Application of regularized deconvolution technique for predicting pavement thin layer thicknesses from ground penetrating radar data

NDT&E International 73 (2015) 1–7

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NDT&E International journal homepage: www.elsevier.com/locate/ndteint

Application of regularized deconvolution technique for predicting pavement thin layer thicknesses from ground penetrating radar data Shan Zhao n, Pengcheng Shangguan 1, Imad L. Al-Qadi 2 Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205N. Mathews Ave., MC-250, Urbana, IL 61801, USA

art ic l e i nf o

a b s t r a c t

Article history: Received 31 August 2014 Received in revised form 23 January 2015 Accepted 2 March 2015 Available online 11 March 2015

In this paper, regularized deconvolution is utilized to analyze GPR signal collected from thin asphalt pavement overlays of various mixtures and thicknesses on a test site. By applying regularized deconvolution and the L-curve method, the overlapped interface was identified in the signal. The thickness of the thin layer was predicted with maximum error of 4.2%, which is less than 1.5 mm, a value well below the layer tolerance during construction. The study shows that the algorithm based on regularized deconvolution is a simple and effective approach for processing GPR data collected from thin pavement layers to predict their thickness. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Non-destructive testing Ground penetration radar Asphalt pavement Thin layer problem Regularized deconvolution

1. Introduction Ground penetrating radar (GPR) is a technique that utilizes electromagnetic (EM) waves to explore the subsurface. This technique has been applied in civil engineering in the United States since 1970s when it was firstly used by the Federal Highway Administration (FHWA) [1]. GPR is commonly applied to find the reinforcement and delamination under concrete slab [2]. In flexible pavement (asphalt pavement), GPR is used to detect free water [3], to estimate the dielectric property of pavement [4], and to estimate the thickness [5] and density [6–8] of asphalt pavement layer. The detailed procedure of applying GPR for subsurface investigation can be found in ASTM standard [9]. One of the most successful applications of GPR on flexible pavement is to estimate the layer thicknesses. Layer thickness is a critical part of the flexible pavement system. It can affect the structural capacity of existing flexible pavement, and can be used to predict the remaining service life of the pavement. For newly constructed flexible pavement, obtaining the layer thickness is essential for the purpose of quality control and quality assurance. The two-way travel time method is the traditional method for obtaining layer thickness from GPR data. The layer thickness can be calculated by knowing the two-way travel time of EM wave within

n

Corresponding author. Tel.: þ 1 217 417 1774; fax: þ 1 201 93 0601. E-mail addresses: [email protected] (S. Zhao), [email protected] (P. Shangguan), [email protected] (I.L. Al-Qadi). 1 Tel.: þ1 217 893 0705; fax: þ 1 217 93 0601. 2 Tel.: þ1 217 265 0427; fax: þ1 217 893 0601. http://dx.doi.org/10.1016/j.ndteint.2015.03.001 0963-8695/& 2015 Elsevier Ltd. All rights reserved.

the layer and the EM wave speed, as shown in Eq. (1): h ¼ ðvΔt Þ=2;

ð1Þ

where h is the layer thickness, Δt is the two-way travel time within the layer, and v is the speed of EM wave, which is given by: pffiffiffiffi v ¼ c= εr ð2Þ where c is the speed of light in free space (3  108 m=s) and εr is the dielectric constant of asphalt pavement layer. According to Snell's law of reflection, the dielectric constant of the asphalt pavement layer can be determined using the following equation:   1 þ ðA0 =Ap Þ 2 εasphalt ¼ ; ð3Þ 1  ðA0 =Ap Þ where εasphalt is the dielectric constant of the asphalt pavement layer, A0 is the amplitude of the reflection from asphalt pavement surface, and Ap is the amplitude of the reflected signal collected over a copper plate, which can be considered as a perfect reflector, placed on the pavement surface. Fig. 1 shows a typical GPR signal reflected from a pavement system consisting of a surface binder whose dielectric constant is ε1 and a leveling binder whose dielectric constant is ε2 . Tx/Rx represents the location of the monostatic antenna. A0 and A1 are the amplitudes of the reflection from the surface and the bottom of the surface binder, respectively. According to Snell's law of reflection, the reflection coefficient at the layer interface has the opposite sign of that at the surface when ε2 o ε1 (assuming the magnetic permeability of asphalt material is equal to that of the free space). Using the two-way travel time method, Al-Qadi et al. [10] reported a mean thickness error of 2.9% for asphalt pavement layers ranging between 100 mm and 250 mm in thickness on a newly built test

