Evaluating a Pavement System Based on GPR Full-Waveform Simulation
Yuejian Cao1 Research Assistant Department of Civil Engineering University of Minnesota 500 Pillsbury Dr SE, Minneapolis, MN 55455 Email:
[email protected] Prof. Joseph Labuz Department of Civil Engineering University of Minnesota 500 Pillsbury Dr SE, Minneapolis, MN 55455 Email:
[email protected] Prof. Bojan Guzina Department of Civil Engineering University of Minnesota 500 Pillsbury Dr SE, Minneapolis, MN 55455 Email:
[email protected] Word Count = 3373 + 10x250 (Figure) + 3x250 (Table) = 6623
1
Corresponding author
TRB 2011 Annual Meeting
Paper revised from original submittal.
ABSTRACT The purpose of this study is to extend the use of ground penetrating radar (GPR) methodology towards more reliable and accurate interpretation of pavement conditions. Utilizing the electromagnetic Green’s function for a layered system due to a horizontal electric dipole, the GPR scan can be simulated over a wide range of pavement profiles. Examples are provided for GPR simulation on a three-layer pavement system. By virtue of this forward model, layer parameters such as thickness and dielectric constant can be optimized to estimate the in-situ values, where the synthetic scan matches the field scan in terms of the minimum time history error. Unlike traditional methods, the proposed analysis allows an evaluation of the relevant pavement properties with no prior assumptions or subjective image adjustments. Keywords: electromagnetic wave propagation, GPR simulation, pavement thickness estimation
TRB 2011 Annual Meeting
Paper revised from original submittal.
Yuejian Cao, Joseph Labuz, Bojan Guzina
2
INTRODUCTION Pavement quality is a major concern for transportation engineers, where the layer thickness is one of the key items associated with the in-situ pavement conditions. Ground penetrating radar (GPR) is an effective non-destructive technique to evaluate the near- and sub-surface conditions in pavements, including layer thickness. Owing to the inherent benefits such as fast, near-continuous field coverage and low implementation cost, the GPR surveys have been gaining popularity among transportation agencies. To obtain more reliable and accurate estimates of thickness conditions under traffic speed, a back-analysis is proposed to interpret the layer properties without a priori assumptions of the pavement conditions. The proposed scheme is based on two key elements: (a) simulation of the GPR scan and (b) estimation of layer properties from the synthetic GPR scan. In the first stage, use is made of the analytic expression for the electromagnetic Green’s function in a three-layer full-space system due to a horizontal electric dipole (HED). With the aid of such forward model, the GPR scans can be simulated over a wide range of three-layer pavement profiles. In the second stage, an effort is made to generate the synthetic GPR scans that are virtually identical to the field scans in terms of minimum misfit of the time history, through a suitable optimization scheme. Once the optimization is performed, the in-situ layer properties such as dielectric constant and thickness associated with the actual scans are well represented by the parameters associated with the synthetic GPR scans. The-state-of-practice GPR applications revolve around the estimate of layer thickness using the travel time technique, where the layer is delineated by the time marker in the received signal. Because the pulse travels back and forth within the pavement structure, the layer thickness h is computed as the product of the travel time ∆t and the pulse velocity v inside the layer: h=v
∆t 2
(1)
where v is related to the speed of light in vacuum c via the dielectric constant ε of the layer: c v=√ . ε
(2)
The travel time technique has been successfully applied to evaluate the pavement profile (7, 13, 14). However, the value of ε is usually assumed in practice, which has been shown to be inconsistent with the in-situ values, and the information about the preassigned layer condition, i.e. the dielectric constant, is actually contained in the amplitude information. Although improvements can be made by implementing additional surveys to determine the in-situ dielectric constant (10) or calibrating through field cores, it is merely a trade-off that reduces the benefits of the GPR technique. GPR EQUIPMENT The GPR equipment (Fig. 1) used in this study is model 4108 air-coupled 1 GHz modified bowtie antennas, manufactured by Geophysical Survey Systems, Inc. (GSSI). Model 4108 is configured as a bistatic antenna system, with dedicated transmitter and receiver antennas positioned at the same elevation and the apertures face downward. In general, without taking into account the complex geometry of the modified bowtie an-
TRB 2011 Annual Meeting
Paper revised from original submittal.
