Use of a non-collinear wave mixing technique to image internal microscale damage in concrete

Linear ultrasound is one of the most widely used tools for the nondestructive evaluation (NDE) of metallic components in the aerospace, manufacturing, and energy industries. Ultrasound is safe and reliable and can provide quantitative information on structural features, e.g., grain size, and damage such as microcracks, throughout the thickness of structural components. The key attribute that enables most successful applications of linear ultrasonic NDE is the use of the scattered wavefield to image internal defects in a component. Ultrasound is most effectively scattered by structural features such as a crack or a void at about the same order of length scale as the wavelength of the dominant frequency of the interrogating wave. In metals, the inherent microstructure, e.g., precipitates and grains, is typically on the nanometer or micrometer length scale. On the other hand, damage becomes practically important when its feature size reaches hundreds of micrometers or larger. In other words, the inherent microstructural features in metals are typically several orders of magnitude smaller than the flaw size of practical importance. Therefore, it is possible to use ultrasound in the MHz range, which generates waves with wavelengths of hundreds of micrometers or millimeters, to image damage of practical importance; these MHz frequency ultrasonic waves can readily penetrate most metallic components, making it possible to image millimeter and smaller length features such as microcracks and other defects throughout the thickness of metallic components.

Unlike metals, concrete is rather heterogeneous with inherent microstructural features ranging in length from nanometers to millimeters or even centimeters. Many damage features (cracks, debonding, voids, etc.) that may significantly reduce the concrete material's integrity are also within this range of length scales. This multiphase, heterogeneous, and multiscale nature of concrete makes the development of linear ultrasound based NDE and monitoring techniques for concrete technically challenging. Successful imaging using ultrasound requires that the ultrasonic wavelength be on the order of a few millimeters, yet the inherent length scale of this heterogeneous material with its fine and coarse aggregates is on this same millimeter length scale and larger. As a result, this heterogeneous nature of concrete makes it impossible to use a high enough ultrasonic frequency to effectively image microscale damage because the concrete's microstructure will scatter the ultrasound. The intrinsic viscoelasticity of concrete further complicates the possibility of ultrasonic imaging in concrete by causing excessive attenuation of higher frequency waveform components, further limiting penetration depth. These physical restrictions have severely limited the application of linear ultrasonic techniques to quantitatively characterize and image microscale damage in concrete.

It is possible to improve the spatial resolution of ultrasonic images (in the 50–100 kHz frequency range) in concrete using array processing techniques,^1–3 but the underlying physics-based limitation of scattering by the heterogeneous microstructure is inherent to a linear ultrasonic technique, making it impossible to image microscale damage that is much smaller than (and, thus, not sensitive to) the centimeter wavelength of the incident waves created by these arrays.

In contrast, nonlinear acoustic techniques have demonstrated high sensitivity to microscale damage in concrete.^4–8 The second harmonic generation (SHG) of Rayleigh surface waves has recently shown to be sensitive to microscale damage in cement-based materials^9–11 such as alkali-silica reaction (ASR) induced microcracks. The basis for the success of these SHG techniques is that the wavelengths of these nonlinear ultrasonic waves do not have to be of the millimeter (or smaller) length scale to sense microscale damage in concrete. It is possible to have the ultrasonic wavelength of the primary wave in an SHG technique much longer than the microscale damage being characterized. So, while linear ultrasonic techniques require the use of high frequency waves to gain sensitivity to microscale damage—and these higher frequency waves have significant attenuation from aggregate scattering—nonlinear ultrasonic techniques can operate at a lower frequency (30 ̶ 60 kHz) that are not scattered by the fine and coarse aggregate, while still being sensitive to microscale damage.

An SHG technique measures the average material nonlinearity along the propagation path of the primary wave, so they are mainly effective in characterizing damage that is uniformly distributed within a known volume (region) of a specimen. A successful application of SHG in concrete used Rayleigh surface waves to characterize uniformly distributed damage such as ASR-induced microcracks in the near surface volume of a specimen;¹¹ this near surface volume is defined by the penetration depth of a Raleigh wave, effectively its wavelength. This limitation makes an SHG approach impractical for the imaging of localized, internal microscale damage in concrete components.