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S. Zhao et al. / NDT&E International 73 (2015) 1–7

section of Route 288 in Richmond, Virginia, United States. Lahouar et al. [11] analyzed GPR data collected from interstate highway I-81 using a kind of multi-offset measurement method – common midpoint method (CMP) – and reported a thickness error ranging from 1% to 15% with a mean error of 6.8%. Liu et al. [12] applied similar CMP method and envelope velocity spectrum analysis to GPR data to measure the dielectric permittivity and thickness of snow and ice cover on a brackish lagoon, and the results possessed a good accuracy. Liu and Sato [13] used another multi-offset measurement method – the common source method – for asphalt layer thickness and EM wave velocity estimation. In the study they first designed a Vivaldi antenna array and then calibrated the phase center using a gypsum model. The results from field experiment shows that the error of asphalt layer thickness estimation is less than 6 mm (10%). The Wide Angle Refraction and Reflection (WARR) method can also be used to measure the EM wave velocity within the surface layer and therefore the dielectric constant and thickness of the surface layer [14]. In a GPR survey, a pavement layer is considered as a thin layer if its thickness is comparable to the wavelength of the received EM pulse.

Fig. 1. Typical GPR signal reflected from a pavement system.

Consequently the two reflections respectively from the surface and from the bottom of a thin layer are so close that they become partly or completely overlapped. In this case, the two-way travel time cannot be easily obtained from the raw GPR signal. Herein, it is referred to as the “thin layer problem”. For GPR system that uses Ricker wavelet as incident signal, the “thin layer problem” becomes significant when layer thickness is around 1.1 times the EM wavelength (defined as the distance between two adjacent negative peaks) as shown in Fig. 2. “Thin layer problem” is GPR incident signal dependent. To address the “thin layer problem”, Loulizi et al. [15] used the multiple reflection model. This method basically assumes the thickness and dielectric constant of each layer. Based on those parameters and the shape of the incident wave, the surface reflection signal is reconstructed and compared with the actual collected signal. The assumption with smallest root mean square error is chosen as the solution. However, this method, which is considered computationally intensive, requires preliminary knowledge of the layer structure. Similar multi-reflection model was used by Oliveira et al. [16] on GPR data collected on multilayer pavement systems to find the thickness and permittivity parameters of each layer. However, in order to present the inverse problem as “well-posed,” preliminary knowledge of the model is required to limit the variables of the problem or the GPR working frequencies. Lahouar et al. [17] used the “match and subtract” method to address the “thin layer problem”. Strong reflections are detected iteratively by a threshold or matched filter detector and then subtracted from the original signal to reveal the weak reflections. An average error of 2.5% was found. Li [18] used a similar independent component analysis (ICA) method on GPR data, and overlapped GPR signal collected on thin asphalt pavement layer was successfully separated by independent component analysis. However, both methods require time to iteratively find the layer thickness and are, therefore, time consuming. A support vector regression method (SVR) was applied by Bastard et al. [19] to the time delay estimation to calculate the pavement layer thickness. The results show that the SVR predictor yields good results in both overlapped (thin pavement) and non-overlapped echoes.

Fig. 2. Pavement reflection (dashed) and impulse response (solid) for layer thickness which is (a) 0.71, (b) 0.93, (c) 1.14, (d) 1.36, (e) 1.57 and (f) 1.79 times of the EM wavelength.

S. Zhao et al. / NDT&E International 73 (2015) 1–7

However, the performance of SVR method at high noise levels remains to be studied. The deconvolution method is a simple and effective alternative for obtaining the thickness from thin asphalt layer. Savelyev and Sato [20] reported the success of the deconvolution method in landmine detection. Al-Qadi and Lahouar [21] also reported good results in estimating asphalt pavement layer thickness using this method. In this paper, the regularized deconvolution method is applied to GPR signal collected in Illinois Route 72 (IL-72) near the Chicago area. The accuracy of this method was found to be acceptable. Advantages of the regularized deconvolution method are: (1) it does not require preliminary knowledge of the pavement system, (2) it is less time consuming than “match and subtract” method and ICA method, and (3) it is feasible and practical at different noise levels.

