Bundesanstalt für Materialforschung und -prüfung

International Symposium (NDT-CE 2003)

Non-Destructive Testing in Civil Engineering 2003
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GPR: From the State-Of-the-Art to the State-Of-the-Practice

Imad L. Al-Qadi
Charles E. Via, Jr. Professor of Civil and Environmental Engineering,
Leader of the Roadway Infrastructure Group, Virginia Tech Transportation Institute, 200 Patton Hall, Virginia Tech, Blacksburg, VA 24061-0105, Tel: 540 231-5262, Fax: 540 231-7532, e-mail: alqadi@vt.edu
Samer Lahouar
Graduate Research Assistant, Virginia Tech Transportation Institute, 3500 Transportation Research Plaza, Virginia Tech, Blacksburg, VA 24061-0536, Tel: 540 231-1504, Fax: 540 231-1555, e-mail: slahouar@vt.edu
Amara Loulizi
Research Scientist, Virginia Tech Transportation Institute, 3500 Transportation Research Plaza, Virginia Tech, Blacksburg, VA 24061-0536, Tel: 540 231-1504, Fax: 540 231-1555, e-mail: amlouliz@vt.edu

Abstract

Determining the dielectric properties of materials is very important for different non-destructive evaluation techniques because these properties are usually affected by the volumetric properties of the materials. Different techniques had been developed during the last decade to measure the dielectric properties of laboratory-prepared samples. However, dielectric-properties estimation in the field is not as well-researched.

This paper explains the different methods that can be used to estimate the dielectric constant of civil structures using Ground Penetrating Radar (GPR). Specifically, the paper focuses on the hot-mix asphalt (HMA) layers of flexible pavements. The first method presented shows how the variations of the HMA's complex dielectric constant can be estimated in the field over the frequency bandwidth of an air-coupled GPR system (500 to 2000 MHz). The second technique also uses an air-coupled GPR system to effectively estimate the dielectric constant of the HMA layer of newly-built pavements. Experimental results showed that this technique achieved an average error of the dielectric constant of 6.7%, resulting in a thickness error of 3.7%. A third technique that uses a combination of air-coupled and ground-coupled GPR systems was found to achieve an average error of approximately 13.8% when used to estimate the dielectric constant of the HMA layer of an old pavement system. This technique resulted in a thickness error of 6.7%. In contrast to this technique, the classic time-domain technique was found, in this case, to achieve an average error of the dielectric constant of approximately 25.4%.

Introduction

Estimating the dielectric properties of materials is very important for many non-destructive evaluation techniques. In fact, the dielectric constant of construction materials can usually be correlated to their volumetric properties and can therefore be used as an indication of defects or distresses within the tested structure. For HMA materials, the dielectric constant can usually be correlated to the density, air voids, asphalt content, and moisture accumulation (Maser 1992). For concrete, the dielectric constant can usually be correlated to the aggregate type, cement to water ratio, and chloride content (Al-Qadi and Riad 1996).

Several studies measured and reported the dielectric properties of HMA on laboratory samples. Al-Qadi (1992) studied the dielectric properties of HMA in the frequency range of 12.4 to 18.0 GHz, using a set consisting of a focused conical horn antenna and an HP 8510B network analyzer. Two types of aggregate were used in preparing HMA specimens: namely, low-absorption limestone and high-absorption piedmont gravel and Conoco AR4000 binder. It was found that for dry HMA specimens, the real part of the dielectric constant ranged from 3.7 to 5.2, while the imaginary part ranged from 0.05 to 0.16. For wet HMA specimens (volumetric water content ranging from 1.2% to 8.2%), the real part of the dielectric constant varied from 4.1 to 5.3, and the imaginary part varied from 0.10 to 0.30. In another study, Shang et al. (1999) used a coaxial apparatus to measure the dielectric properties of HMA over the frequency range of 0.1 MHz to 1.5 GHz. The HMA specimens were prepared using the Ontario wearing surface and binding mixes (HL3 and HL8), with asphalt binder contents varying between 4.0% and 5.5%. Results indicated that asphalt content and mix type did not significantly affect the measured complex dielectric constant. However, moisture content was found to be a predominant factor. The average measured real part of the complex dielectric constant over the frequency range of 8 to 900 MHz was 6.00 ± 0.15 for the dry specimens and 6.52 ± 0.99 for the soaked specimens.

