1. Introduction
Concrete ultrasonic nondestructive testing technology refers to the use of signal processing methods to analyze the changes in acoustic parameters such as wave speed, frequency, and amplitude of ultrasonic waves after passing through the concrete medium, and then to evaluate the mechanical properties and damage status of concrete [
1]. However, concrete is a nonuniform and anisotropic composite material with a wide range of heterogeneous interfaces inside; complex reflection and refraction phenomena will occur when ultrasonic waves propagate through it [
2], making it difficult to measure wave speed changes accurately. However, coda wave interferometry (CWI), developed by seismologists, provides a way to solve this problem [
3]. A coda wave refers to the long tail part that extends behind the direct wave in the waveform [
4]. Compared with direct waves, it is more sensitive to changes in the internal scattering of the medium, so it can be used to identify small changes in concrete [
5,
6]. Coda wave interferometry compares the waveforms at different times to determine the travel time offset change law between the waveforms and then obtains the relative change rate in the wave velocity [
7]. Related research indicates that its wave velocity measurement accuracy can reach up to 0.001% [
8]. Therefore, coda wave interferometry has been introduced into civil engineering as a high-sensitivity monitoring tool, and it has shown great potential and broad application prospects in the health monitoring of concrete structures [
9,
10]. Presently, many scholars have performed a series of concrete ultrasonic nondestructive testing studies using coda wave interference technology. The research directions include stress monitoring [
11,
12], damage estimation [
13,
14], crack positioning imaging [
15,
16,
17], temperature influence, and correction [
18,
19,
20].
This research focuses on the sound velocity response of concrete mechanical behavior under load [
21]. Laboratory sample tests are a common method to obtain the ultrasonic coda wave characteristics of concrete under stress. In the process of uniaxial step-by-step compression, the coda wave velocity first slowly increases with the increase in the stress level and then decreases sharply due to the intensified damage [
22]. For the multi-cycle loading test, after each unloading, the initial wave velocity of re-compression continues to decrease, reflecting the increase in the degree of internal damage to the concrete [
23]. Considering the influence of the number of cycles, the slope of the wave velocity load (stress) function can be used to characterize fatigue damage, which increases with the number of cycles [
24]. In the short-time fixed-loading experiment, the wave velocity change increases with increasing fixed-loading time [
25]. On the other hand, under the action of tensile stress, the wave velocity decreases with the increase in stress; during the loading and unloading processes, the attenuation of the velocity continues to accumulate [
26]. To realize the application of CWI technology in real-world engineering monitoring, the coda wave test was performed on real-size reinforced concrete components, and more attention was given to obtaining local acoustic velocity changes through a reasonable sensor layout. A four-point bending test of reinforced concrete T-beams demonstrated that the coda wave velocity can detect changes in compressive and tensile stresses and accurately locate the position of the neutral axis [
27]. A 16-ton truck was used to carry out on-site load measurement of an old box girder bridge that had never been put into use. The results show that the coda wave velocity changes obtained by different sensor combinations can detect the position of the truck to varying degrees [
28].
The above experimental results qualitatively explain the characteristics of concrete ultrasonic coda waves, but the experiment volume was limited by the research cost. Numerical simulations can perform a large number of simulation calculations on concrete load conditions and damage conditions by adjusting parameter settings, and can effectively eliminate the adverse effects of environmental factors. It is an effective tool for analyzing and interpreting the CWI features of concrete. Using the two-dimensional finite-difference time-domain model within the framework of the locadiff imaging technique, the extended changes in multiple scattering media characterized by coda wave decorrelation can be calculated [
29]. A 2D spectral element method was applied to simulate complex coda signals to study the sensitivity of nonlinear coda interference parameters of samples with local damage, and the research scale was gradually refined: the effective elastic characteristics of the sample, the local crack area, and the effective length of the microcrack [
30,
31,
32]. In order to explore the susceptibility of the coda wave to various damages in the concrete failure process at the micro-scale, a research system of concrete mesostructure generator discrete element calculation of concrete fracture finite-difference simulation of the ultrasonic field was constructed [
33].
To date, relevant scholars have achieved good results in research on establishing the relationship between ultrasonic coda wave characteristics and concrete stress or damage. Larose performed linear regression on the data of coda wave relative velocity change and stress change and defined the estimated value of the nonlinear parameter with an estimation accuracy of 5% for this parameter [
8]. Schurr used the acoustoelasticity constant and nonlinear elastic parameters to estimate the damage degree and proved the two parameters of the damaged samples are typically multiple times higher than those of the damaged samples [
24]. Hafiz used magnitude-squared coherence to evaluate stress change versus ultrasonic waveform change and obtained a test constant as a measure of the sensitivity by linear regression [
34]. Clauß derived the correlation between ultrasonic coda wave relative velocity changes and reinforcement strains, covering 90% of the complex load-bearing behavior in reinforced concrete members, and demonstrated a feasible method for evaluating structural state objectives using ultrasonic coda wave characteristic parameters [
35].
