, O. V. Kondratieva
1
, and A. V. Repin
1, 2
1
Omsk State Pedagogical University, Russia
2
Kirensky Institute of Physics SB RAS, Krasnoyarsk, Russia
Abstract— In microwave methods of the soil moisture remote sensing it is necessary to have
models for determining the complex dielectric permeability (CDP) dependence on moisture, fre-
quency, mineralogy and particle-size distribution. The soil permeability measurement shows that
the basic contribution to the CDP is introduced by free and bound water, and permeability of soil
water depends on a soil type. To establish the influence of particle-size distribution of soil parti-
cles on CDP of the bound and free soil water we carried out the measurements of the frequency
and moisture dependencies of refraction index of artificial sandy-clay mixes having different min-
eral structure and particle-size distribution. The carried out research at the frequencies from
30 MHz up to 4 GHz has shown that the refraction index of free soil water depends on the quartz
granules sizes, as well as on the clay fraction relative content. The characteristic feature of the
free soil water is the increase of refraction index at frequency reduction. This dependence is the
stronger the more clay the sample has. The similar properties are also observed in the bound
water.
1. INTRODUCTION
For algorithms creation of data processing of microwave radiometric and radar remote sensing of
the Earth surface it is necessary to have the model of the complex dielectric permeability (CDP) of
soil which determines the dependence of CDP at a given temperature on moisture, electromagnetic
frequency, particle-size distribution and mineral structure of a soil cover. The basic contribution
to the soil CDP is introduced by a soil moisture being in free and bound water conditions [1]. The
experimental researches have shown, that CDP of various soils depends on particle-size distribu-
tion and mineral structure [1–4]. The frequency dependences analysis of moist soils CDP in the
frequency range from 1 MHz up to 4 GHz has shown that the increase of real and imaginary parts
of CDP occurs at the frequencies below 50 MHz [3, 5] and in some investigations below 500 MHz [6].
This growth is most noticeable for the soils with the large content of clay and organic matter.
However, the dielectric characteristics of the bound and free soil water and the influence on these
values of particle-size distribution and soil mineral structure at frequencies lower than 500 MHz are
investigated insufficiently. In the present work the results of the research of a soil water refraction
index in artificial mixes simulating grounds with different particle-size distribution are given.
2. EXPERIMENT DESCRIPTION
According to the refractive model [1] a complex refractive index of soil ( ˙n = n + jκ =
√
˙ε is the
square root of CDP) is found from the formula
˙n = n
d
+ (n
b
− 1)W
t
+ (n
u
− 1)(W − W
t
) (1)
where n
d
is a complex refractive index of dry soil, n
b
and n
u
— complex refractive indices of bound
and free water, respectively, W
t
is maximum volume fraction of bound water, W is volumetric
moisture. The results of experimental studies show that the parameter of the model n
u
, fitted for
the best correspondence with the experiment, has a value that differs from the refractive index of
free water. Therefore, in the future, this component of the mixture we will call free soil water.
Dielectric measurements of artificial mixes were made by using a vector network analyzer, which
measures the scattering matrix components at the frequency range from 30 MHz to 4 GHz. To
measure CDP at these frequencies the sample under investigation was placed in a segment of coaxial
line with the section of 7/3 mm. The bentonite clay (sample No. 13 in Table 1) and three types of
quartz particles in the form of nearly spherical granules (samples NoNo 1–3) were used to create
mixtures. The mixtures containing quartz granules and bentonite clay in the following proportions
2
by mass: 95 : 5, 70 : 30, 50 : 50 for each type of granules (samples NoNo 4–12) were investigated. As
you can see from the data given in Table 1, the clay content increases with increasing the number
of a sample. Samples NoNo 1, 4, 7 and 10 contain the largest quartz granules, and samples NoNo
3, 6, 9, 12 contain the quartz granules of the smallest sizes.
The mineralogical composition of bentonite is 70% of montmorillonite, 15% of quartz, 3–5% of
feldspar, 3–5% of calcite + dolomite and the mass share of each of other minerals does not exceed
1%.
