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1 588 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 2, APRIL 2006 Semiempirical Electromagnetic Modeling of Crack Detection and Sizing in Cement-Based Materials Using Near-Field Microwave Methods Jagadish Nadakuduti, Member, IEEE, Genda Chen, and Reza Zoughi, Fellow, IEEE Abstract Detection and characterization of cracks in cementbased materials is an integral part of damage evaluation for health monitoring of civil structures. Microwave signals are able to penetrate inside of dielectric materials (e.g., cement-based materials) and are sensitive to local, physical, geometrical, and dielectric variations in a structure. This makes microwave nondestructive testing and evaluation (NDT&E) techniques suitable for inspection and health monitoring of civil structures. Near-field microwave NDT&E techniques offer the added advantage of providing high spatial resolution, requiring simple hardware that may be portable, low power, fast, real time, and robust. Additionally, these techniques are noncontact and one-sided. Besides the need for robust detection, electromagnetic modeling of a microwave probe response to a crack is also an important issue. Such a model can be used to obtain optimal measurement parameters and serve as the foundation for extracting important crack information such as its width and depth. In this paper, the utility of open-ended rectangular waveguide probes for detecting surface-breaking cracks in cement-based materials is discussed. Subsequently, the development of a semiempirical model capable of simulating the crack response is presented. The model described here translates the magnitude and phase of the reflection coefficient as a function of scanning distance into the complex reflection plane and takes advantage of the common shape of these signals for predicting a similar signal from an unknown crack. Finally, this empirical model is used to estimate crack dimensions from a set of measurements. Index Terms Concrete, crack, microwaves, nondestructive testing, structural health monitoring. I. INTRODUCTION NUMEROUS buildings and civil infrastructures, such as bridges and tunnels, are constructed with reinforced concrete (RC) structures. As major capital investments, these structures are typically required to remain in service for 50 years or much longer. Due to the ever-increasing demand and extreme events such as explosives and earthquakes, they are often supporting more loads than they were designed for, while the condition of these structures is deteriorating over the years. As a result, cracks are often seen on the surfaces Manuscript received February 22, 2005; revised August 22, This study was supported by the Missouri Department of Transportation (MoDOT) Grant RI J. Nadakuduti and R. Zoughi are with Applied Microwave Nondestructive Testing Laboratory (AMNTL), Electrical and Computer Engineering Department, University of Missouri Rolla, Rolla, MO USA ( zoughir@umr.edu). G. Chen is with Department of Civil, Architectural, and Environmental Engineering, University of Missouri Rolla, Rolla, MO USA. Digital Object Identifier /TIM of RC structures. After an extreme event, it is important for structural engineers to conduct a damage assessment of the structures in the affected areas. For any RC structure, yielding of steel rebar in tension will occur before concrete crushes in compression and will thus govern the ultimate capacity of the structure. Although concrete cracks may not threaten the safety of the structure, their size and location are directly related to the tensile strain in the steel rebar. Therefore, it would be desirable to assess the condition of steel rebar through the crack pattern and size on the surface of the RC structure. To this end, it is critically important to develop a practical methodology for the detection and characterization of cracks in concrete structures. Microwave nondestructive testing and evaluation (NDT&E) is the process of testing materials and evaluating their various properties (e.g., materials, geometrical, chemical, etc.) by studying the transmission and/or reflection properties of highfrequency electromagnetic signals interacting with them. Among the many advantages offered by microwave NDT&E techniques, noncontact, one-sided inspection capabilities, and the ability of the signals to penetrate inside of dielectric media (i.e., nonmetallic) and interact with their inner structures are the most significant. These techniques employ relatively simple measurement setups, require minimal operator skills, and can be conducted using portable equipment including handheld probes with real-time operational capabilities [1] [3]. The ability of microwave signals to penetrate inside dielectric media makes them suitable for inspecting a wide range of composite structures including cement-based materials such as concrete [1], [4] [16]. Inspection of layered composites using microwave NDT&E techniques for thickness measurement, disbond and delamination detection, impact damage evaluation, etc., has been successfully performed in the past [6] [9]. Limited penetration of microwave signals in metals makes them suitable for examination of surface anomalies such as stressinduced fatigue cracks. These techniques have also been successfully used for surface-crack detection and characterization and detection of corrosion and pitting under paint in recent years [10] [12]. Microwave NDT&E techniques have also been extensively used to evaluate properties of a variety of cement-based materials including concrete. For example, reflection properties of microwave signals have been correlated to compressive strength and to the evaluation of water and saltwater distribution and movement in mortar. Determination of saltwater ingress in cement-based materials is of utmost importance since the /$ IEEE

