Feasibility of detecting embedded cracks in concrete structures by re ection seismology

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1 NDT&E International 34 (2001) 39±48 Feasibility of detecting embedded cracks in concrete structures by re ection seismology Young-Fo Chang a, *, Chung-Yue Wang b, Chao-Hui Hsieh c a Institute of Seismology and Applied Geophysics, National Chung Cheng University, Min-hsiung, Chia-yi 621, Taiwan, ROC b Department of Civil Engineering, National Central University, Chung-li 320, Taiwan, ROC c Department of Geophysics, National Central University, Chung-li 320, Taiwan, ROC Received 26 March 1999; received in revised form 20 April 2000; accepted 18 May 2000 Abstract Re ection seismology has been widely used in the petroleum exploration industry for decades. To improve the capabilities of detecting the depths and lengths of cracks inside a concrete element, an ultrasonic common depth point (CDP) re ection technique was employed in this study. The effectiveness and accuracy of applying the re ection seismology method to detect cracks embedded in concrete structures are discussed. Test results show that simulated blind cracks with certain lengths, dip angles and depths inside concrete specimen can be successfully imaged and identi ed. This study shows that when the signals re ected from the crack are obscure, the CDP signal stacking method is very useful and provides an opportunity to look into the object, which is not possible with traditional ultrasonic methods. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Re ection seismology; Concrete; Crack; Nondestructive evaluation; Data processing 1. Introduction * Corresponding author. Tel.: ; fax: address: seichyo@eq.ccu.edu.tw (Y.-F. Chang). The state of infrastructure in a country re ects economic progress and stability, and indeed, the quality of its peoples' lives. Over time, the environment, and mismanagement reduce the load carrying capacity, serviceability and durability of civil infrastructures. Recently, many engineering agencies have become interested in locating and evaluating defects or damage in civil structures. Concrete structures are common components of civil infrastructures. To evaluate the safety of a concrete structure, the locations and dimensions of cracks and voids must be estimated using nondestructive detecting techniques. Concrete is a heterogeneous material, especially to high frequency ultrasonic waves. Due to the complexity of concrete material and high energy loss for high frequency ultrasonic waves in concrete, small cracks in the concrete structure cannot easily be estimated precisely. It is known that small cracks are the precursors of larger cracks and then affect the strength and durability of concrete structure. It will be useful for evaluation and retro tting of concrete structure if the small cracks can be found early. Although the ability to detect cracks in concrete has improved in recent years [1±3], a high resolution technique for evaluating defects within concrete, especially concrete with steel reinforcement, is still under development. Each nondestructive evaluation method has its own capabilities and limitations and can not be applied to all engineering cases. Up to now, the most popular nondestructive method for detecting surface opening cracks in concrete element is the ultrasonic pitch-catch method [1]. Based on the measurement of the travel time of the ultrasonic waves propagating from the transmitter to the crack tip and to the receiver, the location of the crack tip can be estimated by geometrical relationships if the wave velocity in the concrete is known. The impact-echo method uses a small steel ball to impact the concrete surface and a wide band receiver records the responses from the concrete. By analyzing the spectrum of the measured response signals, the locations of empty ducts and defects like delaminations can be evaluated [4,5]. One can also analyze the dispersion curves of the Rayleigh waves to estimate the depth of horizontal crack [6]. Phase analysis of transient elastic waves has been applied to estimate the depth and dip angle of cracks within concrete [7±9]. Liu et al. [10] and Kuo et al. [11] imaged the crack tip of surface opening crack by using the seismic migration method. The authors of this paper also demonstrated a migration technique to construct a three-dimensional (3D) image of the crack tip of a surface opening /01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S (00)00030-X

