## 4 Concrete Subject to Uniaxial Stress
Only the results from the first loading cycle are presented because the three loading cycles give similar results. The relative velocity change \(dV_{11}/V_{11}\) of the P wave in the parallel direction shows the highest sensitivity (0.268%/MPa) to stress change when the wave propagation and polarization directions align with the stress direction. P wave velocity has the least sensitivity in the transverse direction (\(dV_{22}/V_{22}=0.023\%\)/MPa). These results agree with previous findings by other researchers [37; 38]. However, if the full-length signals were analyzed, the acoustoelastic coefficients calculated from both directions would become very close (0.121%/MPa and 0.105%/MPa). The P wave velocity in the transverse direction was expected to decrease with stress owing to [PERSON]'s effect, but it increased in the uniaxial loading experiment. This behavior was also observed in other studies [37]. The authors believe this phenomenon was caused by the circumferential restraint due to end zone friction when the concrete cylinder is under compression [39; 40]. Figure 12: Zero-cross images of ultrasonic signals show time shifts in the parallel direction and transverse direction with uniaxial stress change. The horizontal axis represents signal time, and the vertical axis represents load steps for a duration of 40 min, with corresponding stress on the left. (**a**) Parallel direction; (**b**) Transverse direction. To investigate the time window effects on measurements of acoustoelastic coefficients, a moving time window with a width of 0.2 ms was used for stretching technique analysis. The center time of the window moved from 0.1 ms to 1.5 ms. Figure 14 summarizes the calculated acoustoelastic coefficients in both directions using different time windows. For a time window before 0.25 ms, the acoustoelastic coefficients measured in two directions have a clear difference, and \(\alpha_{11}\) in the parallel direction is larger than \(\alpha_{22}\) in the transverse direction. After 0.25 ms, which is more than ten times the first arrival time (0.015 to 0.02 ms), the calculated acoustoelastic coefficients in both directions become very close. This indicates that the coda wave does not show directivity toward the stress direction. Although the coda wave velocity still increases with stress level (positive \(\alpha\)), which is similar to the full-length signal result in Figure 13, the \(\alpha\) value measured from the coda wave or full-length signal is different from \(\alpha_{11}\) and any acoustoelastic coefficient \(\alpha_{ij}\) in Equation (7). Compared to the concrete hydration and temperature change experiments, the relative velocity change due to uniaxial loading shows more variation. Weak anisotropy caused by the uniaxial stress results in non-uniform strain and wave-velocity changes in different time windows. In a uniaxial experiment on a concrete cylinder, [PERSON] et al. [12] also noticed large fluctuations of CWI calculated \(dV/V\) with window positions. [PERSON] et al. [37], [PERSON] and [PERSON] [38] reported that the acoustoelastic effect was the most significant when the wave propagated and polarized in the stress direction. Figure 14: Calculated acoustoelastic coefficients in two directions at different time windows. The window center moves from 0.1 ms to 1.5 ms with a window width of 0.2 ms. The first data point represents the stretching technique analysis on the P wave signals. Figure 8:0 Relative velocity change vs. stress by applying stretching technique to the P wave part and full-length signals in parallel and transverse directions. Therefore, the P wave propagating in the stress direction shows the largest velocity change. However, if the full-length signals are analyzed, the relative velocity changes do not show much difference between two directions. In the cylinder test, the acoustoelastic coefficients were \(\alpha_{11}=0.105\,\%\)/MPa in the stress direction, and \(\alpha_{22}=0.121\,\%\)/MPa in the non-stress direction, respectively.