Yuejian Cao, Joseph Labuz, Bojan Guzina
3
R
495 mm
ρ
T
21 0
6 55
mm
mm
FIGURE 1 Model 4108 1 GHz air-coupled GPR (12). tenna, the aperture surface can be simplified as a horizontal electric dipole (HED) antenna, given that the pavement is located at a sufficient distance from the antenna. The so-called far-field region can be estimated by r ≥ 2D2 /λ (3) where D is the maximum overall dimension (aperture width), and λ is the wavelength of the electromagnetic wave (5). Since the overall size of the GPR box is 210 × 556 × 495 mm, a reasonable estimate of D for each antenna is 0.25 m, and the wavelength of a 1 GHz electromagnetic wave in air is λ = 0.3 m. Guided by these two conditions, the far-field is determined as the region with a radial distance beyond 0.4 m. Because the GPR box is placed at about 0.5 m above the ground, the whole pavement system satisfies the far-field condition, allowing the actual antenna to be modeled by the HED antenna. In other words, the GPR system can be simplified to two HED antennas over the pavement, as shown in Fig. 2. ρ
z
R
T d
y
O x
FIGURE 2 Two x-directed HED antennas, transmitter (T ) and receiver (R). TRADITIONAL APPROACH A typical recorded scan from the GPR equipment contains the echo of the feed-point reflection, the direct arrival, and the reflection(s) from each layer interface (Fig. 3). To process and display the GPR image, the reflection amplitudes of a single GPR scan have to be transformed by means of a grey or color scale. These GPR scans are then stacked in the vertical direction so that the
TRB 2011 Annual Meeting
Paper revised from original submittal.
Yuejian Cao, Joseph Labuz, Bojan Guzina
4
variations of the GPR scans can be observed with the aid of the transformed color scale. In Fig. 4, for example, the grey scale is applied, where the brighter color is for a higher positive amplitude. The first two white bands on top represent the feed-point reflection and direct arrival. Below these, the layer profile is denoted by various white bands, from top to bottom, representing the surface, second, and third layer interfaces. Note that the incompleteness of the third layer interface implies deterioration of the signal at the deeper location. 4
x 104 feed-point reflection
Amplitude
3
surface reflection direct arrival
2 1
2nd layer 3rd layer reflection reflection
0 -1 ∆t1
-2 t0
-3 50
100
t1
150
200
∆t2 t2
t3
250 300 Sample
350
400
450
500
FIGURE 3 Single scan from a GPR survey.
2
feed-point reflection
4
direct arrival
Time (ns)
6
surface reflection 8 10 12 14
2nd layer reflection
16
3rd layer reflection
18 20 100
200
300
400
500
600
700
800
900
1000
Scan
FIGURE 4 Typical GPR image from a road survey. In addition, to better delineate various layers in the pavement profile, several user-specified post-processing protocol (filtering, clutter removal, gain adjustment) can be applied to obtain a sharper GPR display. Thus, the near-continuous coverage and fast data collection make GPR an effective technique for pavement applications, provided that the images are suitably interpreted.
TRB 2011 Annual Meeting
Paper revised from original submittal.