2 40 Y.-F. Chang et al. / NDT&E International 34 (2001) 39±48 Fig. 1. Con guration of re ection seismology. crack [12]. The re ection seismology has never been used for detecting cracks in concrete structures before. The dominant wavelength in the concrete will be about 2 cm, if the velocity of concrete is 4000 m/s and the dominant frequency of the propagating waves is 200 khz. The size of the aggregates within the concrete may be greater than 1±2 cm, which is comparable to the wavelength of ultrasonic waves. Therefore, if the wavelength of the waves is less than 1±2 cm, the waves propagating in concrete will be strongly scattered. The high frequency attenuation factor of ultrasonic waves implies that conventional ultrasonic nondestructive techniques are not available to detect small cracks in concrete. Simaan et al. [13] found that a transducer-array method can effectively locate aws, while Green [14] suggested using the geophysical array method to measure and process the weak signals. Cracks and aggregates in the concrete may be analogous to faults and gravel in the earth's crust and can diffract ultrasonic waves as the seismic waves are diffracted in geophysical investigations. Re ection seismology has proved to be ef- cient in exploring geological conditions of the earth's crust. Therefore, it is natural to apply the re ection seismology method to the detection of small cracks in concrete structures. In this feasibility study, simulated cracks with different depths, sizes and dip angles will try to be imaged by an ultrasonic re ection method. Hopefully, the results obtained from this study can eventually provide civil engineers with a high resolution method to detect cracks within concrete structures. 2. Re ection seismology Re ection seismology has been accepted as an effective method in petroleum engineering to explore for hydrocarbons. A detailed theory of re ection seismology can be found in text books [15,16], while a summary is given here. The multi-sources and multi-receivers are distributed on the surface of a two-layer system to generate and pick up the ultrasonic waves (Fig. 1), respectively. Offset is the distance between the source and receiver. The near offset and far offset are the distances from source to rst receiver and last receiver in a spread, respectively. When source 1 is triggered, 48 receivers in spread 1 simultaneously record the re ected echoes from the interface of the two-layer system. After the source 1 shot, the source and all receivers move forward a unit distance, then source 2 is triggered and the 48 receivers in spread 2 record the re ected echoes, and so forth. The middle point between source 1 and receiver 1 on the interface of the two-layer model is the common depth point (CDP) CDP 1 and the middle point between source 1 and receiver 2 is the CDP 2, and so on. The fold number is de ned as the number of time histories having the same CDP and the time histories will be stacked (added) together. In this con guration, the CDP 1 and CDP 2 have 1- fold and CDP 3 has 2-fold. The example of the arrangement of the sources and receivers for a 5-fold CDP on the concrete specimen is shown in Fig. 2a. The time histories having different offsets but the same CDP are sorted to a CDP gather which is a side-by-side display of time histories. A synthetic CDP gather based on the model Fig. 2a is shown in Fig. 2b. The normal moveout (NMO) is the time difference of the echoes re ected from the CDP between the zero offset measurement (source and receiver located at same point) and some offset measurement. Before stacking (adding) the time histories in a CDP gather, the NMO corrections for the time histories are required. Fig. 2c shows the NMO corrections for the time histories so that all the peaks and troughs will be added in phase. After stacking, the new time history can be considered as the echoes recorded directly above CDP using the singleprobe pulse-echo method. The section is constructed by side-by-side display of the new time histories and contains information of any cracks presented in the concrete.

