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Dep. of Earth and Ocean Sciences, Univ. of British Columbia, 6339 Stores Road, Vancouver, BC, Canada V6T 1Z4
* Corresponding author (cfnichol{at}hotmail.com)
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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Abbreviations: DC, direct current • MTDR, MoisturePoint TDR instrument • PIN, positive-intrinsic-negative diodes • TDR, time domain reflectometry • TEM, transverse electric and magnetic mode • TTDR, Tektronix TDR instrument
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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While TDR methods have gained wide acceptance and usage in soils, relatively less attention has been given to TDR's application to high electrical conductivity materials such as mining waste. In these materials, conventional TDR probe designs and signal analysis techniques fail to provide sufficiently accurate estimates of the sample dielectric properties. This paper describes an approach to design an automated TDR system for the measurement of water content in unsaturated mine waste rock. The TDR system is used in both a laboratory column experiment and a field-scale experiment (Nichol et al., 2000). In our application, a high soil water electrical conductivity (5–20 dS m-1) caused by oxidizing sulfide minerals in the mine waste leads to poor signal quality using conventional TDR techniques. Sufficient signal amplitude could not be reliably obtained using a short probe of conventional design. Two techniques for obtaining improved signals were selected: (i) waveform differencing using remote diode shorting (Hook and Livingstone, 1992), and (ii) the use of a resistive probe coating (Kelly et al., 1995; Ferré et al., 1996; Mojid et al., 1998). Our aim is to derive a method to reliably collect waveforms that can be interpreted by automated waveform fitting to derive an estimate of travel time and hence apparent dielectric permittivity.
In this paper, we test both techniques for the collection of interpretable waveforms in high electrical conductivity media. We first provide a brief summary of the TDR method and discuss how it is affected by bulk soil electrical conductivity. We then describe the relevant theory of waveform differencing by remote diode shorting and the use of probes covered with a high-resistance coating. A series of experiments are then presented. The first examines the performance of a short (160 mm) uncoated probe using water solutions of variable electrical conductivity. The second experiments analyse the performance of the waveform differencing method using the remote diode shorting method and manual short circuits under the same conditions as the first experiments. We then examine the performance of a coated probe under the same conditions for both conventional TDR waveform collection and analysis, and using the remote-diode shorting method. We next present the performance of a coated probe in silica sand saturated with water solutions of varying electrical conductivity. A last experiment demonstrates a practical means of compensating for the effect of a probe coating on the estimation of sample dielectric permittivity.
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THEORY |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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app), the bulk electrical conductivity (
DC), and in certain circumstances, the frequency-dependent real and imaginary parts of the complex sample dielectric permittivity (Hoekstra and Delaney, 1974; Dalton et al., 1984; Topp et al., 1988; Heimovaara et al., 1996; Friel and Or, 1999). Time domain reflectometry measures the propagation of a fast rise time, step voltage pulse through a coaxial cable to a waveguide (probe) in contact with the sample. Part of the incident pulse energy reflects back to the TDR instrument from each impedance change in the transmission line and probe, with a full reflection of the remaining pulse energy at the end of the probe. The sum of the incident voltage and reflected pulse voltage measured at the TDR instrument is plotted in time and presented as a waveform. The arrival of reflected energy at the TDR instrument causes a change in voltage over time, and thus a deflection of the waveform. The apparent velocity (
app) of the pulse along the probe is determined from the probe length (L) and the arrival times of the reflections from the head and end of the probe (to, t1). The relative dielectric permittivity of the medium surrounding the probe is related to the velocity of a electromagnetic wave propagating in the transverse electric and magnetic mode (TEM) along a waveguide by:
 | [1] |
Successful TDR measurement of the sample dielectric permittivity requires collecting a waveform in which the pulse travel time at the probe head and probe end can be accurately determined. In conventional waveform analysis, the timing of a reflection is determined using two lines fitted to the deflection of the waveform caused by the arrival of reflected pulse energy. The first is a tangent line fit to the steepest slope of the rising or falling limb of the deflection. The second line is either a horizontal line fit to the predeflection waveform (flat-tangent method), or a tangent fit to the slope of the predeflection waveform (dual-tangent method) (Hoekstra and Delaney, 1974; Topp et al., 1982). The time of the intercept of the pre and postdeflection lines is the arrival time of the reflected pulse energy. The dual-tangent method is more accurate for high electrical conductivity solutions (Wraith and Or, 1999) and is used as the reference method for the alternate methods we examined.
