Short Abstract

The research presented in this paper deals with the application of the GPR technique to the physical characterisation of concrete. The details and results of an experimental study on the effect of concrete moisture upon radar waveforms propagating through concrete laboratory slabs are reported here in. Radar measurements were performed using a commercial GPR system with 1.5 GHz ground-coupled antenna.

The concrete slabs were conditioned so as to get an homogeneous moisture distribution. The samples were partially dried and sealed, and the water saturation was assessed by weighing. Moreover, electrical resistivity measurements were carried out on each concrete sample in order to provide complementary information regarding the moisture of the concrete.

Interesting results concerning the aptitude ability of radar the GPR technique systems for the characterisation of the moisture state of concrete were obtained and will be discussed in the paper The attention is focused on amplitude, velocity and spectral content of the recorded waveforms. The attention was focused on amplitude, velocity and spectral content of the recorded waveforms. In particular, the behaviour of the transmitter-receiver direct wave was found very influenced by the moisture of concrete. At least, a part of Tthese experimental results was were also simulated examined and simulated using a simple dielectric model of heterogeneous mixtures.

1 Introduction

Currently, the GPR technology is more and more implemented on site by civil engineers with the aim of detecting buried dielectric interfaces (concrete delamination, steel rebar, tension ducts, etc.) or measuring depth or thickness of material layers. However, excepted some specific papers [1,2,3], the aptitude of GPR for the physical characterisation of construction materials was very little studied by researchers and is almost never used by engineers concerning concrete.

The physical characterisation of concrete using radar systems consists at last in resolving an inverse problem of wave propagation. Currently, the analysis of the direct problem is conducted through a systematic study on the effect of concrete characteristics upon its HF electromagnetic properties and upon the radar measurement.

Thus, in the field of the radar NDT of concrete, this paper deals with the ability of this technology for the physical characterisation of the concrete. In particular, an experimental study was conducted on concrete laboratory slabs in order to analyse the dependence of radar measurements on the water content of concrete. Then, the experimental results were simulated using a simple dielectric mixture model.

2 Theoretical background

2.1 Electromagnetic properties of concrete
During its propagation in concrete, an electromagnetic (EM) wave is modified in relation with the EM properties of the material: the electrical conductivity, s, the dielectric permittivity, e, and the magnetic permeability, m. The latter property equals the free space permeability m₀ since concrete is a non-magnetic material (m₀ = 4p.10^-7 H/m).

Concrete permittivity and conductivity are complex properties expressing respectively the ability of the material for the electrical polarisation of polar molecules and for the ionic conduction of free charged particles. These properties are defined from a theoretical point of view, in order to separate the basic electrical phenomena. However, in the usual range of radar frequencies (~100 to 3000 MHz), EM waves are influenced by these two properties, and it is impossible to distinguish their effects. Thus, an effective permittivity, e_e, is defined, which takes electrical conductivity and dielectric permittivity into account. The expression of the effective permittivity is given by Eq.1.

(1)

In this expression, the effects of e' and s" are added to produce the real part e'_e of the effective permittivity. This part represents the capacity of concrete to store EM energy. On the other hand, the imaginary part, e"_e, results from e" and s', expressing the EM energy losses.

The permittivity e_e is generally divided by the permittivity of air e₀, which is a real number (e₀ = 8.854.10^-12 F/m). A relative permittivity e_r is thus defined, as expressed in Eq.2:

(2)

The real part e'_r of the relative permittivity is usually known as the dielectric constant. The dielectric constant primarily influences the wave velocity. The imaginary part, e"_r (loss factor), represents the losses of energy due to absorption. It greatly influences the attenuation of the wave. The absorption of electromagnetic energy in concrete is primarily due to ionic conduction and dielectric relaxation. The losses due to conduction result from friction existing between moving free charges and fixed particles. The dielectric relaxation corresponds to the movement of polar molecules, which tend to direct their dipolar moment parallel to the electric field. During the rotation, friction occurs between molecules, leading to energy losses. In concrete, the relaxation mechanism essentially concerns free water molecules contained in the pores.

