A novel ultrasonic-velocity-based concrete carbonation monitoring method based on step-wise stretching technique

Abstract

Carbonation is a common and slow process that occurs in cement-based material, resulting in durability degradation of reinforced concrete structures. In this research, the relative velocity change (dv/v) of both ultrasonic direct waves and coda waves are extracted based on the step-wise stretching method for concrete carbonation monitoring. To this end, two-dimensional mesoscale models are established to investigate the ultrasonic propagation behaviors and assess the effectiveness of direct waves and coda waves on concrete carbonation monitoring. The numerical results indicate that direct waves could evaluate the initial carbonation, but exhibit limited sensitivity for severe carbonation. Conversely, the dv/v values of coda waves show a linear correlation with carbonation depth in all conditions. Accelerated concrete carbonation experiments are conducted to validate the numerical findings. The experimental results and numerical findings mutually corroborate, validating the effectiveness of velocity changes of coda waves on all-stage concrete carbonation monitoring. This research contributes a novel method for monitoring concrete carbonation and enhances the understanding of ultrasonic wave propagation in concrete.

Keywords

Concrete carbonation ultrasonic direct waves ultrasonic coda waves step-wise stretching technique ultrasonic velocity

Introduction

Carbonation is a widespread and slow chemical reaction in concrete involving the interaction of atmospheric carbon dioxide (CO₂) and hydration products.¹ Carbonation reduces the pH value of concrete,² which will destroy the passivating film around the steel bar and trigger the corrosion process once the carbonation front reaches the steel bar.³ Concrete carbonation is significant for predicting the remaining service life of reinforced concrete structures,⁴ especially for the infrastructures exposed to high-concentration CO₂ (e.g., tunnels and industrial plants).⁵ Therefore, it is necessary to monitor concrete carbonation.

The most widely used concrete carbonation assessment approach is phenolphthalein indicator, which relies on a pH threshold of 10 to distinguish carbonated and non-carbonated concrete. This method is hard to measure the semi-carbonation zone with a pH range of 10–13 and underestimates the carbonation depth.^6–8 Moreover, the phenolphthalein testing method is destructive to structures and suspected to be carcinogenic to operators.⁹ Empirical prediction models¹⁰ have been developed to estimate carbonation depth by leveraging water cement (w/c) ratio and service time. However, the predicting results may be inaccurate because a simple mathematical model cannot consider the complex external factors, such as harsh service environment and poor construction quality.

Global vibration characteristics (frequency, mode shape, and damping) have been widely used for structural condition monitoring,¹¹ but suffer from low sensitivity to small damages.¹² The acoustic emission (AE) technique, as a sensitive and non-destructive testing method,¹³ relies on the stress waves generated by the material fracture events,^14,15 while the concrete carbonation is a slow process involving the absorption of CO₂ rather than the material fracture. Consequently, the AE technique faces challenges to monitor concrete carbonation.

Nonlinear ultrasonic methods have shown the strength in monitoring concrete carbonation because of the high sensitivity to minor damages. Bouchaala et al.¹⁶ utilized the nonlinear resonant acoustic spectroscopy (NRUS) technique to assess concrete carbonation. The results revealed a substantial 300% increase in nonlinear parameters, while the linear indicator exhibited a mere 5% increment. However, the NRUS technique may be impractical for large-scale concrete structures because it requires resonance of the entire structure. Kim et al.¹⁷ utilized nonlinear Rayleigh surface wave to evaluate concrete carbonation, and the results showed that this method was very sensitive to carbonation. Nevertheless, the inspection range of Rayleigh wave is inherently limited by the effective penetration depth, which is approximately one wavelength. Consequently, nonlinear parameters will lose the sensing capacity once the carbonation depth exceeds the effective penetration depth of Rayleigh wave. Additionally, the formation of Rayleigh wave requires the structure’s depth to be more than twice the effective penetration depth.¹⁸ This implies that the inspection depth using Rayleigh wave-based methods cannot be indefinitely increased by lowering the excitation frequency in a specific structure. Moreover, the explicit relation between the nonlinear parameters^16,17 and carbonation depth has not yet to be established, which impedes nonlinear ultrasonic methods for predicting the remaining carbonation service life of concrete structures.

