Reverse-Time Migration Imaging of Ground-Penetrating Radar in NDT of Reinforced Concrete Structures

: The evaluation and inspection of steel bars in reinforced concrete structures are critical for prolonging the service life of buildings. In this regard, ground-penetrating radar (GPR) has been a crucial alternative due to its non-invasiveness and convenience. This paper reports the experimental activities on a test-site area inside a camp in Shanghai, China. To assess the concrete structures of the building, GPR was employed for the detection and localization of rebars in columns, beams, and ﬂoors. From the GPR B-scan proﬁles acquired using a high-frequency antenna, the exact quantity of reinforcements was identiﬁed according to the hyperbola responses. Considering the difﬁculty of inferring the exact position and the scale of the rebars, we applied reverse time migration (RTM) to collapse the hyperbolic response and retrieve the target in a migrated image. To verify the effectiveness of the RTM algorithm, we carried out an experiment on a concrete model with three reinforced bars. We also utilized the RTM algorithm to process the B-scan proﬁles collected in a column that was later excavated. The imaging results validated the capacity of RTM in localizing and shaping rebars. Then, we employed the RTM algorithm for the GPR B-scan data collected from the other column. Based on the imaging proﬁle, the quantity and positions of the rebars were correctly determined. Moreover, the thickness of the protective layer was evaluated according to the migrated result. These results demonstrate that GPR combined with RTM could provide useful foundation data for structural evaluation.


Introduction
Ground-penetrating radar (GPR) has been a high-efficiency near-surface geophysical method widely applied in many application fields, such as hydrological monitoring [1][2][3], landmine detection [4][5][6], geological exploration [7,8], lunar exploration [9,10] and civil engineering [11,12]. As an effective tool in non-destructive testing (NDT), GPR is commonly adopted to evaluate concrete structures and detect reinforcements in civil engineering [13,14]. Specifically, the main applications of GPR in reinforced concrete materials and structures are [15]: (1) the location of reinforcing bars; (2) the detection of rebar corrosion; (3) the estimation of the rebar size; (4) the evaluation of the concrete cover; (5) the structural detailing of anchorages and joints in major structures/infrastructures; (6) the assessment of concrete characteristics by analyzing the material dielectric properties.
Zhou et al. [16] used GPR in combination with the electromagnetic induction (EMI) method to accurately locate reinforcing bars. Chang et al. [17] reported a physical model based on the use of digital image GPR for measuring the radius of reinforcing steel bars in concrete. Shaw et al. [18] developed a neural network approach to automate the estimation of the rebar size diameter from data collected with the transducer axis parallel and orthogonal to the bar orientation. Tesic et al. summarized corrosion inspection of reinforced concrete using GPR over the past two decades [19]. Tarussov et al. adopted computer-assisted visual interpretation to eliminate the anomalies unrelated to structural defects and filter out random noise [20]. For detection and localization of reinforced bars,

Theory
In 2D situation, the propagation of the TM mode electromagnetic wave follows the equations as: where H x and H y represent the magnetic field in the X and Y directions, respectively; E z is the electric field in the Z direction; σ is the conductivity, σ m is the equivalent specific reluctance; ε is the dielectric constant; µ is the magnetic conductivity. H n+1/2 x (i, j + 1/2) = DA * H n−1/2 x (i, j + 1/2) − DB * E n z (i, j + 1) − E n z (i, j) ∆y (5) H n+1/2 y (i + 1/2, j) = DA * H n−1/2 where Assuming that the travel-times of reflections are twice that of the reflector-to-receiver times, the energy of reflections received by receivers can back-propagate to locations of reflectors with half the real velocity. The expression of the inverse time extrapolation formula of the electromagnetic field is as follows: H n−1/2 where The wavefield is propagated through Equations (8)-(10) from the maximum time to time = 0. The wavefield at time = 0 is the migrated wavefield, that is: where I and E denote wave fields at zero time and between zero time and the maximum, respectively.