2. Regularized deconvolution on GPR signals It is assumed that the pavement reflection system is a linear time-invariant system. The incident signal is the input signal. The output signal is the GPR signal reflected by the pavement structure. The output GPR signal can be considered as the convolution of the incident signal and the pavement impulse response. This relation is shown in Eq. (4). Z 1 yðt Þ ¼ hðt Þneðt Þ ¼ eðt  uÞhðuÞdu ð4Þ 0

where y(t) is the pavement reflection signal, e(t) is the incident wave (inverse of copper reflected signal), and h(t) is the impulse response. h(t) can be calculated if y(t) and e(t) are known. This process is called deconvolution. One method of deconvolution is to take the Fourier transform on both sides of Eq. (4) to get the impulse response in frequency domain and then convert it back to time domain. However, this method introduces errors during the Fourier transform and inverse Fourier transform and the results will, therefore, be less accurate compared with time domain deconvolution [22]. In practice, all the collected GPR signals are in discrete shape (discrete signal). Therefore, the equation above could be written in

3

the matrix format below: y ¼ Eh;

ð5Þ

where y is the vector of y(t); h is the vector of h(t), and E is the Toeplitz matrix constructed by e(t). Then, the deconvolution is simplified as: h ¼ E  1 y:

ð6Þ

Fig. 2 shows the simulated output signal from a two-layer asphalt pavement model with different thicknesses. The incident signal in the simulation is the same as the one used by air-coupled antenna in this study. The incident signal is a Ricker wavelet with an EM wavelength duration of 0.5382 ns having an arbitrary amplitude. The dashed lines show the GPR signals which are generated by convoluting the incident GPR signal with Dirac delta functions at the surface and the bottom of the asphalt pavement layer. The amplitude of Dirac delta functions represent the proportion A0 =Ap shown in Eq. (3) and can be used to calculate the dielectric constant for each layer. For example, an impulse amplitude of 0.3 of the surface reflection means A0 =Ap ¼ 0:3; therefore, the dielectric constant εasphalt is 3.45 as calculated by Eq. (3). The locations and amplitudes of Dirac delta function are simply assumed by the authors for the purpose of demonstration. Fig. 2(a)–(f) shows the increase in layer thickness from 0.71 times of the wavelength to 1.79 times of the wavelength. For the Ricker wavelet-type of incident signal used in this study, the length of the wavelet is around twice the length of the EM wavelength. Fig. 2(c)– (f) shows that the two peaks can be seen directly because the thickness is relatively large; however, Fig. 2(a), (b) shows that the second reflection is masked by the surface reflection, resulting in difficulties in obtaining the two-way travel time. The two solid vertical lines in each figure represent the impulse response calculated by using Eq. (6) after determining the incident GPR signal. The amplitudes of these two impulses are respectively A0 and A1 , as shown in Fig. 1. In Fig. 2, the amplitude of the impulse responses is magnified to better show the locations of the surface and the bottom of the asphalt pavement layer. Finding the locations of the interface in the “thin layer problem” by applying Eq. (6) is only valid for simulated GPR signal when no noise is added. In practice, real GPR signal contains noise.

Fig. 3. (a) Original signal with white noise, (b) Impulse response directly deconvoluted (c) L-curve and (d) Impulse response after regularized deconvolution.

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As an inverse problem, the deconvolution method is an ill-posed problem, which means a small change in the input would lead to a huge fluctuation in the solution (h(t)). Fig. 3(a) is generated by adding white noise N(0, 5002) to the original signal, shown in dashed line in Fig. 2(b). The result of direct deconvolution, shown in Fig. 3(b), is meaningless. The Tikhonov regularization method [23] is used to address this ill-posed problem. The solution of impulse response is modified as follows:  1 h ¼ E T E þ αI E T y; ð7Þ