Yuejian Cao, Joseph Labuz, Bojan Guzina
5
In this setting, however, it must be recognized that the vertical axis in Fig. 4 is travel time, which must be converted to depth by assuming the wave speed, i.e. the dielectric constant in each layer. For the traditional travel time technique to work, the dielectric constants (ε) and travel time (∆t) are the only information needed to find the layer thickness, as shown in Eqn. (1) and (2). However, there are instances where difficulties arise in obtaining one or both of these parameters. For example, the in-situ dielectric constants are typically unknown. In fact, these values are usually assumed and the corresponding profile is affected by the assumptions. In addition, each peak in the temporal GPR record represents a pulse reflected back from a layer interface. During the field survey, the peak may be overwhelmed by ambient noise, thus increasing the difficulty of identifying the travel time between interfaces. This latter problem is often dealt with by a user-specified gain adjustment applied to selected portions of the time histories. Furthermore, it is known that layer properties are governed not only by dielectric constants, but also by the magnetic permeability and electrical conductivity. Although in the scope of pavement materials, which are non-magnetic and have similar magnetic permeability as air, the electrical conductivity can vary for the different materials (7). It is important to note that partly because of the conductivity, the energy of the electromagnetic wave dissipates during propagation, meaning in a high conductive material the electromagnetic wave vanishes faster than that in a low conductive material. Unfortunately, attenuation is generally not considered in a standard interpretation. As a consequence of these sources of error, layer thickness determined by Eqn. (1) is to a large extent an approximation. Currently, the error for the layer thickness estimated by the travel time technique is around 7.5% compared to core data (11). The error may be reduced by gathering additional information to estimate the in-situ conditions (10). Nevertheless, no attenuation factor is considered, which still hampers the accuracy to interpret the GPR survey. Information on the physical properties of the pavement is carried by the electromagnetic wave in terms of the travel time and the amplitude of the waveform. By taking only part of the available information, the traditional travel time technique inherently has less capability to efficiently interpret the GPR scan. Therefore, it is advantageous to treat the GPR measurement in a more comprehensive fashion to interpret the pavement profile. The proposed approach is based on the simulation and analysis of the waveform for electromagnetic wave propagation in a layered system. Because the entire electromagnetic response is available, this approach can provide enhanced interpretation of the pavement profile from the GPR measurements. GPR SIMULATION Under the assumed configuration (Fig. 2), GPR measures the x-component of the electric field at point R due to an x-directed HED at point T . In this study, a three-layer pavement system (air, asphalt, and base layers) is investigated. As shown in Fig. 5, each layer is characterized by the thickness hj , dielectric constant εj , permeability µj and conductivity σj (j = 0, 1, 2), where the air and base layers are two half-spaces, i.e. h0 = h2 = ∞. For the asphalt and base layers, the variation of the parameters is shown in Table 1. Note that ε0 = 8.8542 × 10−12 F/m, µ0 = −7 4π × 10q N/A2 and σ0 = 0 S/m in region 0 (air). The wave number for each region is defined as kj = ω µj εej , where εej = εj + iσj /ω and ω = 2πf is the angular frequency. For a three-layer system, the analytic solution of the electric field due to an electric HED in the air is available in the literature (9).
TRB 2011 Annual Meeting
Paper revised from original submittal.
Yuejian Cao, Joseph Labuz, Bojan Guzina
6
r2=ρ2+(z—d)2 R
zˆ ε0 µ0 σ0
T d
z
ρ
ε1 µ1 σ1
h1
Region 0
ˆρ
Region 1
ε2 µ2 σ2
Region 2
FIGURE 5 Three-layer system. TABLE 1 Parameter Ranges Asphalt Region 1 Base Region 2 εj (F/m)
3ε0 ∼ 12ε0
4ε0 ∼ 20ε0
µj (N/A2 )
µ0
µ0
σj (S/m)
10−4 ∼ 10−1
10−4 ∼ 10−1
As detailed in (9), in region 0 (air), the horizontal fields in polar coordinate shown in Fig. 5 can be calculated by hX i −ωµ cos φ ∓F (ρ, z ± d) + F (ρ, z + d) ρ0 ρ1 4πk02 hX i ωµ Gφ (ρ, φ, z, ω) = sin φ ∓F (ρ, z ± d) + F (ρ, z + d) φ0 φ1 4πk02
Gρ (ρ, φ, z, ω) =
(4)
√ with ρ = x2 + y 2 , cos φ = x/ρ, sin φ = y/ρ. The expressions for Fρ0 , Fφ0 , Fρ1 , and Fφ1 can be found in (9), where all have the integral forms of F (ρ, z) =
Z ∞ 0
f (λ)Jν (ρλ)e−λz dλ
(5)
where Jν is the Bessel function of the first kind with integer orders (ν = 0, 1, 2); f (λ) is the response in the transformed domain which is different for Fρ and Fφ ; λ is the transformed variable that is independent of εj and hj . It is observed that the total integrand f (λ)Jν (ρλ)e−λz is subjected to fast decay when λ → ∞ due to the exponential term, which enables the integration on a truncated integral path, i.e. Z ∞ 0
f (λ)Jν (ρλ)e−λz dλ ∼
Z λmax 0
f (λ)Jν (ρλ)e−λz dλ
(6)
where λmax is the truncation point. Generally, such integral equation has no closed-form, and it needs to be evaluated from numerical integration. As a matter of fact, the highly oscillating nature of the Bessel function Jν (λ) for large argument λ would result in difficulties for the general technique such as n-point
TRB 2011 Annual Meeting
Paper revised from original submittal.