Previous research^12–14 has successfully demonstrated the effectiveness of wave mixing techniques for nonlinear ultrasonic detection of internal microscale damage in metallic specimens such as plasticity and fatigue damage. Wave mixing for nonlinear ultrasonic characterization is based on the fact that material nonlinearities such as microscale damage causes interactions between two intersecting ultrasonic waves due to cross-mixing, which can lead to the generation of a third, mixed wave with a frequency and wave number equal to the sum or difference of the incident waves.¹⁵ The technique in Ref. 12 mixes two non-collinear waves generated with angle-beam transducers to create a mixing zone at a specific location inside a specimen, while the collinear approach of Refs. 13 and 14 requires access to both sides of a specimen for proper nonlinear wave mixing. By using proper timing of the two incident ultrasonic waves, each of these approaches enables a scanning procedure to image internal plasticity driven damage in a metal component.

The objective of the work presented here is to demonstrate the effectiveness of a non-collinear wave mixing technique to image internal, microscale damage in concrete. Following the approach in Ref. 12, imaging of internal microscale damage in concrete is accomplished with non-collinear mixing of two incident waves created by two angle-beamed transducers. The 40 kHz frequency of these two mixing waves is selected such that its wavelength is large enough to not be scattered by the coarse aggregate of the concrete. However, the third, mixed wave is sensitive to the presence of any microscale damage induced material nonlinearity in the mixing zone; the location of this mixing zone is determined by the timing and angles of the incident mixing waves. Scanning and imaging of internal microscale damage is accomplished by manually adjusting the location and timing of the two incident angle-beamed transducers. Note that this wave mixing approach images internal damage with a third, mixed wave with a known frequency and arrival time that is directly proportional to any material nonlinearity such as microscale damage present in the mixing (inspection) zone.

A concrete prism measuring 96.6 × 30.5 × 28.6 cm³ (Fig. 1) is cast around two embedded field-damaged concretes (described subsequently). The cast concrete mixture design consists of 700 kg/m³ of crushed quartz river sand (Lambert Sand and Gravel, Shorter, Alabama) with gradation conforming to ASTM C33, 1061 kg/m³ of crushed granitic gneiss coarse aggregate (Vulcan Materials Company Lithia Springs, Georgia) conforming to ASTM C33 #67 gradation, 46 kg/m³ of coarsely ground limestone powder (BARACARB 50, Halliburton), and 409 kg/m³ of portland cement (type I/II, LafargeHolcim). The water-to-binder ratio, by mass, is 0.40. The binder, including a blend of 90% cement and 10% limestone by mass, was designed to reduce chemical and autogenous shrinkage¹⁶ and to reduce temperature rise, which can result in thermal deformation; the intention of this design was to ensure good bonding between the embedded damaged concrete and the host or bulk concrete cast around it. The concrete mixture design satisfies the Georgia Department of Transportation (GDOT) class AAA concrete specification. The concrete is machine-mixed in a 0.255 m³-capacity drum mixer, according to ASTM C192-14, and is cast in a plywood form coated with WD-40 as a formwork release agent. After demolding, the concrete prism is cured at 23 °C and 100% RH for 28 days.

One of the two embedded field-damaged concrete volumes (shown in red color in Fig. 1), denoted as “ASR-damaged,” was cored from a concrete roadway, I-675 (Atlanta, Georgia), that experienced internal microcracking, propagating into surface cracking, in a damage pattern associated with alkali-silica reaction (ASR); ASR is a well-known deleterious reaction between more disordered (e.g., amorphous) siliceous aggregate minerals and the alkaline pore solution in concrete, which can produce damage when reactants, including moisture, are present in sufficient concentrations. The other embedded field-damaged concrete volume (shown in black color in Fig. 1), denoted as “fire-damaged,” was obtained from spalled concrete pieces from a precast concrete bridge girder, I-85 (Atlanta, Georgia), that experienced significant fire damage. Damaged concrete from the field was preferred for this study over laboratory-induced damage under accelerated or extreme conditions because they are better representative of real damage. Figure 2 shows the images of companion concrete samples for the encased concrete and the embedded concrete damage. Since the damaged concrete pieces are from the field, their concrete mixture proportions are not available. However, GDOT concrete specification requires the aggregates to be all natural sand for fine aggregate and granitic gneiss for coarse aggregates—similar to the aggregates used in the encased concrete. For typical precast girders (fire-damaged concrete), the maximum size of aggregate (MSA) of course aggregate should be less than 19 mm (0.75 in.—as shown in Fig. 2) and w/b less than 0.44 to meet class AAA specification. The mixture design of the encased concrete also meets the same class AAA specification. For concrete pavements that are designed for exposure to high vehicular traffic, GDOT requires concrete mixtures to meet at least class 2 specification (i.e., w/b less than 0.50, and cement content greater than 335 kg/m³). The MSA of coarse aggregates from the ASR-damaged specimens is around 25 mm (1 in.)—as shown in Fig. 2.

