# Fracture Behaviour of Concrete with Reactive Magnesium Oxide as Alternative Binder
## 3 Experimental Results and Discussion
### Fracture Energy  
The results of the fracture energy after 28 days of curing are shown in Figure 5a-d and Table 4, as well as their standard deviation and percent variation relative to RC for each substitution ratio. As can be seen there, the fracture energy decreases with the use of reactive MgO. This can be explained because \(\mathrm{G_{F}}\) is directly related to the interaction between cement matrix and aggregates. Therefore, the greater the replacement of cement with MgO, the lower the amount of CSH produced and the greater the amount of Mg(OH)\({}_{2}\) produced, reducing the properties of the cementitious paste (as inferred from the results of Table 3) and, consequently, the \(\mathrm{G_{F}}\) of the concrete mixes [9; 10; 50; 51]. The mixes with MgO from Canada and Australia are the most affected, with a reduction of approximately 50%, relative to RC, for ratio of 20%. In addition to being related to the hydration products formed by the MgO, these mixes have a higher w/b ratio and \(\mathrm{K_{F}}\) decreases with the increase of this ratio, as observed by [PERSON] and [PERSON] [50].  
Figure 5: Splitting force versus crack mouth opening displacement (CMOD) curves for mixes: C, S0, S1, A, and RC (**a**), 5% (**b**), 10% (**c**), 20% of MgO (**d**).  
Figure 5b shows that the tenacity of the mixes with MgO from Australia (A) at 5% (Figure 5b), 10% (Figure 5c), and 20% (Figure 5d) of substitution is lower than that of the mixes with other MgO's. The best results are observed in the mixes with MgO's S0 and S1, as shown in Figure 5b-d. As seen in Figure 5a-d, when the amount of MgO increases, the splitting force-CMOD curve tends to be flatter. Furthermore, CMOD increases with the incorporation of MgO. This increase occurs because the modulus of elasticity of concrete increases with the use of the expansive agent (MgO), improving the quality of concrete [31, 48], as was observed in the analysis of results of the modulus of elasticity.  
The peak splitting force will also increase for the mixes with MgO S0 and S1, in relation to the RC mix. A similar behavior was observed by [PERSON] et al. [31], when they studied the effect of expansive agents, including MgO, in concrete with FA. The authors observed that toughness exceeded 1.1 times that of the reference concrete between 28 and 60 days using this type of agents.  
As \(\mathrm{G_{F}}\) and \(\mathrm{K_{I}}\) are correlated parameters. In Figure 6a it is found that there is a real logarithmic correlation between these parameters with an R\({}^{2}\) of 0.96. On the other hand, \(\mathrm{G_{F}}\) and the compressive strength of each type of concrete mixes are also correlated with a strong quadratic fit (R\({}^{2}\) between 0.93 and 0.99), as shown in Figure 6b. This occurs because one of the most relevant parameters that determine the fracture energy of normal strength concrete is the w/b ratio [52], as is also the case of compressive strength. However, some other properties can also affect the value of \(\mathrm{G_{F}}\), such as the relative strength between aggregates and cement paste [52].  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mix**} & \multicolumn{6}{c}{**28 Days**} \\ \cline{2-7}  & \(\mathbf{G_{F}}\) **(N/m)** & \(\mathbf{\sigma}\) & \(\mathbf{\Delta_{RC}}\) & \(\mathbf{K_{I}}\) **(MPa-m\({}^{12}\))** & \(\mathbf{\sigma}\) & \(\mathbf{\Delta_{RC}}\) \\ \hline RC & 141.1 & 10.3 & - & 2.27 & 0.0