Bundesanstalt für Materialforschung und -prüfung

International Symposium (NDT-CE 2003)

Non-Destructive Testing in Civil Engineering 2003
Start > Contributions >Lectures > Radar 1: Print

Determination of dielectric properties of insitu concrete at radar frequencies

J Davis, Y Huang
Department of Electrical Engineering & Electronics, University of Liverpool, UK
SG Millard,JH Bungey
Department of Civil Engineering,University of Liverpool, UK

Abstract

Ground penetrating radar (GPR) is becoming increasingly popular as a completely non-destructive method for assessing the integrity of concrete structures. However, one difficulty that test engineers have is in relating radar signal return times to the geometric location of a sub-surface feature. It is necessary to have a prior knowledge of the concrete relative permittivity to know the speed of a radar signal in the concrete. The relative permittivity is very sensitive to the moisture content of the concrete & hence may not be uniform within the concrete depth. This paper reports on the development of a wide-band TEM horn antenna system suitable for field applications. The system operates in the frequency domain over the range 300MHz - 3 GHz. An inverse modelling procedure has been developed to determine the profile of a varying relative permittivity with depth. Initial validation trials were carried out on sheets and sandwiches of dielectric material. Tests were then carried out on laboratory test slabs of both cement mortar and concrete. These slabs were pre-conditioned to give a varying moisture profile with depth. Initial results are presented that show the system has a good potential for field use.

Introduction

The use of sub-surface radar has gained increasing popularity within the Civil Engineering community over the past two or three decades. It offers a means of investigating beneath an accessible surface in a totally non-destructive way and giving valuable information about buried inclusions and faults at depths beyond the range of other techniques. One of the difficulties in extracting useful results from a GPR investigation lies in the quantitative interpretation of results. When interpreting a reflected radar signal collected in the time domain, the return time cannot be converted into a distance without foreknowledge of the speed of propagation. This speed is determined by the dielectric and magnetic material properties and is given by:

(1)

where
c = the speed of light in free space,300mm/ns,
mr = the relative magnetic permeability and
er= the relative dielectric permittivity.

Concrete is essentially a non-magnetic material with a relative magnetic permeability of unity. It has been found [1] that the principal factor influencing the concrete permittivity is the amount of moisture contained within the concrete pores, which often varies with increasing depth below the surface. The relative permittivity of concrete typically varies from a value of about 6 for naturally dry concrete to 12 for saturated concrete.

Determination of the dielectric properties of concrete

The recent development of a wide band TEM horn antenna at Liverpool is intended to address this problem. Unlike most commercial time domain radar equipment, this horn operates in the stepped frequency domain, transmitting a steady-state sinusoidal signal over a range of frequencies from 300MHz-3.0GHz. An inversion routine was developed to determine the dielectric properties of the concrete that caused a reflection. This is significantly more difficult and more fraught with problems than a more conventional presentation of time domain output in a graphical format. However it offers the possibility of a more direct characterisation of the physical properties of the concrete, which cannot otherwise be obtained.

Development of Tem horn antenna

A high fidelity transverse electromagnetic (TEM) horn antenna was developed to give a number of required characteristics:

  • Wide bandwidth
  • Near linear phase characteristics
  • Constant polarisation
  • Near constant gain
  • Low return loss

Two prototype antennas were built, each comprising two divergent 1mm thick copper (or aluminium) plates, connected to a network analyser via an N-type coaxial adaptor.

Inversion of radar results

In order to evaluate the electrical properties of the concrete from measurements taken using the TEM horn antenna in the frequency domain, an inversion procedure was developed [2,3,4] to reconstruct the multi layer permittivity profile that produced these results. The complete inverse modelling process comprises three distinct sections,

  • Forward model,
  • Mean square error function (MSE) and
  • Global optimisation or minimisation algorithm.

Forward model
The forward model is derived from a profile designed to represent the anticipated dependence of permittivity and conductivity on depth and frequency for flat, uniformly thick layers. The model incorporates a Cole-Cole frequency dependence[5] and allows the profile to be divided into distinct regions. Each region has dielectric properties that may be either homogeneous or can vary with depth in a linear, exponential or parabolic manner, depending upon the model in use.