GPR incident signal); the dielectric constant of asphalt concrete is assumed 6. After construction, GPR survey was conducted at six static locations in each section. A 2.0 GHz (center frequency) air-coupled antenna manufactured by Geophysical Survey Systems, Inc. was used in the study, as shown in Fig. 5. The designed thicknesses of each section were validated by taking cores from the same locations where the GPR data were collected and the thicknesses are included in the name of each section (e.g. section F-mix-50.8 has the thickness of 50.8 mm).

where α is the regularization parameter. A larger α will result in a smooth solution; however, a smaller α better fits the data. Therefore, it is necessary to determine a proper α. One choice is to use Morozov criteria, where α is selected based on the signal noise level (in decibel). The drawbacks of the Morozov method are its numerical complexity for large vectors [24] and that it requires the knowledge of the noise level. Another method is the L-curve method; its basic principle is to plot the norm of solution norm(h) versus the norm of residue norm(Eh-y) based on different α level; the curve is usually L-shaped. Thus, α is selected at the inflection point of the L-curve as indicated by the arrow in Fig. 3(c). The second method is applied to deconvolute the signal shown in Fig. 3 (a). The result is shown in Fig. 3(d). It can be seen that the second peak is found at a sample number of 36 (indicated by an arrow), which is correct after being compared with the simulated signal shown in the solid line in Fig. 2(a). Therefore the thickness can be calculated once the dielectric constant is known.

4. Results and discussion

3. Construction site and data collection A field study was conducted on IL-72 in Hoffman Estates and Barrington in Illinois in October 2010 [25]. Asphalt concrete overlays with different layer thicknesses and mixture types were constructed on concrete pavement on two lanes in both directions. Below the surface binder, a leveling binder layer was first placed to make the total overlay (leveling binder plus surface binder) thickness equal to 50.8 mm, as shown in Fig. 4. Only the surface binder layer thickness is calculated in this study. The material of the leveling binder is a sprinkle mix without chips with less expensive materials (and it usually has a lesser dielectric constant than the surface binder). Table 1 shows a summary of a total of six different mixtures. The layer thicknesses, in terms of EM wavelength, are calculated knowing that the duration of EM wavelength is 0.5382 ns (according to the

Fig. 6 shows the result at the left lane of 25.4-mm-quartzite section as an example of GPR signal before and after deconvolution. Fig. 6(a) is the GPR signal collected over a flat copper plate. Fig. 6(b) features a raw pavement reflection signal truncated from the original signal and shows that the second peak is hidden under the surface reflection. Fig. 6(d) is the impulse response deconvoluted using α selected based on the L-curve, as shown in Fig. 6(c). It can be seen that the second peak is clear as indicated by an arrow. In addition, it should be noted that the fluctuation after the second peak is caused by the interference of the pavement structure underneath the surface layer and should thus be ignored. Table 2 shows the results in all sections after deconvolution with regularization parameter obtained from the L-curve method.

Table 1 Summary of different mixtures used in construction and their layer thicknesses. Mixture

Binder type

Asphalt content (%)

Friction mix Quartzite mix

PG 70- 5.1 22 PG 70- 5.8 22

4.75-mm SMA

PG 70- 7.3 22

Sprinkle mix Fiber-slag mix 12.5-mm SMA

PG 70- 6.1 22 PG 70- 5.7 22 PG 76- 6.0 22

Fig. 4. Design thicknesses of leveling binder and wearing surface.

Aggregate

Layer thickness (mm)

Thickness in terms of EM wavelength

Dolomite and slag Quartzite and dolomite Dolomite and quartzite Dolomite

38.1/50.8

1.16/1.54

25.4/31.8

0.77/1.16

19.1

0.58

25.4/31.8

0.77/1.16

25.4/31.8

0.77/1.16

50.8

1.54

Dolomite and slag Dolomite and slag

S. Zhao et al. / NDT&E International 73 (2015) 1–7

The dielectric constant of the surface asphalt layer and the EM wave velocity is determined by Eqs. (3) and (2), respectively. It should be noted that for layers thinner than 38.1 mm (1.16 times of the EM wavelength), the regularization parameter α given by the L-curve method is larger than the optimal value such that the second peak is diminished. In these cases, using a decreased α value makes the second peak clearer. All α values are shown in Table 3. Thinner layers are more susceptible to α value; however, a reduction in α would influences the shape or the amplitude of the signal only; and it doesn't affect the arrival time of the two peaks, which mainly affect the results. In practice, the alpha value given by L-curve method could be directly used if no further adjustments are desired.