This paper presents various methods for estimating the dielectric properties of HMA layers in the field, using GPR. Validation of the different techniques, using GPR data collected in the field, is also presented.

Ground Penetrating Radar System Description

The principle of the GPR system used in this study (impulse radar) is based on sending an electromagnetic (EM) pulse through the antenna to the pavement surface and then recording the reflected pulses from the internal interfaces, where there is a contrast in the dielectric properties as depicted in Figure 1. The measured time difference between the reflected pulses (i.e., t1 or t2) can be used in conjunction with the dielectric properties of the surveyed layer to determine its thickness. The thickness of the HMA layer, for example, could be computed according to equation (1):

(1)

where h is the HMA layer thickness, t1 is the EM wave two-way travel time through the layer as shown in Figure 1, c is the speed of light in free space (c = 3x 108 m/s), and e r is the dielectric constant of the HMA layer. Similar expressions could be developed for the other layers.

Fig 1: Typical GPR Reflections from a Pavement System.

Electronically, impulse GPR systems function in the following manner: A trigger pulse is generated in the radar control unit. This trigger pulse is sent to a transceiver where it is modulated and amplified to become a bipolar transmit pulse with a much higher amplitude and bandwidth. The generated pulse is then sent through the transmitting antenna to the ground. After a short time (10 to 100 nanoseconds, depending on the antenna used), the reflected signal is collected by the receiving antenna and is transmitted to the receiver circuitry, where it is filtered and digitized. The produced data is finally displayed for immediate interpretation and is stored on a magnetic media for later processing.

Depending on the way antennas are used, GPR systems are classified as air-coupled (or launched) or ground-coupled systems. In air-coupled systems, the antennas (usually horn antennas) are typically 150 to 500mm (6 to 20 in) above the surface. These systems give a clean radar signal and allow for highway speed surveys. However, because part of the EM energy sent by the antenna is reflected back by the pavement surface, the depth of penetration is limited. In contrast, a ground-coupled system's antenna is in full contact with the ground, which gives a higher depth of penetration (at the same frequency) but limits the speed of the survey.

Fig 2: GPR Van Used during the Survey Showing Antennas Configuration.

The control unit of the GPR system used in this study allows data acquisition through two different channels simultaneously. Therefore, both air-coupled and ground-coupled antenna systems can be used simultaneously. As depicted in Figure 2, the air-coupled system is composed of a pair of separate horn antennas (bistatic: one serves as a transmitter and the other as a receiver) working at a central frequency of 1 GHz. The ground-coupled system is comprised of a single antenna (monostatic operating as transmitter and receiver) working at a central frequency of 900 MHz

In-situ HMA Dielectric Constant Estimation versus Frequency

As part of an ongoing research project at the Virginia Smart Road (Al-Qadi et al., 2000-a), 35 copper plates were embedded during construction at the different layer interfaces of 12 different flexible pavement systems in order to characterize the dielectric properties of the different pavement materials (Al-Qadi et al., 2000-b). Use of GPR to characterize the in-situ dielectric properties of the SM-9.5D SuperPaveTM mix versus frequency is presented in this paper. The study was based on collecting GPR scans over an SM-9.5D wearing surface layer, underneath which a 914x1219mm (3x4 ft) copper plate was placed during pavement construction. The ratio of the Fourier transform of the measured reflected signal to that of the incident signal (typically considered as the GPR-reflected signal collected over a copper plate placed at the pavement surface) represents the overall measured reflection coefficient:

(2)

where F{} is the Fourier transform, f is the frequency of the signal, and Yr(t) and Yi(t) are the reflected signal from the pavement surface and the incident signal, respectively. Practically, the Fourier transform is computed using a fast Fourier transform algorithm.

