Improving TDR for use with fine-grained soils
THOMAS, A.M., CURIONI, G., FOO, K.Y., ATKINS, P.R., ROGERS, C.D.F. AND CHAPMAN, D.N.
This paper is reproduced from the following source and is copyright 2010 FSST Organizing Committee and not to be reproduced in any manner without their permission:
Thomas, A.M., Curioni, G., Foo, K.Y., Atkins, P.R., Rogers, C.D.F. and Chapman, D.N. (2010) "Improving TDR for use with fine-grained soils", First International Conference on Frontiers in Shallow Subsurface Technology, 20-22 January 2010, Delft, The Netherlands, pp 169-172.
Time-Domain Reflectometry (TDR) provides a robust and widely used method for the monitoring and characterisation of soils using user-friendly cable testers. However, the simplicity of common TDR practice, often utilizing only measurements of reflection distances for electromagnetic signals in probes, causes a number of difficulties when applied to fine-grained soils, largely because they can be electromagnetically dispersive: that is their dielectric 'constants' vary with frequency. This paper therefore considers two ways in which TDR data can be made to greater use in geotechnical disciplines: supplementing TDR with frequency-domain data, and addressing the issues of standardisation and data sharing.INTRODUCTION
For many geotechnical applications, soils may be dominated by the fines fraction (e.g. silt and clay), may exhibit significant swelling and shrinkage, are often electromagnetically dispersive, have maximum water contents significantly greater than the dry porosity, and can even be in the form of wet slurries containing more than 90% water by volume. For such applications, there are few data available on both the geotechnical and electromagnetic properties. Such soils, defined for geotechnical purposes as having particle sizes <425µm, cause significant signal attenuation and loss tangents, limiting the potential accuracy of 'universal' mixing models for estimating soil water content. In a more positive light, the magnitude of electromagnetic dispersion has been shown to provide useful clues to the geotechnical properties of fine-grained soils. However, electromagnetic dispersion, and related attenuation, erodes the frequency spectrum of the TDR pulse resulting in dielectric data based on an unknown measurement frequency. A simple example of the problem is provided in Figure 1(a), which shows apparent permittivity data for fine-grained soils compared to the widely used Topp et al. model . As expected, the figure shows that the Topp et al. model provides a useful approximation for water contents up to approximately 40% by volume - the most apt for the empirical measurements upon which it was based. However, volumetric water contents of 40% and greater can be seen from Figure 1(a) to depart significantly.
Figure 1. TDR data in fine-grained soils (a) compared to the Topp et al. model and (b) compared to HF QWA data at 1GHz.
In Figure 1(b) the same TDR data are compared to data derived from quarter-wavelength analysis at higher frequencies of 1GHz (HF QWA). The greatest departure of the two data sets occurs close to 40% volumetric water content: at the maximum dry density. TDR in fine-grained soils therefore includes variations in apparent permittivity due to the loss tangent and the decrease in the dominant signal frequency. For QWA data, based on network analyzers, the geotechnically most appropriate water-content-to-apparent-permittivity relationship has been shown to be well described by the work of Wensink . For TDR, however, there is still difficulty in that the widely used models do not adequately represent the higher water contents and so soil-specific calibration is still required.
SUPPLEMENTING TDR WITH FREQUENCY-DOMAIN DATA
One means of overcoming the difficulties associated with dispersion is to undertake measurements directly in the frequency domain, either removing the need for TDR altogether or by providing complimentary measurement data. The latter is obviously preferable, as it allows for improved data while preserving the robustness, and relative low cost, of TDR. For instance, complementary frequency-domain data derived during laboratory TDR soil-specific calibration could provide apparent permittivity-to-dispersion relationships that could then be utilised in the field. A relatively simple method of achieving this is to use QWA , based largely upon the work of Heimovaara et al. . QWA is generally undertaken using complex reflection coefficients requiring accurate measurement of phase differences between transmitted and reflected signals, and careful correction of the measured phase. However, QWA may also be undertaken using the return loss (i.e. magnitude of the reflection coefficient - Figure 2(a)), as this can provide data without phase correction, in soils with significant loss tangents. Therefore, while being unsuitable for low water content soils, for many fine-grained soils return loss QWA allows a potentially simple, and relatively low cost, method of obtaining frequency-domain apparent permittivity data, potentially using simple scalar network analyzers. It is also relatively simply modelled, and so useful for parameter matching.
Figure 2. Return loss measurements for distilled water (a) in a coaxial cell and (b) using two different TDR probes with fixed cables.