2 NADAKUDUTI et al.: MODELING OF CRACK DETECTION AND SIZING IN CEMENT-BASED MATERIALS 589 presence of sufficient concentration of free chloride ions can lead to the onset of corrosion in reinforcing steel embedded in concrete structures [13] [17]. Cure-state monitoring and water-to-cement (w/c) ratio determination in mortar and concrete have also been successfully investigated using these techniques [18], [19]. Polarization of microwave signals is another useful and practical attribute, which makes these techniques suitable for detecting defects possessing a particular orientation such as surface-breaking cracks in metals and composite structures [20]. This paper presents the principle of detecting surfacebreaking cracks in mortar and hardened cement-paste samples. Additionally, the foundation of a semiempirical model predicting the response of an open-ended rectangular waveguide probe scanning such a crack, as a function of measurement parameters including the frequency of operation, standoff distance (i.e., the distance between the probe aperture and the sample under test), and crack dimensions (i.e., width and depth), is presented. II. EXPERIMENTAL FOUNDATION AND PREVIOUS WORK As mentioned earlier, the primary advantages of near-field microwave NDT&E techniques are their ability to perform noncontact and one-sided inspection of surface-breaking and interior flaws in dielectric composite structures and materials. When a material is irradiated by and is in the near field of an open-ended rectangular waveguide probe, the local dielectric and geometrical properties of the material determine the complex (i.e., magnitude and phase) reflected signal characteristics measured by the probe. Commonly, the reflection coefficient, which is the complex ratio of the reflected to transmitted signals referenced to the probe-aperture plane, is measured and recorded as the probe scans over the test material. For an inhomogeneous mixture such as mortar or concrete, the local dielectric properties vary depending on the composition of its constituents [e.g., (w/c) ratio, sand-to-cement (s/c) ratio, and coarse aggregate-to-cement (ca/c) ratio, and the relative size of coarse aggregates]. The reflection coefficient measured at the probe aperture is a function of local composition as well as the presence and dimensional properties of anomalies such as surface-breaking cracks. Consequently, by studying the properties of the reflection coefficient, the properties of the anomaly, in this case a surface-breaking crack, may be determined. When investigating surface-breaking cracks, the measured magnitude and/or phase of the reflection coefficient, as a function of scanning distance, is used to determine the presence and the attributes of the crack. This is referred to as the crack characteristic signal [21] [23]. In this paper, crack characteristic signals (for both magnitude and phase of the reflection coefficient) are used to evaluate the response of the probe to cracks of various dimensions and to different measurement parameters such as the operating frequency and standoff distance. This paper is preceded by a preliminary investigation that was conducted on mortar and concrete samples with artificial surface-breaking and interior cracks [24]. In that study, the properties of crack characteristic signals and their dependence on various measurement parameters such as standoff distance, operating frequency, incidence angle, and the polarization orientation of the irradiating electric field with respect to the long axes of a crack were examined. Optimization of these measurement parameters, to increase crack-detection sensitivity, was also performed. The success of this preliminary investigation led to the examination of stress-induced cracks by statically loading rebars protruding out of cylindrical RC samples [25]. This subsequent study resulted in demonstrating the capability of near-field microwave techniques for detecting surface-breaking cracks as a function of applied load (i.e., increasing crack opening). As in all nondestructive evaluation methods, it is imperative that the probe response to an anomaly be modeled in order to optimize the measurement parameters for enhanced detection and to enable extracting useful information about the anomaly, such as crack dimensions [26]. This paper describes the development of a semiempirical forward model for simulating the response of an open-ended rectangular waveguide probe to surface-breaking cracks in mortar and hardened cement paste samples. The