Yuejian Cao, Joseph Labuz, Bojan Guzina
7
Gaussian quadrature method. In order to speed up the integration, one efficient approach is to find approximation that can be integrated in closed-form (8). As a result, the kernel function g(λ) = f (λ)e−λz can be represented by polynomials over an arbitrary interval with the aid of the Lagrange interpolation formula, where the error is subjected to the increment of the interval ∆λ, i.e. g(λ) = g(λ0 + p∆λ) =
4 X
Ai (p)g(λi )
(7)
λ0 = λ−3 + 3∆λ
(8)
i=−3
where p=
λ − λ0 , ∆λ
∆λ =
and Ai (p) = (−1)i+4
λ4 − λ−3 , 7
p(p − 4)(p2 − 1)(p2 − 4)(p2 − 9) (3 + k)!(4 − k)!(p − k)
(9)
Meanwhile, the Bessel function Jν (λ) is represented by closed-form expression via the ascending series of the Bessel function for small λ (1): !k
Jν (λ) =
λ2 !ν ∞ − 4 λ X 2 k=0 k!(ν + k)!
(10)
and the asymptotic expansion of the Bessel function for large λ (1): s
Jν (λ) ∼
"
#
2 P (ν, λ) cos φ − Q(ν, λ) sin φ . πλ
(11)
Eventually, it can be shown that the integral Eqn. (6) can be integrated in closed-form along the truncated integral path with the aid of Eqn. (7–11). Furthermore, the x-component of the received HED is obtained by trigonometric relations from Gρ and Gφ via Gx (x, y, z, ω) = Gρ (x, y, z, ω) cos φ − Gφ (x, y, z, ω) sin φ
(12)
Gy (x, y, z, ω) = Gρ (x, y, z, ω) sin φ + Gφ (x, y, z, ω) cos φ The Green’s function in Eqn. (12) can be thought of as the frequency response function associated with certain pavement systems. Thus, using the x-component of the Green’s function in f (x, y, z, t) can be generated via the inverse Fourier transform Eqn. (12), the GPR time history E x F −1 [X]: f (x, y, z, t) = F −1 [E (x, y, z, ω)] E (13) x x where Ex (x, y, z, ω) = Gx (x, y, z, ω) · I(ω)
(14)
is the GPR response in the frequency domain. The I(ω) in Eqn. (14) represents the signature of the excitation current source, which varies from different GPR antennas.
TRB 2011 Annual Meeting
Paper revised from original submittal.
Yuejian Cao, Joseph Labuz, Bojan Guzina
8
Therefore, by using the three-layer electromagnetic wave propagation model, synthetic GPR time histories for an asphalt-base configuration can be generated, as shown in Fig. 6. It is worth noting that the direct arrival is not shown because it contains no information about the pavement profile. The first echo is the reflection from the surface; the second echo is the reflection from the interface between the asphalt and base layer.