The classical ultrasonic pulse velocity (UPV) method, relying on the velocity of transmitting waves, has been explored to evaluate concrete carbonation.^19,20 The results in research¹⁹ demonstrated that UPV values fluctuated in the initial stages and increased in late stages of carbonation. Another study²⁰ concluded that the UPV technique may be challenging for carbonation evaluation. The disparate results in the two studies^19,20 arise from the low resolution of UPV technique to carbonation. In recent years, direct wave interferometry (DWI)^21,22 was proposed to the improve the resolution of direct wave to small changes by using the stretching method to extract the relative velocity changes.

Other than the direct-wave-based method, coda wave techniques employ the late-arriving wave packets for damage detection and condition monitoring.^23–25 Coda waves contain rich information about the medium.^26,27 First, numerous sampling events though the long propagation trajectories confer coda waves with high sensitivity to subtle changes.^28,29 Second, the waves from various directions endow coda waves with a large sensing range, enabling coda wave techniques to detect concrete carbonation beyond the transducer path.³⁰ The classical coda wave interferometry (CWI) method^31–37 computes dv/v by utilizing a fixed reference signal that is obtained at the beginning of measurement.^37,38

In recent years, the step-wise stretching method using moving reference signal has been employed to solve the difficulty of CWI in analyzing signals with severe changes.^39,40 Then, the proposed step-wise coda wave interferometry (SCWI) method was adopted for condition monitoring of concrete structures⁴¹ because of the high sensitivity to subtle changes and stability to large variations. Meanwhile, the step-wise stretching method also possesses the robustness to external disturbances because of the flexibility in selecting the reference signal.

In this study, the step-wise stretching method is applied on both direct waves and coda waves to extract carbonation-induced ultrasonic velocity changes. Two-dimensional mesoscale concrete models are established to investigate the wave propagation behaviors and assess the performances of direct waves and coda waves on concrete carbonation monitoring. The scattering effect of aggregates on ultrasonic waves extends the sensing range of direct waves beyond the direct depth, thus allowing early-stage carbonation assessment using direct waves. However, the surface-concentrated feature limits direct waves for severe carbonation evaluation. On the other hand, the linear relationship between dv/v of coda waves and carbonation depth is observed in all-stage carbonation. The dv/v of coda waves is inferred to be proportional to the square root of carbonation time based on the numerical results and classical concrete carbonation model.^42,43 Subsequently, accelerated carbonation experiments are conducted to validate the numerical results and findings. The flowchart of this study is shown in Figure 1. This research contributes a novel coda-wave method for all-stage concrete carbonation monitoring in a non-destructive and real-time manner and enhances the understanding of ultrasonic wave propagation behaviors in concrete.

Ultrasonic propagation mechanism and signal processing method

Ultrasonic waves in carbonated concrete

Concrete carbonation initials from structural surface and develops along the depth direction, resulting in the enhancement of the mechanical characteristics of concrete and the subsequent alteration of ultrasonic waves. The ultrasonic waves would be scattered and reflected by the aggregates and boundaries in concrete,⁴⁴ as shown in Figure 2. According to the path summation theory of ultrasonic waves, the waveform in a location of the wave field could be expressed as:

u (t) = \sum S_{p} (t)

(1)

where p represents all possible paths including direct wave and scattered waves. Direct waves are the first arrivals in the recorded waveform, which contains the waves propagating along the direct path between transducers and the waves scattered by the aggregates near the surface. Coda waves are the late-arrival wave packets consisted with multiple scattered and reflected waves. When a perturbation, τ_p, occurred in the medium, the perturbed wave field u_p(t) could be expressed as:

u_{p} (t) = \sum_{p} S_{p} (t - τ_{p}) .

(2)

The ultrasonic waves propagating through the carbonated area would be altered. Ultrasonic velocity directly correlates with the elastic properties and density of the inspected structures.⁴⁵ Hence, the ultrasonic velocity changes of both direct waves and coda waves are explored to monitor the concrete carbonation.

