Fully noncontact nonlinear ultrasonic characterization of thermal damage in concrete and correlation with microscopic evidence of material cracking

Cement and Concrete Research 123 (2019) 105797

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Fully noncontact nonlinear ultrasonic characterization of thermal damage in concrete and correlation with microscopic evidence of material cracking Chenglong Yang, Jun Chen

T

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Department of Civil Engineering, School of Transportation Science and Engineering, Beihang University, 37 Xueyuan Road, Haidian District, Beijing 100191, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Concrete Thermal cracking Nonlinear ultrasonic Elastic wave velocity inversion X-ray computed tomography

This paper investigates the degradation of concrete integrity under the rising temperature using a nonlinear ultrasonic second harmonic generation (SHG) technique based on a fully non-contact approach. The microscopic cracks accumulated during the course of thermal damage is then analytically and experimentally quantified by the elastic wave velocity inversion method and X-ray computed tomography (CT) technique, respectively. The nonlinear parameter calculated by the non-contact SHG technique not only shows a higher sensitivity to the damage growth than traditional macroscopic ultrasonic parameter such as wave velocity, but also presents an excellent correlation with microscopic quantified crack density by showing a proportionally increase with the propagation distance of ultrasonic waves. The experimental findings in this work indicate that the non-contact SHG technique can truly reveal the progressive microscopic cracking of concrete through the macroscopic nondestructive measurements and is suitable for the assessment of globally distributed damage with a high sensitivity and reliability.

1. Introduction With the increasing height and distribution density of buildings, fire disaster is becoming a significant challenge for the building safety. As the most commonly used construction material, concrete however does not have a very good fire-resistant performance. Extensive experimental studies have shown that the typical physical and mechanical properties of concrete such as compressive strength and Young modulus are significantly decreased when subjected to high temperatures, and this loss is not recoverable even if the temperature falls back [1–3]. As a porous multiphase mixture, concrete undergoes complex physical and chemical procedures when exposed to high temperatures such as the interfacial water evaporation, decomposition of C-S-H gel, thermal expansion and debonding of cement paste and aggregates. Eventually thermal damage will be presented in the form of distributed cracking throughout concrete. It is thus a critical issue to characterize progressive cracking due to thermal treatments of concrete based on a nondestructive evaluation (NDE) approach. The contact type defect of concrete cracks due to thermal treatments leads to the nonlinear behaviors of ultrasonic waves propagating in concrete [4,5]. Based on the principle of nonlinear ultrasonic, various ultrasonic-based NDE techniques are emerging in recent years due to their highly sensitive response to the structural defects, and four types

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of experimental techniques are developed according to different nonlinear ultrasonic phenomena [6–29]. Kim et al. [6,7], Chen et al. [8] Shah et al. [9–11] developed the second harmonic generation (SHG) technique for the damage characterization of concrete and rock subjected to mechanical and thermal loading, where the relative amplitude of second harmonic was considered to correlate with material damage. Warnemuende and Wu [12], Chen et al. [13], Kober and Prevorovsky [14], Van Den Abeele et al. [15,16] and Hong et al. [17] proposed the wave modulation method to observe sidebands due to modulation effect, and the defined nonlinear parameter showed better sensitivity than phase velocity of ultrasonic wave for the assessment of material deterioration. In recent years, the nonlinear resonance spectroscopy method gained a lot of attention in nondestructive evaluation society because it estimated the nonlinear parameter by simply analyzing the variation of self-resonance of structures [18,19]. For example, Payan et al. [20], Park et al. [21] and Rashidi et al. [22] used the nonlinear resonance spectroscopy technique for the assessment of thermal and delayed ettringite formation damage of concrete, respectively. Chen et al. [23], Lesnicki et al. [24,25], Boukari et al. [26] and Rashetnia et al. [27] deployed the nonlinear resonance spectroscopy method for the monitoring of time-variant alkali-silica reaction and freeze-thaw damage of cement-based materials. In addition, Antonaci et al. [28,29] developed nonlinear ultrasonic scaling subtraction method in which the

Corresponding author. E-mail address: [email protected] (J. Chen).

https://doi.org/10.1016/j.cemconres.2019.105797 Received 11 January 2019; Received in revised form 19 June 2019; Accepted 19 June 2019 0008-8846/ © 2019 Elsevier Ltd. All rights reserved.