model provides the probe response as a function of crack dimensions and measurement parameters, namely, the standoff distance and the frequency of operation. This model is subsequently used to extract crack dimensions from measured crack characteristic signals. III. SAMPLES Two different sample arrangements were used to produce cracks with varying widths (openings) and depths. In the first arrangement, which was used to record measured crack characteristic signals as a function of crack width, two mortar blocks with dimensions of mm were prepared with a (w/c) ratio of 0.55 and an (s/c) ratio of These mortar blocks were then placed next to each other to produce cracks with various widths, as shown in Fig. 1(a). Consequently, for this arrangement, the resulting crack depth would be 200 mm, representing a deep crack (i.e., a crack with a large electrical depth). Electrically deep cracks cause no reflected signal from the end of the crack. Thus, the crack characteristic signals obtained from this arrangement are independent of crack depth. The second arrangement was used to obtain measured crack characteristic signals as a function of crack depth. For this purpose, a notch was cut in an existing cement paste cube, with a (w/c) ratio of 0.35 and dimensions of mm, using a hacksaw. Notches produced in this way had a fixed width of 1.14 mm and varying depths, as shown in Fig. 1(b). This arrangement provided for simulating cracks with a fixed width and varying depths. IV. MEASUREMENT APPROACH Once an electromagnetic model describing the interaction of the open-ended rectangular waveguide probe and a crack is developed, it needs to be validated. To this end, it is necessary to conduct measurements to obtain crack characteristic signals as a function of all pertinent parameters such as standoff distance, crack width and depth, and operating frequency. Consequently, both arrangements, as shown in Fig. 1(a) and (b), were scanned

3 590 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 2, APRIL 2006 Fig. 2. (a) Magnitude and (b) phase of reflection coefficient for a 2-mm-wide deep crack at 10 GHz, as a function of standoff distance. Fig. 1. (a) Arrangement 1: two mortar blocks used to simulate deep cracks with varying widths. (b) Arrangement 2: cement-paste cube with a notch representing a crack with a fixed width and varying depth (not to scale). using an X-band ( GHz) open-ended rectangular waveguide probe with aperture dimensions of 22.8 by 10.1 mm. The magnitude and phase of the reflection coefficient, referenced to the waveguide aperture, were measured using a calibrated HP8510C vector network analyzer as a function of scanning distance over the samples. When necessary, the dielectric properties of the cubes were measured using a full-wave electromagnetic formulation that had already been developed for cement-based material characterization [27]. A typical set of measurements in which arrangement 1, with a crack width of 2 mm, was scanned at a frequency of 10.0 GHz, as a function of standoff distance (from 0.5 to 5.0 mm in steps of 0.5 mm), is shown in Fig. 2(a) and (b), corresponding to the magnitude and phase of the reflection coefficient (i.e., crack characteristic signals), respectively. The small degree of asymmetry in the crack characteristic signals is primarily attributed to the not-so-sharp edges of the crack produced using the two mortar blocks. Additional measurements will be presented in conjunction with the modeling effort in the next section. V. S EMIEMPIRICAL ELECTROMAGNETIC MODEL An electromagnetic model facilitates measurementparameter optimization for crack-detection purposes. Additionally, subsequent to detecting a crack, it is necessary to extract crack width and depth information from crack characteristic signals. Consequently, a forward electromagnetic model capable of simulating the crack characteristic signal as a function of crack dimensions and other measurement parameters must be developed. A. Complex Representation of Crack Characteristic Signals as a Function of Various Parameters By observing the magnitude and phase of crack characteristic signals shown in Fig. 2, it is evident that these signals do not follow any particular pattern. A new approach is presented here in which the magnitude and phase of the crack characteristic signal are combined to produce a complex-plane representation of the crack characteristic signal. Fig. 3(a) and (b) shows the magnitude and phase of the crack characteristic signal for a deep crack with a width of 2 mm at a standoff distance of 3.5 mm and at a frequency of 10 GHz. Fig. 3(c) shows the representation of these two signals in the complex plane. The complex-plane representation of a crack characteristic signal looks similar to the impedance plane diagrams in eddy-current testing [2]. This observation was a motivating factor for