Step-wise stretching method

The fundamental of the stretching method to calculate dv/v of ultrasonic waves is that the signal is uniformly stretched or compressed by the changes of the medium. The perturbed signal is stretched to achieve maximal alignment with the reference signal at a selected time window. The cross correlation coefficient, CC(ε), between the stretched signal u_p(t(1+ε)) and the reference signal u_r(t) is calculated:

CC (ε) = \frac{\int_{t_{1}}^{t_{2}} u_{r} (t) u_{p} (t (1 + ε)) d t}{\sqrt{\int_{t_{1}}^{t_{2}} u_{r}^{2} (t) d t \int_{t - T}^{t + T} u_{p}^{2} (t (1 + ε)) d t}}

(3)

where ε is the stretching factor, u_r(t) is the reference signal, u_p is the perturbed signal, and u_p(t(1+ε)) is the perturbed signal after stretching. t₁ and t₂ determine the time window for stretching operation. The stretching factor ε_max maximizing the cross-correlation coefficient is regarded as dv/v:

ε_{max} = d v / v .

(4)

The residual decorrelation coefficient (DC), which can be used to assess the efficiency of extracting dv/v values, can be calculated based on the CC(ε_max):

DC = 1 - CC (ε_{\max}) .

(5)

The time window containing only direct waves corresponds to DWI analysis. While the selection of time window for CWI analysis should satisfy two criteria: (1) the start point should be sufficiently late to ensure long-distance propagation of coda waves and (2) the end point should ensure reasonable signal quality.^46,47 It has also pointed out that the long time window is beneficial for CWI to simplify data processing procedures³⁰ and obtain reliable results.⁴⁸ The CWI and DWI have their own superiorities⁴⁹ and should to be selected or combined carefully by considering the specific applications. A demonstration of the stretching operation on the direct waves of two signals is shown in Figure 3.

The stretching method based on the fixed reference signal may fail to extract the real dv/v value if the signal undergoes critical phase shift. Niederleithinger et al.³⁹ and Wang et al.⁴⁰ innovatively proposed the SCWI technique based on the step-wise stretching method to address the limitation of CWI on critical changes. The step-wise stretching method decomposes the significant changes into multiple processes, and the stretching factor describing dv/v in each step could be expressed as follows:

\begin{matrix} ε_{1} = \frac{v_{1} - v_{0}}{v_{1}}, ε_{2} = \frac{v_{2} - v_{1}}{v_{2}}, \cdot \cdot \cdot, ε_{i} = \frac{v_{i} - v_{i - 1}}{v_{i}} \cdot \cdot \cdot, \\ ε_{n} = \frac{v_{n} - v_{n - 1}}{v_{n}} . \end{matrix}

(6)

Based on Equation (6), it could be obtained that

\begin{matrix} 1 - ε_{1} = \frac{v_{0}}{v_{1}}, 1 - ε_{2} = \frac{v_{1}}{v_{2}}, \cdot \cdot \cdot, \\ 1 - ε_{i} = \frac{v_{i - 1}}{v_{i}} \cdot \cdot \cdot, 1 - ε_{n} = \frac{v_{n - 1}}{v_{n}} . \end{matrix}

(7)

By multiplying the above expression, the following equation can be obtained:

(1 - ε_{1}) (1 - ε_{2}) \cdot \cdot \cdot (1 - ε_{i}) \cdot \cdot \cdot (1 - ε_{n}) = \frac{v_{0}}{v_{n}} .

(8)

Inverting Equation (8), we obtain

\frac{v_{n}}{v_{0}} = \frac{1}{(1 - ε_{1})} • \frac{1}{(1 - ε_{2})} • \cdot \cdot \cdot • \frac{1}{(1 - ε_{i})} • \cdot \cdot \cdot \frac{1}{(1 - ε_{n})} .