2.2 Significance of the water content
Concrete is an heterogeneous material, which can be simply decomposed into three phases: a solid phase, including all the solid components (aggregates, hydrated components, anhydrous cement, etc.); a gaseous phase (air); and a liquid phase, which is a conductive solution. The sum of the volume fractions of air and saline solution equals the total porosity of the material.

The relative permittivity of the solid phase is a real number usually lying between 3 and 5, depending on the mineral composition. The real value of the solid phase permittivity indicates that solid components present negligible losses. The mixture of solid and gazeous phases (dry concrete) gives a non-dispersive medium, i.e. the permittivity is not frequency dependent. The existence of dispersion in concrete results only from the presence of free water in the pores and its significance is governed by the volume water content. That was observed by some authors by the way of concrete permittivity measurements [4,5,6]. An important effect of dispersion is the change in signal shape during propagation.

In concrete, only the permittivity of the pore solution is a complex number. According to Debye's relaxation model, in the radar frequency range (100 to 3000 MHz), the relative dielectric constant of an aqueous solution lies between 40 (high salinity) and 81 (pure water) [7]. The effect of the salinity on the relative loss factor of an aqueous solution is also described by Debye's model. It can be shown that the number of ions dissolved in the pore solution has no effect beyond the relaxation frequency (~ 10 GHz), corresponding to the maximum of dielectric losses. However, regarding radar frequencies, the relative loss factor varies over a wider range (~5 to 500) as the salinity increases.

So, in spite of a relatively low volume fraction value in concrete, the variations in water content lead to large changes in the dielectric properties of the mixture, due to the strong dielectric constant and high loss factor (high salinity of the pore solution). The presence of saline water in the concrete pores also produces a particular polarisation mechanism, known as the Maxwell-Wagner effect [5]. This effect occurs when conductive volumes are contained in a resistive matrix, leading to interfacial polarisation when an external electric field is applied.

3 Experimental details

Concrete samples and moisture conditioning
The tests were carried out on concrete parallelepiped slabs of dimensions 25 cm x 25 cm x 7cm (Fig.1 and Fig.2) [8]. The degree of saturation S was controlled by partial drying and weighing. Then, the slabs were sealed and oven heated in order to distribute the moisture in an homogeneous way. The various degrees of saturation S_i allowed to generate slabs with different electromagnetic properties.

Fig 1: Concrete slab geometry.

Fig 2: Concrete slab and radar equipment.

Radar and electrical resistivity measurement
Radar measurements were carried out with GSSI^Ò equipment(SIR 2000 + 1.5 GHz antennas). The antennas were located against the concrete slabs (Fig.3). Thus, two signals were recorded and analyzed: the Transmitter - Receiver (T-R) direct wave and the reflection generated by the bottom of the slab. In order to highlight the contrast between dry and saturated concrete, amplitudes are normalised in relation to the amplitudes recorded on saturated concrete.

Fig 3: Configuration of radar measurements and recorded signals.

Radar measurements were performed at the middle of the concrete slabs. In order to demonstrate that this measurement position is not affected by border effect, a short radar cross-section of a concrete slab was carried out.

Electrical resitivity measurements were carried out using a commercial Wenner array (RESI by Proceq^Ò).

4 Experimental results

4.1 Effect of concrete moisture on the effective dielectric constant and the propagation velocity
The assessment of the dielectric constant of concrete sample can be carried out using two usual methods reported in [8]. The first method is based on the estimation of the propagation time of the signal reflected by the bottom of the slab. This measurement allows estimating the propagation velocity and to calculate the effective dielectric constant e'_r of the concrete.

The second method consists in analysing the reflection coefficient of the concrete compared to the reflection coefficient of a metallic plate, which can be related to the dielectric constant of the concrete.

Fig 4: Effect of concrete moisture upon the dielectric constant [ Freq ~ 1.5 GHz ].

