# Crushing Performance of Ultra-Lightweight Foam Concrete with Fine Particle Inclusions
## 4 Results and discussion  
### Elastic Modulus of the Samples  
The elastic modulus data obtained from the using the vibrational frequency test are summarized in Table 2 and compared in Figure 1. Each mean value in Table 2 represents the result averaged from nine measurements (3 specimens by 3 repeats). Continuous increase of the elastic modulus was seen for all samples from 7 to 21 days, where the average increase was 7.8% at 14 days and only 2.6% at 21 days. Because of the high accelerator dosage used for mixing, the modulus change of the samples from 14 to 21 days was marginal, indicating that cement hydration in the mixtures was almost complete at 21 days. In terms of standard deviation of the measurements, the samples with a larger sand ratio were less consistent than the others at 7 days but more consistent at the later ages. Figure 1 indicates that elastic modulus decreases for both sand size and sand ratio. The lowest modulus values at all three testing ages are observed with Sample 0.5_850 \(\upmu\)m, which had the largest sand ratio and sand size. On the other hand, the modulus of Sample 0.15_300 \(\upmu\)m is quite close to the control sample. The influence of sand ratio from 0.15 to 0.5 is more significant than increasing the sand size from 300 to 850 \(\upmu\)m in this case. Although the elastic modulus of the fine aggregate is greater than cement paste, the overall trend indicates that the elastic modulus of the composite samples are much reduced at higher sand ratios. However, similar observations have been reported in the literature [12; 19; 27]. As all samples were designed for the same target bulk density, the effective density of foamed paste is lower in samples with higher sand ratios, as shown in Table 1, meaning that less cement is available to support the cellular structure in foam concrete. This should be the main influence from sand ratio. Interestingly, the 7-day modulus values of Samples 0.15_300 \(\upmu\)m and 0.15_600 \(\upmu\)m are slightly higher than Control, and continue to stay close to Control at the later ages. This relationship, however, is not observed for Sample 0.15_850 \(\upmu\)m. Thus, a small amount of sand inclusion has a minimal influence, or even a slight improvement, on the elastic modulus of the foam-sand composite, but this rule does not hold true when the particle size becomes larger. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{4}{c}{**Mean of Elastic Modulus (and Standard Deviation) [MPa]**} \\ \cline{2-6}  & \multicolumn{2}{c}{**7 Days**} & \multicolumn{2}{c}{**14 Days**} & \multicolumn{2}{c}{**21 Days**} \\ \hline Control & 1176 & (31.1) & 1335 & (5.5) & 1365 & (18.5) \\ \hline
0.15\_300 \(\upmu\)m & 1223 & (1.8) & 1361 & (26.0) & 1363 & (17.3) \\ \hline
0.15\_600 \(\upmu\)m & 1245 & (35.8) & 1299 & (14.7) & 1332 & (23.4) \\ \hline
0.15\_850 \(\upmu\)m & 997 & (30.2) & 1071 & (4.4) & 1126 & (7.2) \\ \hline
0.3\_300 \(\upmu\)m & 1081 & (24.8) & 1166 & (23.1) & 1201 & (23.5) \\ \hline
0.3\_600 \(\upmu\)m & 1076 & (20.6) & 1161 & (25.8) & 1202 & (34.6) \\ \hline
0.3\_850 \(\upmu\)m & 975 & (29.4) & 1045 & (27.1) & 1072 & (28.8) \\ \hline
0.5\_300 \(\upmu\)m & 888 & (20.1) & 922 & (24.3) & 931 & (15.8) \\ \hline
0.5\_600 \(\upmu\)m & 762 & (42.9) & 821 & (43.4) & 855 & (33.8) \\ \hline
0.5\_850 \(\upmu\)m & 662 & (49.1) & 709 & (8.9) & 719 & (16.1) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean elastic modulus and standard deviation of the samples. Figure 1: Comparison of the elastic modulus results for all samples. The influence of sand size on elastic modulus is not strong in the samples with the 300- and 600-\(\upmu\)m sand of 0.15 and 0.3 sand ratios, but an increase in particle size to 850 \(\upmu\)m resulted in a substantial reduction for all sand ratios. Seemingly, there is a size threshold between 600 and 850 \(\upmu\)m beyond which leads to a marked modulus reduction.