4 NADAKUDUTI et al.: MODELING OF CRACK DETECTION AND SIZING IN CEMENT-BASED MATERIALS 591 passes over the crack. However, in Fig. 3(c), the crack signal does not retrace to the center of the spiral on the same exact path [the trace without the circles in Fig. 3(c)]. This asymmetry in the crack characteristic signal is primarily attributed to the notso-sharp edges of the crack produced using two mortar blocks. Ideally, the crack characteristic signal is expected to be symmetrical, and thus, only half of it is plotted in the complex-plane plots shown hereon and used for the purpose of electromagnetic modeling. A complex representation of the crack characteristic signal shows that it possesses a common overall shape, represented by the circles in Fig. 3(c). This common shape is preserved in the complex plane irrespective of standoff distance, crack width, and the dielectric properties of the block. Figs. 4 7 show the variation of crack characteristic signal in the complex plane as a function of standoff distance, crack width, crack depth, and operating frequency, respectively. The results show that for all of these cases, the overall shape of the crack characteristic signals are very similar and possess common attributes. Fig. 3. (a) Magnitude and (b) phase of reflection coefficient for a 2-mm-wide deep crack at a standoff distance of 3.5 mm and at a frequency of 10 GHz and (c) complex-plane representation. pursuing the following empirical approach. In Fig. 3, starting point (SP) corresponds to the position where the waveguide probe (including its flange) does not coincide with any part of the crack and is only placed on an infinite half-space of mortar (i.e., crack completely outside of the waveguide probe flange and aperture), and middle point (MP) represents the case when the crack is in the middle of the probe aperture, respectively. The crack characteristic signal in the complex plane resembles a spiral that opens up as the waveguide flange approaches the crack and reaches the tip of the spiral when the crack is exactly in the middle of the waveguide aperture (represented by the circles in Fig. 3). The crack characteristic signal is expected to trace back to the center of the spiral as the waveguide probe B. Modeling Procedure The three necessary steps for simulating a crack characteristic signal in the complex plane require computing the magnitude and phase of the reflection coefficient at the aperture of the open-ended rectangular waveguide probe when the following conditions are met. 1) The probe aperture is placed on an infinite half-space portion of the sample at a given standoff distance in the absence of a crack, as shown in Fig. 8, corresponding to the SP. 2) The crack is situated in the middle of the probe aperture, as shown in Fig. 8, corresponding to the MP. 3) The probe aperture is between the SP and the MP, as shown in Fig. 8, corresponding to the intermediate points. The SP, MP, and the intermediate points are shown in Fig. 9 for a deep crack with a width of 2.0 mm, at a standoff distance of 3.5 mm, and at a frequency of 10 GHz. Half of the crack characteristic signal can be simulated once these points are computed. The other half of the crack characteristic signal is symmetrical as the waveguide passes over the crack to its other side. The first step in simulating the crack characteristic signal involves computing the SP reflection coefficient. This can be accomplished by using a previously developed electromagnetic formulation (referred to as the nlayer code) to calculate the reflection coefficient at the aperture of an open-ended rectangular waveguide radiating into a generally layered medium given the dielectric properties and thickness of each layer including the operating frequency [28]. Fig. 10 shows the comparison between the calculated SPs (solid circle) and the measured crack signals for a 2-mm-wide deep crack for different standoff distances at 10 GHz. The reflection coefficient of the SP was calculated using the nlayer code after having measured the dielectric properties of the sample [27]. The results indicate that the computed SPs at different standoff distances agree well with the measured SPs. The second step involves computing the reflection coefficient for the MP. It is difficult to develop an electromagnetic model

5 592 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 2, APRIL 2006 Fig. 4. Complex-plane representation of crack characteristic signals for a 2-mm-wide deep crack for different standoff distances and at a frequency of 10 GHz. Fig. 6. Complex-plane representation of crack characteristic signals for a 1.14-mm-wide crack with different crack depths, at a standoff distance of 2.0 mm, and at a frequency of 10 GHz. Fig. 5. Complex-plane representation of crack characteristic signals for deep cracks with different widths, at a standoff distance of 0.05 mm, and at a frequency of 10 GHz. that accurately evaluates the reflection coefficient for the MP. The difficulty is primarily due to the fact that the complex nearfield interaction of the probe field properties with discontinuities (presence of a crack in this case) in a dielectric material is rather complex and a direct analytical model cannot be effectively developed. Additionally, the electromagnetic model would need to accurately account for the effect of crack edges. An alternative approach is to compute the reflection coefficient numerically at the MP using a commercially available threedimensional (3-D) electromagnetic-field solver such as the Ansoft high-frequency