Theoretically, the overall reflection coefficient of the considered system (i.e., HMA layer plus copper plate) can be determined using the multiple reflection model presented in Figure 3. It should be noted that the transmitted wave is assumed to be transverse electromagnetic (TEM) and propagating normally to the surface. It is shown oblique in the figure for clarity. As the electromagnetic wave hits the road surface, some energy is reflected, with a reflection coefficient r, and some energy is transmitted through the interface with a transmission coefficient equal to (1+r). The reflection coefficient r is given by equation (3) (Balanis, 1989):

Fig 3: Multiple Reflection Model.

(3)

where er* is the complex dielectric constant of the HMA layer and f is added to show the dependency of the considered values on frequency. The wave then propagates through the HMA layer until it reaches the bottom, just above the copper plate. At this point, the transmitted wave is multiplied by the propagation factor T given by equation (4) (Balanis, 1989):

(4)

where w is the wave angular frequency; d is the HMA layer thickness; and j2 = -1. As soon as the wave hits the copper plate, it is reversed in sign and starts propagating back to the surface, where it is transmitted through the HMA/air interface with a transmission coefficient (1-r). At the same time, another wave at the surface is reflected back inside the HMA layer with a reflection coefficient -r. The process will then repeat until all the transmitted EM energy is attenuated in the HMA layer. The theoretical overall reflection coefficient will be the sum of all the reflected coefficients and is determined using equation (5).

(5)

where the right-hand side of the equation was obtained using the summation expression of a geometric series with a base rT2.

Substituting equations (2) and (4) into equation (5) leads to an equation where r(f) is the only unknown:

(6)

Fig 4: Multiple Solutions for r at 1 GHz.

When solving equation (6) for r, it was found that multiple solutions exist at each frequency. This is depicted, for example, in Figure 4 for the SM-9.5D layer at a frequency of 1 GHz. In this figure,two solutions were found, as illustrated by the circles. The solving procedure starts by computing the function g(r) for different values of r corresponding to physical values of er*. The zeros of the function, thus found, are then used as initial points in a Gauss-Newton method to find the actual solutions with an accuracy of 10-12. These solutions are then sorted to select the best physical solution based on the conversion of both parts of the dielectric constant (i.e. real and imaginary). Figure 5 shows the chosen solution for the SM-9.5D dielectric constant from 500 to 2000 MHz. It should be noted that this data may not be extrapolated to other frequencies. Different dielectric constant values may be obtained at other frequency ranges. The average complex dielectric constant over this frequency range is 5.2-0.1j.

Fig 5: Chosen Solution for the Dielectric Constant of SM-9.5D.

Estimation of Static Dielectric Constant of HMA Layers

In general, the thickness of any pavement layer can be estimated based on equation (1). Assuming that the two-way travel time t can be measured accurately from the GPR reflected signal as pictured in Figure 1, the dielectric constant e r is the only unknown that remaining in equation (1). For new pavement systems, the dielectric constant of HMA can be estimated non-destructively from the GPR-collected signal, based on the following equation (Maser 1996):

(7)

where

  • e HMA is the HMA layer dielectric constant,
  • A0 is the amplitude of the surface reflection, and
  • AP is the amplitude of the reflected signal collected over a copper plate placed on the pavement surface. It represents the negative of the incident signal.

It should be noted that estimating the HMA dielectric constant using equation (7) assumes that the HMA layer is homogeneous and has a uniform dielectric constant throughout its thickness. This assumption is usually valid for new pavements; however, it may not be applied to aged pavements.

