# Effect of Dune Sand on Drying Shrinkage Cracking of Fly Ash Concrete
## 2 Experimental Plan and Method
### Effect of Aggregates on Drying Shrinkage Cracking  
Drying shrinkage cracking typically decreases as the volume of cement paste decreases, while that of aggregate increases [30; 31; 32; 33]. However, mixtures with the same W/B ratios and unit water contents have the same cement paste volume, while the aggregate volume ratio (weight ratio) varies depending on the aggregate types used and the sand-to-aggregate ratio. Regarding the mixture proportions used in this study, when the DS/FA ratio increased with the same unit water content, CS decreased and CA increased. In addition, as the aggregate volume fraction changed, the net time to cracking and stress rate also changed. That is, the change in the volume fraction of the aggregate also affected the shrinkage cracking characteristics of the concrete. As such, the effect of the change in the volume of each aggregate type on the net time to cracking, which is a measure of shrinkage cracking, was also examined in this study. First, based on the mixture with the highest net time to cracking among the mixtures with the same unit water content, the volume change of each aggregate and the change in net time to cracking were calculated for the other mixtures. The volume change of each aggregate and the change in net time to cracking were calculated based on the D20 mixture for the W170 and W160 mixtures. The results are shown in Table 5.  
In addition, the relationship between the change in each aggregate's volume and the change in net time to cracking is proposed in Equation (5) [34]. \[\Delta T_{cr}=a\cdot\Delta DS+b\cdot\Delta CS+c\cdot\Delta CA \tag{5}\]  
where \(\Delta T_{cr}\) is the change in the net time to cracking (days); \(\Delta DS\) is the DS volume change (\(\ell\)); \(\Delta CS\) is the CS volume change (\(\ell\)); \(a\) is the restraint  
Figure 14: Relationship between net time to cracking and stress rate. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Mixture**}} & \multicolumn{3}{c}{**Change in Aggregate Volume (\(\ell\))**} & \multicolumn{1}{c}{**Change in Net**} \\ \cline{2-5}  & **CS** & **DS** & **CA** & **Time to Cracking** \\ \hline W170 & D10 & 92 & \(-\)26 & \(-\)66 & \(-\)0.57 \\  & D40 & \(-\)86 & 53 & 33 & \(-\)0.08 \\  & D60 & \(-\)153 & 100 & 53 & \(-\)0.20 \\ W160 & D10 & 98 & \(-\)31 & \(-\)68 & \(-\)0.85 \\  & D40 & \(-\)107 & 53 & 54 & \(-\)1.92 \\  & D60 & \(-\)179 & 104 & 75 & \(-\)1.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Aggregate volume change and the change in net time to cracking. effect factor of DS affecting the net time to cracking (days-\(\ell\)); \(b\) is the restraint effect factor of CS, which affects the net time to cracking (days-\(\ell\)); and \(c\) is the restraint effect factor of CA, which affects the net time to cracking (days-\(\ell\)). In general, DS has a smooth surface and a round shape. Conversely, CS and CA have rough surfaces and angular shapes. The physical properties of these aggregates may affect the adhesion and binding force between the cement paste and aggregates. That is, an increase in the volume of DS will reduce the restraint effect of the aggregate, and increases in the volumes of CS and CA will increase the restraint effect. In addition, as the size of the aggregate increases, the restraint effect increases, reducing the drying shrinkage [32]. Therefore, the restraint effect of each aggregate can be assumed to adhere to the order of \(0<a<b<c\). Finally, after setting the largest factor c to 1, subject to the restraint effect factor condition of each aggregate type, the restraint factor a was calculated based on the substitution of the second largest factor b (0.99-0.01) in Equation (5). Among the calculated factor values, the ranges of the factors that met the assumption presented above were calculated. Figures 15 and 16 show the results. Figure 16: Analysis results of restraint effect factor of DS and CS (W160 mixtures); \(a\) is the restraint effect factor of DS and \(b\) is the restraint effect factor of CS.