(9)

The overall dv/v could be obtained by using the stretching factors in each step:

\begin{matrix} d v / v = \frac{v_{n} - v_{0}}{v_{0}} \\ = [\frac{1}{(1 - ε_{1})} • \frac{1}{(1 - ε_{2})} • \dots \frac{1}{(1 - ε_{i})} • \dots • \frac{1}{(1 - ε_{n})}] - 1 . \end{matrix}

(10)

The step-wise stretching method also possesses the robustness to disturbances. Assuming that the disturbance occurs in the i-th step of the long-term monitoring of real concrete structures, the short-term event may lead to large variation of stretching factor, ε_i, and overshadow the slow and minor wave velocity change induced by carbonation. Correcting the stretching coefficient in the i-th step as zero is necessary to eliminate the influences of the disturbances on the velocity changes. The correction could be expressed as

\begin{matrix} d v / v = [\frac{1}{(1 - ε_{1})} • \cdot \cdot \cdot • \frac{1}{(1 - ε_{i - 1})} • \frac{1}{(1 - 0)} \\ • \frac{1}{(1 - ε_{i + 1})} • \cdot \cdot \cdot • \frac{1}{(1 - ε_{n})}] - 1 . \end{matrix}

(11)

The correction operation may lead to the underestimation of ultrasonic velocity changes induced by carbonation. For concrete carbonation characterized by extended durations spanning several years to even decades, dv/v caused by carbonation within one measurement interval (e.g., several days or 1 week) is minuscule. Therefore, the correction scheme is suitable to enhance the robustness of the ultrasonic-velocity-based long-term concrete carbonation monitoring.

Numerical study

To investigate ultrasonic wave propagation behaviors in concrete and assess the performances of direct waves and coda waves on concrete carbonation monitoring, two-dimensional mesoscale models considering the heterogeneity of concrete are established using the finite-element (FE) method.

2-D mesoscale modeling

The aggregates in concrete are usually polygonal, and the spherical shape is utilized in this study for convenience. The 3-D simulation of ultrasonic wave propagation in concrete at mesoscopic level requires substantial number of elements, resulting in significant consumption of computing time and memory. Many studies have demonstrated the accuracy and efficiency of 2-D mesoscale model as an alternative to a 3-D model for ultrasonic wave simulation.^50,51 Therefore, a 2-D mesoscale concrete model is established for exploring wave propagation behavior in carbonated concrete. The aggregate gradation is determined by the Walraven formula as follows:

\begin{matrix} P (D < D_{0}) = P_{k} \\ [\begin{matrix} 1.065 {(\frac{D_{0}}{D_{max}})}^{0.5} - 0.053 {(\frac{D_{0}}{D_{max}})}^{4} \\ - 0.012 {(\frac{D_{0}}{D_{max}})}^{6} - 0.0045 {(\frac{D_{0}}{D_{max}})}^{8} + 0.0025 {(\frac{D_{0}}{D_{max}})}^{10} \end{matrix}] \end{matrix}

(12)

where P(D < D₀) is the cumulative volume percentage of the aggregates with the diameters smaller than the sieve D₀ in the cross section, and P_k is the ratio of the volume of all aggregates and the whole concrete specimen. D₀ and D_max are the diameters of the target and maximum aggregates, respectively.

In this research, the dimension of the 2-D mesoscale model is 100 × 300 mm. Without loss of generality, the diameters of aggregates are randomly distributed in four grade ranges. 1–5, 5–10, 10–15, and 15–20 mm corresponds for very fine, fine, middle, and large stone, respectively. The total aggregate ratio is set as 50%, and diameter distribution of generated aggregates is shown Table 1. The mesoscale model is established using commercial FE software, ABAQUS.

Table 1.

Diameter distribution of generated aggregates.

Diameter range (mm)	1–5	5–10	10–15	15–20
Ratio	0.147	0.108	0.076	0.045

The intricate concrete carbonation process is simplified by enhancing the elastic modulus and density of the carbonated mortar, while preserving the properties of non-carbonated mortar and aggregates. The material properties are set based on the results from Refs.,^52–54 and presented in Table 2. As illustrated in Figure 4, Carbonation depth is defined as the depth of mortar with improved density and modulus. Carbonation depths increase from 0 to 70 mm in the step of 5 mm to simulate the concrete carbonation process. The global and local mesh of the mesoscale model is shown in Figure 5. The mesh type is CPS4R and mesh size is set as 1 mm.

Table 2.