∆t
A1
ε1 = 4ǫ0 ε2 = 6ǫ0 σ1 = 2 × 10−4S/m σ2 = 2 × 10−3S/m h1 = 0.1016m
Amplitude
15000 10000
A2 5000 0 -5000 80
100
120
140
160 Sample
180
200
220
240
FIGURE 6 Synthetic GPR scan. In addition, it may be observed from Eqn. (14) that the characteristic of each echo is strictly associated with the current source and the peak amplitude. Since the current source is fixed, the peak amplitude can be used to represent the overall reaction of the impulse due to the layer properties such as dielectric constant and conductivity. Assuming constant conductivities, it can be further observed that the amplitude of the first peak A1 is solely determined by the dielectric constant of the asphalt layer ε1 . Consequently, the amplitude of the second peak A2 is not only affected by the dielectric constants of the base layer ε2 , but also affected by ε1 in the asphalt layer. Moreover, the travel time ∆t represented by the distance between the first and second peaks will be affected by the variation of wave speed due to the variational dielectric constant of the asphalt layer ε1 . In other words, the travel time ∆t is co-determined by both ε1 and h1 . Mathematically, the above observations can be described by the following formulas: A1 = f1 (ε1 ),
A2 = f2 (ε1 , ε2 ),
∆t = f3 (ε1 , h1 )
(15)
where the anonymous functions f1 , f2 , and f3 can be evaluated from the Green’s function in Eqn. (12). OPTIMIZATION OF SYNTHETIC GPR SCAN For the three-layer configuration, the GPR time history is uniquely characterized by all three parameters, namely A1 , A2 , and ∆t (Fig. 6). Comparing the synthetic GPR scan to the measured one, it is found that it is possible to generate a synthetic GPR scan identical to the measured GPR scan by fitting the layer properties (thickness and dielectric constant) to the actual field values. For example, as shown in Fig. 7, no major differences can be recognized between the measured and the
TRB 2011 Annual Meeting
Paper revised from original submittal.
Sam
140 160
Yuejian Cao, Joseph Labuz, Bojan Guzina
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180 200
400
600
800
1000
1200
1400
1600
1800
2000
fitted synthetic GPR scans. Thus, it is intuitive to interpret Scan the layer properties by using a certain optimization scheme to fit the synthetic GPR scan to every measured GPR scan. x 104
Single Scan Comparison
Amplitude
1.5
Measured Synthetic
ε1 = 4.9ε0 ε2 = 6.8ε0 h1 = 83.8 mm
1 0.5 0
-0.5 -1 100
120
140
160
180
200
Sample FIGURE 7 The measured and the fitted synthetic GPR scan. The optimization scheme is developed following Eqn. (15), with the objective functions introduced as g1 (ε1 ) = A1 − Afield = f1 (ε1 ) − Afield 1 1 g2 (ε1 , ε2 ) = A2 − Afield = f2 (ε1 , ε2 ) − Afield 2 2
(16)
g3 (ε1 , h1 ) = ∆t − ∆tfield = f3 (ε1 , h1 ) − ∆tfield which means that the closer the parameters (ε1 , ε2 and h1 ) to their objective values in the field, the smaller are the three objective functions in Eqn. (16). It is worth noting that in Eqn. (16), it is not necessary to fit the dielectric constant ε1 in the second or third equations, which is obtained from the fitted result of the first equation. Thus, the task is simplified to find the root of a single variable function for all three objective functions. GPR SURVEY To evaluate the proposed scheme, experiments were performed to compare the estimated layer thicknesses with sample cores from the MnRoad facility. A total of 11 cores were taken from different cells in the MnRoad low volume road section, with a typical 80-130 mm asphalt layer over the base material. The core data are shown in Table 2. GPR surveys were conducted, and the scans were marked at the core locations. The marked scans were used to interpret the layer thicknesses using the proposed optimization scheme. The estimated asphalt layer thicknesses are shown in Table 3, as well as the errors compared to the core data, i.e. |h − hest | × 100% (17) Error(%) = h where h is core thickness and hest is the estimated thickness using the proposed scheme. From Table 3, the highest error is 6.9%, with a considerably lower average of 2.3%. Moreover, it is important to notice that 7 out of 11 scans have errors less than or equal to 1.1%. The proposed scheme is also capable of providing thickness and dielectric constant profiles from GPR surveys under highway speed. As an illustration, one GPR survey completed by MnDOT was processed by the proposed method. The test site is a section of pavement consisting of
TRB 2011 Annual Meeting
Paper revised from original submittal.