The samples were wetted with distilled water, then were kept in hermetically sealed containers
at a constant temperature (22–25
◦
C) during the day and night to distribute the moisture in the
mixture evenly. The samples with zero moisture were obtained by drying them at a temperature
of 105
◦
C for 12 hours. After conducting the dielectric measurements the sample was weighed and
dried for several hours, then it was weighed again. According to measured data the moisture and
dry bulk density of the sample was calculated.
3. EXPERIMENT RESULTS AND DISCUSSION
In Fig. 1, we show the measured values of the real part of the refractive index depending on the
volumetric moisture W of two samples — pure quartz sand grains with the size of 40–70 microns
(sample No. 2) and the same sand mixed with bentonite clay in the ratio of 70 : 30 in weight
(sample No. 8). The same piecewise linear dependences as shown in Fig. 1 were observed for all
survey results, given this work.
Table 1: The distribution of particles due to their sizes in the studied samples.
No sample
The distribution of particle sizes in mm (in mass fractions)
1–0.25 mm 0.25–0.05 mm 0.05–0.01 mm < 0.01 mm
1 0.133 0.867 0 0
2 0 0.90 0.10 0
3 0 0.042 0.958 0
4 0.128 0.824 0.012 0.036
5 0.002 0.855 0.107 0.036
6 0.002 0.04 0.921 0.037
7 0.105 0.607 0.073 0.215
8 0.012 0.63 0.143 0.215
9 0.012 0.03 0.743 0.216
10 0.086 0.433 0.121 0.359
11 0.02 0.5 0.171 0.359
12 0.02 0.021 0.6 0.359
13 0.04 0 0.242 0.718
1
1,5
2
2,5
3
3,5
4
4,5
00,1 0,20,3
1
2
W , sm
3
/sm
3
n
Figure 1: The dependence of the refractive index due to moisture sample No. 2 (1) and sample No. 8 (2) at
a frequency of 1 GHz.
3
One can see that the regression lines slope angles for the pure sand and sand with bentonite in
the values of the free soil water (for the sand it is the entire range of moisture, but for a mixture of
sand with bentonite it is the value of moisture in excess of 0.12 sm
3
/sm
3
) differ significantly. As it is
seen from (1) the tangent of the inclination angle of regression line is (n
u
−1), hence, the refractive
index n
u
of free soil water in the mixture of sand with bentonite is considerably higher than in
pure sand (9.4 and 8.1, respectively). This difference is larger than the error of measurement. A
relative root mean square error for determining n
u
evaluated by the Monte Carlo method, is equal
to 2.3%.
7
8
9
10
11
0,11 10
1
No 2
3
f, GHz
n
u
SamplesClay 0%
(a)
9
10
11
12
13
0,11 10
4
5
6
f, GHz
n
u
SamplesClay 3,6%
(b)
8
9
10
11
0,11 10
7
8
9
f, GHz
n
u
Samples
Cla
y
21,5%
(c)
8
9
10
11
12
0,11 10
10
11
12
f, GHz
n
u
Samples
Clay 35,9%
(d)
No
No
No
No
No
No
No
No
No
No
No
Figure 2: The values of refractive index of free water, due to the content of clay in the mixtures containing
a variety of quartz granules.
4
6
8
10
0123
No
7
No
10
No
13
f, GHz
n
b
Samples
n
b
Samples
4
6
8
10
0123
9
12
13
f, GHz
n
b
Samples
4
6
8
10
0123
f, GHz
No 8
No 11
No 13
No
No
No
Figure 3: The values of indices of refraction of bound water, depending on the clay content in the mixtures
containing a variety of quartz granules.
4
The measurement n
u
in different samples in the frequency range 0.1–4 GHz are shown in Fig. 2.
You can see that the values of n
u
in sand mixtures without clay are highly dependent on the size
of quartz particles — they decrease with increasing particle sizes (Fig. 2(a)).