For each concrete sample, these two methods were implemented. The averaged results are presented in the Fig.4. The increase in the dielectric constant associated to the increase in the water content is clearly observed. These results present a good agreement with the literature, since the dielectric constant is lying between 4 (for dry concrete) and 8.2 (for saturated concrete). In the figure 5 is presented the related propagation velocity.

Fig 5: Effect of concrete moisture upon the propagation velocity [ Freq ~ 1.5 GHz ].

4.2 Effect of moisture on the amplitude of waveforms
Fig.6 shows the relation between the amplitudes of the two recorded signals and the moisture state of the concrete. Amplitude values are normalised in relation to amplitudes measured on the saturated slab in order to highlight the contrasts between different moisture states. It can be observed a linear increase in the amplitudes of the two signals associated to the decrease in the degree of pore saturation. Linear regressions indeed present good determination coefficients (R²= 0.97 for the T-R direct wave and 0.93 for the bottom reflection). Moreover, differences of 6 dB for the T-R direct wave and 9 dB for the bottom reflection are quantified between dry and saturated states.

Fig 6: Effect of the degree of saturation upon signal amplitude.

The behaviour of the T-R direct wave is particularly interesting for at least two reasons. Firstly, this signal is generally considered as stable reference on radargrams. But, actually, this experiment shows that it is greatly influenced by the water content of concrete. Secondly, the sensitivity of the direct wave to the moisture of concrete is an important factor in the field of the physical characterisation of concrete.

Fig.7 presents the results of electrical resistivity measurements carried out on the concrete slabs. This property is very dependent of the degree of saturation since the electrical conduction in concrete is primarily ionic (or electrolytic) [9]. From a theoretical point of view, the attenuation of radar waveforms and consequently their amplitude are related to the electrical resistivity of concrete. The value of 99 kOhm.cm corresponds to the higher limit of measurement for the resistivimeter used in this study. For this reason, it was not possible to investigate slabs presenting saturation degree lower than 32 %. The observed behaviour is in agreement with the literature [10]. In particular, it can be observed that the electrical resistivity is greatly increased, as the degree of pore saturation becomes smaller than 60-70 %. Physically, the disconnection of the pore solution in this saturation range explains this behaviour.

Fig 7: Effect of the degree of saturation upon the electrical resistivity of concrete.

However, this particular behaviour is not observed concerning the linear variations in the amplitudes of radar waveforms with the degree of saturation. This shows that the amplitude of radar waveforms are just sensitive to the volume fraction of water in concrete and not to the electrical connection of the pore solution. Thus, in the field of the moisture characterisation of concrete, the inversion of radar waveform amplitude may be easier than the inversion of resistivity measurements.

4.3 Effect of moisture on the spectral content of the reflected signal
The Fig.8 shows the relation between the spectral content of the signal reflected by the bottom of the slabs and the degree of saturation of concrete. It can be observed that the centre frequency is approximately lying from 1.18 GHz (saturated concrete) to 1.4 GHz (dry concrete). This behaviour is explained by the electromagnetic dispersion of concrete due to the presence of water. In concrete, high frequencies are generally more attenuated than low frequencies and the importance of this phenomenon is amplified by the presence of water. This dispersion related to the water content was observed by some authors that implemented permittivity measurements on concrete samples using coaxial transmission lines [4,5] or open-ended coaxial probe [6].

This experimental result leads to the conclusion that the dispersion of concrete observed on permittivity measurements is also visible on radar measurement. So, for the characterisation of concrete moisture, the analysis of the variations in the shape of signals should provide interesting information.

Fig 8: Effect of the saturation degree upon the spectral content of the bottom reflection.

5 Direct modeling

5.1 Modeling of the effective dielectric constant of the concrete
The effective permittivity of each concrete slab was simulated using the Complex Refractive Index Model (CRIM), which is a simple mixture law (Eq.3),

(3)

where:
e_r - relative effective permittivity of concrete
e_m - relative permittivity of the solid phase (matrix)
e_a - relative permittivity of the gazeous phase (inclusion - air)
e_sw - relative permittivity of the liquid phase (inclusion - saline water)
f - porosity of concrete
S_w - degree of pore saturation.