Optimisation and mean square error function
The optimisation process comprises the minimisation of a mean square error function (MSE), fe formed directly from the measured reflection coefficient data (G n ), and that generated synthetically from the 'forward' solution (Rn) for N coefficients in the frequency domain i.e

(2)

From a derivation of the global minima of the MSE, the optimum or 'best fit' curve to the measured reflection data can be determined, thus enabling the dielectric parameters of the concrete profile to be reconstructed. To speed up the optimisation routine, the range of possible input parameter values for each layer was restricted to a relative permittivity and conductivity within the feasible range for concrete,
i.e. 6 < e r < 12 and 10-3 < s <10-1 S/m.

Measured reflection coefficients

For the measured reflection data, the experimental radar signal was first corrected for the background signal before conversion from the frequency to time domain using an inverse fast Fourier transformation (IFFT) in order to give an equivalent radar pulse signal reflection. This signal was then time-gated to eliminate any unwanted interference components due to edge diffraction and any mismatch within the signal path. The corrected data set was then converted back into the frequency domain prior to normalisation to the background corrected calibration signal (Figure 1). It is this processed reflection coefficient data that was incorporated into the optimisation algorithm for reconstruction of the dielectric profile.

a) S11 reflection coefficient b) IFFT into time domain
Fig 1: 100mm concrete block measurement

Validation of modelling technique

To evaluate the accuracy of the inversion process, tests were first carried out on several layers of material of known thickness, with homogeneous dielectric profiles. These were sheets of "Tufnol" and "PE500" (Teflon) plastic, whose properties are given in Table 1.

Properties PE500 Tufnol
Relative permittivity2.34.4
Conductivity (S/m)00
Thickness (cm)4.0 or 2.02.5
Table 1: Material properties.

Measurements were first carried out on a single 4cm layer of material of PE500, with the antenna located 50cm away from the surface. The results seen in Figure 2a show a good agreement between the measured result and that modelled using the optimisation procedures described. The inverted dielectric properties shown in Table2 agree well with the expected properties.

Fig 2: Validation of inversion results.

Optimised parameters Layer 1: PE500
Permittivity2.23
Conductivity (S/m)0.006
Thickness (cm)4.3
Table 2: Evaluation of material properties of 1 layer.

Similar measurements were then carried out on a 2-layer and finally a 3-layer composite slab. Results of the 3-layer slab are shown in Figure 2b. From this the inverse modelling of a 3-layer composite slab is seen in Table 3 to give results within approximately 10% of the actual values for each layer.

Optimised parameters Layer1: PE500 Layer 2: Tufnol Layer 3: PE500
Permittivity2.314.492.14
Conductivity (S/m)0.0130 0.009
Thickness (cm)4.62.551.86
Table 3: Evaluation of material properties of 3 layers.

Measurements on concrete specimens

Following these validation tests on materials with well-known dielectric properties, measurements were then taken on cementitious slab specimens. Initially a 50 mm thick mortar slab was cast with dimensions,1.2m x 1.2m. The slab was cast directly against a sheet of PE500 material. It was kept moist for several weeks, until full curing had occurred. Measurements were then taken on the fully water saturated slab. The slab was then allowed to air-dry, after the edges had been painted with a bitumen coating on, to ensure unidirectional drying.

a) S11 : modulus b) S11 : phase
Fig 3: Optimisation fit for 50mm mortar slab.

The results of the optimised forward modelling can be compared with the test measurements from the mortar slab in Figures 3a & 3b. It can be seen here that a very close fit between both the magnitude and phase of the S11 reflection coefficients can be achieved between experimental results and theoretical modelling. The output from this modelling is seen in Figure 4. An exponential decay of the magnitude of the permittivity of the mortar, together with a linear increase in the conductivity with increasing frequency is observed. At any one particular frequency there is an increase in the permittivity and conductivity with increasing depth below the air-drying surface. This is the result that would be expected from an increasingly wet mortar with increasing depth.

Fig 4: Dielectric properties of 50mm mortar slab.

Following the successful measurements of a mortar slab, investigations moved on to study a concrete slab containing coarse aggregates. A 100 mm slab was investigated, where the slab was positioned in the vertical orientation to minimise problems of spurious reflections from the laboratory floor.

Significant problems were first encountered however from multiple reflections arising within the air gap between the mouth of the antenna and the front face of the slab. These problems become serious for thicker concrete specimens where the size of the air gap becomes comparable to the electrical length of the slab. In essence, if a second signal reflection returns to the antenna from the upper concrete surface before the signal reflection from the lower concrete surface arrives, then there can be difficulties in extracting the material properties of concrete. One partial solution to this predicament is to increase the length of the air gap. However there are practical limitations to this approach. Another solution is to use two different positions between the antenna and a calibration metal plate, during the calibration set-up routine[6] in an effort to eliminate the effects of multiple air reflections. This technique has been partially successful but studies are still ongoing to develop an ideal calibration method.