structural simulator (HFSS) v9.0 [29]. The HFSS method can also be used to simulate the entire crack characteristic signal. Fig. 11 shows the comparison between the numerically simulated (using HFSS) and the measured crack characteristic signals for arrangement 2 for a crack width of 1.14 mm and a depth of 5.0 mm, at a standoff distance of 1.0 mm, and a frequency of 10 GHz (measured dielectric constant of 5.95 j1.02 [27]). It can be observed that the HFSS method is capable of simulating the crack characteristic Fig. 7. Complex-plane representation of crack characteristic signals for a 2.0-mm-wide deep crack at a standoff distance of 2.0 mm, as a function of operating frequency. Fig. 8. Schematic of the relative location of the waveguide probe showing the SPs, intermediate points, and the MPs (not to scale). signal given the standoff distance, operating frequency, dielectric property of the mortar sample, waveguide dimensions, and crack width and depth. However, the drawback of this numerical method is the associated relatively long calculation time. For example, in Fig. 11, it took about 1 h to calculate the mag-

6 NADAKUDUTI et al.: MODELING OF CRACK DETECTION AND SIZING IN CEMENT-BASED MATERIALS 593 Fig. 9. Complex-plane representation of the measured crack characteristic signal for a 2.0-mm-wide deep crack, at a standoff of 3.5 mm, and at a frequency of 10 GHz, showing the SPs, intermediate points, and the MPs. Fig. 11. (a) Magnitude and (b) phase of measured and simulated crack characteristic signals for a 1.14-mm-wide and 5.0-mm-deep crack, at a standoff distance of 1.0 mm, and at a frequency of 10.0 GHz. Fig. 10. Comparison of SPs calculated from the nlayer formulation and those obtained from measurements, as a function of standoff distance, for a 2.0-mm-wide deep crack and at a frequency of 10.0 GHz. nitude and phase of the reflection coefficient for a single point. Consequently, it takes more than 15 h to simulate 15 points for half of a crack characteristic signal using HFSS. Therefore, simulating an entire crack characteristic signal, using HFSS exclusively, is fairly time consuming and may not be practical for inverse (i.e., parameter extraction) applications in which crack dimensions are to be extracted from a crack characteristic signal. Consequently, in the overall modeling approach, only the MP reflection coefficient is computed using the HFSS, and the remaining portions of the reflection coefficient are evaluated using the empirical method outlined here. The third step involves the determination of the intermediate points, which comprise of the reflection coefficient at the waveguide probe aperture, with the crack moving from the tip of the waveguide flange to the middle of the waveguide aperture. This is accomplished by using measured crack characteristic signals to generate a database or a set of templates as a function of standoff distance, crack width, crack depth, and operating frequency. Fig. 12(a) shows a set of templates of measured crack characteristic signals as a function of standoff distance for a deep crack [i.e., Fig. 1(a)] with a width of 2.0 mm and at a frequency of 10 GHz. Fig. 12(b) shows the corresponding templates obtained empirically by taking two measured signals from Fig. 12(a) at standoff distances of 0.5 and 4.5 mm. These two measured templates are primarily used to obtain the overall shape of the crack characteristic signal. The standoff distances of 0.5 and 4.5 mm are chosen since from Fig. 12(a), it can be observed that these template signals encompass all possible shapes of crack characteristic signals. Subsequently, crack characteristic signals at the intermediate standoff distances can be obtained by interpolating or extrapolating the two template signals, as shown in Fig. 12(b). In other words, once the template signal is found for a given standoff distance, crack dimensions, and operating frequency, a scaled version of this signal is rotated and translated such that it fits in between the computed SP and MP. Thus, the crack characteristic signal may be simulated in the complex plane for a given standoff distance, crack dimensions, and dielectric properties of the mortar cube. Finally, the simulated crack characteristic signals in the complex plane are unwrapped (i.e., plotted in linear format) to get the magnitude and phase of the reflection coefficient. As shown in Fig. 12(a) and (b),

7 594 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 2, APRIL 2006 Fig. 12. (a) Complex-plane representation of measured crack characteristic signals corresponding to various standoff distances and (b) templates generated by interpolating or extrapolating the measurement signals using the measured results for standoff distances of 0.5 and 4.5 mm for a 2-mm-wide crack. Fig. 13. Complex-plane representation of crack characteristic signals corresponding to various crack widths for a deep crack at a standoff distance of 0.05 mm, and at a frequency of 10 GHz. (a) Measured. (b) Simulated. very good agreement between the measured and simulated crack characteristic signals. good agreement between the measured and simulated crack characteristic signals in the complex plane is obtained. Similarly, templates