3 Y.-F. Chang et al. / NDT&E International 34 (2001) 39±48 41 The advantages of this method are that the signals re ected from the interface will be enhanced and it is not necessary to pick the travel times or the waveform of the re ected echoes for analysis. The necessary data processing can be conducted using a personal computer and the output represents an image of the geometry of the re ecting interface. 3. Experimental program 3.1. Specimens Five concrete specimens (H1, H2, H3, I1 and I2) with different types of simulated cracks and one layered mortar (LM) specimen were made in this study. The LM specimen was used to examine the feasibility of applying the macro-re ection seismology method to a small-scale specimen. It was cast with mortar and polyethylene (PE) plate of 10 mm thickness embedded at a depth of 12 cm; shown in Fig. 3. The weight ratio of the water to cement is about 0.4. The outer dimension of this LM specimen is 24 cm 24 cm 24 cm: The compressional wave velocities of the mortar and the PE plate are 3200 and 2470 m/s, respectively. The concrete specimens with known simulated crack sizes and locations were made. They were cast with cement, sand and aggregate and the mix ratio was 1:2:4 (by weight). Type I Portland cement was used. The aggregate had a maximum size of 25.4 mm. The velocities of the concrete for the compressional waves and Rayleigh waves are 3837 and 1900 m/s. A steel plate of 1 mm thickness was embedded in each concrete block at its designated position during casting of the specimen. After the initial solidi cation of concrete, the thin steel plate was pulled out to create an arti cial crack 1 mm wide in the specimen. The outer dimension of all concrete specimens with arti cial cracks is 20 cm 16 cm 35 cm: All the cracks used in this study are blind plane cracks. Fig. 4 shows a specimen with a crack that has a dip angle of 158, a depth of 6 cm measured from the upper crack tip to the top surface, and a length of 5 cm. Con gurations of all the cracks in the test specimens used in this study are listed in Table 1. The distance between the shot and the crack edge projection on surface is de ned as the surface distance Experiments Fig. 2. The con gurations of (a) a 5-fold CDP arrangement; (b) the synthetic time histories in a CDP gather; (c) NMO correction of the time histories. The experiments were conducted in the Seismic Acoustic Laboratory (SAL), Institute of Geophysics, National Central University in Taiwan. Fig. 5 shows the automatic ultrasonic scanning and data acquisition system used for crack detections in the mortar and concrete specimens by the re ection seismology method. Two pairs of Ultran transducers with diameters of 17 mm (500 khz) and 30 mm (300 khz) were used to detect the cracks with depths of 6 and 13.9 cm, respectively.

4 42 Y.-F. Chang et al. / NDT&E International 34 (2001) 39±48 Table 1 Con gurations of the cracks and acquisition parameters used in the experiments Model con guration type LM H1 H2 H3 I1 I2 Crack tip depth (mm) ± Crack length (mm) ± Dip angle (degree) Total number of shots, N s Total number of traces, N t N t ˆ 48 N s Near offset (mm) Far offset (mm) Transducer (khz) Surface distance a (mm) ± Peak frequency of re ected echoes (khz) Fig. 3. Dimensions of the layered mortar specimen, LM. The measurement and scanning, as shown in Figs. 3 and 4, proceeded along survey lines on the top surface of each specimen. The system is an end-on shooting arrangement wherein the source is at the end of the receiver spread. There are 48 receiver stations in the spread for each shot. The spacing interval between neighboring receiver stations was set as 2 mm. The source's spacing interval was also 2 mm. All the measurement parameters, including the number of shots, recorded traces, near offset and far offset, are listed in Table 1. Based on the geometry of the sources and receivers used in this study, the maximum fold for a CDP is Data processing The data processing was conducted at the Shallow Seismic Seismology (SSS) Laboratory, Institute of Geophysics, National Central University. The amplitudes of the time histories recorded in this study had been conducted and displayed by automatic gain control (AGC). The gain factor a The distance between rst shot and the crack edge projection on the surface. alters in accordance with the amplitude of the input signal in the form of AGC. Up to a certain input level the gain is approximately constant but it reduces progressively for higher input levels. Thus the stronger signals are relatively attenuated and the overall dynamic range is markedly reduced [16]. For seeing the section clearly and consistently, the maximum amplitudes of the histories were normalized to the same level. In order to focus on the feasibility of re ection seismology for detecting cracks inside concrete, only a basic sequence of data processing was conducted. However, other processing techniques such as ltering, deconvolution, and migration can be further applied to improve the data quality and resolution [15±19]. The steps of the data processing procedure are shown in Fig. 6. After scanning over the surface of the specimen, the recorded data was reformatted into the compatible format for the seismic data processing. Then, the recording parameters of the eld geometry were Fig. 4. Dimensions of concrete specimen and crack location used in the experiments. Fig. 5. Acquisition system for crack detection in concrete by the re ection seismology method.