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nonlinear parameter was extracted based on the subtraction between actual signal and scaled reference signal for the analysis of discontinuity and corrosion of concrete. As one of the most frequently used nonlinear ultrasonic methods in recent years, the SHG technique has been very successful in evaluating damage of different materials [30–35]. However, most of previous researches established the experimental setup are based on the contacttype transducers and the reliability of multiple measurements is highly affected by the coupling condition between transducers and structural surface. Lately, Kim et al. [36–38] developed a half noncontact SHG system for the evaluation of concrete shrinkage and carbonation, where a contact type transducer is still required for the signal transmission. Smith et al. [39] tried to further replace the transmitting sensor with an air-coupled one but most of signal strength was lost and could not provide meaningful results. In this paper, a fully non-contact SHG technique is introduced to evaluate the thermal damage in concrete, where a couple of air-coupled transducers instead of traditional contact transducers is used in order to avoid the side effect of coupling condition and improve the measurement reliability. The results from noncontact SHG technique are compared with phase velocity results to validate the sensitivity of nonlinear ultrasonic measurements. The SHG technique is further proved to have the capability to qualify the progressive cracking of thermal damage by showing a high correlation with theoretical calculation of crack density based on elastic wave velocity inversion method and the microscopic scanning results of thermal damage with X-ray CT technique. The main contributions of this study consist of two parts. First, we improve the SHG experimental measurements for the half noncontact system of previous work [36–39] to a fully noncontact system which is validated for its sensitivity and reliability. The air coupling condition of noncontact sensors is constant, which will ensure the measurement reliability. The removable characteristic of experimental setup further facilitates the application possibility of fast inspection. Secondly, previous work generally used external physical parameters as the structural damage indicator, such as rising temperature and increasing loading. Although these parameters are environmental factors inducing damage in the macroscopic scale, they cannot directly indicate the microscopic variation of concrete throughout the course of damage. Therefore, the second contribution of this paper is to establish the direct correlation between nonlinear ultrasonic measurements and microscopic material evidence – crack density calculated from two independent approaches.

Fig. 1. Thermal treatment process of different peak temperatures.

and each group includes one prismatic specimen and two cubic specimens. The number of group label refers to the temperature applied on specimens, where T20 means this group of specimens sit in the room temperature and is used as the control ones. The heating treatment of concrete specimens was conducted through an electric muffle furnace. The heating process is schematically presented in Fig. 1. The heating rate was 15 °C per minute and then each peak temperature was maintained constantly for 2 h. The cooling rate controlled by a hot-air blower was identical with the heating rate. A rapid change in ambient temperature can cause a large temperature gradient between the core part and marginal part of concrete as its low thermal conductivity, thereby resulting in a large internal stress. Therefore, a rapid change of temperature was avoided in order to prevent the secondary damage, via which a high fidelity of thermal damage was ensured. The compressive strength and mass loss of the specimens were measured and listed in Table 2 as the reference value of typical physical and mechanical properties of concrete samples. A considerable mass loss of 5.22% is discovered when the exposed temperature changes from 150 to 300 °C while the compressive strength has a relatively small decrease, indicating that a large amount of water evaporates during this stage and the material integrity is less affected. When the exposed temperature rises from 300 °C to 600 °C, the mass loss is about the half of low temperature range, and the decrease of compressive strength is almost five times that of low temperature range, indicating that concrete samples suffer a significant material deterioration during this stage.