The dielectric permittivity estimated by tangent-line analysis of a TDR waveform is termed the apparent dielectric permittivity (app) because the estimate of dielectric permittivity is not obtained for a single frequency. Frequency domain analyses of TDR waveforms using Fourier transform techniques (Hoekstra and Delaney, 1974; Heimovaara et al., 1996; Friel and Or, 1999) demonstrate that the incident TDR pulse generated by common TDR instruments contains energy in a range of frequencies up to 1.5 GHz. The deflection of the waveform is the integration of the arrivals of all of the frequencies reflected. Tangent-line methods of waveform analysis are biased towards the higher frequencies as these create the sharpest waveform deflections. The frequencies which dominate travel time estimates from tangent line waveform analysis are in the range of 700 MHz to 1.0 GHz (Hoekstra and Delaney, 1974; Heimovaara et al., 1996; Friel and Or, 1999).
Effect of Solution Electrical Conductivity
Ions in solution affect both the waveform quality and the pulse velocity. Direct current (DC) conductance and ohmic losses because of current between the probe conductors dissipate the pulse energy within the waveguide. The energy reflecting from the end of the probe is reduced, the waveform deflection becomes less distinct, contributing to greater uncertainty in tangent-line fitting and travel time determination. In samples with high electrical conductivity, the amplitude of the signal reflected from the probe end may be fully dissipated within the exposed probe conductors and no travel time can be determined. The effect of electrical conductivity on the signal amplitude decreases with a shorter length of probe. The practical lower limit for probe length with common TDR instruments is 0.1 to 0.15 m (Kelly et al., 1995).
Dissolved ions directly decrease the dielectric permittivity of a water solution by reducing the number of highly polarizable water molecules per unit volume and indirectly by the interaction of ions with the electrostatic bonding structure of liquid phase water molecules (Hasted, 1973). In contrast, the DC conductance resulting from ions in solution contributes to the imaginary component of the complex valued dielectric permittivity, leading to an increase in dielectric permittivity. However, at the frequencies which contribute most to tangent-line analysis of a TDR waveform, the DC conductance of water has negligible effect on the pulse velocity (Or and Wraith, 1999). Tabulated experimental measurements of (
)solution for common electrolytes are available in Hasted (1973) and Robinson and Stokes (1959).
The dielectric properties of the water phase in soil differs from that of water in a water solution. Both polar water molecules and dissolved ions interact with mineral surfaces. The dielectric and conductive properties of these diffuse, bonded layers are different from the rest of the water solution (Or and Wraith, 1999). Experiments in saturated and unsaturated soils have shown that increasing the concentration of dissolved ions in soil water increases the measured travel time when soil water content is constant (Wyseure et al., 1997; Sun et al., 2000; Topp et al., 2000). The measured increases in travel time are larger than can be explained by the direct effect of the increased bulk electrical conductivity on the real and imaginary parts of the complex dielectric permittivity (Topp et al., 2000). This indicates that increasing the concentration of dissolved ions in the soil water solution affects other components of the complex-valued dielectric permittivity of the soil/air/water/bound water/dissolved ions mixture in a manner that is not fully understood.
Waveform Differencing and Remote Diode Shorting
Hook et al. (1992) describe a method to improve TDR signal quality using waveform differencing. A raw waveform is first collected from the probe. A short circuit then is created between the signal and ground conductors at the probe head. A second waveform is then collected, termed the shorted waveform. The incident pulse energy will leave the signal conductor and return to the TDR instrument along the ground conductor. This causes a sharp downwards deflection in the shorted waveform. The difference waveform is the difference between the raw waveform and shorted waveform. The timing of the deflection in the difference waveform is determined by tangent-line fitting to derive the travel time for the pulse through the short circuit and back to the instrument. The same process is then repeated with a short circuit created at the probe end.
