HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Full Text Free Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Robinson, D. A. Articles by Friedman, S. P. Search for Related Content PubMed Articles by Robinson, D. A. Articles by Friedman, S. P. GeoRef GeoRef Citation Agricola Articles by Robinson, D. A. Articles by Friedman, S. P. Related Collections Soil Methods/Instrumentation Water Content Time Domain Reflectometry, TDR

A Review of Advances in Dielectric and Electrical Conductivity Measurement in Soils Using Time Domain Reflectometry

^a U.S. Salinity Laboratory, USDA-ARS, 450 W. Big Springs Road, Riverside, CA 92507
^b Dep. Plants, Soils and Biometeorology, Utah State University, Logan, UT 84322-4820
^c Land Resources & Environmental Sciences Dep., Montana State University, Bozeman, MT 59717-3120
^d Dep. of Civil and Environmental Engineering, University of Connecticut, 261 Glenbrook Road, Unit 2037, Storrs, CT 06269
^e Institute of Soil, Water and Environmental Sciences, The Volcani Center (ARO), Bet Dagan 50250, Israel

View larger version (24K): [in a new window]   Fig. 1. (a) The dipole moment of a water molecule. (b) Water molecules randomly aligned (left) and being aligned by an external field (right). This alignment causes the storage of energy described as the real part of the permittivity.

View larger version (23K): [in a new window]   Fig. 2. Three TDR probe designs. Left to right, three-rod probe, two-rod probe, and parallel plate probe.

View larger version (19K): [in a new window]   Fig. 3. A schematic diagram of the TDR main components. The window on the right illustrates two waveforms, one in air and one in water. The dip is caused by an electrical marker in the head of the TDR probe so that the software can locate the start point for travel time analysis.

View larger version (15K): [in a new window]   Fig. 4. Schematic diagram representing the electrical circuit analogy of a transmission line. L, R, C, and G are the line inductance, conductor skin resistance, medium capacitance, and medium conductance per unit length z.

View larger version (23K): [in a new window]   Fig. 5. Left, The apparent permittivity as a function of conductivity for two frequencies, 250 and 750 MHz. Permittivities of 80, 40, and 25 represent water, saturated clay, and saturated sand, respectively. Right, TDR measurements in KCl solutions and KCl saturated glass beads, Eq. [11] fitted using a frequency of 400 MHz as the effective frequency.

View larger version (18K): [in a new window]   Fig. 6. The loss tangent (tan2) as a function of frequency for three differing bulk electrical conductivities.

View larger version (25K): [in a new window]   Fig. 7. Spectrum analyzer measurements for air, water, and a saline solution (data from Friel and Or, 1999). The TDR was connected through a coaxial cell to a spectrum analyzer. The results give the TDR power response as a function of frequency.

View larger version (18K): [in a new window]   Fig. 8. The real permittivity of propanol with some absorbed water. The arrows demonstrate that a 200-MHz signal will "see" a permittivity of 19.0, whereas a signal with a frequency of 1000 MHz will "see" a permittivity of 8.4. The high-frequency signal will therefore travel faster than the low-frequency signal which sees a higher permittivity.

View larger version (19K): [in a new window]   Fig. 9. Waveforms collected with a 0.18-m coaxial cell for air, water, and propanol–water mixtures. Waveforms 1 through 9 have increasing amounts of water. Location A shows how tangent lines were fitted to the waveforms.

View larger version (21K): [in a new window]   Fig. 10. The real permittivity of the propanol–water mixtures corresponding to Fig. 9. The arrows indicate the permittivity values measured from the waveforms in Fig. 9 used to determine the frequency to which they correspond.

View larger version (16K): [in a new window]   Fig. 11. Demonstration of the method used to estimate the highest passable frequency for a given material. tr is the time measured between the signal rising 10 to 90% of the signal magnitude.

View larger version (24K): [in a new window]   Fig. 12. The effective frequencies determined from Fig. 10 and the data of Or and Rasmussen (1999). The filled circles represent the corresponding effective frequency (fmax) calculated using Eq. [14].

View larger version (20K): [in a new window]   Fig. 13. The real permittivity measured for saturated quartz sand and bentonite clay at two water contents. The figure demonstrates the sharply changing real permittivity of moist bentonite below 500 MHz.

View larger version (17K): [in a new window]   Fig. 14. Waveforms from layered water and air with the respective order changed. The shape of the waveforms changes but the travel time remains the same.

View larger version (23K): [in a new window]   Fig. 15. Measurements from Chan and Knight (2001) for the change in velocity averaging. As the wavelength/layer thickness ratio increases above 4, the permittivity averaging changes from refractive index to arithmetic.

View larger version (23K): [in a new window]   Fig. 16. Refractive index and arithmetic averaging of permittivity for layers of Plexiglas and water. As the wavelength/layer thickness ratio increases above 4, the averaging moves from refractive index to arithmetic, as indicated by the arrow (Schaap et al., 2003).