Existing studies have qualitatively analyzed the characteristics of ultrasonic coda waves in the development process of loaded concrete damage. The research objects are mainly concrete strength (C30–C50) samples commonly used in practical engineering [
11,
22,
23,
25]. In this paper, through laboratory experiments and numerical simulations, the correlation between the damage degree of concrete and the ultrasonic coda wave velocity under uniaxial load was studied. A high-strength concrete (C60–C70) ultrasonic coda wave test group was set up to broaden the research scope. Based on the variation curve of concrete coda wave velocity with the percentage of maximum load, a mathematical formula for evaluating concrete damage was fitted. The uniaxial compression simulation model established by this discrete element method can clarify the damage and failure mechanism of concrete. The ultrasonic field simulation model based on digital image processing technology, as an attempt to quantify the relationship between the damage degree and coda wave velocity change rate, provides a feasible platform for further research.
3. Experimental Results and Discussion
3.1. Waveform Cross-Correlation Analysis
The changes in internal damage of concrete were detected through the coda wave interferometry method, mainly to determine the small difference between the coda wave waveforms before and after the concrete is loaded. A comparison of the received signal waveforms before and at the beginning of loading is shown in
Figure 5. In time window 1, the two received signals are completely coincident, which ensures the repeatability of the wave source. In time windows 2 and 3, there is a phase difference between the two signals that gradually increases. Comparing windows 1, 2, and 3 proves that the coda wave is very sensitive to small changes in the random medium of concrete.
The value of the cross-correlation coefficient
ranges from 0 to 1. A value of 0 means that the two waveforms are completely uncorrelated; 1 means that the two waveforms are completely the same [
23].
Figure 6 shows the correlation between the coda wave cross-correlation coefficient and the maximum load percentage of the concretes. Within 50% of the maximum load percentage (A–B–C), the correlation coefficient of each concrete is approximately equal to 1, so the corresponding wave velocity change is linear and uniform [
36]. When the maximum load percentage is between 50–80% (C–D), the cross-correlation coefficient decreases continuously, indicating that coda wave propagation is strongly affected by the internal damage to the concrete, which causes the waveform to be distorted. As the load exceeds 80% of the maximum load percentage (D–E), the cross-correlation coefficient exhibits a larger range of fluctuations based on further reduction, indicating that the typical causing of scatter inside the concrete, that is, the cracks, has further widened or linked up.
3.2. Coda Wave Velocity Change Rate Analysis
The curves of the maximum load percentage–wave velocity change rate of the four strengths of concrete samples are shown in
Figure 7. According to the trend of the changes, the curve can be divided into four parts: strengthening (A–B), stabilizing (B–C), weakening (C–D), instability (D–E).
The strengthening section (A–B) of the curve ranges from 0% to 30% of the maximum load percentage. The coda wave velocity of the concrete sample shows a slowly increasing trend with increasing the load percentage, and the increased speed is negatively correlated with the load increase. This is because, in the early stage of loading, the internal cracks slowly close, making the internal microstructure denser. The stabilizing section (B–C) of the curve ranges from 30% to 50% of the maximum load percentage. The rate of change of the coda wave velocity of the C40 and C50 concrete specimens remained stable. The coda wave velocity changes of C60 and C70 concrete specimens first increase and then tend to be generally stable. It is speculated that within this range, the original microcracks in the concrete are further closed, and at the same time, the material particles are squeezed and elastically deformed. However, with the increase of pressure, the degree of development of internal microcracks may increase slightly. The range of the weakening section (C–D) is approximately 50% to 80% of the maximum load percentage. The wave velocity of the coda wave decreases with the increase of external load. At this time, the closed cracks inside the concrete begin to expand and secondary cracks are generated, causing the wave velocity to drop. The instability section (D–E) ranges from 80% to 100% of the maximum load percentage. In this interval, the coda wave velocities of the four strengths of concrete showed a rapid downward trend with the increase of the load, indicating that the scale of the internal cracks in the concrete continued to increase and gradually connected. Eventually, a macroscopic fracture surface will be formed.
This experiment comprised a coda wave test on a limited number of concrete samples. Due to the complexity and randomness of concrete materials, the relationship between the rate of change of coda wave velocity of uniaxially compressed concrete and its strength grade has not yet been clarified. To complete the research for this aspect, many tests of concretes of various strengths are still needed.
3.3. Coda Wave Velocity Change Rate Fitting
Piecewise linear fitting was performed on the coda wave velocity change curve of the abovementioned concrete uniaxial compression process. The fitting function expression is
, where
.
is the concrete load value,
is the concrete ultimate load value, and
is the ratio of the concrete load value to its ultimate load value; that is, the maximum load percentage. The notations
a and
b are constants. The curve fitting results of four kinds of concrete coda wave velocity change rates are shown in
Table 3. The fitting effect of C70 concrete is poor when the load level is in the range of 30–50% of the maximum load (R
2 = −0.10323). The data show a trend of increasing first and then decreasing. The poor fitting effect is mainly due to the large difference between the maximum value and the minimum value of the data in this group (the difference is equal to 0.00469). However, as shown in
Figure 7, the general trend in this section is the same as that of C60 concrete. It is speculated that the dispersion of the existing data is caused by the complexity of the test material and the deviations in the operating process.