Workflow of RTM
The flowchart of RTM is shown in Figure 1. First, a time-zero correction is applied to the recorded GPR data. After that, the migration velocity is estimated based on prior knowledge or hyperbola fitting. The migration velocity is an essential parameter, which affects the focusing result of hyperbolas. Here, we adopt the iterative velocity estimation method, i.e., an estimation method by a trialand-error process, to determine the migrated velocity [21,30]. Then, the recorded data is inserted at each receiver position as boundary conditions for constant-time iteration. With this extrapolation, all energy converges back to the positions of the reflectors. Finally, we obtain the migrated result to estimate the depths and diameters of the reinforced steel bars. First, a time-zero correction is applied to the recorded GPR data. After that, the migration velocity is estimated based on prior knowledge or hyperbola fitting. The migration velocity is an essential parameter, which affects the focusing result of hyperbolas. Here, we adopt the iterative velocity estimation method, i.e., an estimation method by a trialand-error process, to determine the migrated velocity [21,30]. Then, the recorded data is inserted at each receiver position as boundary conditions for constant-time iteration. With this extrapolation, all energy converges back to the positions of the reflectors. Finally, we obtain the migrated result to estimate the depths and diameters of the reinforced steel bars.

Synthetic Datasets
A synthetic data test is carried out to validate the ability of RTM in detecting and localizing reinforcements in concrete. Figure 2 shows the dielectric constant of reinforcement and concrete model, which is discretized into 600 × 300 grids with a grid size of 1.2 m × 0.6 m. The model contains three reinforced steel bars, which are respectively located at (0.3 m, 0.1 m), (0.6 m, 0.075 m), (0.9 m, 0.05 m). The diameter of each reinforced steel bar is 24 mm which is based on factual circumstance consideration. The relative dielectric constant of the concrete material is 6.
We used an FDTD algorithm [35] to model the propagation of the electromagnetic wave. The offset between the transmitter and receiver is 0.04 m, and the location of the first excitation is at (0.04 m, 0 m). A Ricker wavelet with a center frequency of 2.6 GHz is used for the source excitation. The time window is 5 ns and the number of sampling points in each trace is 1061. A total of 521 times of excitations is conducted, and the horizontal step is 2mm. In this way, a GPR B-scan profile with 521 traces is simulated. Figure 3 shows the simulated B-scan profile, in which the direct wave has been muted and the unit is V/m. From this profile, three hyperbolas with different widths and depths are identified.
To test the ability of the RTM algorithm for noisy data, we added random noise with a value of 5-30% (with an increment of 5% each time) of the maximum amplitude in the simulated signal to the synthetic data. The B-scan with added noise at a different level is shown in Figure 4. From Figure 4a, the random noise of 5% has little effect on the recognition of hyperbolas. When the degree of random noise reaches 20%, there is no crossing between the adjacent hyperbolas. As the random noise increases further to 30%, the left hyperbola is almost invisible; the lengths of the other two hyperbolas are reduced to