View larger version (35K): [in a new window]   Fig. 17. Modeled and measured waveforms for layers of Plexiglas and water. (A) Modeled waveforms for homogeneous dielectric. (B) Modeled waveforms for layered dielectrics. (C) Measured waveforms for layered dielectrics corresponding to those modeled in Fig. 17B. (From Schaap et al., 2003).

View larger version (23K): [in a new window]   Fig. 18. Measurements of the permittivity of coarse grained (700 µm) monosized quartz sand. The data and modeling suggest that for these measurements the averaging remains in the refractive index regime.

View larger version (24K): [in a new window]   Fig. 19. (a) TDR waveform in water. (b) The corresponding scatter function for water measured using TDR and modeled using the Cole–Cole (1941) relation.

View larger version (12K): [in a new window]   Fig. 20. TDR waveforms from deionized water and from a KCl solution. The various voltages used to obtain the reflection coefficient are illustrated.

View larger version (30K): [in a new window]   Fig. 21. Electrical fields in a coaxial cell. Panels I, II, and III show the progression from the relative electrical potential through the relative electrical field intensity to the relative electrical energy storage density, respectively. The graphs correspond to the marked cross section.

View larger version (40K): [in a new window]   Fig. 22. Relative electric field intensity and energy storage density cross-sections for a variety of TDR probe designs. Configurations include (a) two rods, (b) three rods, (c) three rods with the center rod twice the diameter of the outer rods, (d) five rods, (e) parallel plates, and (f) parallel plates with the right-hand plate twice the length of the left-hand plate.

View larger version (56K): [in a new window]   Fig. 23. Four alternative probe designs. The red represents the positive rod and the blue the negative. Upper panels show the change in sampling volume as a function of permittivity. The brown areas represent a permittivity of 3.3 for PVC, and the yellow areas represent a permittivity of 10, common for unsaturated soils.

View larger version (23K): [in a new window]   Fig. 24. Waveforms collected from a two-rod parallel probe with both rods in air, both rods in water, and then one rod in air and one rod in water. One rod was connected to the inner conductor of a coaxial cable and the other to the outer sheath; this was then reversed. In air and water this made no difference. However, the waveform magnitude is affected depending on which rod is connected to the inner conductor of the coaxial cable and the dielectric that rod is in. The travel time remains unaffected.

View larger version (18K): [in a new window]   Fig. 25. The relative energy storage distribution (2) cross sections from between (a) parallel plates and (b) twin rods. The graphs indicate that there is a more even distribution of energy in the sample between plates than between rods.

View larger version (31K): [in a new window]   Fig. 26. A comparison of water content measured during a field drainage experiment using probes constructed from plates (upper diagram) and probes constructed from rods (lower diagram). (From Robinson and Friedman, 2000.)

View larger version (79K): [in a new window]   Fig. 27. Time domain reflectometry probe construction jig.

View larger version (18K): [in a new window]   Fig. 28. A series of waveforms collected in a coaxial cell demonstrating how the waveform travel time increases as the permittivity increases. Tangent lines are fitted to the water waveform, the intersection being the point from which the time is measured.

View larger version (13K): [in a new window]   Fig. 29. Waveforms in ethanol (s = 22) and octanol (s = 10) demonstrating the rounding of a waveform that contains relaxation in the TDR frequency bandwidth (Octanol).

View larger version (21K): [in a new window]   Fig. 30. An example of a waveform in water showing tangent lines fitted at the end of the waveform and the times used to calibrate a TDR probe (Eq. [45]).

View larger version (19K): [in a new window]   Fig. 31. Left, permittivity estimated from calibration of probe adjusting the electrical length of the probe according to measurements in water using the bump apex as a timing reference. The lines on the right-hand diagram show the corresponding locations on the waveform. The correctly calibrated start point lies 0.035 ns to the right of the point B, the bump apex, according to calibration using Heimovaara's calibration method (Eq. [45]).

View larger version (18K): [in a new window]   Fig. 32. The response of TDR waveforms to cable length. The longer cable filters the higher frequency components of the signal, and the waveform becomes more rounded.

View larger version (19K): [in a new window]   Fig. 33. Influence of temperature in shifting the first reflection peak location resulting from the change in travel time along a 10.3-m cable. Arrows indicate the estimated peak location based solely on the travel time change in polyethylene at 1 and 50°C relative to 25°C.

View larger version (92K): [in a new window]   Fig. 34. Contributors to dielectric loss in wet porous media covering a large frequency spectrum. Mechanisms include C, ionic conductivity; DL, charged double layer; X, crystal water relaxation; I, ice relaxation; MW, Maxwell–Wagner relaxation; S, surface conductivity; B, bound water relaxation; W1, principle free water relaxation; W2, second free water relaxation. (Modified from Hasted, 1973, p. 238).