The input data relative to the simulation are given in the table 1. The centre frequency is the average of the values presented in the Fig.8. The porosity of concrete was measured according to a recommended procedure [11].

The pore solution is characterised by a permittivity depending on the concentration of dissolved ions. In order to assess this concentration, a DC conductivity measurement was carried out on a mechanically extracted pore solution. This conductivity allowed estimating the NaCl-equivalent concentration of the solution by inversion of Debye's equations [7] for very low frequencies. The result of this experiment led to a NaCl equivalent salinity of approximately 15 g/l. Then, it was possible to calculate e_sw using Debye's equations at 1.3 GHz.

The Fig. 9 presents the result of the simulation and the radar measurements of the effective dielectric constant of the slabs. One can note a good agreement between experimental and simulated data, leading to the conclusion that CRIM seems to be able to simulate the real effective permittivity of concrete.

Fig 9: CRIM simulation of the effective dielectric constant of concrete.

5.2 Modeling of the amplitude variation with the degree of saturation
The following simulation aims at reproduce the experimental behaviour presented in the Fig.7 concerning the reflection generated by the bottom of the slab. Although the initial electric field E₀ is unknown, it is possible to calculate from a theoretical point of view the variations in the amplitude of the bottom reflection compared to the amplitude measured on saturated concrete.

According to the plane wave approximation, the amplitude E of the electric field at the receiver position is related to the absorption coefficient a, the initial amplitude E₀and the propagation distance d, as presented in Eq.4. The knowledge of the complex effective permittivity (e_e = e '_e - j e ''_e) of the propagation medium allows to calculate the absorption coefficient a, according to Eq.5.

(4)

(5)

The effective permittivity of each concrete slab was simulated using the CRIM and the input data presented in the table 1. Then, an absorption coefficient a_i can be calculated for a degree of saturation i. Thus, in such a slab, the amplitude E_i of the electric field is given by Eq.6. The simulated amplitudes are normalised in relation to the amplitude E_s of the electric fied in saturated concrete (absorption coefficient a_s), which is given by Eq.7.

(6)

(7)

At last, the normalisation leads to the elimination of E₀ from the equation, as presented in Eq.8. Final results A_i are expressed in decibels (Eq.9). In the case of the slab presented in this paper, the propagation distance d of the bottom reflection equals 15.1 cm. Thus, the variations in the normalised amplitude A_i are just depending on the variations in the absorption coefficient, that are simulated according to the CRIM.

(8)

(9)

The simulated and experimental values of A_i are plotted on the Fig.10 as a function of the degree of saturation. It can be observed that experimental data are correctly simulated.

Fig 10: CRIM simulation of the variation in the ampiltude of the bottom reflection.

Actually, a part of the amplitude variation is due to changes in the width of the radiation pattern in relation to the water content. This behaviour was considered as negligible for this study, but complementary FDTD simulations are currently conducted to assess its actual significance.

6 Conclusion

The experimental study presented above shows the sensitivity of radar measurements to the degree of saturation of concrete, and thus the aptitude of the technology for the physical characterisation of the material.

In particular, the behaviour of the transmitter-receiver direct wave was found very influenced by the concrete moisture. This result is particularly interesting because the use of this signal is not depending on the presence of a reflector.

Currently, systematic laboratory studies are conducted in order to evaluate the effect of the physical characteristics of concrete on radar measurements and to define the most significant parameters of the signals regarding the water content. Taking account of the behaviour of the direct wave, a complementary study is also conducted to assess the ability of radar surface waves to characterise the moisture state of concrete.

Finally, the simulation stage leads the conclusion that simple dielectric mixture models as CRIM seem to be able to reproduce the experimental behaviour concerning the variations in the effective dielectric constant or in the absorption coefficient of the concrete slabs. This conclusion is particularly interesting concerning the inverse modeling which will be conducted in a further stage of this research work.

7 References

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