Yuejian Cao, Joseph Labuz, Bojan Guzina
10
TABLE 2 MnRoad Sample Core Thickness Information Core # MnRoad ID Cell Station Thickness (mm) 1
3509BC006
35
7496
114
2
3409BC006
34
7444
127
3
3307BC006
33
6562
111
4
3309BC006
33
6374
114
5
2409BC012
24
15821
89
6
2409BC003
24
16326
89
7
2808BC001
28
18148
111
8
2808BC003
28
18350
102
9
7909BC002
79
19618
95
10
7909BC007
79
19741
114
11
3507BC005
35
7702
102
a HMA layer and underlying base. The survey was performed at 0.3 scan/m over 200 m with a driving speed of 65 km/h. Using the proposed interpretation scheme, the obtained layer properties (ε1 , ε2 , and h) are shown in Fig. 8, where the asphalt thickness variation can be clearly quantified with an average of 91 mm. The results indicate a variation of the asphalt dielectric constant from 3.5ε0 ∼ 7.8ε0 . As a result, it shows the utility of the method in interpreting pavement layer properties without a priori assumptions. Particularly, the interpreted asphalt thickness is compared to that using the traditional travel time technique, with the commonly assumed asphalt dielectric constant of ε1 = 6ε0 . As shown in Fig. 9, the pavement thickness interpreted from the travel time technique contains an average error of 7.6%, with a maximum error of 25%. Furthermore, the synthetic GPR image can be produced directly from the interpreted parameters, exhibiting strong similarity to the measured GPR image, as shown in Fig. 10. As a matter of fact, the measured GPR image may be contaminated by other activities such as the interference from a cell phone signal. On the other hand, the synthetic GPR scan can be generated without any noise, which offers an enhanced visualization, i.e. by removing the ambient noise in the GPR scans, the GPR image becomes less fuzzy and hence during the interpretation of the pavement profile, misidentification can be reduced. CONCLUSION By using the analytic representation of the electromagnetic Green’s function in a layered system, the GPR scans are successfully simulated over a wide range of pavement profiles. Based on this forward model, an interpretation scheme to estimate the layer thickness without a priori assumption of the pavement condition is proposed. The interpreted layer thickness shows very low error compared to the sample core data, indicating the success of this proposed scheme. The results also show the validation of the proposed scheme to process GPR measurements obtained at highway
TRB 2011 Annual Meeting
Paper revised from original submittal.
Yuejian Cao, Joseph Labuz, Bojan Guzina
11
Dielectric (ε0 )
12
εA εB
10 8 6 4 200
400
600
800
1000
1200
1400
1600
1800
2000
1200
1400
1600
1800
2000
1600
1800
2000
Thickness (m)
Scan 0.07 0.08 0.09 0.1
h
0.11 200
400
600
800
1000
Scan FIGURE 8 Road profile summary.
Asphalt layer thickness (m)
0.06 0.07 0.08 0.09 0.1 Proposed method
0.11
Travel time technique εA = 6ε0 0.12
200
400
600
800
1000 1200 Scan
1400
FIGURE 9 Estimated thickness using the proposed method and travel time technique
TRB 2011 Annual Meeting
Paper revised from original submittal.
