Numerically based qualitative evaluation of GPR vertical and horizontal resolutions for reinforced concrete structures

. The GPR is widely used for non-destructive evaluation of reinforced concrete structures. High resolution of detection is needed in order to differentiate between multiple targets present in the host medium. This article aims to numerically study the vertical and horizontal resolutions associated to detection of reinforcing bars buried in a structure made from concrete by means of GPR inspection. Use was made of open source software GprMax2D by considering the three work frequencies: 1GHz, 1.6GHz and 2GHz. The method of scanning is assumed to be according to B-scan protocol which was conducted along a profile traced on the surface of the inspected member. In situ measurements were made for a bridge pillar made of reinforced concrete by the MALÅ CX GPR system with a frequency centred on 1.6 GHz. The obtained results show that the GPR is effective in the examination of reinforced concrete structure and most of the steel bars can be detected. After making correction, the horizontal resolution predicted by a conventional formula was verified. However, the real vertical resolution imposes a minimum distance separating steel bars that is higher than that proposed in the literature. This is due to the high conductivity of steel bars that yields strong reflection of the signal at the first reached bars and which impedes significant secondary reflection from targets located below them.


Introduction
Ground Penetrating radar (GPR) is a device widely used in non-destructive evaluation of reinforced concrete (RC) structures. The principle is based on the emission of an electromagnetic pulse which is centred on frequency belonging to the band 10MHz to 4GHz . The GPR transmitting antenna sends out the pulse into the inspected medium and is partially reflected when it reaches a target having dielectric properties that are different from those of the host medium. The reflected wave is recorded by means of a receiving antenna. The control unit of the GPR enables to process the single traces (A-scan) corresponding to fixed positions of antennas into a B-scan radargram.
This GPR device was judged suitable for the inspection of the sub-surfaces, particularly for the assessment of location of buried pipes in soils and rebars in RC structures. It was successful in monitoring cracks in bridges, roads, pavements and tunnels [1][2][3][4][5]. However, this non-destructive testing technique can involve some shortcomings affecting the stages of data collection, analysis and interpretation. Heterogeneities of the inspected medium may cause a complex reflection pattern which is difficult to understand. This is the case for example of soils containing high concentrations of rocks, gravel, and roots [6]. In the case of a RC structure, multiple steel bars are present and each one of them creates a trace on the radargram. But a given bar will be distinguishable only if the reflected signal is significant. So, a fundamental topic in GPR testing is how to improve the quality of acquired data by considering the best configuration and settings of the GPR device.
One of the most significant factors that should be dealt with in the planning of non-destructive studies based on the GPR is to characterise the horizontal and vertical resolutions that intervene in detection of targets. For appropriate collection of GPR data, radar antennas must be selected for each specific study. This includes in particular the best selection of the work frequency. The GPR's resolution capability is largely influenced by this choice.
The purpose of this work is to investigate numerically both vertical and horizontal resolutions in terms of the work frequency and target depth. Use is made of the GprMax2D software according to B-scan protocol. An example of In-situ GPR measurement is considered at first. Then, extensive simulations are performed in order to determine the practical resolution limits in horizontal and vertical directions. Direct examination of the obtained radargrams is done to determine detectability of steel bars buried in concrete while varying the horizontal or the vertical distance separating them. Discussion is performed about validity of some theoretical formulas that were presented in the literature for the prediction of GPR resolution.

Theoretical background of GPR resolution
The vertical and horizontal resolutions have been estimated through various formulas that were proposed in the literature. Let us consider two reflection events from two adjacent targets which are located on the same vertical, see Fig.1. The reflections are sensed at the time instants 1 t and 2 t . The vertical resolution v ∆ is defined as the minimal depth distance separating the two targets that could be distinguished on the GPR radargram [7][8]. Separation of the traces will be possible if the time delay 2 1 t t ∆τ = − exceeds half the pulse duration denoted p τ . The vertical resolution is then estimated by: where c is the velocity of electromagnetic waves. The horizontal resolution h ∆ is defined as the minimum distance separating two targets, which are located at the same depth from the inspected surface, such that the GPR can detect them separately. A lot of formulas have been proposed in the literature to estimate this resolution [9][10][11][12]. One can find among them the statement illustrated by Fig. 2 for which the horizontal resolution is taken to be the radius of antenna footprint. This latter can be expressed under the following form: where / c f λ = represents the wavelength for the given work frequency f , r ε is the relative dielectric permittivity to depth d of the reflector surface and H R the radius of antenna footprint at depth d , see Fig. 2. Eq. (3) states that the penetration depth is a small fraction of wavelength and decreases versus the GPR frequency. So there is a conflict resulting between decreasing horizontal and vertical resolutions on one hand and increasing the penetration depth on the other hand. A compromise should then be found in order to have sufficient amplitude of the GPR signal and desired resolutions. This depends on the host medium material.

