# Effects of Fineness and Dosage of Fly Ash on the Fracture Properties and Strength of Concrete
## 4 Results and Discussion
### Compressive Strength
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Mixture no.**} & \multirow{2}{*}{**w/cm**} & \multicolumn{4}{c}{**Compressive Strength, MPa \({}^{*}\)**} \\ \cline{3-6}  & & **7 Days** & **14 Days** & **28 Days** & **56 Days** & **91 Days** \\ \hline \multirow{3}{*}{R0} & & 56.5 \(\pm\) 0.26 & 62.1 \(\pm\) 0.29 & 66.1 \(\pm\) 0.28 & 70.3 \(\pm\) 0.20 & 71.2 \(\pm\) 0.38 \\  & & (100\%) & (110\%) & (117\%) & (124\%) & (126\%) \\ \multirow{3}{*}{F1R1} & & 53.0 \(\pm\) 0.17 & 57.3 \(\pm\) 0.33 & 63.0 \(\pm\) 0.26 & 69.8 \(\pm\) 0.31 & 72.4 \(\pm\) 0.41 \\  & & (100\%) & (108\%) & (119\%) & (132\%) & (137\%) \\ \multirow{3}{*}{F1R2} & & 52.2 \(\pm\) 0.20 & 56.0 \(\pm\) 0.34 & 61.4 \(\pm\) 0.24 & 68.7 \(\pm\) 0.36 & 71.7 \(\pm\) 0.45 \\  & & (100\%) & (107\%) & (118\%) & (132\%) & (137\%) \\ \multirow{3}{*}{F2R1} & & 54.6 \(\pm\) 0.12 & 61.9 \(\pm\) 0.29 & 68.2 \(\pm\) 0.26 & 74.2 \(\pm\) 0.25 & 75.8 \(\pm\) 0.34 \\  & & (100\%) & (113\%) & (125\%) & (136\%) & (139\%) \\ \multirow{3}{*}{F2R2} & & 53.3 \(\pm\) 0.15 & 59.2 \(\pm\) 0.19 & 66.8 \(\pm\) 0.36 & 73.1 \(\pm\) 0.35 & 74.6 \(\pm\) 0.41 \\  & & (100\%) & (111\%) & (125\%) & (137\%) & (140\%) \\ \multirow{3}{*}{F3R1} & & 55.7 \(\pm\) 0.23 & 63.5 \(\pm\) 0.35 & 70.3 \(\pm\) 0.35 & 75.8 \(\pm\) 0.29 & 77.9 \(\pm\) 0.34 \\  & & (100\%) & (114\%) & (126\%) & (136\%) & (140\%) \\ \multirow{3}{*}{F3R2} & & 53.9 \(\pm\) 0.14 & 61.5 \(\pm\) 0.29 & 69.1 \(\pm\) 0.19 & 74.6 \(\pm\) 0.23 & 76.5 \(\pm\) 0.28 \\  & & (100\%) & (114\%) & (128\%) & (138\%) & (142\%) \\ \hline \hline \end{tabular} \({}^{*}\) Average value of three specimens.  
\end{table} 
Table 4: Compressive strength of concrete cylinders. early ages, the superior filling effects of the finer fly ash could increase the denseness of the concrete, resulting in increased fracture toughness. After 56 days, the G\({}_{\text{F}}\) values of the fly ash concrete mixtures all exceeded that of the control mixture, except for the mixture F1R2. In addition, it was also found that the increment of the fracture energy for each fly ash concrete from 14 days to 56 days was attained by 21-31%, which was much higher than that of the control concrete (13.6%). This signifies that, during this period, the pozzolanic reaction of fly ash became active, which together with the filling effect, enhanced the fracture toughness of the fly ash concrete. Figure 6 compares the fracture energy, and the compressive strength of all fly ash concretes in the study. The G\({}_{\text{F}}\) was found to increase in conjunction with the compressive strength. This trend compares favorably with the research of [PERSON] [19], [PERSON] [20], and [PERSON] [21]. Nevertheless, these researchers observed smaller increases in G\({}_{\text{F}}\) with increases in compressive strength of high strength concrete. [PERSON] et al. [19] found that an increase in compressive strength of 160% resulted in an increase in G\({}_{\text{F}}\) of only 12%. [PERSON] et al. [20] observed that G\({}_{\text{F}}\) increased as compressive strength increased, but only at a fraction of the rate. [PERSON] et al. [21] found that increases in compressive strength of 29-35% resulted in a G\({}_{\text{F}}\) increase of only 11-13%. In this study, an increase in compressive strength of 10% resulted in a larger increase in G\({}_{\text{F}}\) of around 14% (\(\sim\)13-15%) when the compressive strength varied  
Figure 5: Fracture energy of concretes with various fineness levels and the replacement ratios of fly ash.