Full Text:   <3170>

CLC number: TU4

On-line Access: 2008-01-06

Received: 2007-12-12

Revision Accepted: 2007-12-20

Crosschecked: 0000-00-00

Cited: 0

Clicked: 6003

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.3 P.293-302


A new equation for dielectric permittivity of saturated soils based on polarization mechanics

Author(s):  Ren-peng CHEN, Yun-min CHEN, Wei XU, Zhi-gang LIANG, Wei FENG

Affiliation(s):  MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   chenrp@zju.edu.cn, chenyunmin@zju.edu.cn

Key Words:  Dielectric permittivity, Saturated soils, Polarization, Time domain reflectometry (TDR)

Share this article to: More |Next Article >>>

Ren-peng CHEN, Yun-min CHEN, Wei XU, Zhi-gang LIANG, Wei FENG. A new equation for dielectric permittivity of saturated soils based on polarization mechanics[J]. Journal of Zhejiang University Science A, 2008, 9(3): 293-302.

@article{title="A new equation for dielectric permittivity of saturated soils based on polarization mechanics",
author="Ren-peng CHEN, Yun-min CHEN, Wei XU, Zhi-gang LIANG, Wei FENG",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T A new equation for dielectric permittivity of saturated soils based on polarization mechanics
%A Ren-peng CHEN
%A Yun-min CHEN
%A Wei XU
%A Zhi-gang LIANG
%J Journal of Zhejiang University SCIENCE A
%V 9
%N 3
%P 293-302
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A071620

T1 - A new equation for dielectric permittivity of saturated soils based on polarization mechanics
A1 - Ren-peng CHEN
A1 - Yun-min CHEN
A1 - Wei XU
A1 - Zhi-gang LIANG
A1 - Wei FENG
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 3
SP - 293
EP - 302
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A071620

Based on polarization mechanisms, such as electronic, ionic and orientational polarizations, a new equation for dielectric permittivity of soil is proposed to interpret the dielectric behavior of a mixture like soil, in terms of polarization process of its components and the interactions between its components. The dielectric permittivity is expressed in terms of a frequency-dependent part and a frequency-independent part. These two parts correspond to polarizations occurred at different frequency range. It is a new volumetric mixing model with theoretical background. Based on time domain reflectometry (TDR) measurements of saturated soil samples and test data from literature, comparisons of this model with some well established mixing models show that the curves for saturated sand soils and slurries resulted from the new equation, which agree well with TDR measurements, are close to those calculated from Birchak’s model.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] ASTM D6780-05, 2005. Standard Test Method for Water Content and Density of Soil in Place by Time Domain Reflectometry (TDR). West Conshohocken, PA.

[2] Birchak, J.R., Gardner, C.G., Hipp, J.E., Victor, J.M., 1974. High dielectric constant microwave probes for sensing soil moisture. Proc. IEEE, 62:93-98.

[3] Dirksen, C., Dasberg, S., 1993. Improved calibration of time domain reflectometry for soil water content measurements. Soil Sci. Soc. Am. J., 57:660-667.

[4] Dobson, M.C., Ulaby, F.T., Hallikainen, M.T., El-Rayes, M.A., 1985. Microwave dielectric behaviour of wet soil, part II: dielectric mixing models. IEEE Transactions on Geoscience and Remote Sensing, GE-23(1):35-46.

[5] Friedman, S.P., Robinson, D.A., Jones, S.B., 2006. Review of Geometrical and Interfacial Factors Determining the Effective Permittivity-volumetric Water Content Relationships of Soil and Rocks. Proceedings of the 3rd International Symposium and Workshop on Time Domain Reflectometry for Innovative Soils Applications, Purdue University.

[6] Heimovaara, T.J., 1994. Frequency domain analysis of time domain reflectometry waveforms 1: Measurement of the complex dielectric permittivity of soils. Water Resources Research, 30(2):189-199.

[7] Heimovaara, T.J., Bouten, W., Verstraten, J.M., 1994. Frequency domain analysis of time domain reflectometry waveforms 2: A four-component complex dielectric mixing model for soils. Water Resources Research, 30(2):201-209.

[8] Heimovaara, T.J., de Winter, E.J.G., van Loon, W.K.P., Esveld, D.C., 1996. Frequency-dependency dielectric permittivity from 0 to 1 GHz: time domain reflectometry measurements compared with frequency domain network analyzer measurements. Water Resources Research, 32(12):3603-3610.