Material properties of the finite-element models.

Material	Density(kg/m³)	Elasticmodulus(GPa)	Poisson’sratio
Non-carbonated mortar	2100	26	0.22
Carbonated mortar	2300	30.16	0.22
Aggregate	2700	55.5	0.17

Considering the near-surface characteristic of concrete carbonation and the practicality of surface-installed transducer in field applications, the excitation is applied in the surface to activate ultrasonic waves. The main focus is investigating the propagation behaviors of bulk wave and Rayleigh waves, and the out-plane⁵⁵ rather than the in-plane excitation⁵⁶ is utilized in the model, as shown in Figure 4. The frequency range of 50–150 kHz, locating in the simple scattering regime, is demonstrated to be suitable for damage detection in concrete.⁵⁷ Considering the gradual process of concrete carbonation, the frequency of 150 kHz is selected in this study to enhance the sensitivity to carbonation. Therefore, the 5-cycle sinusoidal signal modulated by Hanning window with central frequency of 150 kHz is adopted as excitation signal, as shown in Figure 6. The vertical displacement in the receiving point is obtained for analysis. The time increment of the simulation is set as 0.5 μs. The free boundary condition that permits wave reflections is employed to maintain consistency with the laboratory tests. The duration of FE simulation is set as 1500 μs to obtain sufficiently long coda waves.

Numerical results

To preliminarily compare the performances of direct waves and coda waves on carbonation monitoring, the simulated signals in the initial carbonation stage and severe carbonation stage are shown in Figures 7 and 8. Figure 7 shows that both the direct waves (0.05–0.08 ms) and coda waves (0.77–0.81 ms) undergo significant shifts as the carbonation depth develops from 0 to 5 mm. When the carbonation depth increases from 45 to 50 mm, the direct waves (0.05–0.08 ms) are quite similar, while that of coda waves (0.75–0.775 ms) still manifests substantial differences, as shown in Figure 8.

The disparate performances of direct waves and coda waves can be attributed to the differences in sensing range. The direct wave is confined to the vicinity of the direct path between the transducers, impeding direct waves for severe carbonation detection. Coda waves encompass cumulative information carried by multiple scattered and reflected waves from various directions, endowing coda waves with the capability to monitor severe carbonation.

Step-wise DWI analysis results

The step-wise stretching method is employed to analyze the direct waves and is referred to step-wise direct wave interferometry (SDWI). The dv/v and DC values of direct waves (0.05–0.08 ms) calculated by SDWI are shown in Figure 9. Direct waves propagate though the vicinity of direct path between transducer and sample the concrete few times, resulting in the low DC values. The largest DC value is observed in the 5-mm carbonation condition, which is attributed to the heightened sensitivity of direct waves to the shallow defects. The dv/v values increase with carbonation depth in initial stages, but tend to stabilize after the carbonation depth exceeds 45 mm. The results indicate that direct waves possess a sensing range of 45 mm along the depth direction, which would be unexpectedly wide for direct waves concentrating on the direct path between transducers.

To provide further clarification regarding this phenomenon, the simulated wave field represented by resultant displacement in the mesoscale model at 0.05 ms is presented in Figure 10. The arrows in Figure 10 indicate the direction of the resultant displacements in different locations, providing insights into the wave propagation behaviors influenced by the presence of aggregates. The P wave, shear wave (S wave), and Rayleigh wave could be identified because of the different vibration modes and velocities. P wave is the first to reach the receiving point, giving rise to the direct waves in the recorded signals. The aggregates alter particle motion direction of P wave, allowing the receiver at the surface to capture the P waves originating from deep area. This phenomenon contributes a relatively wide sensing range along the depth direction. However, the short propagation path still limits the sensing range of direct wave near the surface, which may be overcame by using the coda waves in the recorded signals.

