## 3 Ultrasonic Measurement of Air Void Distribution in Early-Age Concrete
### Attenuation Measurement of Cement Paste for Different Ages  
As mentioned before, the ultrasonic attenuation of the cement paste first needs to be determined as attenuation for the corresponding viscoelastic matrix in concrete, especially during the early ages. The cement paste samples with the same water/cement ratio (0.45) as concrete samples were separately prepared and no air entrainment agent was added during preparation. Then, the air voids in the separately prepared cement paste are mainly capillary pores due to cement hydration. The attenuation of cement paste is mainly generated from its viscoelastic property, and the contribution from the capillary air void structure is limited. The air void structure of the separately prepared cement paste and that of the cement paste in concrete is different, as the air void structure in concrete can be further affected by the added air entrainment agent, air voids entrapped by the aggregate, and the existence of the Interfacial Transition Zone (ITZ) area. Also, due to the relatively small volume fraction (around  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sample** & **Cement Content** & **Coarse Aggregates** & **Fine Aggregates** & **Water** & **Glass Particle** & **Design** & **Air entrainment** \\
**(kg/m3)** & **(kg/m3)** & **(kg/m3)** & **(kg/m3)** & **(kg/m3)** & **(kg/m3)** & **w/\(\epsilon\)** & **Agent (mL/m3)** \\ \hline Type 1 & 334.6 & 1110.7 & 666.4 & 148.4 & 74.0 & 0.45 & 0 \\  & (\(\lx@sectionsign\)\({}^{*}\) = 3.15) & (\(\lx@sectionsign\)\({}^{*}\) = 2.75) & (\(\lx@sectionsign\)\({}^{*}\) = 2.65) & 148.4 & 74.0 & 0.45 & 167.5 \\ \hline Type 2 & 334.6 & 1110.7 & 666.4 & 148.4 & 74.0 & 0.45 & 335.0 \\  & (\(\lx@sectionsign\)\({}^{*}\) = 3.15) & (\(\lx@sectionsign\)\({}^{*}\) = 2.75) & (\(\lx@sectionsign\)\({}^{*}\) = 2.65) & 148.4 & 74.0 & 0.45 & 335.0 \\ \hline \multicolumn{8}{c}{\({}^{*}\)_sg_ is short for specific gravity.} \\ \end{tabular}
\end{table}
Table 1: Lab concrete mixture proportional design for early-age concrete studies.  
25%) of cement paste inside concrete, the influence of the intrinsic capillary air void content of the cement paste on the concrete air void structure is further limited. The influence of the entrained air voids, entrapped air voids, and the air voids in the ITZ area on the ultrasonic attenuation, are all considered during the measurement in this study.  
The cement paste properties are highly impacted by the hydration process. In this study, the ultrasonic scattering measurement was conducted at Day 1, 3, 7, 14, and 28 for both the cement paste and concrete specimen. The calculated cement paste attenuation on the frequency domain based on Equation (10) is shown in Figure 4. A parabolic equation was then used for the curve fitting between the attenuation and corresponding frequency. The fitted equations are depicted as Equations (11)-(14). These fitted equations served as the background attenuation for further inverse analysis of the characteristics of concrete air voids. As the center attenuation used in this study is 500 kHz, the signal is more stable during the range of [150, 550] kHz and this range was applied for the further analysis. It can be observed from Figure 3 that the attenuation of the cement paste matrix decreased with the curing age on the whole frequency domain.  
\[\alpha_{a,f} =-222.8110e-6\times f^{2}+259.3297e-3\times f+23.8052 \tag{11}\] \[\alpha_{a,f} =-371.3589e-6\times f^{2}+362.8550e-3\times f-10.4897\] (12) \[\alpha_{a,f} =-275.0380e-6\times f^{2}+280.7362e-3\times f-5.5200\] (13) \[\alpha_{a,f} =-129.7629e-6\times f^{2}+146.8296e-3\times f+20.7148 \tag{14}\]  
where \(f\) is the frequency range (KHz) and \(\alpha_{a,f}\) is the attenuation (Np/m).