Synthetic Datasets
A synthetic data test is carried out to validate the ability of RTM in detecting and localizing reinforcements in concrete. Figure 2 shows the dielectric constant of reinforcement and concrete model, which is discretized into 600 × 300 grids with a grid size of 1.2 m × 0.6 m. The model contains three reinforced steel bars, which are respectively located at (0.3 m, 0.1 m), (0.6 m, 0.075 m), (0.9 m, 0.05 m). The diameter of each reinforced steel bar is 24 mm which is based on factual circumstance consideration. The relative dielectric constant of the concrete material is 6.
We used an FDTD algorithm [35] to model the propagation of the electromagnetic wave. The offset between the transmitter and receiver is 0.04 m, and the location of the first excitation is at (0.04 m, 0 m). A Ricker wavelet with a center frequency of 2.6 GHz is used for the source excitation. The time window is 5 ns and the number of sampling points in each trace is 1061. A total of 521 times of excitations is conducted, and the horizontal step is 2 mm. In this way, a GPR B-scan profile with 521 traces is simulated. Figure 3 shows the simulated B-scan profile, in which the direct wave has been muted and the unit is V/m. From this profile, three hyperbolas with different widths and depths are identified.
To test the ability of the RTM algorithm for noisy data, we added random noise with a value of 5-30% (with an increment of 5% each time) of the maximum amplitude in the simulated signal to the synthetic data. The B-scan with added noise at a different level is shown in Figure 4. From Figure 4a, the random noise of 5% has little effect on the recognition of hyperbolas. When the degree of random noise reaches 20%, there is no crossing between the adjacent hyperbolas. As the random noise increases further to 30%, the left hyperbola is almost invisible; the lengths of the other two hyperbolas are reduced to nearly half of that in the original image ( Figure 3). Nevertheless, the apexes of the three hyperbolas are still clearly visible.
Remote Sens. 2021, 13, 2020 5 of 17 nearly half of that in the original image ( Figure 3). Nevertheless, the apexes of the three hyperbolas are still clearly visible.

Real Case Datasets
The site is located in a new camp on Changxing Island, Shanghai. To investigate the quality and scale of the reinforcement in the column or beam, GPR measurements were performed. The data was collected using GSSI sir-4000 GPR and an antenna with a center frequency of 2.6 GHZ. In particular, a small wooden bench was used to ensure that the measurements could be conducted from the column's edge, as shown in Figure 5.
The specifications of all columns are the same, i.e., 0.8 m × 0.6 m. Column A was cut to verify the imaging result before testing. In data acquisition, the time window was set to 8.8541 ns; the samples per trace was 512; There were 408 traces in total, and the horizontal step was 2.5mm. Figure 6 shows the B-scan profile of column A, in which the unit is V/m. The length of the survey line is 1.018 m. In this profile, nine hyperbolas (marked by red cycles and numbers) are identified, of which hyperbola 8 and hyperbola 9 are in doubt. nearly half of that in the original image ( Figure 3). Nevertheless, the apexes of the three hyperbolas are still clearly visible.

Real Case Datasets
The site is located in a new camp on Changxing Island, Shanghai. To investigate the quality and scale of the reinforcement in the column or beam, GPR measurements were performed. The data was collected using GSSI sir-4000 GPR and an antenna with a center frequency of 2.6 GHZ. In particular, a small wooden bench was used to ensure that the measurements could be conducted from the column's edge, as shown in Figure 5.
The specifications of all columns are the same, i.e., 0.8 m × 0.6 m. Column A was cut to verify the imaging result before testing. In data acquisition, the time window was set to 8.8541 ns; the samples per trace was 512; There were 408 traces in total, and the horizontal step was 2.5mm. Figure 6 shows the B-scan profile of column A, in which the unit is V/m. The length of the survey line is 1.018 m. In this profile, nine hyperbolas (marked by red cycles and numbers) are identified, of which hyperbola 8 and hyperbola 9 are in doubt.

