## 3 Results and Discussion
### Hardened State Properties
#### 3.4.3. Secant Modulus of Elasticity  
In Figure 7a, a considerable reduction can be observed in mixes with higher cement replacement. At 28 days, the modulus of elasticity of mixes with \(\text{f}_{\text{ad}}=60\%\) exhibited a reduction of about 70% with respect to the RC. While, for the same age, the value of C10 FA20 BA decreased by 49% and that of C20 FA10 BA by 38%. After 91 days, the variation in \(\text{E}_{\text{cm}}\) relatively to that of the reference SCC exhibited the same trend, wherein decreases of 52% and 40% were observed for C10 FA20 BA and C20 FA10 BA, respectively. The values of mixes with \(\text{f}_{\text{ad}}=60\%\) had a reduction greater than 65%. Such decline in performance has been previously reported, wherein reductions of over 50% were observed in mixes with 85% of MIBA as a partial lightweight aggregate replacement when compared to the control concrete after 28 days due to the expansion of concrete as a result of the corrosion of Al [10]. Moreover, [PERSON] et al. [55] reported an expansion of the concrete, caused by the formation of hydrogen as a result of the Al present in MIBA. The small hydrogen bubbles are trapped in the remaining slurry causing an increase in volume.  
Figure 7b presents the relationship between the theoretical values using Equation (6) and the values obtained experimentally, showing some correlation between the \(\text{f}_{\text{cm}}\) and the \(\text{E}_{\text{cm}}\).  
\[\text{E}_{\text{cm}}=22\bigg{(}\frac{\text{f}_{\text{cm}}}{10}\bigg{)}^{0.3} \tag{6}\]  
Comparing the results obtained experimentally with those according to the expression proposed by EC2 [56], as Table 6 shows, it is evident that the evolution of the two curves  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mix**} & \multirow{2}{*}{\(\text{f}_{\text{cm,28}}\)} & \multicolumn{2}{c}{\(\text{f}_{\text{cm,28}}\)} & \multirow{2}{*}{\(\text{f}_{\text{cm,91}}\)} & \multicolumn{2}{c}{\(\text{f}_{\text{cm,91}}\)} \\ \cline{3-6}  & & **EC2** & **Measured** & & **EC2** & **Measured** \\ \hline RC & 55.3 & 3.9 & 4.53 & 65.5 & 4.2 & 4.40 \\ C10 FA20 BA & 14.4 & 1.8 & 2.81 & 16.7 & 2.0 & 3.10 \\ C20 FA10 BA & 24.5 & 2.6 & 2.51 & 26.3 & 2.7 & 3.42 \\ C20 FA40 BA & 6.1 & 1.0 & 1.62 & 8.7 & 1.3 & 2.08 \\ C40 FA20 BA & 8.6 & 1.3 & 2.02 & 10.0 & 1.4 & 2.57 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Splitting tensile strength (\(\text{f}_{\text{cm}}\) in MPa) versus compressive strength (\(\text{f}_{\text{cm}}\) in MPa) determined according to EC2 at 28 and 91 days.  
Figure 7: Modulus of elasticity (\(\text{E}_{\text{cm}}\)) at 28 days (**a**); relationship between \(\text{E}_{\text{cm}}\) and \(\text{f}_{\text{cm}}\) at 28 and 91 days (**b**).  
is similar. However, for values of \(\mathrm{f_{cm}}\), below about 35 MPa, the results recorded in the experimental campaign are lower than those of EC2, corresponding to mixtures with MIBA. On the other hand, the reference SCC presents results superior to those of the EC2 curve. For more advanced ages and greater substitution quantities (\(\mathrm{f_{zd}}\)), the \(\mathrm{E_{cm}}\) is less sensitive to cement substitution by additions than the compressive strength [57]. This fact may be due to the decreasing porosity resulting from the formation of C-S-H by pozzolanic reactions, especially in the interfacial transition zone.