2. Specimens preparation and damage induction Five prismatic specimens with a size dimension of 100 mm × 100 mm × 300 mm and ten cubic specimens with a side length of 150 mm were prepared for the thermal treatment. The mixing materials for concrete specimens included ordinary Portland cement (type P·O 42.5 according to Chinese code GB175-2007), river gravel coarse aggregate with a maximum size of aggregate of 20 mm and natural sand with a fineness modulus of 3.04. Water-cement ratio of 0.45 was chose for the mixing. The detailed mix proportion of concrete specimens is listed in Table 1. The specimens were cured in a standard curing environment (23 °C and 95% relative humidity) for 28 days before subsequent thermal treatments. The concrete samples are divided into five groups labeled T20, T150, T300, T450 and T600, respectively,

3. Elastic wave velocity inversion Based on effective medium theory, important microstructural information of material such as crack density finds a legitimate connection with the elastic parameters (e.g., Young modulus and Poisson coefficient). Considering the well-established relation between the acoustic wave velocities and elastic parameters, elastic wave velocity Table 2 Material property of concrete samples.

Table 1 Mixture proportioning of concrete samples. w/c Water (kg/m3) Cement (kg/m3) Fine aggregate (kg/m3) Coarse aggregate (kg/m3)

0.45 185 420 572 1273

2

Sample

Temperature (°C)

Mass loss (%)

Compressive strength (MPa)

T20 T150 T300 T450 T600

20 150 300 450 600

0 1.27 7.49 8.20 9.65

44.5 42.7 40.2 33.4 21.7

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(EWVI) technique becomes an efficient way to investigate the microstructural features through the macroscopic ultrasonic measurements. The crack density ρ = (1/V)∑i=0Nci3 is defined in effective medium theory [40], where N is the number of cracks in the volume V, ci is the radius of the i-th crack. With the assumption of neglecting the stress interaction between randomly distributed cracks, the relation between the elastic parameters of damaged concrete and those of intact concrete can be expressed as [41]

⎧ E0 = 1 + ⎡1 + ⎪ ⎢ ⎪E ⎣ ⎨ G0 = 1 + ⎡1 + ⎪ ⎢ ⎪G ⎣ ⎩

μ 3⎛ δ ⎛1 − 0 ⎞ ⎛ − 1⎞ ⎞ ⎤ hρ 5 ⎝⎝ 2 ⎠⎝ 1 + δ ⎠⎠⎥ ⎦ ⎜

⎟

μ hρ 2⎛ δ ⎛1 − 0 ⎞ ⎛ − 1⎞ ⎞ ⎤ 5 ⎝⎝ 2 ⎠⎝ 1 + δ 1 + μ0 ⎠⎠⎥ ⎦ ⎜

⎟

(1)

where E (G) and E0 (G0) are the effective and crack-free Young modulus (shear modulus) respectively,μ0 = 0.2 is the crack-free Poisson coefficient, δ is a parameter considering the influence of the fluid bulk modulus, and h = 16(1 − μ02)/9(1 − μ0/2) is a scalar to describe the geometry of the cracks for a non-interactive penny-shaped crack geometry [42]. Afterwards, irrespective of the material density variation, the relationship between the acoustic velocity measurements and the elastic parameters can be expressed as

⎧ E0 = νL0 ⎪ E νL ⎨ G0 νS 0 = ⎪ νS ⎩ G

(2)

where νL (νS) and νL0 (νS0) are the compressional (shear) wave velocity corresponding to the current state and initial state respectively. Combing Eq. (1) and Eq. (2), the crack density can be then related to the variation of compressional and shear wave velocity as expressed in Eq. (3).

ρ= =

Fig. 2. Schematic (a) and experimental setup (b) of X-ray CT technique.

3(1 + υ0 )(νS 0/ νS )2 − 2(νL0/ νL )2 − 1 16(1 − μ0 2 )/9(1 − μ0 /2)

4. X-ray CT imaging

3.6(νS 0/ νS )2 − 2(νL0/ νL )2 − 1 1.896

4.1. Principle

(3)

The X-ray CT technique has been demonstrated to be an efficient method to visualize the 2D and 3D microstructural images of material [44,45]. The schematic of the X-ray CT technique is shown in Fig. 2 (a). The concrete cube is projected on the flat panel detector through a point source generated by an X-ray machine. The locations of the X-ray machine and the flat panel detector are adjusted for an appropriate spatial resolution. The spatial resolution can be expressed as