Fig. 5. GPR data collection [26].

5

Table 2 shows that for 50.8-mm thick layers, the errors range from 3.3% to 8.2%; for 38.1-mm thick layers, the errors range from 6.6% to 7.8%; for 31.8-mm thick layers, the errors range from 4.0% to 14.0%; and for 19.1-mm and 25.4-mm thick layers, the errors range from 4.3% to 54.56%. The error is partially attributed to the GPR system settings. During GPR data collection, the scan length of the GPR signal is set to 12 ns, and the number of samples for each scan is set to 512. The sampling resolution is 12/512 ¼0.0234 ns. The systematic pffiffiffierror of thickness estimation is: δ ¼ 0:0234 ns  ð3  108 = 6Þm=s  ð1=2Þ ¼ 1:4 mm (assume the dielectric constant is 6.0). It will result in a relative error of 5.64% for a 25.4 mm thick layer. Table 2 shows that some sections, especially those with thin layers (25.4 mm and 31.8 mm), have greater average errors than systematic errors (5.6%). The possible reason is that when the dielectric constant is calculated based on Eq. (3), it is assumed that the first peak of the GPR signal represents amplitude of surface reflection A0. In this case, however, the surface reflection partially or completely overlaps with the reflection at the bottom of the surface layer because of the small layer thickness. As a result, the true value of surface reflection amplitude might be different from the amplitude of the reflection pulse shown in the signal as a result of overlapping. The inhomogeneity of the asphalt pavement layer may also contribute to the error. To reduce the error, the data from one core was used to calibrate the dielectric constant of the asphalt pavement layer. The calibrated dielectric constant was then used as the dielectric constant value at the other five locations to calculate the layer thicknesses. The calibrated dielectric constants and the average errors for the other five data are shown in Table 4. It can be seen from Table 4 that the greatest difference of dielectric constant value before and after calibration takes place in the cases of 25.4-mm thick layers, where the surface reflection mostly overlaps with the reflection at the bottom of the surface layer because of the relatively small layer thickness. As a result, the calibration process greatly reduces the prediction error in the cases of 25.4-mm thick layers as shown in Table 4. The prediction errors for sections SMA-19.1 and fiber-slag-25.4 before calibration are 4.3% and 6.9% respectively, which are relatively small. This is

Fig. 6. Results from 2.5-mm-quartzite section. (a) Copper reflected signal, (b) Pavement reflected signal, (c) L-curve and (d) Impulse response.

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Table 2 Layer thickness calculated after deconvolution. Section

Left lane of F-mix-50.8

Test no. Thickness (mm) Error (%)

1 52.76 3.85

Section

Left lane of F-mix-38.1

Test no. Thickness (mm) Error (%)

1 34.26 10.07

Section

Left lane of quartzite-31.8

Test no. Thickness (mm) Error (%)

1 35.28 11.10

Section

Left lane of quartzite-25.4

Test no. Thickness (mm) Error (%)

1 37.13 46.19

Section

Right lane of fiber/slag-25.4

Test no. Thickness (m) Error (%)

1 27.00 6.29

Section

Right lane of sprinkle-31.8

Test no. Thickness (mm) Error (%)

1 35.27 11.08

Section

SMA-19.1

Test no. Thickness (mm) Error (%)

