# Influence of Concrete Strength Class on the Long-Term Static and Dynamic Elastic Moduli of Concrete
## 3 Results and Discussions
### Compressive and Tensile Splitting Strengths  
The compressive strength was measured on 10 cylinders in accordance with SR EN 12390-3 [14]. The load was applied at a constant rate of 0.6 MPa/s (4.71 kN/s). The obtained values are shown in Figure 5.  
Compared to the data presented in [10], when similar tests were conducted on cylinders made from the same mix proportions, the value of the compressive strength increased by 5.81%, 9.23%, and 47.37% for Mixes 1, 2, and 3, respectively. The possible explanation for such a significant increase in the compressive strength value of Mix 3 compared to the other mixes, all other parameters being similar (water/cement ratio, curing conditions, storage conditions), may be related to the fact that Mix 3 contains the highest amount of cement. The statistical analysis confirms the accuracy of the obtained results with COV values of 4.86%, 0.92%, and 1.61% for Mix 1, Mix 2 and Mix 3, respectively. A 8.06% increase in the value of the compressive strength at the age of 365 days (1 year) was reported in [1], whereas a 15.07% increase, at the age of 600 days (1.6 years) was reported in [5]. Neither of the studies had a target compressive strength pertaining to a  
Figure 5: Compressive strength at 6 years. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mix Designation**} & \multicolumn{2}{c}{**Dynamic Poisson’s**} & \multirow{2}{*}{**Standard Deviation**} & **Coefficient of** \\  & \multicolumn{2}{c}{**Ratio, \(\mu_{\text{d}}\)**} & & **Variation** \\ \cline{2-4}  & **-** & **-** & **[\%]** \\ \hline Mix 1 & 0.303 & 0.0202 & 6.68 \\ \hline Mix 2 & 0.316 & 0.0111 & 3.51 \\ \hline Mix 3 & 0.296 & 0.0147 & 4.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Dynamic Poisson’s ratio. certain concrete strength class and the water to cement ratio was 0.4. Additionally, neither of the studies mention the storage conditions of the concrete specimens, after the standard curing age of 28 days, until the tests were conducted. Similar trends were reported in [27] for the control mix, although the authors did not provide any numerical data. The conversion equations from compressive strength to static modulus of elasticity were checked for their accuracy and suitability for being applied to rubberized concrete, although they were not specifically developed and proposed for this purpose. Hence, the equation given by Eurocode 2 [11], Equation (9), and the equation given in ACI 318-14 [28], Equation (10), were investigated. The obtained results are summarized in Table 6.  
\[\mathrm{E_{cm}(t)}=\left(\frac{\mathrm{f_{cm}(t)}}{\mathrm{f_{cm}}}\right)^{0. 3}\times\mathrm{E_{cm}},\text{ where }\mathrm{f_{cm}}=\mathrm{f_{ck}}+8[ \mathrm{MPa}] \tag{9}\]  
\[\mathrm{E_{c}}=4.7\sqrt{\mathrm{f_{c}}^{\prime}} \tag{10}\]  
where \(\mathrm{f_{c}}^{\prime}\) and \(\mathrm{f_{ck}}\) are the compressive strength of concrete obtained from laboratory investigations (MPa), \(\mathrm{E_{c}}\) and \(\mathrm{E_{cm}}\) are the static moduli of elasticity (MPa), and \(\mathrm{f_{cm}(t)}\) and \(\mathrm{E_{cm}(t)}\) are the compressive strength of the modulus of elasticity at the age of 6 years, respectively. It can be observed that both Equations (9) and (10) give quite accurate predictions for the static modulus of elasticity of the three mixes. Equation (9) tends to underestimate the results, yielding conservative values, whereas Equation (10) slightly overestimates the results in the case of Mix 2. The tensile splitting strength was determined in five samples in accordance with SR EN 12390:6 [15]. The specimens were loaded at a loading rate of 0.05 MPa/s (0.4 kN/s). The obtained results are shown in Figure 6. The statistical analysis confirms the accuracy of the obtained results with values for COV of 10.71%, 9.1%, and 3.52% for Mix 1, Mix 2, and Mix 3, respectively.