## 5 Conclusions  
The stretching technique and CWI have been used to measure minor wave-velocity changes in concrete. Their high sensitivity has attracted much research interest in different NDE applications, including evaluation of microcracking damage, healing, stress estimation, temperature effects, etc. However, many researchers starting in this field are often confused about the interpretation of the CWI results. In this study, we present three experimental cases for application of the stretching technique: early-age hydration, temperature change, and uniaxial compressive loading. The first two cases cause homogeneous velocity change. Based on the experimental results, the following conclusions can be drawn:  
1. In very early-age concrete, the P and S wave arrivals can be easily determined using the first arrivals with little error; but after 24 h, the measurement error will increase when the wave arrivals become short and their changes become very slow. Using the P and S wave arrivals at a very early age as the reference values, the stretching technique can then be used to track the changes of wave velocities and Poisson's ratio with high accuracy after 24 h. Because the material property change is homogeneous, stretching analyses concerning the coda wave, the S wave, and the full-length signal give similar results. The stretching technique provides an easy solution to accurately monitor the S wave-velocity change in early-age concrete.
2. Uniform temperature change causes homogeneous velocity change in the concrete, so stretching analysis on the coda wave gives consistent results for different time windows. The P and S wave-velocity change can be calculated by applying the stretching procedure to P and S wave part signals only. If the signal does not show a clear S wave pulse, the S wave-velocity change may be derived from Equation (6). The relative velocity changes \(dV_{p}/V_{p}\) and \(dV_{s}/V_{s}\) due to temperature change can be used to calculate the third-order elastic constants in concrete [16].
3. Uniaxial compressive loading generates non-uniform strain field and velocity changes in concrete. Therefore, the stretching result of the coda wave varies with the window time and does not show directivity to the stress direction. This is because the diffuse wave has random propagation and polarity directions due to multiple scattering in the medium.
4. In order to measure acoustoelastic coefficients or third-order elastic constant using the uniaxial loading test, we must use direct P or S waves which maintain clear propagation and polarity direction. The direct waves give different \(dV/V\) along with the stressed (11) and non-stressed (22) directions. This property may be used to evaluate the stress level in large prestressed concrete structural members [20].  
Conceptualization, methodology B.Z. and J.Z.; software, formal analysis, resources, data curation, investigation, writing--original draft preparation B.Z.; writing--review and editing, supervision, funding acquisition, J.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Nebraska Department of Transportation (NDOT), United States.  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors would like to acknowledge the NDT-CE team members at the University of Nebraska-Lincoln for their help in preparing concrete specimens.  
The authors declare no conflict of interest.