Positive-intrinsic-negative diodes (PIN) can be used to create the short circuits remotely, and thus allow the waveform differencing method to be automated. PIN diodes have a low resistance under a forward-bias DC current and a high resistance under no current or a reverse-bias DC current. Hook et al. (1992) do not provide details or specifications for the diodes used. We used MPN3404 diodes as suggested by the manufacturers of the MoisturePoint TDR system (Environmental Sensors, Victoria, BC, Canada) which incorporates the remote diode method (Young,1998a). The impedance of these diodes, measured at 100 MHz, switches from >5 M
to <0.8 under a forward bias current (On Semiconductor, 2000).
Our experimental waste rock pile allowed for direct burial of the TDR probes on an open soil surface. This removed the requirement for an open-ended probe design that can be inserted into in situ soil materials. The probe construction is based upon a three-rod Zegelin-type probe design (Young, 1998a), with the inclusion of a single PIN diode at the probe head, and two PIN diodes at the probe base. A schematic of the probes is shown in Fig. 1 . The velocity of the TDR pulse within the sample is determined from the difference between the time for the TDR pulse to pass through the probe-head diode, and the probe-end diode. Calibration measurements in materials of known dielectric permittivity allow the measured time to be corrected for the distance between the diodes located within the probe head and end termination structures and the start of the exposed conductors (Nichol et al., 2002).
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3, lower than most soils materials, and therefore the estimate of apparent dielectric permittivity using a coated probe (cp) will always be less than the apparent dielectric permittivity that would have been estimated using an uncoated probe (app).
Three-rod or multi-rod probes are designed to emulate a coaxial cell (Zegelin et al., 1989). A simple analytical solution for the effect of a dielectric material of uniform thickness around the central conductor of a coaxial cell can be derived from Annan (1977).
 | [2] |
Equations have been derived which exactly describe the effects of coatings applied to three-rod or multi-rod probes, but these equations do not have analytical solutions and are solved numerically (Zegelin et al., 1989; Knight et al., 1994, 1997). We therefore test the simpler analytical solution.
All probe designs with a fixed dielectric material within the sampling zone have a nonlinear relationship between the apparent dielectric permittivity estimated directly from the measured travel time and the actual sample dielectric permittivity. This nonlinear relationship means that the sample dielectric permittivity must be uniform along the probe length to properly determine the sample dielectric permittivity (Ferré et al., 1996).
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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Reference raw waveforms with 5000 points in time were collected using a Tektronix 1502C instrument (TTDR) connected to a PC running WAT TDR Version 3.11 (Waterloo Center for Groundwater Research, Waterloo, ON, Canada). All waveform analysis of TTDR waveforms was performed manually using the dual-tangent analysis method. All waveforms are presented as the reflection coefficient displayed against the two-way travel time. This approach represents the currently accepted practice of TDR measurement against which we compare the alternate methods.
Raw waveforms and diode-shorted waveforms with 256 points in time were collected using a MoisturePoint TDR (MTDR) instrument (Environmental Sensors, Victoria, BC, Canada) with firmware Version 1.27. The MTDR instrument was purchased with proprietary software and hardware specifically designed for conducting automated, diode-shorted TDR measurements. Travel times were measured using the automated waveform fitting routines which are included in the instrument firmware. Additional waveforms for presentation and for detailed waveform analysis were collected manually using a PC connected to the MTDR and running the instrument control software ViewPoint Version 1.34. For all measurements, all instrument settings and waveform fitting parameters in the instrument firmware and software were optimized for maximum accuracy and stability of tangent-line fitting. The MTDR instrument warm up time was set to 15 s and a minimum of five measurements were discarded prior to all recorded measurements to ensure the instrument returned a stable value of travel time.