Real Case Datasets
The site is located in a new camp on Changxing Island, Shanghai. To investigate the quality and scale of the reinforcement in the column or beam, GPR measurements were performed. The data was collected using GSSI sir-4000 GPR and an antenna with a center frequency of 2.6 GHZ. In particular, a small wooden bench was used to ensure that the measurements could be conducted from the column's edge, as shown in Figure 5.
The specifications of all columns are the same, i.e., 0.8 m × 0.6 m. Column A was cut to verify the imaging result before testing. In data acquisition, the time window was set to 8.8541 ns; the samples per trace was 512; There were 408 traces in total, and the horizontal step was 2.5 mm. Figure 6 shows the B-scan profile of column A, in which the unit is V/m. The length of the survey line is 1.018 m. In this profile, nine hyperbolas (marked by red cycles and numbers) are identified, of which hyperbola 8 and hyperbola 9 are in doubt. Remote Sens. 2021, 13, 2020 6 of 17  At the same time, two black dotted boxes were utilized to identify hyperbola 8 and 9. Table 1 shows the locations and features of the identified hyperbolas. The four hyperbolas (number 1-4) are normal which denotes the typical hyperbola; the three hyperbolas (number 5-7) are almost overlapped; the hyperbola (number 8) is incomplete and smaller near to 0.9m; the hyperbolas (number 1 and 9) are overlapped, moreover, the hyperbola (number 9) is hardly identifiable.   At the same time, two black dotted boxes were utilized to identify hyperbola 8 and 9. Table 1 shows the locations and features of the identified hyperbolas. The four hyperbolas (number 1-4) are normal which denotes the typical hyperbola; the three hyperbolas (number 5-7) are almost overlapped; the hyperbola (number 8) is incomplete and smaller near to 0.9 m; the hyperbolas (number 1 and 9) are overlapped, moreover, the hyperbola (number 9) is hardly identifiable.    Table 2 shows the positions and features of the identified hyperbolas.
In Figure Table 2 shows the positions and features of the identified hyperbolas.
In Figure 8a Figure 8 shows the accurate amount of the column and the approximate location of each steel bar. However, the precise depth of each reinforced bar is necessary for the determination of the reinforced structure. For the determination and localization of the reinforced bars, we adopted the RTM algorithm to process the data of the four B-scan profiles. Figure 9 shows the imaging results of the synthetic GPR profile presented in Figure 3. We can see that the energy of the hyperbola converges precisely to a region consistent with the scale of the reinforced steel bars. The depth and horizontal position of the left point are 0.1 m and 0.3 m, respectively; the depth and horizontal position of the middle one are 0.075 m and 0.6 m, respectively; the depth and horizontal position of the right one are 0.5 m and 0.9 m. For quantifying the diameters of rebars, an area inside the black-dotted box was enlarged. As the arrow points out, the image inside the box was enlarged into the detail window. We used a circle to mark the identified rebar. Moreover, we scaled the length of the detail window to estimate the diameter.

Synthetic Data Test
The corresponding imaging results of Figure 4a,f are shown in Figure 10a

Real Field Data Test
In this paper, the horizontal axes of all imaging results are 0.01 m longer, and the maximum depth is 0.4 m. The size of the grid is 0.5 mm x 0.5 mm, and the sampling interval is reduced to one-hundredth of the original to satisfy the time stability condition. Figure 11 shows the imaging result of the cut column. We identified and marked seven  Figure 6) collapsed into clouds (number 2-6 in Figure 11) except that the leftmost one, as well as the rightmost one, converged to a striped shape. For quantifying the diameter, we selected an area, i.e., the area inside a black-dotted box. Rebar 4 is marked by a green circle. Table 3 shows the positions and features of the identified rebars. As shown in Figure 12a, the cut side is 0.8 m long. The cut column in Figure 12a demonstrates that the positions of rebars in the imaging result are well retrieved. Notably, as shown in Figure 12b, the black-dotted box surrounds the steel pipe, and the right hyperbola (number 6) is generated by a steel pipe. Figure 12c shows that the real diameter of the rebar is approximately 22 mm.

