# Analysis of the Aggregate Effect on the Compressive Strength of Concrete Using Dune Sand
## 3 Results and Discussion
### Aggregate Effect on Compressive Strength
#### 3.4.1 For \(0<a<b<c\) and \(c=1\)  
Table 4 list the results, with the maximum and minimum values of the effect factors a and b that satisfy Equation (1) under the conditions: \(0<a<b<c\) and \(c=1\). In addition, Figure 10 shows the common ranges of the effect factors of DS and CS for each age. The results indicate that the value of \(a\) generally increased as the value of \(b\) increased. Similarly, the value of \(a\) decreased as the value of \(b\) decreased; however, the decrease in \(a\) was larger than that of \(b\). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Age**} & \multirow{2}{*}{**Mixture**} & \multicolumn{6}{c}{**W170**} & \multicolumn{6}{c}{**W160**} & \multicolumn{6}{c}{**W150**} \\ \cline{2-13}  & & \multicolumn{3}{c}{**D10**} & \multicolumn{3}{c}{**D40**} & \multicolumn{3}{c}{**D60**} & \multicolumn{3}{c}{**D10**} & \multicolumn{3}{c}{**D40**} & \multicolumn{3}{c}{**D60**} & \multicolumn{3}{c}{**D40**} & \multicolumn{3}{c}{**D60**} \\ \cline{2-13}  & **Factor** & \(a\) & \(b\) & \(a\) & \(b\) & \(a\) & \(b\) & \(a\) & \(b\) & \(A\) & \(b\) & \(a\) & \(b\) & \(a\) & \(b\) & \(a\) & \(b\) \\ \hline \multirow{2}{*}{3} & Max. & 0.97 & 0.98 & 0.97 & 0.98 & 0.86 & 0.99 & 0.90 & 0.92 & 0.88 & 0.99 & 0.90 & 0.99 & 0.83 & 0.99 & 0.87 & 0.99 \\ \cline{2-13}  & Min. & 0.01 & 0.55 & 0.01 & 0.39 & 0.02 & 0.53 & 0.02 & 0.65 & 0.03 & 0.64 & 0.02 & 0.53 & 0.02 & 0.69 & 0.02 & 0.61 \\ \hline \multirow{2}{*}{7} & Max. & 0.95 & 0.98 & 0.94 & 0.99 & 0.94 & 0.99 & 0.96 & 0.98 & 0.90 & 0.99 & 0.95 & 0.99 & 0.93 & 0.99 & 0.95 & 0.99 \\ \cline{2-13}  & Min. & 0.04 & 0.72 & 0.02 & 0.42 & 0.01 & 0.45 & 0.02 & 0.69 & 0.01 & 0.62 & 0.01 & 0.50 & 0.01 & 0.65 & 0.02 & 0.57 \\ \hline \multirow{2}{*}{14} & Max. & 0.96 & 0.98 & 0.96 & 0.99 & 0.92 & 0.99 & 0.95 & 0.96 & 0.92 & 0.99 & 0.94 & 0.99 & 0.91 & 0.99 & 0.91 & 0.99 \\ \cline{2-13}  & Min. & 0.01 & 0.71 & 0.01 & 0.40 & 0.02 & 0.46 & 0.01 & 0.67 & 0.03 & 0.62 & 0.02 & 0.51 & 0.03 & 0.66 & 0.01 & 0.59 \\ \hline \multirow{2}{*}{28} & Max. & 0.90 & 0.92 & 0.89 & 0.99 & 0.89 & 0.99 & 0.90 & 0.92 & 0.89 & 0.99 & 0.89 & 0.99 & 0.85 & 0.99 & 0.90 & 0.99 \\ \cline{2-13}  & Min. & 0.02 & 0.67 & 0.02 & 0.45 & 0.02 & 0.48 & 0.02 & 0.67 & 0.02 & 0.45 & 0.02 & 0.48 & 0.02 & 0.68 & 0.01 & 0.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of the calculated aggregate effect factors (\(a<b<c\), \(c=1\)). Figure 10: Common ranges of the effect factors for (**a**) W170, (**b**) W160, and (**c**) W150 mixtures at different ages (\(a<b<c\), \(c=1\)). For the W170 mixtures, the value of \(a\) was in the range of 0.02-0.86, whereas that of \(b\) was 0.55-0.98 at an age of 3 days. Furthermore, at an age of 7 days, the value of \(a\) was in the range of 0.04 to 0.94, whereas that of \(b\) was 0.72 to 0.98, indicating that the influence of DS and CS on compressive strength was more significant at an age of 7 days than at 3 days. At an age of 14 days, the value of \(a\) was in the range of 0.02 to 0.92, whereas that of \(b\) was in the range of 0.71 to 0.98, which were similar to the ranges at 7 days. Finally, at an age of 28 days, the value of \(a\) was in the range of 0.02 to 0.89, whereas that of \(b\) was 0.67 to 0.92, indicating that the influences of DS and CS on the compressive strength decreased slightly at this age compared with those at 7 and 14 days. For the W160 mixtures, the value of \(a\) was in the range of 0.03 to 0.88, whereas that of \(b\) was 0.65 to 0.92 at an age of 3 days. Furthermore, at an age of 7 days, the value of \(a\) was in the range of 0.02 to 0.90, whereas that of \(b\) was 0.69 to 0.98, indicating that the influence of CS on the compressive strength was more significant than at 3 days. At an age of 14 days, the value of \(a\) was in the range of 0.03 to 0.92, whereas that of \(b\) was 0.67 to 0.96. Finally, at an age of 28 days, the value of \(a\) was in the range of 0.02 to 0.89, whereas that of \(b\) was 0.67 to 0.92.