The first experiments determine the effect of solution electrical conductivity on conventional travel time analysis and on the performance of the remote diode shorting method. Waveform and travel time analysis was carried out for a 160/3.2/25 uncoated probe immersed in isothermal water of variable solution electrical conductivity. The probe was connected to the TTDR and MTDR using 6 m of Commscope F660BEF 75 RG6 coaxial cable, a male F-connection termination, and an F-to-BNC adapter. Solution electrical conductivity was altered from 0 to 5 dS m-1 using KCl. Raw waveforms and probe head and end diode-shorted waveforms were manually collected for each solution.
The effectiveness of the MPN3404 diodes as short circuits was assessed by taking waveform measurements using manually created short circuits. For distilled water and for a solution electrical conductivity of 2 dS m-1, 6 gauge Cu wire was used to create a short circuit at the start of the exposed rods and then at the end of the exposed rods. Shorted waveforms of each short circuit were collected using both TTDR and MTDR.
The second experiments address the effect of a resistive coating. Waveform and travel time analysis was carried out for a 281/3.2/25 coated probe using the same experimental setup as the uncoated probe. Electrical conductivity was altered from 1 to 70 dS m-1 using NaCl. The measurements for 30 to 70.8 dS m-1 solutions have some conductive amplitude loss of signal, and different overall probe impedance because of failure of the probe-head seal and invasion of electrically conductive water into the probe head. Conclusions can still be drawn from these results and they are included in the following analysis. No manually created short circuits were tested in these probes because of the presence of the probe coating.
The performance of a 281/3.2/25 coated probe and remote diode method was then assessed for silica sand saturated with electrically conductive water solutions. Water electrical conductivity was altered from 0 to 20 dS m-1 using NaCl. Raw and diode shorted waveforms were collected using the MTDR. Travel time was determined using automated remote diode shorting at the probe head and end. Water solution and bulk soil electrical conductivity were measured independently using a four electrode conductivity cell and conductivity meter.
The effect of the resistive coating on the estimation of sample dielectric permittivity was determined in the final set of experiments. Travel time measurements were made using a coated probe and materials of known dielectric permittivity with low electrical conductivity, the latter determined using a calibrated 295/3.2/25 uncoated probe. Measurements were conducted using the MTDR instrument and averaging a minimum of 15 measurements. For the purposes of these experiments, the best dielectric materials are liquids, which allow simple probe immersion, uniformity of sample and a controlled range of dielectric properties. Organic liquids can be used to obtain a range of dielectric properties. However, the 281/3.2/25 coated probe used in this study was required for other calibration work and the compatibility of the probe construction materials with various organic liquids was not known. To prevent damage to this probe, a more limited range of inert materials was used. Air, oven-dried silica sand, wetted silica sand, methanol, and water were used as dielectric media. Liquids were placed in a 15.2-cm diam. polyvinyl chloride (PVC) container. Granular materials were packed within a 12 by 12 by 63 cm watertight container.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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In contrast, the pathway created by the remote diode short has a low, but finite impedance. Pulse energy does divide between the diode pathway and the probe pathway when it encounters the two impedances in parallel. The diode-shorted waveform collected at 2 dS m-1 at the probe head closely follows the raw waveform (Fig. 3C), indicating that significant signal energy continued past the location of the diode in the probe head, entered the probe and returned reflections from impedance changes within the probe. The transition time of the probe end reflections in the diode-shorted and the raw waveforms indicates that the frequency spectra of the energy pulse transmitted into the probe was similar. The difference between the diode-shorted waveform and the raw waveform represents the energy that returned via the diode. The gradual departure of the diode-shorted waveform from the raw waveform indicates the energy passing through the diode was dominated by lower frequencies. The probe impedance at low frequency (Z
) was calculated from the reflection coefficient at long times using the method of Mallants et al. (1996). The probe impedance is 4000 in distilled water and 20 in 2 dS m-1 water. The MPN3404 PIN diodes used have a rated impedance of 0.8 at 100 MHz. It is clear from Fig. 3 that the MPN3404 diode and our probe impedances are more similar at higher frequencies, and thus remote diode shorting becomes less effective.