Interpretation of the radar measurements on concrete slabs

The same method of reconstructing the dielectric properties as a function of frequency and depth was adopted as for the 50mm mortar slab. The results are shown in Figure5. It was found that the 100mm concrete block had a considerably higher conductivity and signal attenuation than the previous mortar slab. This attenuation may be related to higher moisture levels or may be due to losses resulting from concrete aggregates particles making internal reflections beneath the surface.

Fig 5: Dielectric properties 100mm concrete slab with frequency & depth. Fig 6: Field radar measurements in Liverpool.

Direct measurements of the variation of the moisture content across the slab from the drying of companion prisms indicated a parabolic type dependence of dielectric properties on depth for a slab of this thickness. Figure 5 shows the results of the optimisation fit using a parabolic spatial variation of permittivity and conductivity. The '2D' surface shown in Figure 5a & 5b allows the dielectric properties of the slab to be reconstructed at a given frequency and depth within the block. Investigations are currently in progress to verify the spatial dependence of permittivity that yields the best fit to the optimised data.

In parallel with these laboratory investigations, some field measurements were taken on a reinforced concrete slab of a multi-storey car park, located in Liverpool (Figure6a). This made use of portable, battery powered instrumentation to replace a laboratory based network analyser. The horn antenna was suspended from a tripod arrangement to give a 500mm air gap to the concrete slab (Figure 6b).

Summary and conclusions

A series of measurements have been undertaken under laboratory conditions to establish the validity of an inversion algorithm applied to the reflection coefficient data received from a TEM horn. The results exhibited a close correlation (<10%) between the reconstructed profile and the known dielectric properties.

Tests were then carried out on a 50mm thick mortar specimen to reconstruct the dielectric properties by inversion of the reflection coefficient data. The resulting permittivity and dielectric conductivity parameter values were shown to be both repeatable and plausible when compared with estimates derived from moisture content readings [7].

Measurements on a 100mm concrete slab demonstrated a higher degree of loss. This resulted in a reflection from the far side of the slab being barely distinguishable from the clutter arising from unwanted multiple reflections in the air gap at the front of the slab. This does present a significant problem and the current method appears to be at about the limit (100mm) beyond which reflected power from any discontinuity or far face is no longer measurable.

For the thicker concrete slab, the optimum spatial dependence is still to be determined, but based on prior knowledge of the moisture content variation with depth, a parabolic variation of the dielectric properties appears to offer the most plausible profile at this stage. The results of an optimization exercise designed to confirm this premise produced an acceptable fit to the measured data whilst still maintaining the anticipated frequency dependence exhibited for the 50mm mortar slab (Figure 6).

Acknowledgements

Thanks to due to EPSRC for their financial support for this work (project reference GR/N34130/01).

References

  1. Soutsos MN, Bungey JH, Millard SG, Shaw MR & Patterson A, "Dielectric properties of concrete and their influence on radar testing", NDT&E International, Vol. 34, 2001, pp 419-425.
  2. Davis J, Huang, Y, Millard SG and Nakhkash M, 2002, "Validation of an inversion algorithm for the reconstruction of an inhomogeneous dielectric profile", IEE Radar-2002 conference, Edinburgh, Oct. 2002, pp 232-238.
  3. Zhang J, Nakhkash M, and Huang Y, "Electromagnetic imaging of layered building materials", IOP Publishing, Measurement Science and Technology 2001, pp 1147-1151.
  4. 4. Nakhkash M, Huang Y, Fang MTC, "Application of the multi-level single-linkage method to one-dimensional electromagnetic inverse scattering problem", IEEE Trans. on Antennas and Propagation (ISSN 0018-926X), 1999, 22p.
  5. Cui TJ and Liang CH, "Non-linear differential equation for the reflection coefficient of an inhomogeneous lossy medium and its inverse scattering solutions", IEEE Transactions on Antennas and Propagation, Vol.42, No.5, May 1994, pp621-626.
  6. Nakhkash M, Huang Y, Al-Nuaimy W and Fang MTC, "An improved calibration technique for free-space measurement of complex permittivity", IEE Transactions on Geoscience and Remote Sensing, 2000.
  7. Bungey JH, Shaw MR, Millard SG and Thomas C, "Radar testing of structural concrete", Proc. Int. Conf. GPR'94, Waterloo, Canada, June 1994, Vol.1, pp 305-318.
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