A practical experiment
To have a clear idea about the practical issue of GPR resolution, a real GPR testing was carried out on a reinforced concrete bridge pillar having a diameter of 30cm . Fig. 3 shows a photo of the pillar which was the subject of GPR testing. The figure indicates also the traces of the B-scans that were performed.

Fig. 3.
Photo of the bridge pillar made of reinforced concrete that was tested by the GPR system MALÅ CX; the photo shows the traces along which B-scan was performed.
In the experiment, the GPR system MALÅ CX from the company MALA Geosciences was used. The work centre frequency was fixed at 1.6GHz . The frequency bandwidth is delimited by 0.8GHz and 2.4GHz . The time window was fixed at 9ns . GPR surveys were conducted on an area of the bridge pillar of 60 60cm × , where longitudinal and transverse B-scans were performed along the eight traces shown in Fig. 3.
Some of the collected radargrams are presented in Figs. 4 and 5. These correspond respectively to the horizontal line P7 and the vertical line P1 shown in Fig.  3. The pattern of reflection as obtained in the two radargrams shows the existence of ordered and repetitive hyperbolic signatures. Each signature is linked to a steel rebar. These hyperbolas are quite visible because of the high contrast existing between the steel electric conductivity and that of concrete. Taking the first row of the hyperbolas, one can determine the depth of concrete cover. For the longitudinal B-scan conducted along the profile P1, the depth is about 3cm. Meanwhile for the transverse profile P7, the identified depth is around 5cm.  Based on the radargram shown in Fig. 4, one can determine that the longitudinal rebars have a spacing of 30cm . Fig. 5 shows that the transverse rebars have a spacing of about 15cm . Horizontal resolution in this experiment enables to distinguish without problem between the adjacent steel bars of the first row along the two directions of inspection. Note that the radargrams become noisy and visibility of the traces is reduced after reaching a depth which is comprised between 16cm and 20cm for both of the profiles P1 and P7. This can be attributed to secondary reflections taking place at the rebars with high signal attenuation because of high steel conductivity.
To understand more deeply how vertical and horizontal resolution can change the radargram content, a case of study is simulated in the following.

Simulation of a case of study
In the following a concrete structure containing steel bars having the same diameter of 25mm is modelled by using GprMax2D software under Matlab environment [13]. GprMax2D software enables to simulate propagation of electromagnetic waves based on the finite difference in time domain method. The bars are located according to Fig. 6. The horizontal distance between the bars belonging to the second row is 5cm , while the distance separating those of the third row is 10cm . The first two rows are separated vertically by 5cm , while the second and third rows are distant by 10cm . Fig. 6. Scheme of the simulated concrete structure containing steel bars. Table 1 gives the materials properties used in GPR simulations. They consist of relative permittivity r ε , relative permeability r µ and electric conductivity σ . The calculated wave velocity c in / m ns is given in the last column of this table. GprMax2D enables to obtain a B-scan radargram along the top border of the concrete domain. Normally all targets should show a hyperbola trace which is associated to the reflected amplitude of wave on the steel bar. The expected number of hyperbolas is then 6. To assess this, the resolution is tested in the following for the three work frequencies 1GHz , 1.6GHz and 2GHz .

Horizontal resolution
To study the outcome of simulation in terms of horizontal resolution, reference is made to Eq. (2) in which a new parameter α reflecting geometric attenuation is introduced [14][15][16]. The horizontal resolution is considered under the following form [15]: In the present work, it is proposed to define the coefficient α as the ratio of the reflected signal amplitude from a bar located at the depth of 20cm divided by the reflected signal amplitude from the bar situated at the depth of 5cm . Fig. 7 gives the obtained radargram for the work frequency 2 1.6 f GHz = . From this figure, one can see that it is quite possible to distinguish between the hyperbolas associated to steel bars placed on the first, second and third rows, and presenting an eccentricity with regards to the first column. One can conclude then that the horizontal interval distances of Fig. 6 are within the margin of horizontal resolution. Post-treatment of a B-scan radargram, such as that given in Fig. 7, can be performed under Matlab in order to identify the reflection amplitudes from steel bars. Table 2 gives the obtained numerical results in terms of signal amplitude reflected from the bars as function of their depth and the work frequency.