can be generated as a function of other parameters such as crack width, crack depth, and operating frequency. For example, Fig. 13(a) shows measured crack characteristic signals for a deep crack as a function of crack width at a standoff distance of 0.05 mm (i.e., nearly in contact) at 10 GHz. Fig. 13(b) shows the corresponding simulated crack characteristic signals [for even a wider range of crack width than those shown in Fig. 13(a)]. Once again, the results show VI. RESULTS It is important to discuss the issue of critical parameter extraction, such as crack width and depth, when using a set of simulated crack characteristic signals, which is the ultimate goal of the model that simulates the crack characteristic signals (i.e., probe response to a crack). As an insight into this issue, in Fig. 13(a) and (b), it is evident that the shape of crack characteristic signals may be used to obtain a relatively close estimate of crack width. To demonstrate this point, three blind measurements were conducted, using sample arrangement 1, at

8 NADAKUDUTI et al.: MODELING OF CRACK DETECTION AND SIZING IN CEMENT-BASED MATERIALS 595 Fig. 14. Evaluation of crack width for three unknown cracks (i.e., blind measurements) for deep cracks at a standoff distance of 0.05 mm and at a frequency of 10 GHz. the same standoff distance as the templates shown in Fig. 13(a) (0.05 mm in this case) with an arbitrary crack width by a different person so that the crack width is unknown to the person analyzing the data and trying to obtain the crack width from this measurement. Fig. 14 shows the three crack characteristic signals for blind measurements (the dashed lines) along with a few simulated crack characteristic signals from Fig. 13(b). Here, the shape of the measured signals resemble the simulated ones, as expected. Using Fig. 14, it was determined that the width of cracks associated with the three blind measurements are 1.75, 2.2, and 0.4 mm, respectively. The actual widths of these cracks were 1.8, 2.1, and 0.3 mm, respectively. Clearly, using the simulated crack characteristic signals (i.e., the model) rendered crack widths that are very close to their actual values. Finally, and as mentioned earlier, once a crack characteristic signal is simulated in the complex plane, it may be unwrapped to obtain the corresponding magnitude and phase of reflection coefficient at the waveguide aperture. Figs. 15 and 16 show the results of such unwrapping, illustrating a comparison between the measured and simulated crack characteristic signals. Here, the generated template signals for various standoff distances, as shown in Fig. 12 (for a deep crack with a width of 2.0 mm and at a frequency of 10 GHz), were used to represent the intermediate points. The results show that the simulated crack characteristic signals (i.e., magnitude and phase of reflection coefficient, as a function of scanning distance) match well with the measured signals. This model has the potential to accurately simulate crack characteristic signals for a given standoff distance, operating frequency, waveguide dimensions, and crack width. The results presented here are only for deep cracks, as shown in arrangement 1. For this model to be applied to finitedepth cracks, a corresponding set of template signals must be created. This can be accomplished by conducting a series of measurements on cracks of various dimensions. Fig. 15. (a) Magnitude and (b) phase of measured and simulated crack signals at a standoff distance of 0.5 mm for a deep crack with a width of 2.0 mm and at a frequency of 10 GHz. Fig. 16. (a) Magnitude and (b) phase of measured and simulated crack signals at a standoff distance of 3.5 mm for a deep crack with a width of 1.0 mm and at a frequency of 10 GHz.

9 596 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 55, NO. 2, APRIL 2006 VII. SUMMARY AND DISCUSSIONS The utility of near-field microwave NDT methods for detecting surface-breaking cracks in metals and cement-based structures has been demonstrated in the past. Detection and evaluation of such cracks in RC structures may render valuable information about the health of the structure, in particular, after a seismic event. This paper presented the results of detecting cracks (thin notches) of various widths and depths in mortar and hardened cement-paste samples at a wide range of standoff distances and in the X-band frequency range ( GHz) using an open-ended rectangular waveguide probe. Additionally, a semiempirical electromagnetic model was developed to simulate the response of this probe to the presence of a crack, as a function of scanning distance over the crack. This model was based on studying the complex-plane representation of the magnitude and phase of the reflection coefficient at the waveguide aperture as the probe scans a crack. It was found that the representation of a crack with a given width and depth in the complex plane possesses a common shape that may be used to obtain the complex-plane representation of other cracks from it. Subsequently, the complex-plane representation of magnitude and phase of the reflection coefficient may be unwrapped to obtain these two parameters as a function of scanning