# Crushing Performance of Ultra-Lightweight Foam Concrete with Fine Particle Inclusions
## 4 Results and discussion
### Micro-CT Investigation on the Influence of Particle size  
The experimental results from both the vibrational frequency test and the penetration test indicate that sand size affects the material performance of the foam-sand composite samples, especially at the large sand ratio of 0.5. It has been known that the mechanical behavior of cellular solid material is primarily determined by the solid property (e.g., solid modulus) and the morphology of the foam structure (e.g., void size distribution) [13; 18; 23]. In this case, the solid modulus is related to the cement paste and sand; however, this factor remains unchanged under the same sand ratio of 0.5. Therefore, it is more likely that the size of the sand inclusion makes a difference in the foam crushing behavior by affecting the cellular paste matrix. To study the influence of the inclusion size, the specimens of Samples of 0.5 sand ratio, along with the control sample were further scanned using micro-CT. These samples were selected because they reflected the greatest contrast between the control and composite samples based on the mechanical tests. A sample scan of each sample is shown in Figure 4, along with the corresponding processed image highlighting the different material phases and a 3D reconstruction showing the foam structure. The 3D reconstruction represents a smaller 2500 \(\times\) 2500 \(\times\) 2500 \(\upmu\)m\({}^{3}\) volume being extracted from the center of each CT scan. Due to the density difference, the sharp contrast made it easy for segmenting between air void and solid phases, while it was more challenging to separate out the sand particles from the cement paste, as the density of C-S-H solid is close to that of the sand [39]. Figure 3: Loading responses of all the samples at (**a**) 7, (**b**) 14, and (**c**) 21 days. Figure 4: A representative micro-CT scan, corresponding phase segmentation, and 3D reconstruction of samples (**a**) Control, (**b**) 0.5_300 \(\upmu\)m, (**c**) 0.5_600 \(\upmu\)m, and (**d**) 0.5_850 \(\upmu\)m, where the micro-CT scan has a side length of 5000 \(\upmu\)m and the 3D reconstruction has a side length of 2500 \(\upmu\)m.  
To further validate the CT test, the volume fractions of the three phases measured from the 3D reconstruction of each sample were compared with the theoretical values calculated based on the mixture design, as shown in Table 3. In general, the measurement achieves a decent agreement with the theoretical volume for all four samples, especially the void content. Due to the difficulty of separating the paste and sand, the variation on these two phases is greater. With respect to the composite samples, a greater deviation is observed in Sample 0.5_600 \(\upmu\)m, but still within a reasonable range. In terms of the spatial distribution of sand, the 3D reconstruction shows that no particle agglomeration in the inspected volumes and these mixtures are generally homogeneous. The segmentation images in Figure 4 confirm the increment on sand size from Sample 0.5_300 \(\upmu\)m to 0.5_850 \(\upmu\)m. Since the amount of sand inclusion was identical across the three samples, the sand population declines with the particle size. Seemingly, the sand particles in Samples 0.5_300 \(\upmu\)m and 0.5_600 \(\upmu\)m are more included in the cement paste, but those in Sample 0.5_850 \(\upmu\)m are less confined by the cellular matrix. Regarding the air void size, Sample Control in Figure 4a has the smallest voids among the four samples. This difference is mainly caused by the lower effective density of the foamed paste in the composite samples (see Table 1), and thus less confinement to the air bubbles in fresh cement paste before setting. These larger voids can be partly attributed to the presence of sand as well, as the interaction between the solid sand particles to the soft air bubbles reduces the stability of the foamed paste during mixing [17; 23; 32].