Amplitude Depth
The amplitudes given in Table 2 are next used to calculate the geometric attenuation parameter α for each work frequency. The obtained results are as follows: 1 0.32 α = for the frequency 1 f ; 2 0.30 α = for the frequency 2 f and 3 0.27 α = for the frequency 3 f . From Table 2, one can see that the amplitudes decrease with frequency. The geometric attenuation decreases also with frequency. As H R decreases in its turn with frequency, no conclusion can be made regarding the effect of frequency on horizontal resolution limit before calculating the resolution from Eq. (4). Table 3 gives the obtained values of H R and h ∆ as function of the work frequency and depth. ∆ versus the depth for a given work frequency.  Table 3, it is seen that the horizontal resolution limit decreases at a given depth with the work frequency. It is seen also that the horizontal resolution limit is largely affected by depth. It almost doubles when the depth passes from 5cm to 20cm .
To test further the horizontal resolution limit as predicted by Eq. (4), examination of the aspect of the obtained radargram was performed. Simulations are conducted by varying the horizontal interval distance separating the steel bars in a row placed at a given depth. Fig. 8 gives the radargram in the case of 3 2 f GHz = for the interval distance 5cm and depth 20 d cm = . It is clear in Fig.8 that interference has occurred and detection of the two bars is impossible. Only one hyperbola trace appears in the radargram. This observation is conform with the horizontal resolution limit which is in this case, as given in Table 3, equal to 6.2cm . Considering the work frequency 2 1.6 f GHz = and varying the interval distance separating two adjacent steel bars that are placed in a row at a given depth, Table  4 gives the conclusion in terms of detectability, or presence of interference. This was determined after studying each simulated radargram. Table 4 corroborates the results given on Table 3. No detection is possible when the horizontal distance separating two adjacent bars is lesser than the horizontal resolution limit predicted by Eq. (4).

Vertical resolution
As shown by Eq. (1), the vertical resolution v ∆ depends on the width of the pulse emitted by the GPR antenna as well as the wave velocity in the host medium. The pulse width can be estimated from the work frequency to be roughly 1/ This gives for the vertical resolution the value / 2 v ∆ = λ . To test numerically this theoretical resolution limit, numerical simulations have been conducted with the work frequency 2 1.6 f GHz = by varying the vertical distance separating two adjacent steel bars. Qualitative evaluation of detectability was performed then through studying the obtained radargram. The conclusions are reported in Table 5. Comparison is also done with the vertical resolution predicted by means of Eq. (1). This latter is given in the last column.  Table 5, it is seen that / 2 v ∆ = λ predicts the observed vertical resolution limit only for the depth of 5cm . The numerically determined vertical resolution limit is found to be larger than that predicted by Eq. (1) for depths exceeding 10cm . This is because of shadowing effect induced by the upper bar, which impedes the emitted signal to hit the lower bar with significant intensity such that it could provoke a reflected signal that can be sensed. The theoretical formula as given in Eq. (1) does not take into account this shadowing effect which is of huge importance in practice. Its predictions underestimate the real vertical resolution.

Conclusions
Considering concrete structures reinforced with steel bars, numerical simulations which were oriented towards evaluating qualitatively horizontal and vertical resolutions have been performed in this work. This was achieved by means of GprMax2D software. Comparison was made with two conventional formulas that were introduced in the literature to estimate GPR resolution in both directions. It was found that the equation predicting the horizontal resolution gives accurate results with respect to the observations made. This former should then be corrected by taking into account geometric attenuation as mentioned in the present work. However, the theoretical predictions regarding the vertical resolution hold only for shallow depths. Large errors are observed when using the formula of vertical resolution for deep targets. So, in practice detection will only be possible for bars that are separated vertically with a minimal distance that is larger than that predicted by the theoretical formula. This observation may be understood if one considers the shadowing effect which occurs in reality when two bars are placed vertically one above each other.