The ASR results from an internal chemical reaction that produces mechanical damage (e.g., microcracking) due to a swelling of the ASR gel product,¹⁷ while fire damage is induced from the surface and results in cracking from differential thermal response of the aggregate and paste and decomposition of the cement hydration products. While both samples are expected to exhibit microscale damage, the extent and pattern of damage is expected to differ. Because these embedded, damaged concrete volumes are obtained from real (aged) structures, details on their composition are not available.

Companion samples from both field-damaged concretes that are from close proximity to the embedded concretes, and companion samples that are cast together with the same concrete mixture as the concrete prism are characterized by light microscopy (i.e., petrography). An optical microscope (Leica MZ6), coupled with a color camera (SPOT Insight 12Mp sCMOS) and a short-wave ultraviolet (UV) lamp, is used for petrographic imaging. Multiple sections of ∼10 mm each in thickness are cut from the damaged concrete samples (both fire and ASR-damaged) using an isopropanol-cooled saw with a 0.4-mm thick, low-concentration/medium-grit diamond wafering blade to avoid the creation of new microcracks from cutting. Immediately after cutting, the samples are washed with isopropanol and dried under a vacuum. Frequent nitrogen gas purging is performed during drying to avoid high vacuum pressures, again to minimize the creation of new microcracks. The dried slices are embedded with low viscous epoxy resin (EpoThin 2, Buehler) containing 0.5% (w/w) fluorol yellow 088 dye (Setareh Biotech LLC) using a vacuum impregnator (SimpliVac, Buehler). The dyed epoxy, which penetrates into the cracks, appears bright yellow in color when incident with short-wave UV light. After curing the epoxy, the samples are polished gradually down to 0.25 μm fineness, with isopropanol as a coolant, and petrographic imaging is carried out. Polishing with multiple, increasingly fine grits ensures the presence of dyed epoxy only within the cracks and pores in the prepared samples.

Petrographic images in Fig. 3 show the cast concrete (i.e., undamaged concrete encasing the two damaged pieces), fire-damaged concrete, and ASR-damaged concrete. In the undamaged sample, no significant cracks are observed in the paste or mortar region (i.e., the region surrounding the coarse aggregates). However, a few 5–10 μm-wide microcracks are observed within the coarse aggregate particles, likely formed during their production through mechanical crushing of rock. In the ASR-damaged concrete, several microcracks—about 20 μm wide—are observed, both passing through and around multiple coarse aggregate particles. Also, ∼20 μm-wide cracks are present within the paste matrix between the aggregate particles. In the fire-damaged sample, in addition to the 5–10 μm-wide microcracks within the coarse aggregate particles, also observed in the undamaged samples, a more significant amount of microcracks (∼20 μm wide) are present in the paste and mortar region.¹⁸ This could be due to a differential thermal response of the paste and aggregate as well as paste shrinkage due to the decomposition of hydration products with fire exposure.¹⁹ For the same reasons, debonding is also observed around the coarse aggregates, in some cases showing delamination between paste matrix and aggregates. In addition, 30–50 μm-wide cracks are also formed within the paste matrix connecting the gaps (formed from debonding) around the coarse aggregates. In the fire-damaged concrete, the cracks observed are typically empty (i.e., do not contain gel or hydration products). The cracks in the ASR-damaged sample within the coarse aggregates are wider than those observed in the fire-damaged concrete and tend to be filled with more fluorescing epoxy, which may have displaced ASR gel products.

This work employs the mixing of two incident shear waves to generate a third, mixed longitudinal wave. These primary waves are chosen for the following reasons, noting that the desired third waves are obtained only when the resonance condition is satisfied by two incoming primary waves. There are five theoretical cases that satisfy the resonance condition for non-collinear mixing.¹⁵ We then considered the following theoretical and practical factors: the availability of high-fidelity low frequency transducers; the scattering effect that limits the frequency to below approximately 100 kHz for longitudinal waves (50 kHz for shear waves) in concrete; the sample dimensions with respect to the wavelength; generation efficiency (higher frequencies are more efficient); and the nature and propagation direction of the third wave to determine that only the shear-shear and shear-longitudinal cases are practical. Between these two, the shear-shear case is chosen for simplicity in implementation. The two incident (fundamental) vertically polarized shear waves (SV) propagate in-plane with respect to the x–y axes (Fig. 4) with identical frequencies, $f1$⁠. Then, the characteristic equation for the nonlinear wave mixing is given by¹⁵ 

