## 5 Conclusions  
In this paper, the second-harmonic generation technology of longitudinal waves and the ultrasonic penetration detection method were used to measure the non-linear carbonation parameters of concrete with two different water-cement ratios and moisture content as well as different ultrasonic incident frequencies during the carbonation process. Although the non-linear parameters in this study are relative, the applicability of the SHG technology of longitudinal waves to quantitatively assess carbonated concrete is verified. The following conclusions are drawn from the experiments:  
Figure 11: Variation ratio of nonlinearity parameters of CI, CII, and CI-W.  
Figure 12: Non-linear parameters versus carbonation progress.  
* The non-linear parameters of ultrasonic waves with frequencies of 75 kHz and 100 kHz are larger than the frequency of 50 kHz. This indicates that the smaller wavelength (higher frequency) of the longitudinal wave has a better resolution to the relative non-linear parameters of carbonated concrete.
* The dryness and humidity of concrete CI also affect the relative non-linear parameters. However, the rates of change (CI: 62.73%, CI-W: 60.25%, carbonation depth: 15 mm) for the non-linear parameters before and after carbonation are similar for the two moisture content samples.
* The relative non-linear parameters for the two specimens with different water-cement ratios vary significantly during the carbonation process. In this study, CII (\(w/c=0.53\)) has a higher initial relative non-linear parameter than CI (\(w/c=0.47\)). The carbonation progress of concrete can be well reflected by changes in the relative non-linear parameters. The relative non-linear parameters decrease with the carbonation depth (the completely carbonated zone).
* Although the water-cement ratio, moisture content of concrete, and ultrasonic frequency are different in this study, there exists a relationship between the relative non-linear parameters of longitudinal waves and the concrete carbonation process. This demonstrates the feasibility of quantitative assessment in concrete carbonation with the relative non-linear parameters of longitudinal waves. Based on this, further studies of quantitative assessment in different types of concrete could be undertaken to identify a common relationship.  
When a non-linear ultrasonic longitudinal wave is used to evaluate concrete carbonation, the selection of signal frequency, waveform, excitation power, and ultrasonic transmission distance can affect the magnitude of non-linear parameters. Depending on the transmission distance of ultrasound in the concrete, suitable ultrasound parameters will be selected to detect changes in the non-linear parameters during the carbonation process. Considerably more work needs to be conducted considering various factors (temperature, humidity, attenuation, etc.) to determine a common relationship between the quantitative measurements of carbonation depth for different concretes and the non-linear parameters of longitudinal ultrasound.  
Conceptualization, J.Z., K.C., J.W.; methodology, J.Z., K.C.; software, J.Z., K.C.; writing--original draft preparation, J.Z. and J.W.; writing--review and editing, J.Z., J.W. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Thank you to [PERSON] and [PERSON] for their assistance in revising the language.  
The authors declare no conflict of interest.