To validate this technique of in-situ dielectric-constant measurement, different GPR surveys were conducted as a quality control-quality assurance (QC/QA) for a newly-built three-lane pavement section of Route 288 in Richmond, Virginia (APAC 2001). Three HMA layers were evaluated in this project.

In order to ensure that the HMA layers were homogeneous for the GPR survey, the GPR measurements were conducted on each of the HMA pavement layers just a few hours after they were placed. For each of the three lanes, GPR surveys were conducted on three lateral positions: center of the lane, right wheel path, and left wheel path. Figure 6 shows the variations of the dielectric constant of the three HMA layers along the test-section in the center of the center lane. This figure shows that for all the layers, the dielectric constant is around 5, except for some locations where it varies slightly. The regions of relatively low dielectric constant (for example around 50m for the HMA intermediate layer 2) are usually susceptible to having a low density. An increase in air voids implies a decrease in the global dielectric constant of the mix. Moreover, because the three HMA layers have approximately identical dielectric constants, discrimination between the individual layer interfaces can be difficult to achieve using GPR surveys at the top of the HMA intermediate 2 layer.

Fig 6: Dielectric-Constant Variation of the HMA Layers at the Center of the Center Lane.

To verify the accuracy of the estimated dielectric-constant values based on the GPR data, stationary GPR measurements were collected near the locations where some cores were extracted. These stationary measurements were then used to estimate the dielectric constant at these positions based on equation (1) and using the measured thickness (from the cores) and the two-way travel time measured from the GPR data. Table 1 presents the correlation between the HMA base layer dielectric constant measured from cores (i.e., based on equation (1)) and the dielectric constant estimated from the GPR data (i.e., based on equation (7)). According to this table, the dielectric-constant error varies between 0 and 20.8%, with an average of 6.7%. Table 1 also shows the correlation between core thickness and the thickness estimated from GPR data. The thickness error varies between 0 and 12.9%, with an average of 3.7%. The reported error could be due mainly to the fact that the positions where the GPR scanning was performed did not always correspond exactly to the core locations. It should be noted that the error of the estimated layer thickness is approximately half the error of the dielectric constant (Lahouar et al. 2002).

Layer Thickness Estimation of Old Pavements

Use of equation (7) to determine the HMA dielectric constant assumes that: (1) the layer is composed of the same material (constant eHMA) throughout its entire thickness, (2) it doesn't have any overlays or repaired sections, and (3) it does not present defects such as moisture or stripping. In fact, the presence of diverse layers of different ages and compositions within the HMA layers may be difficult to detect in the received GPR signal. The contrast in the dielectric constants may not be large enough to produce a relatively high reflection indicating the presence of a different layer. Therefore, equation (7) is only reliable for new or defect-free pavements (Saarenketo, 2000). The examination of typical in-service pavement cores reveals that the above assumptions are ideal and rarely exist. This is due to the variability in materials used in construction in addition to multiple maintenance and rehabilitation projects that usually occur during the service life of most pavement systems.

Core # Thick. (mm) GPR Thick. (mm) Thick. Error (%) GPR Time (ns) GPR Dielectric Constant Core Dielectric Constant Dielectric Constant Error (%)
111312712.91.9375.26.620.8
21081090.91.6525.25.31.8
31091122.41.7395.45.75.3
41131130.01.7345.35.30.0
51011053.91.5825.15.57.5
6951005.31.5455.45.99.8
71071113.71.7155.45.87.1
81091100.91.6845.35.41.8
996971.01.5015.45.52.1
1098971.01.5035.45.32.1
1192901.61.3605.14.94.5
121051071.91.6185.15.33.7
131041061.91.6275.35.53.7
141021052.91.6285.45.75.6
1510611912.31.8655.57.020.7
161101209.11.8235.26.216.0
S295961.001.4094.95.02.1
Average1041083.7   6.7
Table 1: Correlation between Core Dielectric Constant and GPR Dielectric Constant of HMA Base Layer.