distance (i.e., crack characteristic signal). Finally, this model was used to determine the width of several cracks whose widths were not disclosed to the person analyzing the data. The results showed that using this approach, one is able to closely estimate crack dimensions from a measured crack characteristic signal. Most civil structures use concrete, and not mortar, and cement paste as their primary building material. Concrete is an inhomogeneous medium formed by a mixture of cement powder, water, fine aggregate (sand), and coarse aggregate (rocks). Generally, the size of coarse aggregates ranges between 5 20 mm. The X-band waveguide probe is suitable to inspect concrete with such sizes of coarse aggregates to detect cracks with an opening on the order of a few tenths of a millimeter. Operating at higher frequency bands will result in detecting smaller cracks, but the reflected signal will be more sensitive to the presence of coarse aggregates. On the other hand, operating with lower frequency band waveguide probes results in concrete that appears more homogeneous, thereby lowering the overall clutter in the signal. However, lower frequency band probes are limited in detecting cracks with a small opening. It is expected that when inspecting a concrete structure, the same approach as that used in this paper can be used. 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Zoughi, Microwave reflection and dielectric properties of mortar subjected to compression force and cyclically exposed to water and sodium chloride solution, IEEE Trans. Instrum. Meas., vol. 52, no. 1, pp , Feb [15] S. Peer, K. E. Kurtis, and R. Zoughi, An electromagnetic model for evaluating temporal water content distribution and movement in cyclically soaked mortar, IEEE Trans. Instrum. Meas., vol. 53, no. 2, pp , Apr [16] S. Peer and R. Zoughi, Comparison of water and saltwater movement in mortar based on a semi-empirical electromagnetic model, IEEE Trans. Instrum. Meas., vol. 53, no. 4, pp , Aug [17] S. Peer, R. Zoughi, and K. E. Kurtis, Electromagnetic modeling of saltwater ingress in mortar at microwave frequencies, in Proc. 20th IEEE Instrumentation and Measurement Technology Conf., Vail, CO, May 20 22, 2003, vol. 1, pp [18] K. J. Bois, A. D. Benally, P. S. Nowak, and R. Zoughi, Cure-state monitoring and water-to-cement ratio determination of fresh portland cementbased materials using near-field microwave techniques, IEEE Trans. Instrum. Meas., vol. 47, no. 3, pp , Jun [19] K. Mubarak, K. J. Bois, and R. Zoughi, A simple, robust, and on-site microwave technique for determining water-to-cement ratio (w/c) of fresh portland cement-based materials, IEEE Trans. Instrum. Meas., vol. 50, no. 5, pp , Oct [20] R. Zoughi, G. L. Cone, and P. Nowak, Microwave nondestructive detection of rebars in concrete slabs, Mater. Eval., vol. 49, no. 11, pp , Nov [21] C. Huber, H. Abiri, S. I. Ganchev, and R. Zoughi, Analysis of the Crack Characteristic Signal using a generalized scattering matrix representation, IEEE Trans. Microw. Theory Tech., vol. 45, no. 4, pp , Apr [22] C. Huber, H. Abiri, S. Ganchev, and R. Zoughi, Modeling of surface hairline crack detection in metals under coatings using open-ended rectangular waveguides, IEEE Trans. Microw. Theory Tech.,vol. 45,no. 11, pp , Nov [23] C. Yeh and R. Zoughi, A novel microwave method for detection of long surface cracks in metals, IEEE Trans. Instrum. Meas., vol. 43, no. 5, pp , Oct [24] J. Nadakuduti, R. Zoughi, X. Ying, and G. Chen, Microwave near-field techniques for detection of stress-induced cracks in cement-based materials, in Proc. Structural Health Monitoring & Intelligent Infrastructure Conf., Tokyo, Japan, Nov , 2003, pp

10 NADAKUDUTI et al.: MODELING OF CRACK DETECTION AND SIZING IN CEMENT-BASED MATERIALS 597 [25] J. Nadakuduti, R. Zoughi, and G. Chen, Empirical modeling of surface crack detection in concrete using open-ended rectangular waveguide, in Proc. 31st Annu. Review Progress Quantitative Nondestructive Evaluation (QNDE), Golden, CO, Jul , 2004, pp [26] C. Yeh and R. Zoughi, Sizing technique for surface cracks in metals, Mater. Eval., vol. 53, no. 4, pp , Apr [27] K. J. Bois, A. D. Benally, and R. Zoughi, Multimode solution for the reflection properties of an open-ended rectangular waveguide radiating into a dielectric half-space: The forward and inverse problems, IEEE Trans. Instrum. Meas., vol. 48, no. 6, pp , Dec [28] S. Bakhtiari, N. Qaddoumi, S. I. Ganchev, and R. Zoughi, Microwave noncontact examination of disbond and thickness variation in stratified composite media, IEEE Trans. Microw. Theory Tech., vol. 42, no. 3, pp , Mar [29] Ansoft HFSS v9.0, 2003, Pittsburgh, PA: Ansoft Corp. Jagadish Nadakuduti (S 00 M 04) received the B.Tech. degree in electronics and communication engineering from Jawaharlal Nehru Technological University, Hyderabad, India, in 2002 and the M.S. degree in electrical engineering from University of Missouri, Rolla, in From 2002 to 2004, he was a Graduate Research Assistant at the Applied Microwave Nondestructive Testing Laboratory (AMNTL), University of Missouri. Currently, he is an Electromagnetic Compatibility (EMC)/Regulatory Engineer with the Kyocera Wireless