1 20.16 5.81

2 50.84 0.07

2 34.43 9.64

2 35.33 11.26

2 38.80 52.76

2 27.37 7.76

2 36.86 16.10

3 52.01 2.39

3 36.13 5.17

3 34.35 8.18

3 39.23 54.43

3 27.52 8.34

3 36.32 14.40

Right lane of F-mix-50.8 4 52.24 2.84

5 52.68 3.71

6 52.30 2.95

Avg. 52.14 2.63

1 55.06 8.39

2 48.69 4.15

3 49.83 1.92

4 49.51 2.54

5 49.86 1.85

6 50.46 0.67

Avg. 50.57 3.25

4 35.32 7.29

5 34.35 9.84

6 34.35 9.84

Avg. 35.59 6.58

4 35.06 10.42

5 34.92 9.98

6 37.91 19.41

Avg. 35.71 12.48

4 36.39 43.25

5 37.22 46.53

6 36.82 44.96

Avg. 36.84 45.03

4 33.03 4.03

5 32.80 3.32

6 35.04 10.37

Avg. 32.88 3.96

Right lane of F-mix-38.1 4 34.41 9.69

5 36.73 3.60

6 34.78 8.72

Avg. 35.12 7.82

1 35.92 5.73

2 37.21 2.33

3 36.41 4.43

Right lane of quartzite-31.8 4 34.35 8.18

5 35.35 11.34

6 36.52 15.03

Avg. 35.20 10.85

1 34.62 9.03

2 37.18 17.10

3 34.59 8.94

Right lane of quartzite-25.4 4 41.20 62.19

5 39.47 55.39

6 39.73 56.40

Avg. 39.26 54.56

1 36.85 45.09

2 37.52 47.71

3 36.24 42.66

Right lane of fiber/slag-31.8 4 26.44 4.06

5 26.45 4.13

6 28.11 7.17

Avg. 27.15 6.88

1 32.09 1.06

2 31.37 1.20

3 32.96 3.81

Right lane of sprinkle-25.4 4 36.01 13.43

5 37.26 17.37

6 35.39 11.46

Avg. 36.19 13.97

1 33.86 33.31

2 33.96 33.72

3 34.37 35.33

4 34.37 35.32

5 35.00 37.81

6 34.82 37.10

Avg. 34.40 35.43

2 45.74 9.96

3 45.74 9.96

4 48.09 5.33

5 47.64 6.22

6 49.01 3.52

Avg. 46.63 8.22

SMA-50.8 2 20.03 5.13

3 19.75 3.68

4 19.76 3.73

5 20.46 7.40

6 19.10 0.24

Avg. 19.88 4.33

1 43.52 14.33

Table 3 Regularization parameter α for all sections. Section

α

Section

Left lane of F-mix-50.8 Left lane of F-mix-38.1 Left lane of quartzite-31.8 Left lane of quartzite-25.4 Right lane of fiber/slag-25.4 Right lane of sprinkle-31.8 SMA-19.1

1.30Eþ 07 3.20E þ 07 1.30Eþ 07 5.00E þ 06 2.00E þ 06 7.90Eþ 06 5.00E þ 05

Right lane Right lane Right lane Right lane Right lane Right lane SMA-50.8

mainly because the SMA and fiber/slag mixtures have metal materials inside, which cause higher surface reflection amplitudes and partially eliminate errors due to signal overlapping. For the sections whose thickness are equal or greater than 38.1 mm, the largest prediction error is 8.2% before calibration, which suggests good performance of the algorithm even without calibration. Overall, the estimation errors for each section range from 2.5% to 54.6% before calibration while the estimation errors range from 0% to 4.2% after calibration. Therefore, calibration can effectively reduce the mean thickness error for the sections with large estimation error because of signal overlapping.

5. Conclusions Regularized deconvolution is an algorithm that could be used on GPR signals to calculate the impulse response of the pavement system. This approach would increase the resolution of overlapped

α of of of of of of

F-mix-50.8 F-mix-38.1 quartzite-31.8 quartzite-25.4 fiber/slag-31.8 sprinkle-25.4

1.30E þ07 3.20E þ07 8.00E þ 06 8.00E þ 06 7.90E þ06 2.00E þ 06 1.30E þ07

pulses, and address the “thin layer problem” (the problem of predicting pavement layer thickness, which is comparable to the wavelength of the EM pulse). During a GPR survey conducted on newly built asphalt concrete overlays with different mixture type and thickness on IL-72 in Hoffman Estates, Illinois and Barrington, Illinois, GPR measurements were taken at six static coring locations in each section. The regularized deconvolution method was utilized on raw GPR signal using the regularization parameter α given by L-curve method. One of six data was used to calibrate the dielectric constant of asphalt concrete layer. The thickness calculated using regularized deconvolution was then compared with the ground truth. Among all sections, the maximum error was 4.2%, which is less than 1.5 mm. In summary, the error in predicting the thin asphalt layer thickness using the regularized deconvolution algorithm is acceptable and less than the construction tolerance (usually 5 mm in the State of Illinois). The regularized deconvolution of GPR signal can be used to accurately predict asphalt layer thickness at different