When you add clay (a clay fraction is the fraction consisting of particles smaller than 10 microns)
to the samples of quartz sand which differ in size of granules, even in small amounts (3.6% by mass)
first we can observe, the reduction of disparities n
u
, in mixtures with different sizes of quartz grains,
secondly, we can see a considerable increase of the refractive index at the frequencies below 1 GHz
for all samples containing clay. The difference in the refractive indexes of free soils water for
the samples containing the same amount of clay but having different sizes of quartz granules is
comparable to the accuracy of measurements (Fig. 2(b)).
In mixtures containing 21.5% clay, the influence of quartz particles on n
u
increases and the
differences in n
u
exceed the measurement error. The data given in Fig. 2(c) show that in mixtures
containing the largest quartz granules, n
u
is of the largest value, i.e., the influence of the size of
grains mixed with clay is opposite to their influence in the sand samples.
In samples with high clay content (Fig. 2(d)) the influence of the size of quartz grains remains
the same. In sample No. 13 has that has the largest clay content the refractive index of free soil
water has a value of about 9 at frequencies 2–4 GHz and considerably increases with decreasing
frequency (up to 20.8 units at a frequency of 100 MHz). The higher the clay content is in the
sample, the larger n
u
increases with decreasing frequency (Fig. 2).
Figure 3 shows the frequency dependence of the refractive index of bound n
b
water in the
samples NoNo 7–13. You can see that the values of n
b
increase with increasing clay content at all
frequencies. We can also see, an increase in n
b
with a decrease of frequency. Sample No. 13 with the
largest clay content takes the highest value n
b
. Having the same clay content, the values of indices
of refraction of bound water weakly depends on the size of quartz grains. There is a decrease n
b
in the size of granules, but the differences are comparable to the accuracy of determining the n
b
(relatively root mean square error is equal to 7%).
A regression analysis, which shows the dependence of n
u
and n
b
on proportion of different
fractions was made. This dependence is presented by the following equation:
n
t
= k
1
x
1
+ k
2
x
2
+ k
3
x
3
+ k
4
x
4
(2)
where x
1
is a fraction part with a particle size of 1–0.25 mm, x
2
is the proportion of fractions with
particle sizes of 0.25–0.05 mm, x
3
is share fractions with particle size of 0.05–0.01 mm and x
4
is a
share fraction with particle size of less than 0.01 mm, k is coefficients of regression. Similar calcu-
lations were used for bound water. Table 2 presents regression coefficients for multiple frequencies.
Table 2: The frequency dependence of the coefficients of the regression equation.
f, GHz
Free soil water Bound soil water
k
1
k
2
k
3
k
4
R
2
k
1
k
2
k
3
k
4
R
2
0.5 24.01 10.01 9.07 13.10 0.69 9.89 5.519 8.08 11.85 0.87
1 16.66 9.60 8.26 10.63 0.8 7.01 4.74 6.47 9.26 0.88
2 17.02 9.72 8.29 8.65 0.94 8.93 4.27 5.32 7.27 0.96
3 15.55 9.54 8.28 8.57 0.95 9.31 3.977 5.32 6.95 0.99
4 16.65 9.30 8.08 8.77 0.89 8.93 3.39 5.07 6.91 0.93
4. CONCLUSION
Dielectric measurements of samples with different structure in the frequency range from 30 MHz
to 4 GHz were made. It was found out that the refractive index of free soil water in the sand soil
increases with decreasing the size of the mixture. It was found out that with decreasing frequency
the increase of the refractive index of free soil water is observed in samples containing clay content.
Moreover, the intensity of increasing depends on the amount of clay. This is also particularly true
for the bound water. Regressive dependences for finding the refractive mixture indices at different
frequencies due to the particle-size distribution mixture were found out.
5
REFERENCES
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2. Curtis, J. O., “Moisture effects on the dielectric properties of soils,” IEEE Trans. Geosci.
Remote Sensing, Vol. 39, No. 1, 125–128, January 2001.
3. Campbell, J. E., “Dielectric properties and influence of conductivity in soils at one to fifty
megahertz,” Soil Sci. Soc. Am. J., Vol. 54, 332–341, 1990.
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soil properties,” Instrumentation and Measurement Technology Conference, 1999, IMTC/99,
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