At the probe end, a similar division of pulse energy occurs as at the probe head. Connecting diodes across the end of the probe conductors requires the presence of a probe termination structure, similar to the probe head, to house the diodes. Energy is reflected and transmitted at both the end of the exposed waveguides, and again at the diodes, which connect the end of the center conductor to ground within the probe end termination structure. At 2 dSm-1 (Fig. 3D), the higher final amplitude of the diode-shorted waveform than in distilled water (Fig. 3B) indicates a greater proportion of the energy was reflected back along the signal conductor, instead of through the diode short.
In high conductivity systems, the combination of the effects of imperfect diode shorting at the probe head and end leads to large errors in travel-time estimation, and hence water content. The automated instrument-determined travel time for varying solution conductivity is shown in Fig. 5 , with the theoretical travel time calculated from Eq. [1], and the travel time estimated from the manually created shorts in Fig. 4. The travel time estimated using manually created shorts does not include travel time within the probe head and end termination structures from the diodes to the ends of the exposed conductors. The automated determination of travel time increased by 6 ns. Remote-diode shorting hinders travel time estimation under the conditions examined. In contrast, manually fitted tangent-line analysis of the manual short circuit data presented in Fig. 4 determined no change in travel time greater than the uncertainty in the analysis, similar to the results of manual tangent-line fitting to the raw waveforms in Fig. 2.
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5 dS m-1 for a 0.16-m probe.
Coated Probes in Water
The performance of coated probes is first assessed using conventional waveform analysis. Raw waveforms for solution conductivities between 1 to 70.8 dS m-1 collected using the TTDR are shown in Fig. 6
. The raw waveforms from 1 to 20 dS m-1 indicate little signal amplitude loss and a consistent trend in probe impedance. The transition time of the probe head reflections is similar for 1 to 70.8 dS m-1. No attempt was made to precisely match the impedances of the cable, connectors, and probe head. Multiple reflections are seen between 67 and 73 ns caused by these impedance changes and the start of the exposed conductors. The accidental penetration of high electrical conductance water into the probe head causes the sharp drop in probe-head impedance observed in the lowest three waveforms. The multiple internal reflections originating from within the probe base are smoothed out at higher electrical conductivities.
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The waveform differencing method was assessed for coated probes using only the remote diode shorting method as no manual short circuits could be created because of the presence of the probe coating. The diode waveforms collected at 1 (Fig. 7A,B)
and 20 dS m-1 (Fig. 7C,D) are presented in Fig. 7, with the probe head waveforms on the left (Fig. 7A,C) and the probe end waveforms on the right (Fig. 7B,D). In contrast to the uncoated probes, the overall probe impedance calculated from the final reflection coefficient remains high throughout the range of solution electrical conductivities presented. The probe impedance at low frequency changes from 6000 to 1000 from distilled water to 20 dS m-1. The impedance contrast between the shorted diode and the probe remains high and therefore the diode acts as a better short circuit than in uncoated probes. The probe head diode-shorted waveforms indicate negligible changes in the slope and intercept of the diode waveforms between 1 and 20 dS m-1. The probe head diode-difference waveforms eliminate internal reflections within the probe head, and are smoother and more easily interpreted using tangent-line analysis than the raw waveforms in Fig. 6.
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Detailed investigation of changes in frequency content of the TDR pulse, and changes in the dielectric permittivity of soil/air/water/bound water/dissolved ions mixtures are best determined using frequency domain techniques where it is possible to determine both the real and imaginary parts of the complex dielectric permittivity across all the frequencies in the TDR pulse (Hoekstra and Delaney, 1974; Heimovaara et al., 1996; Friel and Or, 1999). This type of analysis, using both uncoated and coated probes, would increase our understanding of the effects of high concentrations of dissolved ions on dielectric permittivity, TDR signal frequency content and on the apparent dielectric permittivity derived from tangent-line analysis.
These methods are not currently suited to automation in a field situation, and therefore we have focussed our analysis on conventional travel time measurements in this paper. We are primarily concerned with signal quality, and obtaining a waveform interpretable by automated waveform fitting. The results obtained in saturated silica sand indicate that a coated probe is sufficient to determine a measurement of travel time and hence apparent dielectric permittivity, but that apparent dielectric permittivity alone is not sufficient to determine the water content of a soil containing a high electrical conductivity water solution. Calibration of the apparent dielectric permittivity to water content for mine waste material is presented further in Nichol et al., 2002.