The wave velocities were measured by the transmission through of ultrasonic pulse waves [43] and the results are listed in Table 3. The calculated crack density corresponding to different exposed temperatures are presented in Table 3 as well. When the exposed temperature of concrete changes from 20 °C to 150 °C, only the free water in the pores evaporates, and very little new cracks appear, leading to a slow increase in crack density. With the increase of exposed temperature, the dehydration shrinkage and thermal expansion result in the continuous development of cracks. In addition, the difference in thermal expansion coefficient of each component in concrete further accelerates the growth of cracking. As a result, in the temperature range of 450 °C and 600 °C, the crack density increases with a rapid speed and reaches up to 12.9% at 600 °C.

R=

20

150

300

450

600

Compressional wave velocity (m/ s) Shear wave velocity (m/s) Crack density (%)

3745.3

3311.2

2901.9

2364.1

1304.1

2436.6 0

2200.7 0.13

1753.2 1.07

1284.7 3.34

708.2 12.93

(4)

where d is the pixel size, n = Sski/Scon is the image magnification with respect to the entity, and Scon (Sski) represents the size of the concrete cube (the skiagraph). When d and Sski are fixed, the spatial resolution increases as the size of concrete cube decreases. With consideration that the maximal aggregate size in concrete is about 20 mm, the cube specimens for the CT scanning were carved with a suitable size of 25 mm × 25 mm × 25 mm. The image magnification was thus 200% with a spatial resolution of 0.098 mm. In this CT scanning, three crosssections in the directions of x, y and z were selected via the rotating platform as shown in Fig. 2(a). The direction was adjusted by the rotating platform supporting the concrete cube. A series of skiagraphs were acquired by the flat panel detector and transferred to a workstation for the subsequent analysis. The image of CT internal chamber is shown in Fig. 2(b).

Table 3 Wave velocity and the volumetric porosity corresponding different exposed temperatures. Exposed temperature (°C)

d d S = = d· ski n Scon/ Sski Scon

3

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20oC

150oC

450oC

300oC

600oC

Fig. 3. 3D reconstruction images of concrete cubes after thermal treatment.

chemical changes are also exacerbated. Accordingly, the colorized region undergoes a large expansion, indicating a large number of cracks generate, propagate and coalesce at the exposed temperature of 600 °C. The volume fraction Dν of the colored region in the concrete cube (i.e., volumetric porosity) for every exposed temperature is calculated according to an established equation [43] as

4.2. Volumetric porosity by spatial reconstruction The reconstruction of concrete cubes was performed using 3D visualization software AVIZO. Subsequently, the pores and cracks in concrete was reconstructed as the colorized regions as shown in Fig. 3, and the different colors denote the disconnection between them. It is observed that there exist some small pores in the specimen at the room temperature, and the damage develops slightly at the temperature range of 20 °C to 300 °C. When the temperature reaches 450 °C, C-S-H gel begins to dehydrate, calcium hydroxide in aggregate begins to decompose and the influence of the difference in thermal expansion coefficient of concrete components is also gradually increasing. These effects result in the generation of a large number of disconnected microcracks, which is manifested by the diverse regions of generated colors. When the temperature continues to reach 600 °C, calcium carbonate begins to decompose and the aforementioned physical and

Dν =

VPore × 100% VTotal

(5)

where VPore and VTotal are the volumetric voxel numbers of pore and entire sample, respectively. The calculated volumetric porosity is then plotted against exposed temperature in Fig. 5. The volumetric porosity changes slightly at the temperature range of 20 °C to 300 °C. After the exposed temperature exceeds 300 °C, the volumetric porosity gradually increases and eventually reaches 20.8% at 600 °C. 4

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20oC

150oC

300oC

450oC

2 mm

600oC

Fig. 4. CT images of concrete cubes after thermal treatment.

have no obvious fracture, and some hairline cracks appear on the specimen T300. As the temperature rises, more cracks appear and become conspicuous, and the cracks in specimen T600 expand significantly and coalesce into continuous fractures encircling the aggregates. The classification and underlying generation mechanism of these cracks were briefly introduced by taking specimen T600 as an example. A large number of cracks appear at the interface between the

4.3. Areal porosity Another important feature of damaged material which the X-ray CT technique can present is the 2D images of cracks of concrete crosssections. One representative image for every exposed temperature is exhibited in Fig. 4. The dark region is identified as the pores and cracks as their high transmissivity for X-ray. The specimen T150 is found to 5

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Fig. 5. Volumetric porosity and areal porosity calculated by X-ray CT technique with respect to exposed temperature.

