## 4 The Air Void Size Distribution and Dynamic Modulus Analysis of the Hardened Stage
### Compare Measured Air Void Size Distribution with ASTM C457 at Hardened Stages  
The obtained air void size distribution and volume fraction from the ultrasonic scattering measurement were further compared with the ASTM C457 test on Day 28. The ASTM C457 tests were conducted with the flatbed scanning methods [41]. The cylinder samples were cut into slabs (7.62 cm (3 in) \(\times\) 10.16 cm (4 in)) and the surface was carefully polished with grinder. The surfaces were then painted with black marker pen and powdered with calcium silicate. The prepared samples are shown in Figure 10. After processing, the white spots represent air voids existing in concrete specimens. Comparing these three samples, it is clear that the whitened areas increase with the added air entrainment agent dosage. To obtain the size distribution and volume fraction of air voids, the prepared samples were scanned and analyzed with the BubbleCounter [41] embedded in ImageJ software [42]. The comparison between the ultrasonic scattering measurement results and the ASTM C457 results is shown in Figure 11a-c, respectively. The corresponding correlation coefficients on the whole size range are 88.86%, 96.88%, and 90.75% for Samples 1-3 separately. The distribution parameters are shown in Table 3. It is clear that the average size and standard deviation for the small air voids decrease and increase respectively with the air entrainment agent content. The air void fraction obtained with  
Figure 10: Scanned pattern of concrete slabs from the ASTM (American Society for Testing and Materials) C457 Test. (**a**) The scanned results of Sample Type 1; (**b**) The scanned results of Sample Type 2; (**c**) The scanned results of Sample Type 3d; (**d**) The demonstration of the Interfacial Transition Zone (ITZ) area (Area **d**) in Sample Type 1; (**e**) The demonstration of the ITZ area (Area **e**) in Sample Type 2; (**f**) The demonstration of the ITZ area (Area **f**) in Sample Type 3.  
ultrasonic scattering techniques is around 3.4%, 6.8%, and 10.0% for Samples 2-4, which are very close to the ASTM C 457 measured values of 3.4%, 6.9%, and 10.1% for tested samples. The size distribution of the small air voids (0.1-1.2 mm) are shown in Figure 12, where a-c represent the non-entrained concrete (Sample Type 1), entrained concrete with regular entrainment dosage (Sample Type 2), and entrained concrete with double entrainment dosage (Sample Type 3), respectively. On the range of small air voids, the correlation coefficient between the ultrasonic scattering measurement results and ASTM C457 measured results are 93.98%, 93.75%, and 71.33%, for Sample Type 1, 2, and 3, respectively. The closeness of both the size distributions curve and volume fraction between these two results demonstrates the feasibility of the ultrasonic scattering measurement method. Figure 11: Comparison between the air void size distribution measurement with ultrasonic scattering and ASTM C 457 methods. (**a**) The comparison for Sample Type 1; (**b**) The comparison for Sample Type 2; (**c**) The comparison for Sample Type 3. Figure 12: Comparison of the air void size distribution in the small size range. (**a**) The comparison of the experimental result and the theoretical result on the small-size air voids range for Sample Type 1; (**b**) The comparison of the experimental result and the theoretical result on the small-size air voids range for Sample Type 2; (**c**) The comparison of the experimental result and the theoretical result on the small-size air voids range for Sample Type 3. As shown in these figures, the volume fractions of both small air voids and large air voids decrease with the curing age. Particularly, a peak shift from about 1.2 mm to about 0.3 mm can be observed for small air void distribution from Sample Type 1 to Type 3. In contrast, the peaks of the large air void distribution are relatively stable among these three samples.