Effect of Probe Coating
The apparent dielectric permittivity estimated using a coated probe must be related to the apparent dielectric permittivity of the soil to accurately estimate water contents. The third set of experiments determined the measured travel time for both a coated probe and an uncoated probe in materials with different dielectric permittivity. Apparent dielectric permittivity for coated and uncoated probes were estimated from these measured travel times using Eq. [1]. The apparent dielectric permittivity (cp) derived from a coated probe is plotted against the apparent dielectric permittivity (app) determined with an uncoated probe in Fig. 11
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It is now possible to assess the accuracy of a coated probe for the determination of the apparent dielectric permittivity of a high electrical conductivity sample. A 0.4 ns change in the measured travel time was noted in the previous discussion of the performance of coated probes in solutions between 1 and 70 dS m-1 (Fig. 6). The highest solution electrical conductance, 70.8 dS m-1, corresponds to a NaCl concentration of 0.77 mol L-1 (Mojid et al., 1998). Using the data tabulated in Hasted (1973), the dielectric constant would be expected to decrease from 80.7 to 69. Using Eq. [1], the two-way travel time in an uncoated probe of the same length as the coated probe should decrease by 1.3 ns. The actual decrease in measured travel time for the coated probe is affected by the probe coating. Using the best fit curve (Fig. 9C), this calculated change of dielectric permittivity would correspond to a change in measured dielectric permittivity from 29.3 to 27.3 and a travel time difference of 0.38 ns. This corresponds to the measured 0.4 ns change in travel time between 1 and 70 dS m-1. The coated probes are therefore sensitive enough to determine small changes in the dielectric permittivity.
Recommendations
The method of waveform differencing for determination of the travel time is accurate for high electrical conductivity samples (Fig. 4) when the waveguides are perfectly shorted. As this method requires a raw waveform with an end reflection, it has the same upper limit of solution electrical conductivity as does the interpretation of raw waveforms. The remote diode method of creating short circuits using the MPN3404 diodes recommended by Young (1998) is inaccurate for media with high electrical conductivities. The MPN3404 diodes have frequency-dependent impedances that are incompatible with our probe design. The results obtained for the remote diode method may be improved by the use of diodes other than the MPN3404 that have lower impedance characteristics at frequencies of 700 MHz to 1 GHz. We have not investigated alternate diodes, but can recommend that any diodes selected can be easily checked for performance by measuring diode waveforms of an uncoated probe in an electrically conductive water solution. The presence of significant signal amplitude in the diode-shorted waveform is an indication of unsuitable diode characteristics.
Measurement of apparent dielectric permittivity in high electrical conductivity systems requires the use of a probe coating to obtain an interpretable waveform. Our three-rod Zeglin-type probe with a coating on the center rod obtained interpretable waveforms in both water solutions and saturated silica sand. The accuracy of the probe head measurements for coated probes (Fig. 7) demonstrates that probe head travel time for coated probes is more easily determined using remote diode shorting, even with the MPN3404 diode. The accuracy of locating the probe-end reflection using conventional waveform analysis (Fig. 6) indicates that probe base travel time can be determined from the raw waveform using a dual-tangent method. No probe-end diodes or terminal block (Fig. 1) are therefore required. An empirical correction (Fig. 9) for the probe coating should be derived by TDR measurements in liquids of known dielectric properties. The calibration media should have dielectric permittivities close to the range of expected dielectric permittivities in the soil and calibration of individual probes is required. The use of a resistive coating permits the determination of travel time and hence apparent dielectric permittivity in high electrical conductivity systems. Further work using frequency domain techniques is required to investigate the changes in apparent dielectric permittivity with both soil water content and the concentration of dissolved ions in the soil water solution.
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ACKNOWLEDGMENTS |
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Received for publication May 10, 2001.
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
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