[9] Hilhorst, M.A., Dirksen, C., Kampers, F.W.H., Feddes, R.A., 2000. New dielectric mixture equation for porous materials based on depolarization factors. Soil Sci. Soc. Am. J., 64:1581-1587.

[10] Looyenga, H., 1965. Dielectric constant of heterogeneous mixtures. Physica, 31(3):401-406.

[11] Lorrain, P., Corson, D.R., 1980. Electromagnetic Fields and Waves. Freeman, W.H., San Francisco, p.504-535.

[12] Maxwell-Garnett, J.C., 1904. Colours in metal glasses and metal films. Trans. Royal Society, London, 203(1):385-420.

[13] Powers, M.H., 1997. Modeling frequency-dependent GPR. The Leading Edge, 16(11):1657-1662.

[14] Ramo, S., Whinnery, J.R., van Duzer, T., 1994. Fields and Waves in Communication Electronics (3rd Ed.). John Wiley, New York, p.187-220.

[15] Robinson, D.A., Friedman, S.P., 2001. The effect of particle size distribution on the effective dielectric permittivity of saturated granular media. Water Resources Research, 37(1):33-40.

[16] Robinson, D.A., Friedman, S.P., 2002. The effective permittivity of dense packings of glass beads, quartz sand and their mixtures immersed in different dielectric backgrounds. J. Non-crystalline Solids, 305(1-3):261-267.

[17] Robinson, D.A., Friedman, S.P., 2003. A method for measuring the solid particle permittivity or electrical conductivity of rocks, sediments, and granular materials. J. Geophys. Res., 108(B2):2076.

[18] Robinson, D.A., Friedman, S.P., 2005. Electrical conductivity and dielectric permittivity of sphere packing: measurements and modelling of cubic lattices, randomly packed monosize spheres and multi-size mixtures. Physica A: Statistical Mechanics and its Applications, 358(2-4):447-465.

[19] Roth, K., Schulin, R., Fluehler, H., Attinger, W., 1990. Calibration of TDR for water content measurement using a composite dielectric approach. Water Resources Research, 26(10):2267-2273.

[20] Santamarina, J.C., Klein, K.A., Fam, M.A., 2001. Soils and Waves. John Wiley & Sons Ltd., West Sussex, UK.

[21] Sen, P.N., Scala, C., Cohen, M.H., 1981. A self-similar model for sedimentary rocks with application to the dielectric constant of fused glass beads. Geophysics, 46(5):781-795.

[22] Siddiqui, S.I., Drnevich, V.P., 1995. Use of Time Domain Reflectometry for the Determination of Water Content and Density of Soil. FHWA/IN/JHRP-95/9, Purdue University, West Lafayette.

[23] Sihvola, A., 1999. Electromagnetic Mixing Formulas and Applications. Institution of Electrical Engineers, Herts, Stevenage, UK.

[24] Silberstein, L., 1895. Untersuchungen über die Dielectricitätsconstanten von Mischungen und Lösungen. Annalen der Physik und Chemie, 292(12):661-679.

[25] von Hippel, R., 1954. Dielectric Materials and Applications. The MIT Press, Cambridge.

[26] Topp, G.C., Davis, J.L., Annan, A.P., 1980. Electromagnetic determination of soil water content: measurements in coaxial transmission lines. Water Resources Research, 16:574-582.

[27] Wang, J.R., 1980. The dielectric properties of soil-water mixtures at microwave frequencies. Radio Science, 15:977-985.

[28] Whalley, W.R., 1993. Considerations on the use of time-domain reflectometry (TDR) for measuring soil water content. European Journal of Soil Science, 44(1):1-9.

[29] White, I., Knight, J.H., Zegelin, S.J., Topp, G.C., 1994. Comments on “Considerations on the use of time-domain reflectometry (TDR) for measuring soil water content” by W.R. Whalley. European Journal of Soil Science, 45(4):503-508.

[30] Wobschall, D., 1977. A theory of the complex dielectric permittivity of soil containing water: the semidisperse model. IEEE Trans. on Geoscience Electronics, 15(1):49-58.

[31] Yu, X., Drnevich, V.P., 2004. Soil water content and dry density by time domain reflectrometry. Journal of Geotechnical and Geoenvironmental Engineering, 130(9):922-934.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE