Soil electromagnetic mapping for enhanced GPR utility location

Oct 24, 2008

1. INTRODUCTIONThe Mapping the Underworld (MTU) project combines the expertise of four UK universities in an effort to provide new geophysical utility location equipment that will dramatically improve on the accuracy of current equipment (see [1] for more information). In order to achieve this goal, it has been recognised that there is a need to optimise the usefulness of data output by GPR equipment through knowledge of the electromagnetic (EM) properties of the soil. This aspect of the project can be considered an essential element as it is soil, and in particular the clay fraction, that determines the degree of signal loss that will occur and the velocity of the signal in the ground.

This required knowledge of soil EM properties can be considered to comprise two distinct elements. Firstly, where access can be made to the soil, direct measurement of soil EM properties can be made. Secondly, where this is not achievable, it is desirable to be able to predict the impact soil will have on utility location equipment signals, including how this impact will vary with the signal frequency. This latter aspect also opens the possibility of geographically mapping soil properties, and the use of such maps as a tool for planning informed utility location surveys.
It is, however, obvious that undertaking a mapping exercise, using measured EM data over large areas, would be an impracticable proposition. This problem has led to consideration of factors common to both EM signal propagation in soils and geotechnical properties. While it may seem implausible that such diverse properties as these can provide predictive linkages, it has been identified that both are highly dependent on the nature of pore water and the mineralogy of the soil mineral particles.
This paper details the approach being followed by MTU in order to achieve both site measurement and a predictive methodology that will allow geotechnical data to be used in mapping soil EM properties. While the approach is currently being developed for use in the United Kingdom, it is expected that it could be equally applicable in other countries.
2. THE THEORY BEHIND SOIL EM MAPPING
2.1 The EM Parameters
An important aspect of both measurement and prediction of soil EM properties is an understanding of the propagation of signals. The two main parameters associated with GPR are attenuation (i.e. the degree to which a signal decays with distance) and the signal velocity, from which the depth to a reflection will be determined. These two parameters can be determined from knowledge of the permittivity, magnetic permeability and conductivity of the material through which propagation occurs, which in simple terms can be summarised as follows:
Permittivity (ε): A measure of the signal energy that can be stored in a material, through separation of charges (e.g. ions, protons, electrons) in a material. Permittivity is divided between a real part representing the storage of energy (ε’) and an imaginary part representing loss mechanisms that degrade energy storage (ε”). The permittivity of a material is generally expressed in terms of its ratio to the permittivity of a vacuum, and is known as the relative permittivity or dielectric constant (ε’r).
Magnetic permeability (μ): A measure of signal energy stored in a material due to the lining up of atomic and sub-atomic particle spin directions. As with permittivity, magnetic permeability can be divided into real (μ’) and imaginary (μ”) aspects, although in practice most soils are considered to have simple magnetic properties and so loss mechanisms are often ignored. It is also commonly referred to as a relative property based on its ratio to the magnetic permeability of a vacuum (μ’r).
Conductivity (σ): A measure of the degree to which a soil allows the passage of direct current (DC) electrical charge through it. In most soils the conductivity is ionic, being dependent on the prevalence and mobility of ions in the pore water.
2.2 Attenuation and Velocity
From knowledge of the above parameters, the attenuation (α) and transmission (β) constants of a material can be determined, using Equations 1 and 2 [2].
Once the attenuation constant has been determined, the signal amplitude reduction with depth can be easily determined, for any depth, using Equation 3. This decay in amplitude is illustrated in Figure 1 (after [3]) where signal 1 ignores attenuation and signal 2 includes for its effects. Signal attenuation is a significant aspect in the difficulty associated with detecting reflected GPR signals, due to the limited sensitivity of detection equipment.
Similarly, the signal velocity can be determined using Equation 4. While it may appear from the cancellation of frequency in Equations 2 and 4 that the velocity (V ms-1) is frequency independent, the frequency dependence of the pore water properties invalidates this assumption.
2.3 Loss Mechanisms
A final consideration in this brief introduction is the nature of the imaginary part of the permittivity. This factor is of particular relevance to the EM properties of soils as it plays a significant part in the frequency dependence of the response of pore water to a signal. As can be seen in Equation 5, the imaginary permittivity comprises two aspects, these being dipolar losses and losses associated with the conductivity.
Dipolar losses (ε”P) are a peculiarity of the properties of water that cause loss of EM signal energy as heat, and is the property exploited extensively for microwave heating. Due to the separation of charges within a water molecule, it will tend to rotate in response to a signal, and energy is stored in the hydrogen bonds affected by the rotation. However, as the frequency increases, the molecules become unable to rotate in time with the signal and energy is lost (a process termed relaxation). This effect, for a simulated soil exhibiting relaxation around a frequency of 500MHz, is illustrated in Figure 2.
The effects of conductivity as a loss mechanism reduce, as shown in Figure 2 and Equation 5, in proportion to the signal frequency and so are a significant factor in the low frequency impact of soils on GPR signals. As seen in Figure 3, which illustrates low frequency effects, increased conductivity is associated with significant reductions in signal velocity in comparison to that which would occur due solely to the effects of the real permittivity (and therefore is also associated with significant signal attenuation).
2.4 Modelling Dispersive Systems
As seen above, the effects of relaxation phenomena and conductivity can cause significant variations in the EM properties of soils with frequency, and such soils are known as dispersive soils. Also, as dipolar relaxation and conductivity both depend on the presence of water, understanding the dispersive effects of pore water are central to predicting soil EM properties. Fortunately, while the process of relaxation appears a complex task to model, the processes involved have been well studied. A suitable mathematical relationship for water relaxation, known as the Havriliak-Negami model, is detailed in Equation 6 [4], which provides both the real and imaginary permittivity.
3. MEASURING SOIL EM PROPERTIES
3.1 Measurement Systems
Two testing scenarios are important in terms of soil EM properties measurement. Firstly, laboratory testing is necessary in order to obtain high quality data for soils in a range of states, including varied water contents and degrees of consolidation. Secondly, field testing is necessary in order to validate the laboratory data and, where access to the soil is possible during a utility location survey, to obtain accurate data for fine tuning the location equipment.
A number of measurement methods will be adopted, in order to maximise available data on soil EM properties. However, one method in particular is currently being developed due to its ability to allow compatibility between laboratory and field testing data. This method is known as Resonant Frequency Analysis (RFA) and relies on the predictability of the maxima and minima that occur in the signal strength to frequency relationships that occur in a transmission line or waveguide [5]. The frequencies at which these maxima/minima points occur is related to the frequency dependent apparent permittivity (ε*r - see below) of the soil and the length of test cell or probe used, as detailed in Equation 7. The signal strength to frequency relationship is measured using a Vector Network Analyser (VNA).
3.2 Apparent Permittivity
The use of apparent permittivity as a measure of soil EM properties has become very popular since the early 1980s, due to it being the main form of data output from Time Domain Relectometry (TDR, see [6]). The apparent permittivity can be directly related to signal velocity (V ms-1), as shown in Equation 8.
TDR measurements are based simply on measurement of the time taken for an electrical pulse to reflect from the end of a probe, from which the velocity can be calculated and the apparent permittivity derived. The reason for the popularity of TDR is its ability to provide data on water content and conductivity of soils using the apparent permittivity. However, in its general form, TDR is limited to a single apparent permittivity value of most relevance to higher frequencies. Therefore, RFA is being used to extend TDR data to cover a frequency range that permits dispersion effects to be measured. This compatibility is being taken advantage of in the design of test cells and probes, which are basically modified versions of those used in TDR, but with improvements to the cable connection to allow their use with either a VNA or TDR equipment.
3.3 Test Cells and Probes
The laboratory testing cell is illustrated in Figure 4 and is simply a coaxial transmission line, consisting of a small diameter metal rod centred within a hollow metal cylinder, the two being connected together electrically by the end plate. In this design, soil is placed within the annulus and a swept frequency signal passed through it to measure the reflected signal strength. However, this form of test apparatus is limited by the need to insert soil, which causes the obvious limitation that it cannot be inserted into the ground for field measurements. Therefore, the probe illustrated in Figure 5 has also been developed.
The probe functions in the same manner as the cell, with the two outer conductors taking the place of the outer cell wall. By using a combination of cell and probe, which can be used both for RFA and TDR measurements, it is expected that a wide range of field and laboratory data can be gathered.
4. PREDICTING SOIL EM PROPERTIES
4.1 Soil Phases
In its simplest representation, soil can be considered to comprise mineral particles, water and air. While this representation can hold true for soils with low specific surface area (SSA), such as sands, increases in SSA (due to increased clay content) bring with them an additional phase that is important for soil EM studies, this being water that is bound to mineral particles and so able to behave electromagnetically in a different manner to free water. This view of soil as a four phase material is illustrated in Figure 6.
Values of relative permittivity quoted for these four soil phases are 4.5-7 for mineral particles, 1.0 for air, 3.5-3.8 for electrically bound water and 81.0 for free water [7]. However, as for many other aspects of soil EM research, these values hold well only for the higher frequencies associated with TDR, so prediction of their variations over all GPR frequencies is of particular importance.
4.2 Bound and Free Water
The need to distinguish between bound and free water relates to the significantly different effects they have on GPR signals. While unconfined water exhibits relaxation centred around frequencies up to 17GHz, the poor intermolecular bonding between bound water molecules means that relaxation occurs in the GPR frequency range. As illustrated in theory in Figure 2, this conspires to cause significant complexity in predicting soil EM parameters up to a frequency of approximately 1GHz, due to the effects of variations in real permittivity, dipolar losses and conductivity losses.
In contrast, improved bonding of water molecules in the more viscous free pore water leads to higher relaxation frequencies and less variation in EM properties above 1 GHz. This is illustrated in Figure 7, which shows frequency domain variations in apparent permittivity of a wide range of soil fines (≤425 μm) close to their liquid limits, as measured using the MTU measurement cell.
It is important to note that the differences between bound and free water electromagnetically are paralleled in clay geotechnical research due to the Stern double layer, which comprises a fixed layer (the Helmholtz layer) and a diffuse layer (Gouy’s layer) of water molecules and adsorbed ions [8].
While further research is required to determine whether the bound and free water, as they relate to EM properties, correspond directly with the Stern double layer system, there is evidence to suggest that the bound water comprises only a single monolayer of water molecules (see e.g. [9]).
It should also be noted that it is not only the charged clay mineral particle surfaces, binding water molecules to them, that cause relaxation effects at low frequencies. It has been identified that such effects are also associated with other particle types due to the reduced potential for hydrogen bonding around uncharged and hydrophobic surfaces. For example, low frequency relaxations have been observed in sands [10] and this effect is illustrated in Figure 8, which shows frequency domain variations in apparent permittivity for a saturated sample of Leighton Buzzard sand. However, due to the low SSA of non-clay soils, this effect could be considered to have only a limited impact on prediction.
4.3 Variations with Water Content
From the above discussions, it can be expected that increases in water content will not necessarily be accompanied by proportional increases in apparent permittivity. Due to the electromagnetic nature of bound and free water, it could also be expected that the impact of increasing water content will be reduced until the transition between the two types of water occurs. This is illustrated in Figures 9 and 10 (after [11]), which show variations in both apparent permittivity and conductivity, in a Kaolinite clay, with changes in water content.
The effect of SSA on the water content at which the transition occurs between bound and free water is further illustrated in Figure 11 [after 12], for a wide range of soil textures. As can be seen in the figure, predictability of the apparent permittivity of soils, at different water contents, becomes more complex as the clay proportion increases.
Predicting the overall EM parameters of a soil from those of its individual constituents is central to creating a prediction methodology. However, this aspect causes a great deal of confusion due to the wide range of mixing models available, with at least twenty two different models to choose between (see for example [13]). These models can, in terms of their usefulness for prediction and mapping, be categorised loosely as either overly simplistic, suitable only for certain scenarios and potentially of use for predicting soil EM properties in both the frequency and water content domains.
An example of the first category is volumetric mixing, which is based on a pro-rata proportioning of the permittivity of each phase according to the overall volume each occupies. However, while simple volumetric mixing is adequate for simple mixtures, it has proved inadequate for complex, often largely inhomogenous, soils and so has proved of little use for predicting soil properties. The rise in popularity of TDR since the early 1980s has illustrated that a different approach to soil EM prediction is possible and can provide accurate relationships between apparent permittivity and volumetric water content. Probably the most widely used of these relationships is the Topp model [6], shown in Equation 9.
The Topp model has proved accurate for all but highly dispersive soils, and has found extensive use in the monitoring of soil water content using TDR. Unfortunately for prediction and mapping for GPR use, it is an entirely empirical model based on TDR measurements. It therefore exemplifies the category of models that are suitable only for certain scenarios, in this case for higher frequencies (e.g. around 1GHz).
The limitations of empirical TDR-based models are partly addressed by models that are of potential use in prediction and mapping. These are based around considering the fact that bound and free pore water act differently in terms of their EM properties. A popular example is the De-Loor model [9], which is based on the theoretical interactions between disc-shaped particles in soils. For a four phase soil system, this model reduces to Equation 10 [14].
For TDR use, the De-Loor model has proved more reliable than the Topp model, due to its ability to account for variations in bound water content. Also, together with other similar models, it is of particular significance since it includes sufficient parameters to allow the effects of variations in soil density and specific surface area to be modelled. However, further work is required to identify the most appropriate model for prediction and mapping, which will itself require much future work measuring the EM properties of a wide range of soils in an equally wide range of states.
However, it should be noted that the more appropriate models require advance knowledge of the proportion and permittivity of each phase. Therefore, for prediction and mapping purposes, they rely on a separate ability to predict frequency domain variations in pore water EM properties. A central aspect of this is the ability to determine the proportion of bound and free water present in a soil, particularly for clays where the amount of bound water will be significant.
4.5 Predicting Bound and Free Water Content
As the liquid limit of a soil is highly dependent on SSA, it could be considered sensible to assume that it can be used to provide a measure of the amount of bound and free water in a soil. This has been investigated using the MTU test cell to measure apparent permittivity of soil fines close to their liquid limit, as shown in Figure 7. As it can be expected that the more stable values of apparent permittivity above approximately 1 GHz will be associated with free pore water only, these values for each of the soils in Figure 7 have been plotted in Figure 12 against water content.
It can be seen from Figure 12 that there appears to be a linear relationship between these two parameters, suggesting that the proportion of free water is indeed proportional to the liquid limit when the soil is saturated. This is perhaps to be expected, as the Topp model illustrates that there are relationships between apparent permittivity and water content at the higher frequencies. However, as illustrated in the figure, the Topp model does not accurately predict the EM properties of saturated, dispersive, clays at the low dry densities associated with the liquid limit (a purpose for which it was not, of course, designed). Therefore, for such soils, Figure 12 may provide a useful method for measurement of total, bound and free water contents using RFA techniques.
At lower water contents, and lower void ratios associated with higher degrees of consolidation, this relationship between free water and liquid limit will obviously become invalid. However, as bound water is represented simply as the difference between total and free water contents, the liquid limit becomes a useful tool for determining how much water is tightly bound to mineral particles, in terms of the EM response. This relationship provides a very useful possibility for prediction and mapping, in that it could be exploited to allow determination of the parameters required for modelling dispersion and for use in mixing models (i.e. the amount of bound and free pore water). For instance, with a reduction in void ratio from that associated with the liquid limit, it could be expected that the bound water volume will remain unchanged, and that the free water volume will reduce (with some increase in the amount of bound water due to increased SSA with increased consolidation and dry density).
Further research will be required to determine whether this relationship holds true when the thickness of the free water layer becomes small in comparison to the bound water layer, but there is some evidence to suggest that such an assumption may provide useful predictions for clay soils. For instance, the data in Figure 13 show frequency domain variations in apparent permittivity for an undisturbed sample of London Clay (measured using the MTU probe) and the same soil mixed with water until close to its liquid limit (measured using the MTU cell). Although there is a difference in water content between the values for undisturbed soil and soil at the liquid limit (volumetric water contents of 50 and 70% respectively), the most apparent difference between the two is a reduction in the contribution of free water properties at the higher frequencies, and increased bound water effects at lower frequencies due to the significant difference in SSA.
If a prediction and mapping system is to be based on the liquid limit of soils (and potentially the plastic limit as a measure of changes between elastic and viscous pore water properties) it is obvious that it will require validation through measurements of a wide range of clay soils.
6. FUTURE WORK
Four main areas of research have been identified for continuation of this work. Firstly, it is necessary to investigate further the properties of saturated clays over a wide range of states, in order to determine the effects of pore size on the EM properties. This is to be addressed through use of the MTU probe to measure variations in EM properties during consolidation of clay samples.
Secondly, to date the research has focussed on the properties of the sand-size particles and smaller (i.e. the fraction 2mm or less in size) but, for field use, the prediction methodology will need to incorporate the effects of larger inclusions. This will largely be addressed through probe measurement of soil EM properties in the field, which can then be related to laboratory tests of the ≤2mm fraction.
Thirdly, the variations in conductivity of soils, particularly in terms of their relationship to geotechnical parameters, requires investigation. This will be achieved through measurements of conductivity values at low frequencies in the laboratory, and will be carried out as an integral part of the consolidation tests.
Finally, a semi-empirical model will be constructed around the formulae presented in this paper, together with relationships determined for quantifying bound and free water. The model will be tested through field measurements of soils compared to laboratory determinations of the geotechnical properties. Once a suitably accurate model is available, the potential for its use in geographical mapping of soil EM properties will be investigated.
7. CONCLUSIONS
At first sight, linking geotechnical properties to EM properties, in order to provide data for informed GPR utility location, appears an almost impossible task. However, it is apparent that the relationships between attenuation, velocity and soil EM parameters are well documented and available for use in modelling, from which prediction and mapping methodologies can be progressed. Furthermore, methods already exist to model variations in the EM parameters associated with relaxation of pore water.
Also, much work is available from previous research relating to mixing models to quantify the EM properties based on those of its constituents (i.e. minerals, air, bound and free water). Some of these models can be discounted for the purposes of this research, due to their being suitable only for specific uses, and it is expected that others may prove unsuitable when applied to the full frequency and water content ranges of interest to GPR surveys. However, of most significance is that current mixing models illustrate that there is potential for constructing a prediction methodology.
From the above, it is apparent that prediction of soil EM properties, to an accuracy level suitable for informed GPR utility location, is not quite as daunting as may otherwise be assumed. However, it is also apparent that the central challenge in such prediction is determining the water content and, in particular, determining the proportion of water that exhibits relaxation at low frequencies (i.e. the bound water) and the associated relaxation frequency.
In terms of this problem, it has been identified that the proportion of bound water appears directly proportional to the liquid limit of a soil. This relationship could be expected as the role of the specific surface area of a soil (which is related to the liquid limit) has previously been identified as being related to bound water limits. However, the degree to which the proportions of bound and free water could vary due to differences in the mineral surface charge, presence of ions, etc., was unknown; based on recent tests reported herein, it is now thought that it may be insignificant in terms of developing prediction systems.
Further work is required to extend this relationship to a wide range of soil states, as well as to determine whether it is possible to predict the conductivity of a soil from knowledge of geotechnical properties (based on increased ion content as specific surface area increases). The MTU project intends to address this research need through EM measurements of soils during consolidation, which is possible through use of the RFA probe developed previously. This will allow EM data to be obtained for a wide range of saturated clays over an equally wide range of void ratios (and therefore degrees of consolidation). By obtaining data during consolidation, rather than testing individually consolidated samples in different states, it is hoped not only to gather a large amount of data on soil EM properties more quickly, but also expected that the data will allow prediction of the variations in EM properties that will occur due to variations in the local degree of consolidation of soils in situ.
Obviously, prediction systems are intended for use during field GPR utility location surveys and so validating the models in the field is of significant importance. This problem has been addressed through development of the probe and cell based on widely used TDR equipment, which is intended to provide a robust measurement system that is also compatible with data obtained using TDR measurement equipment.
Finally, once a prediction system has been developed, to an accuracy considered suitable for GPR use, it is intended that this will be developed into a method of geographically mapping soil EM properties. It is hoped that this will be achieved in partnership with the British Geological Survey (BGS), which holds widespread records of soil conditions within the UK. Through uniting a prediction methodology with an extensive database of soil properties, it is hoped that the mapping system will provide useful data for GPR utility location equipment over wide geographical areas and frequency ranges.
8. ACKNOWLEDGEMENTS
The authors gratefully acknowledge the financial and other support provided by the UK’s Engineering and Physical Sciences Research Council (EPSRC) and UK Water Industry Research (UKWIR).
9. REFERENCES
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[14] Dobson, M.C., Ulaby, F.T., Hallikainen, M.T. and El-Rayes, M.A. “Microwave Dielectric Behaviour of Wet Soil. Part II: Dielectric Mixing Models”, IEEE Transactions on Geoscience and Remote Sensing, 1985, Vol. 23, 35-46

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