Corporation, San Diego, CA. Genda Chen received the B.S.C.E. and M.S.C.E. degrees in civil engineering from the Dalian Institute of Technology, Dalian, China, and the Ph.D. degree in civil engineering (structural engineering and earthquake engineering) from the State University of New York at Buffalo in Prior to joining to the University of Missouri- Rolla in 1996 as Assistant Professor, he was a senior structural engineer in a bridge consulting firm, called Steinman Consulting Engineers, New York, NY. Since 2002, he has been an Associate Professor. His primary research contributions deal with the dynamic response reduction with supplemental damping and control devices, damage detection and health monitoring, and earthquake hazard assessment and mitigation of civil infrastructure. He has authored or coauthored 30 refereed journal papers and over 75 conference papers. He was an organizing member of several national and international conferences. For his innovative research work in the area of smart structures and sensor development with coaxial cables, he was invited to present papers during several U.S. Japan and U.S. Korea workshops. He has also been invited to lecture at several universities in Japan and China. He was the founding faculty advisor of the Earthquake Engineering Research Institute (EERI)/University of Missouri Rolla (UMR) Student Chapter. He was a founding member of the recently established Natural Hazard Mitigation Institute at UMR. Reza Zoughi (S 85 M 86 SM 93 F 06) received the B.S.E.E., M.S.E.E., and Ph.D. degrees in electrical engineering (radar remote sensing, radar systems, and microwaves) from the University of Kansas, Lawrence. From 1981 until 1987, he was at the Radar Systems and Remote Sensing Laboratory (RSL), University of Kansas. Currently, he is the Schlumberger Distinguished Professor of Electrical and Computer Engineering at the University of Missouri Rolla (UMR). Prior to joining UMR in January 2001 and since 1987, he was with the Electrical and Computer Engineering Department, Colorado State University (CSU), Fort Collins, where he was a Professor and established the Applied Microwave Nondestructive Testing Laboratory (AMNTL). His current areas of research include developing new nondestructive techniques for microwave and millimeter-wave inspection and testing of materials (NDT), developing new electromagnetic probes to measure characteristic properties of a material at microwave frequencies, and developing embedded modulated scattering techniques for NDT purposes, in particular, for complex composite structures. He held the position of Business Challenge Endowed Professor of Electrical and Computer Engineering from 1995 to 1997 while at CSU. To his credit, he has over 300 journal publications, conference proceedings and presentations, technical reports, and overview articles. He is also the author of a graduate textbook entitled Microwave Nondestructive Testing and Evaluation Principles (New York: Kluwer, 2000) and the coauthor with A. Bahr and N. Qaddoumi of a chapter on Microwave Techniques in an undergraduate introductory textbook entitled Nondestructive Evaluation: Theory, Techniques, and Applications (edited by P. J. Shull, Amsterdam, The Netherlands: Marcel Dekker, 2002). Dr. Zoughi has received two Outstanding Teaching Commendations, an Outstanding Teaching Award, and the Dean of Engineering Excellence in Teaching Award since at UMR. He was voted the most outstanding teaching faculty seven times by the junior and senior students at the Electrical and Computer Engineering Department, CSU. He received the College of Engineering Abell Faculty Teaching Award in He is the 1996 recipient of the Colorado State Board of Agriculture Excellence in Undergraduate Teaching Award (only one faculty recognized for this award at each of the three CSU system campuses). He was recognized as an honored researcher for seven years by the CSU Research Foundation. He is the holder of seven patents, all in the field of microwave nondestructive testing and evaluation (NDT&E). He has given numerous invited talks on the subject of NDT&E. He is a member of Sigma Xi, Eta Kappa Nu, and a Fellow of the American Society for Nondestructive Testing (ASNT). He is an Associate Technical Editor for the IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, Research in Nondestructive Evaluation, andmaterials Evaluation, servedas the Guest Associate Editor for the Special Microwave NDE Issue of Research in Nondestructive Evaluation in 1995, and served as a Coguest Editor for the Special Issue of Subsurface Sensing Technologies and Applications: Advances and Applications in Microwave and Millimeter Wave Nondestructive Evaluation. He served as the Research Symposium Cochair for the ASNT Spring Conference and 11th Annual Research Symposium in March 2002 in Portland, OR, and as the Technical Chair for the IEEE Instrumentation and Measurement Technology Conference (IMTC2003) in May 2003, Vail CO. He served as the Guest Editor for the IMTC2003 special issue of the IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT. He is also a member of the Administrative Committee (AdCom) of the IEEE Instrumentation and Measurement Society ( ).