where $f2$ is the frequency of the mixed wave, given as $2f1$⁠; $c1$ and $c2$ are the phase velocities at which the fundamental and mixed waves propagate; and $α$ is the angle between the two fundamental (incident) waves. A mode-conversion technique using a Teflon wedge is employed to create each of the two fundamental incident shear waves; the longitudinal wave from a longitudinal wave transducer (T₁ or T₂) is converted to an in-plane shear wave in the concrete prism specimen as shown in Fig. 4. The measured longitudinal and shear wave speeds in the concrete prism are 4200 and 2513 m/s, which leads to $α=106.5°$ by Eq. (1). The measured longitudinal wave speed in Teflon is 1450 m/s and the wedge angle is then 27.5° by Snell's law to generate shear waves.

Two longitudinal wave transducers (T₁ and T₂) with a center frequency at 50 kHz (Ultran GRD50-D50) and a third receiving transducer (R) at 100 kHz (Ultran GRD50-D100), all with diameters of 5 cm, are used to generate the fundamental waves and detect the mixed wave, respectively. Note that the receiving transducer (R) is placed on the top surface of the concrete prism, so it detects the forward mixed wave that is reflected back from the bottom surface of the concrete prism specimen.¹² This setup facilitates a one-sided approach for imaging. Two separate excitation setups consisting of a function generator (Agilent Model 33250A) and a power amplifier (ENI 240L or ENI 1040L) synchronously excite the two transmitting transducers. The 40 kHz input tone burst signal has four cycles to avoid an overlap with reflection signals due to the wedge geometry. To extract the mixed wave signal component at 80 kHz, the detected ultrasonic signals are band pass-filtered; filtering is performed in two stages using Butterworth filters (Krohn-Hite: Model 3202 and Model 3988) connected in series with cutoff frequencies set at 70 and 90 kHz. The input and output gains in the second stage are adjusted to 6 and 20 dB in order to compensate the gain loss during filtering and further amplify the output signal to the level 10–100 mV. This target voltage is chosen to get a sufficiently high signal-to-noise ratio (SNR) and to avoid nonlinear distortion of the amplifier in the filter. The received signals are averaged 256 times to achieve a minimum SNR of 60 dB. A simple geometrical analysis shows that the diameter of the fundamental shear wave beams in the concrete is about 3.5 cm, which forms an intersecting (mixed) volume of approximately 230 cm³ with the diameter of an equivalent sphere being 3.95 cm. Taking into account the beam divergence, the spatial resolution of this measurement setup is in the range of 6.5–8.4 cm. This resolution is comparable to the size of the ASR and fire-damaged inserts in the concrete prism of Fig. 1.

Scanning is accomplished by adjusting the distance between the two wedges to change the depth (y axis per Figs. 1 and 4) of the mixing volume (or inspection zone), while moving the two wedges together (with the same separation distance) moves the inspection zone along a horizontal line (z axis per Figs. 1 and 4) with that given depth. In this way, it is possible to image internal zones of the concrete prism at five different depths and five different locations (25 inspection zones) within a prescribed horizontal y–z plane. The wedges are coupled to the concrete specimen with high vacuum grease. Each measurement at a single inspection zone is repeated five times, with the wedges removed and then recoupled to the concrete specimen for each individual measurement. This procedure quantifies a potential lack of repeatability due to output variability caused by any inconsistency of the contact conditions.

Figure 5 shows typical received (mixed) time domain signals, with Fig. 5(a) being the signal when the mixing volume coincides with the known location of the ASR damage, and Fig. 5(b) is the signal when the mixing volume is at a generic “undamaged” location. Based on the time delay, the signal following the first mixed wave signal corresponds exactly to the arrival time of the second echo from the bottom surface. Note that this procedure does not need to use a polarity switching technique²⁰ since the output signals without any postprocessing are large enough, have a Gaussian shape, and are well isolated from a potential interference of other unwanted second harmonic signals. This is because the nonlinearity of the damaged concrete (ASR and fire) is much higher than that of normal undamaged concrete and the concrete prism specimen is large enough that the location of the individual second harmonic waves is well separated.

