# Crushing Performance of Ultra-Lightweight Foam Concrete with Fine Particle Inclusions
## 4 Results and discussion
### Micro-CT Investigation on the Influence of Particle size
Another observation is that the sand particles in Samples 0.5_300 \(\upmu\)m (Figure 4b) and 0.5_600 \(\upmu\)m (Figure 4c) are smaller than the large air voids in the cellular matrix; however, the particle size is evidently larger in Sample 0.5_850 \(\upmu\)m (Figure 4d). This difference may be relevant to the greater drop on elastic modulus and crushing strength of samples with the 850 \(\upmu\)m sand. To compare the void systems of the four samples quantitively, their void size distributions were extracted from the 3D reconstructions, as shown in Figure 5. As the air voids that are intersected by the model boundary does not reflect the actual void size, those intersected voids were not counted for the statistical analysis. As a result, the effective model volume was different for each sample. This artifact was compensated by renormalizing the effective model volume back to 2500 \(\times\) 2500 \(\times\) 2500 \(\upmu\)m\({}^{3}\). A back calculation using the normalized distributions confirmed that the deviation to the actual bulk density of each sample was less than 5%. In the four specimens, voids larger than 800 \(\upmu\)m were not observed, which is generally in agreement with the visual inspection. Possibly, air bubbles larger than this size cannot be sufficiently confined by the fresh mixture during mixing. According to Figure 5a, the log-scaled void population of Sample Control reduces rather linearly as a function of void size. As suggested by the other three samples, the sand inclusion results in fewer small voids and an increase of large voids. This point is better reflected in Figure 5b, as the volume distribution progressively moves to bigger voids with larger sand added. Since a standard aqueous foam was used for casting all mixtures and the only difference was the volume of foam added, ideally, the normalized void size distribution should not shift across different samples. Therefore, the influence on void size distribution must be induced by either the foamed paste or/and the particle inclusion before setting. Figure 5a shows that the overall distributions of Samples 0.5_300 \(\upmu\)m and 0.5_600 \(\upmu\)m are close to the controlled sample from 100 to 450 \(\upmu\)m but consistently higher at larger \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Void Content [\%]**} & \multicolumn{2}{c}{**Paste Content [\%]**} & \multicolumn{2}{c}{**Sand Content [\%]**} \\ \hline
**Sample** & **Calculated** & **Measured** & **Calculated** & **Measured** & **Calculated** & **Measured** \\ \hline Control & 71.1 & 70.9 & 28.9 & - & 0.0 & - \\ \hline
0.5\_300 \(\upmu\)m & 76.8 & 75.6 & 18.0 & 18.9 & 5.2 & 5.5 \\ \hline
0.5\_600 \(\upmu\)m & 76.8 & 77.4 & 18.0 & 16.8 & 5.2 & 5.8 \\ \hline
0.5\_850 \(\upmu\)m & 76.8 & 75.8 & 18.0 & 19.3 & 5.2 & 4.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Theoretical volume fractions and measurements from the 3D reconstructions. sizes. The remarkable reduction at 50 \(\upmu\)m can be mainly attributed to the diminished stability of small air voids, which have a higher tendency of merging under the reduced paste confinement. Based on the gradual rightward shift of the three distributions in Figure 5b, the larger sand seems to further induces formation of larger voids at the expense of smaller ones. In comparison, the 850-\(\upmu\)m sand has a more profound impact on the void distribution. According to Figure 5a, the void population is dramatically reduced before 300 \(\upmu\)m and consistently increased beyond 400 \(\upmu\)m. In correspondence, its void volume is concentrated at a larger size in Figure 5b. This significant change on the void system can be only reasonably associated with the fact that the 850 \(\upmu\)m sand is more likely to be affected by the void population. Figure 5: Statistics of the void (**a**) population and (**b**) volume distribution of the micro-CT specimens. These results have been normalized by a unit volume of 2500 \(\times\) 2500 \(\times\) 2500 \(\upmu\)m\({}^{3}\).