Fig. 6. Crack density and volumetric porosity of concrete cubes determined by two techniques respectively after thermal treatment.

gravel and the mortar, which is attributed to two factors: the deterioration of the cementation ability of mortar because of the decomposition of the C-S-H gel, and the shear stress at the interface because of the difference in the thermal expansion coefficient between the gravel and the mortar. Some cracks also appear around the pores, which is attributed to the vapor pressure. There are also joint cracks between these interfacial cracks and the pores as the path of energy transfer and release inside concrete. In addition, a large number of microcracks appear inside the mortar mainly due to the shrinkage of mortar. Three cross-sectional CT images are captured in the direction of each coordinate axis, and these 9 CT images are analyzed to obtain the average areal porosity of the concretes at every exposed temperature as shown in Fig. 5. The calculation of areal porosityDsis based on the following equation [44],

(Ultran NCG50-D50) with the central frequency of 50 kHz after the amplification by a power amplifier (Krohn-Hite 7500). Based on Snell's law as shown in Eq. (7), the air-coupled transducer was settled at a tilt angle of 11o to the normal line of specimen's top surface to generate Rayleigh waves in concrete.

Ds =

1 9

S

∑ S Pore

× 100%

Total

θcr =

νair νcon

(7)

where θcr is the critical incident angle to generate the Rayleigh wave, vair is the acoustic velocity in air and vcon is the compressional wave velocity in concrete. The leaky Rayleigh wave was then captured by another air-coupled transducer (Ultran NCG100-D50) with the central frequency of 100 kHz. After the amplification by a pre-amplifier (Krohn-Hite 7602), the received signal was averaged 64 times and eventually recorded by a digital oscilloscope (Tektronix MDO3012) with a sampling frequency of 10 MHz. The air-coupled transducers were installed on a self-designed sliding track, through which the wave propagation distance was adjustable. When propagating in nonlinear elastic materials, the spectrum of ultrasonic waves is observed to contain a second harmonic component. Subsequently, the nonlinear parameter, which is the coefficient of nonlinear term of constitutive relation of damaged material, can serve as an indicator to evaluate damage. The details about relation between nonlinear parameter and second harmonic generation have been extensively documented [30–33,36–38], and only the final expression is shown in this paper as below

(6)

where SPore and STotalare the areal pixel numbers of pores and entire cross-section, respectively. It is seen that the areal porosity presents a similar variation trend to the volumetric porosity. The comparison between the volumetric crack density by EWVI method and the volumetric porosity by X-ray CT technique is also considered. A similar variation trend is found as shown in Fig. 6, which shows the accuracy of the measurements obtained by EWVI method and X-ray CT technique. It is also noteworthy that the volumetric crack density at each temperature obtained by EWVI method is always smaller than the volumetric porosity calculated by CT images since the volumetric porosity includes pores and other disconnections in material in addition to the penny-shaped cracks considered in the EWVI calculation.