SCWI analysis results

The start point of time window analysis is designated at 0.25 ms to ensure the sufficient scattering events of coda waves. And the end point is set as 1.5 ms by making the trade-off between the sensitivity and signal-to-noise ratio.⁵⁸ The dv/v and DC values of coda waves (0.25–1.5 ms) calculated by SCWI are shown in Figure 11. The dv/v values display an ascending trend with the increase of carbonation depth, indicating the efficiency of coda waves on concrete carbonation monitoring. Moreover, the dv/v values exhibit an almost linear relation with carbonation depth, denoted as D. The coefficients are about 0.00023, and the corresponding R-square value is more than 0.99. Based on those results, the relation between dv/v of coda waves and carbonation depth could be expressed as:

d v / v = k_{1} D

(13)

where k₁ is the coefficient linking dv/v and carbonation depth. However, the accurate carbonation depth may be challenging to be obtained in the laboratory tests, which may impede the validation of the numerical findings though accelerated carbonation experiments. The carbonation depth is well known to be proportional to the square root of carbonation time according to the classical concrete carbonation model^59,60:

D = k \sqrt{t}

(14)

where k is the carbonation coefficient and t is the carbonation time. Therefore, the following relation among dv/v, carbonation depth, and carbonation time is inferred:

d v / v = k_{1} D = k_{1} (k \sqrt{t}) = k_{2} \sqrt{t}

(15)

where k₂ is the coefficients that correlate dv/v with the square root of carbonation time. Then, the numerical findings described in Equation (12) could be validated by using the relation between dv/v of coda waves and carbonation time in the laboratory experiments.

The coda waves manifest higher DC values than direct waves, which is caused by the accumulated defect information in the coda waves.^61,62 Elevated DC values of coda waves are particularly observed at the carbonation depth of 10 mm. The wave field in mesoscale model at 1.05 ms is shown in Figure 12. The wave field represented by resultant displacement exhibits a very complicated presentation, while the Rayleigh waves could be identified at the surface with remarkable vertical displacement. The other components in the wave field are the multiple scattered P and S waves. The receiver at the surface could receive all the three kinds of waves, and the performances of coda waves could be explained by the features of the three basic components. In concrete, Rayleigh waves with frequency of 150 kHz have a penetration depth of about 13 mm. Once the carbonation depth exceeds the effective penetrative depth, the Rayleigh wave components lose the sensing ability. Therefore, the DC value is largest in the depth of 10 mm and become smaller when the value is larger than 15 mm. The multiple scattered P and S waves from deep locations could also be received by the receiver in the surface, giving rise to the coda part in the recorded signals. These multiple scattered waves from deep area enable the coda waves to have a wider sensing range and an enhanced capacity for severe carbonation monitoring.

Experimental study

Numerical results have provided insights into the wave propagation behaviors in concrete and established the relations among dv/v of coda waves, carbonation depth, and carbonation time. To validate the numerical results, ultrasonic measurements are implemented on concrete prism subjected to accelerated carbonation.

Experimental setup

Prism specimen with dimension of 100 × 100 × 300 mm is cast for accelerated carbonation testing.⁵⁹ The w/c is 0.6 and detailed mixture proportions are listed in Table 3. Specimens are cured for 28 days, and dries in drying chamber (60°C) for 2 days before accelerated carbonation. One-dimensional penetration of CO₂ is achieved by sealing five surfaces of specimens with epoxy resin. Then, the specimens are placed into the accelerated carbonation chamber with CO₂ concentration of 20%, relative humidity of 70%, and temperature of 20°C. Ultrasonic measurements are conducted every 2 days by keeping the specimen in the chamber to maintain the consistent conditions. The overall experimental setup is shown in Figure 13(a).

Table 3.

Concrete mixture proportion (kg/m³).

w/c	Water	Cement	Coarse aggregate	Fine aggregate
0.60	197.33	327.92	1152.54	706.39

The excitation signal with a frequency of 150 kHz, as shown in Figure 6, is generated by the data acquisition (DAQ) system (SC-HY-PZT-2.0; Sanchuan Inc., Jiangsu, China) to activate ultrasonic actuator. Ultrasonic signals received by the sensor are amplified 40 dB by a pre-amplifier and sent to the DAQ system, as shown in Figure 13(b). The sampling frequency is 2 MHz. By considering the practicability in field applications, the ultrasonic transducers encapsulated by the mixture of epoxy and cement power⁶³ are installed on the exposed surface of the specimen to generate and receive ultrasonic waves. The distance between the transducers is 200 mm, as shown in Figure 13(c).

