## 2 Early-Age Concrete
To show the overall trend of velocity change with age, all signals are stacked together to form an image with axes of signal time (horizontal) and concrete age (vertical), as shown in Figure 4. This method has been used by [PERSON] et al. [26; 27] to manually trace the P or S wave arrivals based on the trend of waveforms. It can be seen that the P wave arrival times (very early part before 0.09 ms) show very little change during the entire monitoring period, while the coda waves show a clear and measurable time shift with aging. The coda wave has a similar changing trend to the S wave but becomes more pronounced at a later time, and the coda wave signals still maintain a good correlation (clear trend) during the entire monitoring period. Figure 5 gives the calculated relative wave-velocity change between signals recorded at ages of 75 th hour and 80 th hour. A moving time window with a width of 0.1 ms and a step of 0.05 ms is used for stretching analysis. It can be seen that different time windows give the same \(dV/V\) results. The cross-correlation coefficient \(CC(\varepsilon_{max})\) calculated at each moving time window is above 0.99, which indicates a very weak distortion between these two signals. To study the window effect, the stretching method was applied to four time windows for all signals: P wave part, S wave part, coda wave part, and the full-length signal to measure the velocity change during concrete hydration. Figure 6 shows the relative velocity change calculated from the four time windows. All curves indicate that the wave velocities increase with the age of concrete. Similar results were obtained on the coda wave, full-length signals, and the S wave windowed signals. This result is consistent with the conclusions given by [PERSON] [28], and [PERSON] [6] that the S wave energy dominates the diffuse wave. P wave has a smaller \(dV/V\) than S wave, which supports conclusions from previous studies [29; 30; 31]: the relative S wave velocity increases faster than the P wave velocity during the early-age-cement-hydration stages. This phenomenon is related to the microstructure development in early concrete. Continued cement hydration contributes to the formation of the solid phase which increases the shear modulus and shear wave velocity, while the P wave velocity is affected to a lesser degree because the P wave can propagate in both the fluid and solid phases. Figure 4: Stacked ultrasonic signal image shows the trend of time shifts in early-age concrete. Figure 5: Relative velocity change calculated at different time window locations, between two signals collected at the 75 th and 80 th hours. It is well known that Poisson's ratio decreases when fresh concrete changes from a fluid-like state to a solid state. Although Poisson's ratio can be calculated from the ratio of \(V_{p}\) to \(V_{s}\), the very slow change of velocities after 24 h of concrete age will induce large errors in wave velocity measurements and Poisson's ratio calculation. At a very early age \(t_{0}\), the wave velocities (\(V_{p0},V_{s0}\)) can be measured with relatively small errors due to large travel times, and a reference Poisson's ratio \(\
u_{0}\) could be reliably determined. Then \(\
u_{1}\) at a later age can be calculated based on the relative velocity change in P wave and S wave using the following relationship (Equation (4)):  
\[\frac{1-\
u_{1}}{1-2\
u_{1}}=\frac{V_{p}^{2}}{2V_{s}^{2}}=\frac{(1+\Delta V_{p }/V_{p0})^{2}}{(1+\Delta V_{s}/V_{s0})^{2}}\frac{1-\
u_{0}}{1-2\
u_{0}} \tag{4}\]  
In this study, we used the P wave and S wave velocities at 30 h in the concrete cylinder as a reference, which were 4211 m/s and 2470 m/s. The Poisson's ratio is calculated as 0.238 using Equation (5)  
\[\
u=\frac{V_{p}^{2}-2V_{s}^{2}}{2\Big{(}V_{p}^{2}-V_{s}^{2}\Big{)}} \tag{5}\]  
Figure 6 also shows the development of Poisson's ratio with concrete age up to 5 days. The Poisson's ratio decreases from 0.238 at 30 h to 0.23 at 58 h and then stays constant.