βb =

A2 A12 x

(8)

5. Damage evaluation by air-coupled SHG technique

where A1 (A2) is the amplitude of the fundamental component (the second harmonic component), x is the propagating distance of ultrasonic wave. When the propagating distance is settled, the relative nonlinear parameter is expressed as

5.1. Experimental system

βa =

The schematic of the experimental system for air-coupled SHG measurements is shown in Fig. 7(a) and the image of air-coupled system is demonstrated in Fig. 7(b). A function generator (Rigol DG1022) was applied to trigger a tone-burst sinusoidal signal at a low frequency of 50 kHz to reduce acoustic scattering [38] because the wavelength at second harmonic frequency is approximately 25 mm, larger than the maximum size of aggregates of 20 mm used in our experiments. The peak-to-peak voltage of the signal changed from 1 V to 3 V with a step of 0.2 V. The signals were then fed into an air-coupled transducer

A2 A12

(9)

5.2. Measurements for settled propagation distance In this section, the wave propagation distance was set to be constant at 14 cm. A Hanning window is imposed to a captured time-domain signal shown in Fig. 8(a) to get a steady part of signal for the subsequent process. The spectra of the windowed signal for every input signal amplitude is then obtained through the fast Fourier transform (FFT) as shown in Fig. 8(b). In the frequency domain, the amplitude of 6

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Fig. 7. Schematic (a) and experimental system (b) for air-coupled SHG measurements.

5.3. Measurements for variable propagation distance

fundamental frequency and second harmonic frequency signal are termed as M1 and M2 respectively. Due to the linearity of FFT, M1 and M2 in frequency domain are regarded as A1 and A2 in Eq. (8). As shown in Fig. 9, the correspondence between A2 and A12 for different input signal amplitudes presents an excellent linear relation. Accordingly, the slope of the linear fitting line is regarded as the nonlinear parameter βb. The variation of βb with respect to exposed temperature is presented in Fig. 10, showing that βb is positively correlated with the exposed temperature and the increase of βb accelerates while the temperature increases. The coefficient of variation of βb which ranges from 1.2% to 5.7% is small enough to ensure the accuracy of the measurements. The reliability of developed noncontact SHG measurements is further validated through a comparison of coefficient of variation with contact SHG measurements, as shown in Fig. 11. It is seen that the coefficient of variation of noncontact measurements of nonlinear parameter is averagely 16% of that of contact measurements.

In this section, the propagation distance x was regulated via the rotary handle on the sliding track. Combining Eqs. (8) and (9), the relative nonlinear parameter βa can be expressed as

βa = βb/ x

(10)

The nonlinear coefficient βb with respect to the propagation distance at different exposed temperatures is calculated and plotted in Fig. 12. It is observed that the sensitivity of βb to thermal damage increases when the propagation distance becomes larger. For example, the maximal change rate of βb is about 1100% for the propagation distance of 18.5 cm, and about 300% for the propagation distance of 14 cm. The increased change rate of nonlinear parameter corresponding to longer propagation distance is reasonable because the thermal cracks are spread out all over the entire specimen and the material nonlinearity has the cumulative effect if the ultrasonic wave travels longer length or larger area of specimen. The accumulation of material 7

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Fig. 10. Variation of nonlinear parameter βb with respect to exposed temperature.

Fig. 8. Fully air-coupled SHG measurements (a) time-domain signal, (b) frequency-domain signal.

Fig. 11. Comparison of coefficient of variation between noncontact and contact SHG measurements.

Fig. 9. Nonlinear parameter βb obtained from the linear relationship of A2 and A12.

nonlinearity was also found in the assessment of concrete carbonation [38], which is also globally distributed throughout samples as thermal damage. As shown in Fig. 12, when the exposed temperature is settled, the

Fig. 12. Nonlinear coefficient βb with respect to the propagation distance at different exposed temperatures.

8

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(1) Cracks presented on concrete cross-sections due to different mechanisms is captured by the 2D images of X-ray CT technique, and different types of interior porosity including cracks, pores and disconnections are visualized by the 3D reconstruction of X-ray CT technique. The areal and volumetric porosity calculated from 2D images and 3D reconstruction images are used to quantify thermal damage in different dimension and they are consistent with each other. (2) On the other side, the volumetric crack density using EWVI method which only considers the penny-shaped cracks is calculated based on the measurements of wave velocities and the variation of volumetric crack density is in an agreement with the porosity parameters quantified by X-ray CT technique. The variation pattern of these parameters indicating material crack and porosity could be explained by the physical and chemical phenomena occurring in different phases of the thermal treatment of concrete. (3) The fully non-contact SHG technique is demonstrated to be an excellent method to qualify thermal damage of concrete for the stability and sensitivity of the measurements. The nonlinear parameters, βb for settled propagation distance and βa for variable propagation distance, are found to have a similar tendency to the volumetric crack density with the increase of exposed temperature. The sensitivity of nonlinear parameters to exposed temperature is also shown to be impressive by comparing with the phase velocity measurements. Particularly, the nonlinear parameter βb is proportionally increased with the propagation distance of ultrasonic waves, indicating the non-contact SHG has the advantage to assess the accumulation of distributed material deterioration such as thermal damage owing to the characteristic of removable air-coupled transducers.