Experimental results

Phenolphthalein testing results

Phenolphthalein testing is conducted in the final stage to intuitively demonstrate the carbonation process. As shown in Figure 14, phenolphthalein testing results show that the specimen are carbonated along the depth direction after the accelerated carbonation experiment. However, this method is destructive to structures, and the carbonation degree is often underestimated because of the limited pH sensing range of phenolphthalein indicator.^6–8

Time-domain waveform analysis results

The experimentally measured signals in early-stage and late-stage carbonation conditions are shown in Figures 15 and 16. Both the direct waves (0.07–0.11 ms) and representative segment of coda waves (0.62–0.69 ms) are shifted forward after the first 2-day carbonation. The changing degree of direct waves after the first 2-day accelerated carbonation is not as pronounced as the simulation presented in Figure 7. The reason is that the 2-day accelerated carbonation may not result in the 5-mm carbonation depth.

When comparing the signals obtained from 28- and 30-day carbonation condition, the direct waves (0.06–0.011 ms) are quite similar, while the representative segment of coda waves (0.72–0.77 ms) still exhibit notable differences, as shown in Figure 16. This phenomenon demonstrates that the carbonation depth has exceeded the sensing range of direct waves, while coda waves remain capable of detecting carbonation. It is noted that the waveform shifting degree in the coda waves of the late-stage carbonation (Figure 16) is not as significant as the changes observed in the initial carbonation (Figure 15). The reason is that concrete carbonation increases fast in the beginning and develops slowly in the late-stage carbonation according to classical carbonation model.^59,60

SDWI analysis results

The dv/v and DC values of direct waves (0.06–0.011 ms) calculated by SDWI are shown in Figure 17. Both the dv/v and DC in day 24 exhibit abnormal changes, as shown in Figure 17(a). The reason is that the air conditioning system of the carbonation chamber malfunctioned in day 23 and the temperature reached about 50°C. The chamber malfunction lasted about 10 h, which may lead to irreversible variations of both concrete and bonding layer of transducers. The sudden decrease of dv/v caused by the chamber malfunction in this step overshadows the slow and minor velocity change induced by carbonation. The errors caused by the disturbed interval (day 22–24) are eliminated by correcting the stretching factor as zero, according to Equation (11). As shown in Figure 17(b), the corrected dv/v values increase with carbonation in initial stages, while tend to be stable after 26-day carbonation. This changing pattern aligns with numerical results, underscoring the sensing capacity of direct waves in early-stage carbonation and the limitation for severe carbonation conditions.

SCWI analysis results

The correction operation is also conducted on the coda waves to remove the negative influence of chamber malfunction on carbonation monitoring. And the corrected dv/v and DC values of coda waves (0.25–1 ms) are shown in Figure 18. The DC values of coda waves are larger than the counterparts of direct waves because of the accumulation defect information in the late-arrival wave packets.

The dv/v values generally exhibit increasing trend in the whole carbonation process, demonstrating the sensing capacity of coda waves for all-stage concrete carbonation monitoring. To validate the inference described in Equation (14), curve fitting is applied to the dv/v data in Figure 18. Although the R-square value is smaller than the corresponding one in Figure 11 causing by the measuring noises in experiments, the results support the reasonability of the inference that dv/v is proportional to the square root of accelerated carbonation time. The results validate the accuracy of the numerical results and findings and demonstrate that it is promising to monitor and predict the concrete carbonation by calibrating the coefficient, k₂, for a specific concrete structures.

To substantiate the accuracy of the findings of this research, the relations between carbonation depth and accelerated carbonation time of different kinds of concrete from Liu et al.⁶⁴ are shown in Figure 19. Carbonation depth is observed to follow a power function in relation to the accelerated carbonation time, with an index of approximately 0.493. The correlation in Figure 19 aligns congruently with the dv/v-accelerated carbonation time depicted in Figure 18, which further demonstrates the potential and applicability of the SCWI method for concrete carbonation monitoring and prediction.

