# Effect of Slag Particle Size on Fracture Toughness of Concrete
## 4 Results and Discussion
### Fracture Energy  
In this research, fracture energy (\(\mathrm{G_{F}}\)) was determined using a notched beam in a three-point bending test. Load-deflection curves were plotted from the tests. The energy absorbed in the test to failure is represented by the area below the load-deflection curve for the specimen. The area represents the fracture energy per unit area of the fracture surface. The \(\mathrm{G_{F}}\) was calculated using Equation (1). Concrete specimens were tested at 14 and 56 days. Results are presented in Table 4. At earlier ages (14 days), the \(\mathrm{G_{F}}\) values of each slag mixture are mostly less than that of the reference mixture, except slag mixture 56R2. In addition, the concrete containing more slag (40%) presented smaller \(\mathrm{G_{F}}\) than that with less slag content (20%) for various ages. Nevertheless, the presence of the finer slag has a beneficial effect on the \(\mathrm{G_{F}}\) of concrete. As shown in Figure 5, increasing the fineness level of slag leads to an increase of the \(\mathrm{G_{F}}\) value of concrete. Even at an earlier age of 14 days, the \(\mathrm{G_{F}}\) value of the mixture with finer slag (56R4) is in turn higher than that of the mixtures 55R4 and 54R4 for a similar slag replacement ratio of 40%. This implies that although the pozzolanic reaction of slag does not yet fully occur at early ages, the superior filling effect and more active hydration reaction of the finer slag can increase the density of concrete, resulting in an increased fracture resistance. After 56 days, the \(\mathrm{G_{F}}\) value of the slag mixtures almost exceeds that of the reference mixture. In addition, it is also found in Table 4 that the increment of fracture energy for each slag concrete from 14 days to 56 days is attained by 18-24%, which is much higher than that of reference concrete (10.1%). This signifies that, during the period, the pozzolanic reaction of slag activates, associating with the filling effect to enhance the fracture toughness of the slag concrete. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Mixture No.**} & \multicolumn{2}{c}{**Compressive Strength (MPa)**} & \multicolumn{2}{c}{**Fracture Energy (N/m)**} \\ \cline{2-6}  & **14 Days** & **56 Days** & **14 Days** & **56 Days** & **Increment N/m (\%)** \\ \hline S0 & 60.7 & 65.5 & 74.3 & 81.8 & 7.5 (10.1) \\ S4R2 & 59.2 & 67.7 & 71.2 & 84.5 & 13.3 (18.7) \\ S4R4 & 58.7 & 66.9 & 65.7 & 78.4 & 12.7 (19.3) \\ S5R2 & 60.1 & 69.1 & 72.1 & 89.1 & 17.0 (23.5) \\ S5R4 & 59.5 & 68.4 & 69.8 & 85.3 & 15.5 (22.2) \\ S6R2 & 62.3 & 70.3 & 76.5 & 94.6 & 18.1 (23.7) \\ S6R4 & 61.0 & 70.5 & 73.9 & 92.1 & 18.2 (24.6) \\ \hline \end{tabular}  
* Average value of two specimens  
\end{table} 
Table 4: Fracture energy of the concrete. Figure 4: The average compressive strength of slag concrete versus the fineness of ground granulated blast furnace slag (GGBS). Figure 6 compares fracture energy with the compressive strength of all slag concretes in the study. The \(\mathrm{G_{F}}\) is found to increase in conjunction with the compressive strength. This compares the trend favorably with the studies by [PERSON] [22], [PERSON] [23], and [PERSON] [24]. Nevertheless, the other studies observed smaller increases in \(\mathrm{G_{F}}\) with the increases in the compressive strength of high-strength concrete. [PERSON], [PERSON], and [PERSON] [22] found that \(\mathrm{G_{F}}\) increased as compressive strength increased, but only at a fraction of the rate. [PERSON], [PERSON], and [PERSON] [23] reported that an increase in compressive strength of 160% resulted in an increase in \(\mathrm{G_{F}}\) of only 12%. [PERSON], [PERSON], and [PERSON] [24] found that increases in compressive strength of 29% and 35% resulted in a \(\mathrm{G_{F}}\) increase of 11% and 13%, respectively. In this study, an increase in compressive strength of 10% resulted in a larger increase in \(\mathrm{G_{F}}\) of around 18%. This implicates the unique effect of using finer slag on the enhancement of the fracture resistance of concrete.