The nonlinearity parameter β in the mixing volume has the following proportionality:

where $A1$ and $A2$ are the amplitudes of the fundamental waves and $A3$ is the amplitude of the third, mixed wave. Equation (2) is valid for plane wave interactions and requires a correction for the diffraction effects, or the finite source sizes and the variations of propagation distances of the fundamental and mixed nonlinear waves in this research. Equation (2) is then modified to

where $A0$ is the wave amplitude at the surface of the circular source, D is the diffraction correction function for a circular piston source,²¹ $d1$ is the distance propagated by the fundamental wave (from the source to the center of mixing volume), and $A3$ is the mixed wave amplitude at the center of mixing volume. Since one can measure only diffracted nonlinear waves, i.e., $A3D(f2;d2)≡A3′$⁠, with $d2$ being the distance propagated by the nonlinear wave, while β will be compared for different inspection zones, a relative nonlinearity parameter is defined in terms of the measured mixed wave signal $A3′$⁠,

Note that the common factor $A02$ is omitted and only the linear diffraction is corrected in Eq. (4). $β′$ is called the nonlinearity parameter hereafter for simplicity. Figure 6 shows the diffraction corrections, i.e., $1D2(f1;d1)D(f2;d2)$⁠, for the five measurement depths where images are determined. It is seen that the diffraction effect is quite significant and, thus, must be corrected for in the ranges of frequency and propagation distance in this measurement setup. Also interesting is that the measurement locations are close to the start of the far-field distance.

Figure 7 shows cross-sectional images of nonlinear wave amplitudes for three representative y–z plane slices in the concrete prism. As shown in Fig. 1, the first cross-sectional image [Fig. 7(a)] includes only the undamaged (cast concrete), while the second [Fig. 7(b)] and third [Fig. 7(c)] ones include the ASR- and fire-damaged regions. The nonlinearity parameter in the undamaged section varies with an average value 0.048 and a standard deviation for 25 locations 0.021 [Fig. 7(a)]. This is because the size of the mixing volume is not sufficiently large when compared with the aggregate sizes (5–19 mm). The ASR- and fire-damaged zones are clearly seen in Figs. 7(b) and 7(c) and are easily differentiated from the surrounding undamaged concrete. The average nonlinearity parameter of the ASR and fire-damaged zones are 0.242 (with the standard deviation 0.029) and 0.214 (with the standard deviation 0.019), respectively. Note that these standard deviation values are from five repeated measurements for each inspection zone. The image contrasts for the regions containing the ASR and fire-damaged zones are 5.07 and 4.49, respectively. Figure 8 summarizes these results.

The increased nonlinearity in the ASR and fire-damaged regions corroborates well with the increased microcracking observed in these damaged regions from petrographic analysis (Fig. 3). Even though the variations of the nonlinearity parameter in the surrounding concrete are significant in general, the nonlinearity of the damaged volumes is significantly larger and can be easily distinguished from the inspection zones without any damage. This result demonstrates the feasibility of using the proposed nonlinear mixing technique to image internal microscale damage throughout the volume of a concrete component.

An additional advantage of using this wave mixing approach is that there are direct, physics-based relationships between measured nonlinear ultrasonic wave properties and specific microscale features and damage like microcracks.²² This should allow for the development of quantitative damage characteristics from the measured nonlinearity parameters throughout the thickness of a concrete component.

This work demonstrates the feasibility of using a non-collinear wave mixing technique to image internal microscale damage throughout the interior volume of a relatively large (28 cm thick) concrete specimen. This wave mixing approach allows for the use of incident waves with frequencies low enough to not be scattered by the inherent heterogenous, concrete microstructure, while leveraging the sensitivity of nonlinear waves to features with length scales well below their wavelength. Scanning and imaging is accomplished by manually adjusting the locations of the two incident waves. Future work will explore the use of phased array transducers to accomplish the scanning without having to physically move the transducers. A knowledge of the wave speeds in concrete plus synchronization of the waveform timing pinpoints the location of the mixing zone—the specific volume of concrete being imaged. Finally, advanced wave filtering and a knowledge of linear wave mechanics allows for the isolation of the mixed wave. The viability of the proposed technique is demonstrated by examining a concrete prism (28 cm thick) with known internal microscale damage.

This is the first known instance of using ultrasonic waves to image internal microscale damage in concrete, and these results can be exploited for the development of an ultrasonic imaging procedure of internal microscale damage in thick concrete components.

This research was partially supported by ARPA-E under Contract No. DE-AR0001137.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.