5 Y.-F. Chang et al. / NDT&E International 34 (2001) 39±48 43 used to initiate the analysis. The processing sequences for the enhancement of signals such as CDP sorting, NMO correction and CDP stacking were used for stacking and improving the recorded data and nally displaying the stacked section. 4. Results Fig. 6. Major steps of the data processing used in this study Layered mortar specimen (LM) The LM specimen is the rst specimen to be scanned in this study. The shot gather is a side-by-side display of time histories recorded by the 48 receivers in a spread for a shot. Fig. 7 is an example of shot gather for the specimen LM. In this shot gather, the most dominant events ªR1º that occurred at about 77 ms for channel 1 and 86 ms for channel 48 are the re ected P-waves from the upper mortar±pe plate interface (R1). The events ªR2º later than ªR1º 8 ms are the waves re ected from the lower PE plate±mortar interface (R2) and the relative amplitudes of the re ections ªR1º and ªR2º is about ªR2º is contaminated by the side lobe (tail) of ªR1º and is not easy to see. Other events named ªR3º 1 ªMR1º 1 ªMR2º occurred at about 155 ms, in which ªR3º represents the P-waves re ected from the bottom mortar±air interface (R3) of the specimen. ªMR1º represent the multi-re ection of ªR1º and ªMR2º is the incident of ªMR1º and re ected at R2 interface. The events ªPSº are the P-waves incident and re ected at the R1 interface which travel to the receivers as S-waves. The events ªDº denote the direct P-waves from the source to the receivers along the top surface, and ªRaº denote the Rayleigh waves propagating along the surface. The dominant frequency of the re ected events ªR1º is about 400 khz by Fourier analysis. Since 500 khz transducer was used on this specimen, only little high frequencies energy of the re ected echo are attenuated during propagation in LM specimen. The processed distance±depth section of specimen LM is shown in Fig. 8, where the Y-axis on the left is the travel time of the echoes and is converted to depth in mm on the right side. The X-axis represents distance along the survey line on the top surface of the LM specimen. From this gure, the interface R1 can be located clearly at the depth of 120 mm. If the fold numbers are too small to decrease the Fig. 7. The shot gather of shot #11 of LM model.

6 44 Y.-F. Chang et al. / NDT&E International 34 (2001) 39±48 Fig. 8. A stacked section of LM model by the re ection seismology method. noise at the right and left boundary of the survey line then the noise at the boundary will be stronger than at the middle of the section. Some small noisy events exist at depth 168 (105 ms, close to the right and left boundaries and caused by ªPSº events), 264 (165 ms, close to the left boundary and caused by ªMR1º 1 ªMR2º events) and 288 (180 ms, close to the center and right boundary and caused by ªPPPSº events) mm. Although the events ªR3º are contaminated by the events ªMR1º and ªMR2º, the interface R3 is still can be identi ed in the section at a depth slightly greater than 240 mm. These results show that if there are no large inclusions (sand and aggregates), the re ection seismology method used for large scale (earth eld) problems can be successfully applied to small scale problems such as the structural elements of civil infrastructures. Fig. 9. The shot gather of shot #26 of the crack model H1 (dip angle ˆ 08, crack length ˆ 5 and depth ˆ 6 cm).