Discussions

The low sensitivity of UPV to concrete carbonation primarily stems from the low resolution of velocity extraction method and the errors introduced by the transducer re-installation during the measurements. The sensitivity of direct waves to concrete carbonation has been notably enhanced by employing the fixed transducers and the step-wise stretching method for extracting the relative velocity changes. This advancement allows direct waves to assess the initial carbonation. However, the efficacy is curtailed when addressing severe carbonation due to the surface-concentrated characteristic of direct waves. Conversely, coda waves, benefiting from a broader sensing range and heightened sensitivity, could monitor the all-stage concrete carbonation. Furthermore, the step-wise stretching method enhances the robustness of coda waves against severe changes and external disturbances. Consequently, the combination of coda waves and step-wise stretching method enables the comprehensive monitoring of concrete carbonation monitoring at all stages.

The performances of direct and coda waves to the incipient and severe damages are different from the results in our earlier work.⁵⁸ The main reason of the differences is the different wave propagation behaviors. The direct waves and coda waves are guided inside the waveguide,⁵⁸ which would reverberate in the rebar and repeatedly sample the damage until the waves are fully attenuated. Therefore, the sensitivity and robustness are highly related to the position in the recorded waveforms (i.e., direct and coda waves). In this research, the direct waves are the P wave concentrating near the surface, and the coda waves are the superposition of the multiple-scattered P and S waves and the Rayleigh waves. Therefore, the appropriate utilization of ultrasonic direct waves and coda waves for damage detection and condition monitoring require the deep understand of wave propagation behavior in different applications.

The long-term carbonation monitoring poses a challenge to the sustained functionality of the transducers. This study has utilized the epoxy-cement mixture protected transducer⁶³ to address the requirement. However, the long-term performance of the ultrasonic transducers needs to be verified in the future work. Regarding the issue of bonding layer deterioration, Sun et al.⁴⁹ implemented a strategy of reinstalling the transducers to achieve ultrasonic-based long-term alkali-silica monitoring of concrete. The disturbances from sensor reinstallation could be eliminated by using the step-wise stretching method in this research. Temperature variations, particularly in field applications with strong ambient changes, exert a considerable influence on ultrasonic wave velocity-based carbonation monitoring. Temperature compensation techniques^65,66,67 will be explored on SCWI-based carbonation monitoring in the future work. The present study has established a proportional relationship between dv/v and both carbonation depth and square root of the accelerated carbonation time. It is essential to calibrate the corresponding coefficient for varied concrete structures with different mixture. Once the coefficients are calibrated, the concrete carbonation monitoring and prediction could be achieved using the proposed method.

Conclusions

In this study, the relative velocity changes of ultrasonic direct waves and coda waves extracted by the step-wise stretching method are innovatively introduced for concrete carbonation monitoring. Numerical simulations are utilized to investigate the performances of SDWI and SCWI on concrete carbonation monitoring and facilitate the understanding of ultrasonic wave propagation behaviors in concrete. Then, accelerated carbonation experiments are conducted to validate the numerical results and findings. The main conclusions of this study are as follows:

The scattering effect of aggregates on ultrasonic waves endows the direct waves sensing capacity beyond the direct path on the concrete surface, thereby facilitating the evaluation of initial concrete carbonation. However, direct waves exhibit very low sensitivity to severe carbonation because of the limited sensing range.

The dv/v of coda waves obtained from SCWI shows linear relation with the carbonation depth in numerical simulations, supporting the inference that dv/v is proportional to the square root of carbonation time based on the classical carbonation model. The inference is further validated through accelerated carbonation experiments, reinforcing the confidence in the accuracy and reliability of both numerical and experimental results.

The SCWI technique possesses the robustness to external disturbance and could be utilized for long-term concrete carbonation monitoring in non-destructive and real-time manner. The established relation between dv/v and carbonation degree helps to predict the service life of carbonated concrete structures.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors sincerely acknowledge the support from National Natural Science Foundation of China (Grant Number: 52020105005) and Shanghai Rising-Star Program of China (Grant Number: 23QA1409600).

ORCID iD

Qingzhao Kong

Data availability

Data will be made available on request.

References

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