Yuejian Cao, Joseph Labuz, Bojan Guzina
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TABLE 3 Compare Layer Thickness Estimation with Sample Core Data Core # Thickness (mm) Estimated (mm) Error (%) 1
114
107
6.1
2
127
128
0.8
3
111
110
0.9
4
114
109
4.4
5
89
90
1.1
6
89
92
3.4
7
111
111
0.0
8
102
109
6.9
9
95
94
1.1
10
114
114
0.0
11
102
101
1.0
speeds. ACKNOWLEDGMENT Support was provided by the Minnesota Department of Transportation, the Local Road Research Board of Minnesota, and the MSES/Miles Kersten Chair. This work reflects the views of the authors who are responsible for the facts and accuracy of the data. REFERENCES [1] Abramowitz, M., and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, U.S. Govt. Print. Off., Washington, 1964. [2] Al-Qadi, I. L., S. Lahouar, and A. Loulizi, In Situ Measurements of Hot-Mix Asphalt Dielectric Properties, NDT and E International, Vol. 34, No. 6, 2001, pp. 427-434. [3] Al-Qadi, I. L., and S. Lahouar, Detection of Asphalt Binder Aging in Flexible Pavement by Ground Penetrating Radar, Materials Evaluation, Vol. 63, No. 9, September, 2005, pp. 921-5. [4] Al-Qadi, I. L., S. Lahouar, A. Loulizi, Ground-Penetrating Radar Calibration at the Virginia Smart Road and Signal Analysis to Improve Prediction of Flexible Pavement Layer Thicknesses, Virginia Transportation Research Council, 2005. [5] Balanis, C. A., Antenna Theory : Analysis and Design, John Wiley & Sons, New York, 1997. [6] Cao, Y., B. B. Guzina, J. F. Labuz, Pavement Evaluation using Ground Penetrating Radar, Minnesota Department of Transportation, 2008. [7] Daniels, D. J., Ground Penetrating Radar, Institution of Electrical Engineers, London, 2004.
TRB 2011 Annual Meeting
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Measured Measured GPR GPR Image Image
Sample Sample
100 100 120 120 140 140 160 160 180 180
200 200
400 400
600 600
800 800
1000 1000
1200
1200 Scan Scan
1400 1400
1600 1600
1800 1800
2000 2000
1600 1600
1800 1800
2000 2000
(a) Measured GPR image
Synthetic Synthetic GPR GPR Image Image
Sample Sample
100 100 120 120 140 140 160 160 180 180
200 200
400 400
600 600
800 800
1000 1000
1200
Scan 1200 Scan
1400 1400
(b) Synthetic GPR image
Amplitude Amplitude
Single Scan Comparison x 1044 Single Scan Comparison x 10 10 GPR FIGURE images: (a) measured and (b) synthetic. 1.5 Measured 1.5 Measured ε = 4.9ε Synthetic 1 0 1 ε1 = 4.9ε0 Synthetic 1 [8] Guzina, B. B., Seismic Responseε2of=Foundations and Structures in Multilayered Media, Ph.D. 6.8ε0 ε2 = 6.8ε0 0.5 0.5 of Colorado, 1996. thesis, University h1 = 83.8 mm h1 = 83.8 mm 0 0 [9] King, R. W. -0.5 P., M. Owens, and T. T. Wu, Lateral Electromagnetic Waves : Theory and -0.5 Applications to-1Communications, Geophysical Exploration, and Remote Sensing, Springer-1 1001992. 120 140 160 180 200 Verlag, New York, 100 120 140 160 180 200 Sample Sample [10] Lahouar, S., I. L. Al-Qadi, A. Loulizi, T. M. Clark, and D. T. Lee, Approach to Determining in Situ Dielectric Constant of Pavements: Development and Implementation at Interstate 81 in Virginia, Transportation Research Record, No. 1806, 2002, pp. 81-87. [11] Maser, K. R., Measurement of as-Built Conditions using Ground Penetrating Radar, Structural Materials Technology : An NDT Conference., 1996. [12] Roberts, R., GSSI, Personal communication, Jan. 2010. [13] Scullion, T., Ground Penetrating Radar Applications on Roads and Highways, Texas Transportation Institute, 1994. [14] Saarenketo, T., and T. Scullion, Road Evaluation with Ground Penetrating Radar, Journal of Applied Geophysics, Vol. 43, No. 2-4, 2000, pp. 119-138.
TRB 2011 Annual Meeting
Paper revised from original submittal.
