# Effects of Fineness and Dosage of Fly Ash on the Fracture Properties and Strength of Concrete
## 4 Results and Discussion
### Critical Stress Intensity Factor  
The critical stress intensity factor (K\({}^{\text{S}}_{\text{IC}}\)) is the stress intensity factor calculated at the critical effective crack tip, using the measured maximum load. In this research, the K\({}^{\text{S}}_{\text{IC}}\) was determined with a notched beam in a three-point bend test, using a closed-loop testing machine under the crack mouth opening displacement control. Load-CMOD curves were plotted from the tests. The K\({}^{\text{S}}_{\text{IC}}\) was calculated using Equation (2). Concrete specimens were tested at 14 and 56 days. As seen in Table 6, results showed that the related tendency of the K\({}^{\text{S}}_{\text{IC}}\) of concrete was similar to that of the G\({}_{\text{F}}\). At an early age (14 days), most of the K\({}^{\text{S}}_{\text{IC}}\) values of the fly ash concrete were lower than that of the control concrete (R0) but exceeded that of R0 after 56 days. This implies that the additional pozzolanic reaction of fly ash with Ca(OH)\({}_{2}\) in the concrete became active during the period between 14 and 56 days, which led to the enhancement of K\({}^{\text{S}}_{\text{IC}}\) of the fly ash concrete.  
It was also found that concrete containing finer fly ash presented larger K\({}^{\text{S}}_{\text{IC}}\) values. This can be observed in Figure 7, which shows that the increase in the fineness level of fly ash led to an increase in the K\({}^{\text{S}}_{\text{IC}}\) values of concrete at various ages. In other words, the K\({}^{\text{S}}_{\text{IC}}\) of the mixture F3R2 with finer fly ash was in turn higher than that of F2R2 and F1R2, for the same fly ash replacement ratio of 20%. Furthermore, the K\({}^{\text{S}}_{\text{IC}}\) of F3R1 \(>\) F2R1 \(>\) F1R1 for a similar fly ash replacement ratio of 10%. The reason for attaining this result is that the finer fly ash particle had a larger surface area, exhibiting a more  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mixture no.**} & \multicolumn{2}{c}{**Compressive Strength (MPa)**} & \multicolumn{2}{c}{**Critical Stress Intensity Factor (N \(\times\) m\({}^{-3/2}\)) \({}^{*}\)**} \\ \cline{2-5}  & **14 Days** & **56 Days** & **14 Days** & **56 Days** \\ \hline R0 & 62.1 \(\pm\) 0.29 & 70.3 \(\pm\) 0.20 & 1.030 \(\pm\) 0.0127 & 1.231 \(\pm\) 0.0212 \\ F1R1 & 57.3 \(\pm\) 0.33 & 69.8 \(\pm\) 0.31 & 0.964 \(\pm\) 0.0121 & 1.289 \(\pm\) 0.0189 \\ F1R2 & 56.0 \(\pm\) 0.34 & 68.7 \(\pm\) 0.36 & 0.908 \(\pm\) 0.0136 & 1.218 \(\pm\) 0.0210 \\ F2R1 & 61.9 \(\pm\) 0.29 & 74.2 \(\pm\) 0.25 & 1.025 \(\pm\) 0.0135 & 1.342 \(\pm\) 0.0250 \\ F2R2 & 59.2 \(\pm\) 0.19 & 73.1 \(\pm\) 0.35 & 0.999 \(\pm\) 0.0128 & 1.310 \(\pm\) 0.0244 \\ F3R1 & 63.5 \(\pm\) 0.35 & 75.8 \(\pm\) 0.29 & 1.135 \(\pm\) 0.0131 & 1.402 \(\pm\) 0.0260 \\ F3R2 & 61.5 \(\pm\) 0.29 & 74.6 \(\pm\) 0.23 & 1.085 \(\pm\) 0.0120 & 1.389 \(\pm\) 0.0272 \\ \hline \hline \end{tabular} \({}^{*}\) Average value of two specimens.  
\end{table}
Table 6: Critical stress intensity factor of concrete.  
Figure 6: Fracture energy versus compressive strength of fly ash concrete.  
active pozzolanic reaction, and thus resulting in an increase in the strength and fracture resistance (K\({}^{\text{S}}_{\text{IC}}\)).  
The stress intensity factors of fly ash concrete in the fracture test were compared to compressive strength, as seen in Figure 8. As shown in the figure, the two values of stress were nearly linearly related. The relationships shown in Figure 8 are of some importance because based on the close relationship between the particle size of fly ash and the compressive strength (Figure 4), the stress intensity factor increases with the increase of the fineness level of fly ash.  
Figure 8: Stress intensity factor versus compressive strength of fly ash concrete.  
Figure 7: Stress intensity factor of concrete with various fineness levels, and the replacement ratio of fly ash.