However, it should be noted that measurements such as shown in Figure 2(a) rely on removal of cable effects by calibrating at their ends. For field monitoring it is necessary to take measurements of the combined effects of the probe and cable. This causes difficulties for QWA because it introduces additional resonances into the data. However, as can be seen from Figure 2(b), it is still possible to obtain useful QWA data from the return loss in some circumstances: for instance, where there are significant losses and the probe resonances dominate the lower frequency response. Such QWA data can also allow estimation of the TDR measurement frequency and could allow many currently installed TDR probes to provide some evidence of the magnitude of electromagnetic dispersion. Furthermore, for new TDR installations, minor adaptations to the probe heads could allow laboratory characterisation of cables, including temperature effects, to allow modelling of the cables for removal of their effects. As can be seen in Figure 2(b), a commercial probe will require at least three models: one each for the probe, probe head and cable. However, this is no different to multi-section models employed in TDR inversion and could allow much improved return loss measurements for TDR probes. Portable network analysers are now very sophisticated, available at lower prices than a high-end TDR unit, and can supplement TDR data for enhanced laboratory calibration and occasional field measurement. Frequency analysis of TDR data could also be used, in which case a network analyser could serve to validate the conversion. Performing QWA on inverted TDR data involves transforming time-domain reflection coefficient data into the frequency-domain as exemplified by Heimovaara et al. . To illustrate this, TDR measurements were carried out using a TDR100 as shown in Figure 3, resulting in both complex and return loss reflection data that could be used with QWA. High resolution TDR data can be represented in the frequency-domain using software processing, allowing data acquisition and conversion to be automated. This has the potential for increasing the accessibility of frequency analysis techniques such as QWA to a wider range of users, as well as in situations where a network analyzer is unavailable.
Figure 3. Measurements for distilled water in a coaxial cell derived from inversion of TDR reflection data: (a) complex reflection coefficient (real part S11) and (b) return loss.
STANDARDISATION AND DATA SHARING
At the GPR08 and IWAGPR09 conferences, workshops were held to consider issues important to stakeholders involved in soil spectroscopy and ground-penetrating radar. A questionnaire was used at IWAGPR09 to estimate the importance of ten issues that can be approximately described as: (1) greater laboratory/field correlation; (2) correlations between electromagnetic testing methods, including codes of practice; (3) the need for agreed calibration standards; (4) a need for overview data on a wide range of soils; (5) a need for detailed data on a small number of soils; (6) a need to develop agreed mixing models; (7) a need for a greater understanding of the properties of soil pore water; (8) a need for widespread geophysical property mapping; (9) a need to share data more openly; and (10) other issues. The averaged responses to the questionnaire (0 = no importance, 10 = very important), are shown in Figure 4. All nine defined issues were considered very significant, and will be fully reported on soon. Also, all of the issues are highly relevant to TDR use in fine-grained soils. For instance, a complete understanding of soil electromagnetic properties can only come from data sharing that allows an overview of geospatial variations. A comparison can be made to genome sequencing, in which researchers are able to make advances through individual gene measurements, but also contribute to an overall database that allows overview research on the genome. Similarly, TDR literature often provides details on small numbers of soils, but the quantitative data are generally not shared and often may not provide exact sampling locations and full geotechnical characterisations.
However, adequate data sharing is difficult to achieve if widely accepted calibration standards and codes of best practice are not in place. There appears, therefore, to be a need to consider developing methods to ensure data inter-compatibility, in order to allow greater sharing of electromagnetic data for fine-grained soils. Potentially a need may also exist to consider funding routes to allow development of those methods and their embodiment in a data repository. This is not just an important issue in terms of effective TDR research, as such standards and data sharing may also have a role to play in aiding development in third-world countries. For instance, one respondent to the questionnaire stated we must consider '...other scenarios in the world like Africa and Latin America, to encourage the young researchers in those parts of the world'. If we are to encourage those young researchers then it is important openly and publicly to share soil measurement data, as well as related, agreed, measurement techniques. Indeed, it could even be argued that funding bodies should insist on such data sharing, and more widespread soil electromagnetic testing, if their investments in science are to receive morally, ethically and socially acceptable returns. Some of these issues could be addressed by emulating other areas of technology where community-led open-source projects allow long-term maintenance of software libraries for many uses, and could do the same for standardised, community-led, TDR data processing tools (e.g. MatLab/Simulink libraries). This would aid young researchers, particularly in third-world countries, to rapidly extend on the work of the current TDR community, allowing research into the more fundamental problems of how to use it to ensure their soils can provide food to an ever-increasing population in a world facing major climate changes.
Figure 4. Questionnaire responses to various issues discussed at GPR08 and IWAGPR09.
For many geotechnical applications, TDR needs to provide frequency-domain data to meet its full potential, such as through soil-specific laboratory calibration, and occasional field measurement, using compatible techniques such as QWA. The relatively low cost of TDR is an important factor; however now the low cost of portable network analysers allows their parallel use to enhance TDR. However, it can be argued that while individual soil TDR measurements are of significant benefit to the studies they are part of, lack of quantitative data sharing limits the potential for those data to contribute to a wider understanding of soils as a whole and their geographical variations. Also, the current lack of community-led projects to provide agreed and accessible software tools for fully utilising TDR data may even limit its potential for addressing the soil science needs associated with developing countries and those facing significant difficulties due to climate change. Therefore, this paper does not intend to prescribe methods for improving TDR in fine-grained soils. Rather, it is intended to promote debate on the potential for developing open-source, widely shared, data and software tools to allow enhanced data-intercompatibility and consideration of dispersion.
 Thomas, A.M., Chapman, D.N., Rogers, C.D.F., Metje, N., Atkins, P.R. and Lim, H.M. 2008. Broadband apparent permittivity measurement in dispersive soils using quarter-wavelength analysis, Soil Science Society of America Journal, 72(5), pp1401-1409.
 Heimovaara, T.J., de Winter, E.J.G., van Loon, W.K.P. and Esveld, D.C. 1996. Frequency-dependent dielectric permittivity from 0 to 1 GHz: Time domain reflectometry measurements compared with frequency domain network analyzer measurements, Water Resources Research, 32(12), pp3603-3610.