To overcome this problem, an average value of the dielectric constant throughout the HMA layer should be computed. This improvement can be achieved using a common midpoint (CMP) technique, as illustrated in Figure 7a. In this case, the HMA layer dielectric constant is computed based on the reflection times t1 and t2, obtained respectively from a monostatic and a bistatic antenna. The layer dielectric constant, er, is computed according to equation (8):

(8)

where x is the distance between the two antennas of the bistatic system. It should be noted that because the HMA dielectric constant is determined from the reflections at the bottom of the layer (point P), it represents an average value and therefore accounts for any internal inhomogeneities.

Fig 7: (a) Common Midpoint Configuration, (b) Modified Common Midpoint Configuration.

The configuration depicted in Figure 7a can be modified to suit the antenna configuration of the GPR system used for this research (i.e., a bistatic air-coupled antenna system and a monostatic ground-coupled antenna, Figure 2), as shown in Figure 7b. The layer dielectric constant is then found after solving for the incidence and transmission angles, q i and qt , and the distance x1, knowing the two-way travel times t1 and t2 (computed from the ground-coupled and air-coupled responses, respectively), the distance x0 between the bistatic transmitter and receiver, and the height d0 of the air-coupled system above ground. A simple algorithm could be used to estimate the HMA dielectric constant using the second configuration (Lahouar et al. 2002) according to the following equations:

(9)

(10)

(11)

The modified CMP technique was used to analyze GPR data collected form a 17-mile, 4-lane section of an old pavement system: Interstate I-81 located in south-west Virginia. Figure 8 shows the dielectric-constant variations of the HMA layer versus distance, as estimated by the CMP technique. For this section of the pavement, the dielectric constant was found to have an average value around 4.5.

Fig 8: Dielectric Constant Variation of the HMA of an Old Pavement.

The performance of the CMP dielectric-constant estimation technique has shown that it outperforms the classic time-domain technique. In fact, comparisons between the thickness results obtained by this technique and test cores showed an average absolute error of 6.8% (Lahouar et al. 2002). The same data analyzed using the classic time-domain technique, showed an average absolute error of 12.7%. A summary of the results found by both techniques is presented in Table 2. Since the dielectric-constant error is almost double that of the thickness error, the CMP technique achieved a dielectric-constant error of 13.6%, whereas the classic time-domain technique achieved an error of 25.4%. It should be noted that the high errors found in this case emphasizes the difficulties encountered in the analysis of GPR data collected over old pavements.

Conclusions

Various techniques used to estimate the dielectric constant of HMA layers in the field were presented. It was shown that the dielectric-constant variations of the HMA layer versus frequency could be accurately computed using GPR by placing a copper plate underneath the layer during the construction of the pavement. Because this approach could be applied only in research, it was shown that the static (or average) dielectric constant of the HMA layer could usually be estimated effectively, using an air-coupled GPR system, for new pavements. For old pavements, however, it was found that it would be better to use a combination of ground-coupled and air-coupled GPR systems in a modified common depth-point configuration in order to obtain an accurate dielectric-constant estimates.

Core # Core Location* Core Thickness
(mm)
GPR Thickness
(mm)
CMP Method
GPR Thickness
(mm)
Classic Method
Absolute Error
(%)
CMP Method
Absolute Error
(%)
Classic Method
1n7.003373223784.312.1
2n9.003113033992.628.4
3n11.003683504595.024.6
4n12.903433223776.110.0
5n14.003303593748.713.3
6n15.502982742728.28.8
7n16.4527931032211.015.5
8s16.003053133112.71.8
9s15.4026730832415.521.3
11s15.2226729630611.014.5
14s14.952862833151.010.1
17s14.682923033013.72.9
21s10.643753454057.98.1
22s7.003563313776.95.8
Mean Error (%)6.812.7
Table 2: Correlation between Core Thickness and GPR Thickness for I-81 Data.

References

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