Real Field Data Test
In this paper, the horizontal axes of all imaging results are 0.01 m longer, and the maximum depth is 0.4 m. The size of the grid is 0.5 mm x 0.5 mm, and the sampling interval is reduced to one-hundredth of the original to satisfy the time stability condition. Figure 11 shows the imaging result of the cut column. We identified and marked seven reinforcements (number 1-7) by red circles, of which the positions are (0. 16 Figure 6) collapsed into clouds (number 2-6 in Figure 11) except that the leftmost one, as well as the rightmost one, converged to a striped shape. For quantifying the diameter, we selected an area, i.e., the area inside a black-dotted box. Rebar 4 is marked by a green circle. Table 3 shows the positions and features of the identified rebars. As shown in Figure 12a, the cut side is 0.8 m long. The cut column in Figure 12a demonstrates that the positions of rebars in the imaging result are well retrieved. Notably, as shown in Figure 12b, the black-dotted box surrounds the steel pipe, and the right hyperbola (number 6) is generated by a steel pipe. Figure 12c shows that the real diameter of the rebar is approximately 22 mm.   Figure 8a-d, respectively. Similarly, the unit is V/m. We marked all identified rebars by circles and numbers. Table   Figure 8a-d, respectively. Similarly, the unit is V/m. We marked all identified rebars by circles and numbers. Table 4 shows the quantity, positions, and features of the identified rebars. Figure 13a,c contain one less reinforcement than that in Figure 13b,d. The depths of the identified reinforced bars in Figure 13a,d are less than 10 cm, which are mainly 0.6 m and 0.5 m, respectively. Conversely, the depths of rebars in Figure 13b,c are more than 10 cm, which are mainly 0.11 m. In Figure 13 b,c, the collapsed energy is mainly dotted except that the first one in Figure 13b and the fifth one in Figure 13c are striped. The focused hyperbolas are mainly curved in Figure 13a,d except for the first one in Figure 13a which is striped. 4 shows the quantity, positions, and features of the identified rebars. Figure 13a,c contain one less reinforcement than that in Figure 13b,d. The depths of the identified reinforced bars in Figure 13a,d are less than 10 cm, which are mainly 0.6 m and 0.5 m, respectively. Conversely, the depths of rebars in Figure 13b,c are more than 10 cm, which are mainly 0.11 m. In Figure 13 b,c, the collapsed energy is mainly dotted except that the first one in Figure 13b and the fifth one in Figure 13c are striped. The focused hyperbolas are mainly curved in Figure 13a,d except for the first one in Figure 13a which is striped.

Discussion
In the synthetic data test, the locations of identified rebars are (0.3 m, 0.1 m), (0.6 m, 0.75 m), and (0.9 m, 0.5 m), respectively, which are consistent with the real ones. For quantifying the diameter, we enlarged an area inside a black-dotted box. As shown in Figure 9, the rebar is marked. Notably, the box is 0.2 m wide, i.e., the real diameter must be from conversion. By conversion, the diameter of the identified rebar is approximately 24.2 mm and the error is 0.2 mm. This result validates the ability of the RTM algorithm. By noisy experiment, we find that the positions of identified rebars are equal to the previous ones. This result proves the stability of the RTM algorithm.
In the paper, the dataset of the cut column A is provided first. We identified nine hyperbolas of which hyperbola 1-7 are clear. Hyperbola 8 is small but curved so that it, as well as hyperbola 9, is in doubt. The hyperbolic energy (number 9) is very weak and overlapped with hyperbola 1. Specially, we made use of black-dotted boxes to identify hyperbola 8 and 9. However, the migration image shows seven identified rebars that correspond to hyperbola 1-7, i.e., we identified disturbing energy in mistake for hyperbolas. To verify the capability of the RTM algorithm on the real case dataset, we cut the column. As shown in Figure 12, the horizontal distance of the seven bars are 8.3 cm, 21 cm, 34 cm, 48.8 cm, 63 cm, 68.5 cm, and 74.5 cm, respectively. Table 3 shows that the relative locations of the identified rebars are consistent with those of the real ones. Moreover, the identified rebar (number 6) is a steel pipe. To quantify the diameter, we selected one black-dotted box that surrounded the identified rebar 3 and 4. Obviously, rebar 4 has been retrieved better. By conversion, the interpreted diameter is about 20.4 mm. The error is 1.6 mm. Nevertheless, the other rebars are retrieved worse, i.e., there exists some degree of error that has an influence on the interpretation. On the other hand, the diffraction wave is suppressed well.
Based on the imaging result of column A, we utilized the RTM algorithm to process the real case datasets of column B which included four sides. From the B-scan profiles, the hyperbolic energy in Figure 8a,d are stronger. Clearly, the energy of the diffraction wave is more powerful with less depth of the rebar. In Figure 13b,c, the hyperbolas collapse better. The results prove the ability of suppressing the diffraction wave of the RTM algorithm. Figure 14 shows the reinforced concrete structure inferred from the imaging results shown in Figure 13. The arrow denotes the direction of the survey line and the red rectangle represents the position of 10 cm below the column surface; the black circles represent the steel bar. As shown in Figure 14, the left and front thicknesses of the protective layer are less than 10 cm; the right and back thicknesses are more than 10 cm. However, the cover thickness of reinforcements in a concrete structure is required to be less than 10 cm.
Remote Sens. 2021, 13,2020 15 of 17 hyperbolic energy in Figure 8a,d are stronger. Clearly, the energy of the diffraction wave is more powerful with less depth of the rebar. In Figure 13b,c, the hyperbolas collapse better. The results prove the ability of suppressing the diffraction wave of the RTM algorithm. Figure 14 shows the reinforced concrete structure inferred from the imaging results shown in Figure 13. The arrow denotes the direction of the survey line and the red rectangle represents the position of 10 cm below the column surface; the black circles represent the steel bar. As shown in Figure 14, the left and front thicknesses of the protective layer are less than 10 cm; the right and back thicknesses are more than 10 cm. However, the cover thickness of reinforcements in a concrete structure is required to be less than 10 cm.