7 Y.-F. Chang et al. / NDT&E International 34 (2001) 39±48 45 Fig. 10. The stacked section of the crack model H1 (dip angle ˆ 08, crack length ˆ 5 cm and depth ˆ 6 cm) by the re ection seismology method Horizontal crack specimens (H1, H2, H3) Three horizontal crack models were made in this study. Fig. 9 shows the 26th shot gather of crack model H1 with a 5 cm long horizontal crack embedded at a depth of 6 cm in the concrete block. The surface distance between the shot 26 and crack is 20 mm. The dominant events denoted by ªRaº is the Rayleigh waves propagating along the top surface. The signals ªR1º re ected from the crack and direct P- waves ªDº are very weak. The converted waves and multi-re ections could not be veri ed in the shot gather, but they can be clearly identi ed in the previous laminated LM mortar specimen. The aggregates in the concrete scatter and attenuate the waves and result in a relatively strong surface waves. This is the main factor that makes the sectional signals very noisy. The echoes re ected from the crack are not easy to be identi ed, the channel number is less than 25 especially. Where the ªR1º arrived later Rayleigh waves are strongly contaminated by the large amplitude and low frequency Rayleigh waves. This section shows that it is impossible to pick the re ected echo ªR1º using an A-scan, even the B-scan is also very dif cult. The dominant frequency of the re ected echoes is 200 khz (Table 1), a lot of high frequency energy were attenuated by the concrete. The stacked section of the H1 crack specimen is shown in Fig. 10. In this gure, the true location of the crack is marked by a straight line LR and extends from CDP number 66 to number 116. The echo is not processed by zero phase lter which the phase shift is zero for all frequencies and the echo begins before time zero. Since the concrete is a high attenuation (low Q) material for high frequency ultrasonic waves, the shape of echo changes during propagation. The high frequencies waves will be attenuated more than the low Fig. 11. The stacked section of the crack model H2 (dip angle ˆ 8, crack length ˆ 3 cm and depth ˆ 6 cm) by the re ection seismology method.

8 46 Y.-F. Chang et al. / NDT&E International 34 (2001) 39±48 Fig. 12. The stacked section of the crack model H3 (dip angle ˆ 08, crack length ˆ 5 cm and depth ˆ 13.9 cm) by the re ection seismology method. frequencies ones. The nite size effect of the transducers will cause uncertainty in the crack position. Therefore, the position of the crack in the section will be reported at the onset of the echoes. The darkest area AB, which is identi ed as the crack re ection event, is about 13±15 mm deeper than the true depth of the crack. The length of AB is greater than the crack's true length of 50 mm. This is because the diameters of the transducers are 17 mm. The transducers can excite and record the ultrasonic wave even when the location of the center of the transducer is beyond the range of the crack. Other events shown in Fig. 10 are noises, which were coherent at some distances and time ranges, and can be stacked constructively after the data processing. But the continuity and length of any stacked constructively noises are not as good as area AB. As with the previous LM model, the intensity of the noise is stronger at the right and left boundary than at the middle section of the survey line. A horizontal crack (H2) with length of 3 cm located 6 cm deep was detected using the same acquisition parameters as crack model H1 except that the total number of shots is 38 since the crack length is shorter than in specimen H1. The stacked section for specimen H2 is shown in Fig. 11. In this gure, the true position of the crack is straight line LR. The image of the crack is recognized as the events between points A and B. The crack image splits at CDP 87, which was caused by part collapse of concrete after pulling out the thin steel plate. The energy level, continuity and length of the noises are relatively stronger compared with the signals from the H1 model. But, the image of the crack still can be recognized in this case. The stacked section of a 5 cm long horizontal crack (H3) Fig. 13. The stacked section of the crack model I1 (dip angle ˆ 08, crack length ˆ 5 cm and upper crack tip depth ˆ 6 cm) by the re ection seismology method.