Fig. 13. Comparison of nonlinear parameter βa, βb and phase velocity with respect to crack density.

nonlinear coefficient βb has an excellent linear correlation with the propagation distance where the coefficient of correlation is as high as 0.987. Based on Eq. (8), the slope of the fitting lines represents the relative nonlinear coefficients βa. The phase velocity (i.e., the compressional wave velocity shown in Table 3) has been proved to be a typical parameter to characterize concrete damage [46,47] and is thus used here as a comparison with the nonlinear parameter of SHG measurements. The relative change rates of phase velocity and nonlinear parameters βb and βa which are calculated through macroscopic ultrasonic measurements are plotted against the crack density calculated through EWVI analysis in Fig. 13. First, a large advantage in the sensitivity of nonlinear parameters to cumulative thermal damage is verified. For instance, the maximal change rates of βb and βa corresponding the largest crack density are about 300% and 2000%, respectively, while the maximal change rate of phase velocity is 65%. Furthermore, as shown in Fig. 13, both two nonlinear parameters have the similar variation tendency and are positively correlated with the volumetric crack density. It is seen that the nonlinear parameters do not increase proportionally with the volumetric crack density and the increasing rate tends to be smaller at the larger crack density. Although more experiments should be conducted to provide more data for the verification of current observation, some preliminary explanation could be given here as the possible reason. As mentioned by previous research [4,5], the nonlinear ultrasonic behaviors are primarily caused by the clapping effect of penny-shaped cracks. While the width of cracks grows to a certain range, the ultrasonic wave may not have sufficient energy to generate the clapping of cracks and the nonlinear ultrasonic effect could be attenuated. From the 2D X-ray CT images of concrete cross-section, the crack width actually becomes larger and larger corresponding to the increased volumetric crack density. Thus the increased nonlinearity due to newly born smallwidth cracks may be partially deducted by the old large-width cracks, which eventually results in the slower increase of nonlinear parameter.

In conclusion, the proposed non-contact SHG technique is feasible to characterizing degradation of concrete integrity caused by thermal treatments. The defined nonlinear parameters present an excellent correlation with quantified damage indexes calculated from both analytical method and image extraction technique, indicating the potential of SHG technique to qualify the microstructural defects of concrete. The non-contact feature of the proposed technique can effectively minimize the measurement errors due to the coupling between sample and transducers and improve the measurement flexibility for large scale inspection by adjusting the transducer distance. It is noteworthy that the detection depth of non-contact SHG technique is circumscribed due to wavelength scale of propagating depth of Rayleigh surface waves, making the proposed technique inappropriate for the application in concrete structures with damage occurring at very deep spots. The best application prospect of the proposed technique is the damage detection of concrete pavement and the near surface cracking assessment of most other structures.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment 6. Conclusions and remarks The work is financially supported by National Key Research and Development Program of China (Grant No. 2018YFB1600202), National Natural Science Foundation of China (Grant No. 51308020) and Natural Science Foundation of Beijing Municipality (Grant No. 8162027). The assistance from Dr. Lifeng Fan at Beijing University of Technology on the X-ray CT measurements is appreciated.

A fully non-contact SHG technique is developed from the previous contact and half noncontact SHG systems for the characterization of thermal damage of concrete. The nonlinear ultrasonic results are further correlated with direct microscopic evidence of material cracking. The following conclusions can be drawn based on the experimental results and analysis: 9

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C. Yang and J. Chen

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