Conclusions
Here, we carried out GPR measurements combined with the RTM algorithm in the localization of reinforcements. We first used a synthetic example to test the ability of the proposed strategy. After the RTM processing, the hyperbolas converged to the region consistent with the real model. Even for noisy data, whose signal-to-noise ratio is too low to identify the response of the hyperbolas, the diffraction energy was collapsed correctly to the positions of the rebars. In addition, the error between the estimated diameter and the real diameter was less than 1 mm. These results demonstrate the capability of the RTM algorithm in reinforcement detection.
Following this, we performed an on-site test to determine the quantity and locations of reinforced steel bars of buildings. Before measurements, we tested the proposed strategy again on a cut column. The migration image shows that the hyperbolic reflections are well focused. The interpreted quantity and positions of the rebars were verified by the

Conclusions
Here, we carried out GPR measurements combined with the RTM algorithm in the localization of reinforcements. We first used a synthetic example to test the ability of the proposed strategy. After the RTM processing, the hyperbolas converged to the region consistent with the real model. Even for noisy data, whose signal-to-noise ratio is too low to identify the response of the hyperbolas, the diffraction energy was collapsed correctly to the positions of the rebars. In addition, the error between the estimated diameter and the real diameter was less than 1 mm. These results demonstrate the capability of the RTM algorithm in reinforcement detection.
Following this, we performed an on-site test to determine the quantity and locations of reinforced steel bars of buildings. Before measurements, we tested the proposed strategy again on a cut column. The migration image shows that the hyperbolic reflections are well focused. The interpreted quantity and positions of the rebars were verified by the real result on column A. The consistency between the migrated result and the fundamental structure of the column further shows the effectiveness of the strategy. However, the error of diameters reaches 1.6 mm, i.e., 7.2%. Finally, we used the RTM algorithm to process the GPR data measured from column B. The results show that the diffraction wave is well suppressed. According to the imaging result of the four sides, we retrieved a reinforced concrete structure, which illustrates that the protective layer thickness of the column is partly qualified.
In summary, the proposed RTM algorithm can help with suppressing the hyperbolic reflections to localize and detect concrete reinforced bars. However, the accuracy of estimation of diameters on real case datasets is a problem. We will investigate other methods to improve the accuracy.
On the other hand, the reinforced concrete structural problem is related to the prevention and the solution of construction safety hazards. When the signal attenuation is significant, energy compensation should be incorporated with the RTM to better resolve the concrete structure.