9 Y.-F. Chang et al. / NDT&E International 34 (2001) 39±48 47 Fig. 14. The stacked section of the crack model I2 (dip angle ˆ 308, crack length ˆ 5 cm and upper crack tip depth ˆ 6 cm) by the re ection seismology method. and 13.9 cm deep is shown in Fig. 12. The acquisition parameters of this test are also listed in Table 1. When the crack depth increases, the travel distance of re ected echo also increases. Hence, lower frequency waves must be used in order to have lower attenuation. When the crack is relatively deep in the specimen, the re ected echoes from the crack to the detector may be later than the surface waves. All signals arriving after the surface waves will be contaminated and will not be easily recovered since the surface waves are the dominant noise in the section and they are dif cult to eliminate. The location of the crack can barely be recognized in the stacked section plot (Fig. 12) because the noises are stronger than that in the stacked section plots of the H1 and H2 models Inclined crack specimens (I1, I2) Two inclined crack models, I1 and I2, were made in the study. The corresponding parameters used for each specimen are listed in Table 1. The dip angle of the inclined plane crack is measured between the horizontal surface and the crack plane. The depth of each crack is de ned as the distance from the top surface of the specimen to the shallower tip of the crack. The length of the cracks is 5 cm. When the crack is inclined in the concrete, the ray paths of the re ected echoes from the crack are never symmetrical about the midpoint between the source and receiver. Besides, the energy of re ected echoes is more weak and dif cult to stack than in the case of a horizontal crack. If the crack is inclined, the extent of the crack image in the processed section would be longer than the true crack length and the imaged dip angle will be less than the true dip angle of the crack. In addition, the position of the echoes will shift up and translate some distance depending on the value of dip angle [19]. Fig. 13 shows the stacked section for inclined crack specimen I1 with a dip angle 158, in which the true location of the crack is marked by a straight line LR and the crack re ected echoes are identi ed as events between A and B. The re ected echoes from the crack are always about a 13± 15 mm deeper than the true crack (see Figs. 9 and 10), but in Fig. 13 they seem to be very close to the position of the true crack this is because that the crack is not horizontal and the crack image is shifted to the left. Although there is some perturbation in the re ected echoes, we can still recognize the re ected echoes from the crack. The positions of the re ected echoes can be moved to their true positions by further data processing [15±19], but that is not of concern in the current study. Fig. 14 shows the stacked section of specimen I2 with a crack at a dip angle 308. Since the echoes re ected from the inclined crack are not easy to distinguish from the background noise and the echo re ected from horizontal layer is assumed in the process. Therefore, it is dif cult to locate the crack straightforward from the section. 5. Discussion The other concrete specimens (for examples, the horizontal crack with depth 13.9 cm and length 3 cm, and incline cracks with dip angle 458/depth 6 cm/length 5 cm, dip angle 608/depth 6 cm/length 5 cm, dip angle 158/depth 13.9 cm/ length 5 cm) which does not shown in this study were scanned, but the results are not good enough to see the crack image. Consequently, this method cannot detect all kinds of cracks in concrete. It is not the only method of the nondestructive evaluation and it cannot solve all the problems. This method can only detect some cracks, horizontal crack especially. Based on the attenuation characteristics of ultrasound, the normal-incident transducer used in experiments, and this

10 48 Y.-F. Chang et al. / NDT&E International 34 (2001) 39±48 method assumed that the echo re ected from the horizontal layer, we can nd from the experimental results that the shallow, horizontal and large cracks are easier to be detected than the deep, inclined and small cracks. The probability of successful locating the crack in concrete depends on a number of factors such as the knowledge of the background of concrete (i.e. the mixture proportions and age of the concrete, how the structure was constructed, how it worked and was maintained, where the possible crack will be produced and what size is the possible crack), and the evaluation methods (destructive and nondestructive) used to detect the crack. The probability increases if more knowledge of the concrete have been known and more evaluation methods were used to locate the crack, otherwise the probability will be low. It is not only the blind crack that this method can detect. Some other objects such as the surface-opening crack, cavity, honeycomb, ducts and steel reinforcement, which have large contrast of the acoustic