Combined with
Table 3, a mathematical formula for concrete damage under uniaxial compression based on the rate of change in coda wave velocity is constructed:
In the above formula, is the slope of the fitted straight line for each interval. Considering the discreteness of individual data, the overall law of the experiment is , , , and . is a constant and depends on the strength of the concrete.
5. Discussion
In this paper, four types of concrete test blocks, namely C40, C50, C60, and C70, were tested under uniaxial compression to study the coda wave velocity changes during the damage process in concrete of different strengths. The stretching technique was used to analyze the ultrasonic coda signal of concrete with different strengths of concrete under uniaxial stepwise compression. Both the correlation coefficient and the rate of change of coda wave velocity can reflect the internal damage degree of concrete under load. According to the slope of the rate of change of coda wave velocity, the relationship curve between the rate of change of coda wave velocity and the percentage of maximum load during uniaxial compression can be divided into four sections: strengthening, stabilizing, weakening, and instability. The turning points of adjacent sections are 30%, 50%, and 80% of the maximum load percentage. A concrete damage fitting formula based on the relationship between the rate of change of the coda wave velocity and the percentage of the maximum load under uniaxial compression is established. The slope of the coda wave velocity change rate is greater than or close to 0, the internal microcracks in the concrete are closed, and the particles are squeezed and deformed. The slope of the coda wave velocity rate change between −1 and 0 indicates that the initial concrete cracks are propagating and new cracks are initiating and developing. When the slope of the coda wave velocity change rate is less than −1, the internal cracks of the concrete will be connected and link up, then the block will slide under the action of external force, causing macroscopic rupture. It is worth noting that within the scope of this study, no clear relationship between the ultrasonic coda wave signal characteristics of uniaxially compressed concrete and its intensity level was found. Due to the discrete nature of concrete materials, a lot of experimental research is still needed on this problem.
The simulation method is used to capture the whole process of uniaxial compression concrete damage and destruction. Damage cracks should first appear at the weak interface between aggregate and mortar. As the load increases, the original cracks and the new cracks that are generated continue to expand and connect. In the end, the concrete was severely damaged and its bearing capacity was lost, and the damage was in the form of double “C”-shaped macroscopic cracks. This method provides images of different degrees of damage for concrete ultrasonic field simulation. The digital image processing technology was used to extract aggregate, cement mortar, and crack information from concrete images of different degrees of damage. The concrete damage model established by processing grayscale images by threshold segmentation technology simulated the propagation of ultrasonic coda waves in concrete with different damage levels and quantitatively calculated the coda wave velocity change rate. The results show that the concrete wave velocity change rate obtained by the numerical simulation is consistent with the overall change trend obtained by the experiment, and the expected effect is achieved. Because the numerical modeling requires a lot of trial calculations and adjustment, within this research period, only the uniaxial compression simulation and the ultrasonic field simulation of the C40 concrete was completed. In the later stage, it is still necessary to optimize the numerical simulation, so as to realize the ultrasonic field numerical simulation of a large number of concrete damage processes using the above method and provide a database for related research.
Based on the perspective of correlating the characteristics of ultrasonic coda waves with the damage and failure process of concrete structures, only the compressive failure of pure concrete was studied in this work. However, in practical engineering, structural components are usually made of reinforced concrete, and the failure modes of components under different mechanical effects are complex. This study simplifies the research problem but can provide a basis for further research on the ultrasonic coda wave characteristics of reinforced concrete members under complex mechanics.
6. Conclusions
In this paper, a combination of tests and simulations is used to explore the ultrasonic coda wave characteristics of uniaxially compressed concrete. The main conclusions are as follows:
The ultrasonic coda signal is processed by the stretching technique. The cross-correlation coefficient and the relative change in coda wave velocity are very sensitive to small changes in the concrete. The regularity of the relationship between the change rate of the coda wave velocity and the percentage of the ultimate load is more significant than the cross-correlation coefficient.
According to the slope of the curve, the relationship curve between the concrete coda wave velocity change rate and the maximum load percentage is divided into four sections, namely strengthening (the slope is greater than 0), stabilizing (the slope is approximately equal to 0), weakening (the slope is between −1 and 0), and instability (the slope is less than −1). The internal damage changes of the concrete corresponding to the curves of the four sections are pore compaction, grain deformation, crack propagation, and block slip in sequence.
Using the PFC uniaxial compression simulation, the image of the internal damage development process of the concrete can be obtained, and the ultrasonic field simulation of the concrete damage and rupture process can be completed by further combining the image processing technology. The calculation results obtained by the above methods are in line with expectations. However, in the process of PFC modeling, it is necessary to perform trial calculation and calibration of multi-parameters to match the experimental results. Due to the uniqueness of concrete compression test results, the obtained damage rupture model (C40) is not suitable for simulating the compressive failure mode of concrete with various strengths. The modeling method of concrete compressive failure still needs to be further optimized.
The numerical simulation method of concrete ultrasonic coda wave characteristics established in this paper is conducive to the simulation calculations for many concretes and provides a feasible method for further obtaining a more accurate quantitative relationship between concrete damage degree and coda wave characteristics.