S. Zhao et al. / NDT&E International 73 (2015) 1–7

7

Table 4 Dielectric constant and mean thickness prediction error before and after calibration for all sections. Section

Left lane of F-mix50.8 Left lane of F-mix38.1 Left lane of quartzite-31.8 Left lane of quartzite-25.4 Right lane of Fiber/ Slag-25.4 Right lane of Sprinkle-31.8 SMA-19.1

Dielectric constant

Mean thickness error (%)

Before calibration (mean)

After calibration

Before calibration

5.31

5.87

2.63

2.86

5.00

4.12

7.82

1.82

4.47

5.41

10.85

1.03

3.91

6.92

54.56

2.58

5.64

6.21

6.88

2.23

4.03

5.41

13.97

1.91

3.67

4.12

4.33

1.37

Section

After calibration

noise levels. It is also a simple and effective technique to address the “thin layer problem”. The algorithm could also be applied on a two-dimensional GPR profile obtained from an antenna array to generate a thickness profile or to identify possible pavement flaws. References [1] Morey RM. Ground penetrating radar for evaluating subsurface conditions for transportation facilities. USA: Transportation Research Board; 1998 (http://trid.trb.org/view.aspx?id=476597). [2] Chang CW, Lin CH, Lien HS. Measurement radius of reinforcing steel bar in concrete using digital image GPR. Constr. Build. Mater. 2009;23(2):1057–63. [3] Al-Qadi IL, Ghodgaonkar D, Varada V, Varadan V. Effect of moisture on asphaltic concrete at microwave frequencies. IEEE Trans Geosci Remote Sens 1991;29(5):710–7. [4] Al-Qadi I, Lahouar S, Loulizi A. In situ measurements of hot-mix asphalt dielectric properties. NDT E Int 2001;34(6):427–34. [5] Al-Qadi I, Lahouar S. Measuring layer thicknesses with GPR–theory to practice. Constr Build Mater 2005;19(10):763–72. [6] Al-Qadi IL, Leng Z, Lahouar S, Baek J. In-place hot-mix asphalt density estimation using ground-penetrating radar. Transp Res Rec: J Transp Res Board 2010;2152(1):19–27. [7] Shangguan P, Al-Qadi IL. Calibration of FDTD simulation of GPR signal for asphalt pavement compaction monitoring. IEEE Trans Geosci Remote Sens 2014;53(3):1538–48. [8] Shangguan P, Al-Qadi I, Coenen A, Zhao S. Algorithm development for the application of ground-penetrating radar on asphalt pavement compaction monitoring. [ahead-of-print]. Int J Pavement Eng 2014:1–12. [9] ASTM D6432 - 11. Standard guide for using the surface ground penetrating radar method for subsurface investigation. [10] Al-Qadi I, Lahouar S, Loulizi A. Successful application of ground-penetrating radar for quality assurance-quality control of new pavements. Transp Res Rec: J Transp Res Board 2003;1861(1):86–97. [11] Lahouar S, Al-Qadi I, Loulizi A, Clark T, Lee D. Approach to determining in situ dielectric constant of pavements: development and implementation at interstate 81 in virginia. Transp Res Rec: J Transp Res Board 2002;1806(1):81–7. [12] Liu H, Takahashi K, Sato M. Measurement of dielectric permittivity and thickness of snow and ice on a brackish lagoon using GPR. IEEE J Sel Top Appl Earth Obs Remote Sens 2014;7(3):820–7.

Right lane of F-mix50.8 Right lane of F-mix38.1 Right lane of quartzite-31.8 Right lane of quartzite-25.4 Right lane of Fiber/ slag-31.8 Right lane of sprinkle-25.4 SMA-50.8

Dielectric constant

Mean thickness error (%)

Before calibration (mean)

After calibration

Before calibration

After calibration

5.48

6.21

3.25

2.43

4.80

4.12

6.58

0.91

3.98

4.70

12.48

4.24

4.02

8.45

45.03

0.00

4.96

5.41

3.96

2.86

3.77

6.92

35.43

0.00

7.18

6.21

8.22

3.34

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