impedance between them and the concrete, can still be detected by this method. Nevertheless, a better result of this method is predicted if more energy re ected from the objects can be detected. Theoretically, this method can be applied to detect multiple or jointed cracks inside concrete members much like the faults in the earth. If 3D patterns or locations of the crack are desired, then 3D re ection seismology acquisition techniques and data processing methods can be adopted. Migration techniques can move the image of an inclined crack from its apparent position to the true position and other data processing techniques can improve the resolution of the image. However, this was not part of the current study and will be considered in a future research. In this study, only two probes, one source and one receiver, were used in the experiments by moving the source and receiver step by step along the survey line. In eld applications, labor and time can be saved if a multi-source multi-receiver system is used. 6. Conclusions The ability of detecting cracks in concrete relies strongly on the capability of the sensing system, techniques and theories of detection, and signal processing techniques for recorded data. The ultrasonic system and data processing techniques, that were used in this study, demonstrate that horizontal cracks of length 3 cm, depth 6 cm deep and of length 5 cm, depth 14 cm and an inclined crack with a 158 dip angle, 6 cm deep can be imaged successfully. Although not all the cracks in concrete can be detected, some of the small cracks in concrete structures can be detected by the re ection seismology method, that other ultrasonic nondestructive methods would miss. This paper shows that the more weakness of the echoes re ected (or diffracted) from the crack, the more measurements from different surveying angles (offsets) are required for the stacking process in order to make a correct estimation of the crack. The quality and resolution of the signals can be improved by stacking the measurements after some necessary correction. Acknowledgements The authors thank Prof. Chien-Ying Wang for the permission to use the processing package to analyze the scan data. The support of this study by the National Science Council of Taiwan, ROC under Contract No. NSC E is deeply appreciated. References [1] Blitz J, Simpson G. Ultrasonic methods of nondestructive testing. London: Chapman and Hall, [2] Wu TT, Liu PL. Advancement on the nondestructive evaluation of concrete using transient elastic waves. Ultrasonics 1998;36:197±240. [3] Buyukozturk O. Imaging of concrete structures. NonDestruct Test Eval Int 1998;31:233±43. [4] Sansalone M, Carino NJ. Impact-echo method: detecting honeycombing, the depth of surface-opening cracks, and ungrouted ducts using the impact-echo method. Concrete Int: Des Construct 1988;10:38±46. [5] Sansalone M, Carino NJ. Detecting delaminations in concrete slabs with and without overlays using the impact-echo method. ACI Mater J 1989;86:175±84. [6] Liu SW, Datta SK, Ju TH. Transient scattering of Rayleigh±Lamb waves by a surface-breaking crack: comparison of numerical simulation and experiment. J Nondestruct Eval 1987;10:111±26. [7] Wu TT, Fang JS. Crack depth measurement of a concrete specimen using phase identi cation of transient elastic waves. J Chin Inst Civil Hydraul Engng 1996;8:337±42. [8] Wu TT, Fang JS. Inverse determination of surface-breaking cracks in concrete using transient elastic waves. Part I: numerical forward simulation. J Chin Inst Civil Hydraul Engng 1997;9:627±36. [9] Wu TT, Fang JS. Inverse determination of surface-breaking cracks in concrete using transient elastic waves. Part II: experiment and inversion. J Chin Inst Civil Hydraul Engng 1997;9:637±45. [10] Liu PL, Tsai CD, Wu TT. Imaging of surface-breaking concrete cracks using transient elastic waves. NonDestruct Test Eval Int 1996;29:323±31. [11] Kuo MK, Lin TR, Liu PL, Wu TT. Locating the crack tip of a surfacebreaking crack. Part I. Line crack. Ultrasonics 1998;36:803±11. [12] Chang YF, Wang CY. Detecting the 3-D image of the surface opening crack in concrete by ultrasonic transducer arrays. J Nondestruct Eval 1997;16:193±203. [13] Simaan M, Hussain A, Hanna MT. Nondestructive detection of aws in material using transducer array. J Nondestruct Eval 1987;6:47±55. [14] Green RE. Nondestructive evaluation of constructed facilities. Proceedings of the US±Korea±Japan Trilateral Seminar, Honolulu, p. 153±66. [15] Dobrin MB, Savit CH. Introduction to geophysical prospecting. 4th ed. New York: McGraw-Hill, [16] Kearey P, Brooks M. An introduction to geophysical exploration. 2nd ed. Oxford, UK: Blackwell Scienti c, [17] Gardner GHF. Migration of seismic data. Society of Exploration Geophysicists, [18] Yilmaz O. Seismic data processing. Society of Exploration Geophysicists, [19] Chun JH, Jacewitz CA. Fundamentals of frequency domain migration. Geophysics 1981;46:717±33.

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