# Analysis of the Aggregate Effect on the Compressive Strength of Concrete Using Dune Sand
## 3 Results and Discussion
### Aggregate Effect on Compressive Strength
#### 3.4.2 For \(0<c<b<a\) and \(a=1\)  
Table 5 lists the results, with the maximum and minimum values of effect factors \(b\) and \(c\) that satisfy Equation (1) under the conditions: \(0<c<b<a\) and \(a=1\). In addition, Figure 11 shows the common ranges of the effect factors of CS and CA for each age. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c} \hline \multirow{2}{*}{**Age**} & \multirow{2}{*}{**Mixture**} & \multicolumn{8}{c}{**W170**} & \multicolumn{8}{c}{**W160**} & \multicolumn{8}{c}{**W150**} \\ \cline{2-13}  & & & **D10** & & **D40** & & **D60** & & **D10** & & **D40** & & **D60** & & **D40** & & **D60** \\ \cline{2-13}  & **Factor** & \(b\) & \(c\) & \(b\) & \(c\) & \(b\) & \(c\) & \(b\) & \(c\) & \(b\) & \(c\) & \(b\) & \(c\) & \(b\) & \(c\) & \(b\) & \(c\) \\ \hline
3 & Max. & 0.97 & 0.96 & 0.99 & 0.98 & 0.99 & 0.84 & 0.98 & 0.97 & 0.99 & 0.93 & 0.99 & 0.94 & 0.99 & 0.90 & 0.99 & 0.89 \\ \cline{2-13}  & Min. & 0.44 & 0.01 & 0.62 & 0.01 & 0.61 & 0.01 & 0.32 & 0.02 & 0.45 & 0.01 & 0.55 & 0.02 & 0.44 & 0.01 & 0.51 & 0.02 \\ \hline
7 & Max. & 0.96 & 0.95 & 0.99 & 0.91 & 0.99 & 0.92 & 0.96 & 0.95 & 0.99 & 0.93 & 0.99 & 0.94 The results indicate that the value of \(c\) generally increased as the value of \(b\) increased. Similarly, the value of \(c\) decreased as the value of \(b\) decreased; however, the decrease in \(c\) was larger than that of \(b\). For the W170 mixtures, the value of \(b\) was in the range of 0.62 to 0.97, whereas that of \(c\) was 0.01 to 0.84 at an age of 3 days. Furthermore, at an age of 7 days, the value of \(b\) was in the range of 0.65 to 0.96, whereas that of \(c\) was 0.02 to 0.91, indicating that the influence of CA on the compressive strength was more significant compared than at 3 days. At an age of 14 days, the value of \(b\) was in the range of 0.63 to 0.98, whereas that of \(c\) was 0.01 to 0.84. Figure 11: Common ranges of the effect factors for the (**a**) W170, (**b**) W160, and (**c**) W150 mixtures at different ages (\(a>b>c\), \(a=1\)). of \(c\) was 0.01 to 0.90. Finally, at an age of 28 days, the value of \(b\) was in the range of 0.68 to 0.80, whereas that of \(c\) was 0.02 to 0.79, indicating that the influence of CS and CA on the compressive strength at 28 days decreased compared to the other ages. For the W160 mixtures, the value of \(b\) was in the range of 0.55 to 0.98, whereas that of \(c\) was 0.02 to 0.93 at an age of 3 days. Furthermore, at an age of 7 days, the value of \(b\) was in the range of 0.55 to 0.96, whereas that of \(c\) was 0.02 to 0.93. At an age of 14 days, the value of \(b\) was in the range of 0.55 to 0.91, whereas that of \(c\) was 0.02 to 0.90. Finally, at an age of 28 days, the value of \(b\) was in the range of 0.68 to 0.80, whereas that of \(c\) was 0.02 to 0.79, indicating that the influence of CS and CA on the compressive strength at 28 days decreased compared to the other ages. For the W150 mixtures, the value of \(b\) was in the range of 0.51 to 0.99, whereas that of \(c\) was 0.02 to 0.89 at an age of 3 days. Furthermore, at an age of 7 days, the value of \(b\) was in the range of 0.47 to 0.99, whereas that of \(c\) was 0.02 to 0.96, indicating that the influence of CA was slightly more significant than at 3 days. At an age of 14 days, the value of \(b\) was in the range of 0.49 to 0.99, whereas that of \(c\) was 0.02 to 0.93. At 28 days, the value of \(b\) was in the range of 0.49 to 0.99, whereas that of \(c\) was 0.01 to 0.91. Based on the obtained values, the common ranges for \(b\) and \(c\) for all ages were obtained. For the W170 mixtures, their common ranges for \(b\) and \(c\) were 0.68 to 0.80 and 0.02 to 0.79, respectively. For the W160 mixtures, the common ranges were the same as those of the W170 mixtures. Furthermore, for the W150 mixtures, the common ranges for \(b\) and \(c\) were 0.51 to 0.99 and 0.02 to 0.79, respectively, which were larger than those of the W170 and W160 mixtures. Overall, for all mixtures, the common ranges of \(b\) and \(c\) were 0.68 to 0.80 and 0.02 to 0.79, respectively.