## 6 Conclusions  
In this work, correlations between variables were statistically analyzed, and empirical equations were developed to calculate (1) compressive strength as a function of UPV and \(RI\); (2) the static modulus of elasticity as a function of UPV; and (3) the dynamic modulus of elasticity as a function of compressive strength and \(RI\). The results are framed for concrete with a nominal compressive strength of 40 MPa and a/c = 0.45, prepared in a 312 L mixer, and then manually molded according to the specimens detailed in Section 2.2. Based on the findings of this research, the following conclusions are drawn. * From the relation between the Reinforcement Index and the mechanical properties, it is concluded that there is a linear correlation between \(RI\) and compressive strength with a correlation coefficient of 0.79. The higher the \(RI\), the lower the compressive \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Author** & **Equation** & **Method** & **Fibers** & \(V_{f}\) (\%)** & **Id** \\ \hline \({}^{*}\) & \(E_{c}\) = 0.0049 \(\times\) UPV + 6.2271 & Indirect & Polypropylene & 0, 0.4, 0.8, 1.2\% & Equation (16) \\ \({}^{[19]}\)** & \(E_{c}\) = (1.06 \(\times\) 10\({}^{-}\)(4)\(\times\) UPV\({}^{2}\)) \(-\) 1.156 \(\times\) UPV + 3210 & Direct & Steel & 0, 0.5, 1.3, 1.5, 2, 2.5\% & Equation (17) \\ \hline \hline \end{tabular} \({}^{*}\)Current research study.  
\end{table} 
Table 7: Static modulus of elasticity prediction equations based on UPV. Figure 24: Normalized comparison between dynamic modulus of elasticity prediction equations based on the reinforcement index and compressive strength. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Author** & **Equation** & **Method** & **Fibers** & **Vf (\%)** & **Id** \\ \hline \({}^{*}\) & Ed\_ind = (7.5084 + 0.0137 \(\times\)\(RI\)) \(\times\) (fc)\({}^{*}\)0.5 & Indirect & Polypropylene & 0, 0.4, 0.8, 1.2\% & Equation (18) \\ \({}^{[24]}\) & Ed\_dir = (5920 \(-\) 9.4 \(\times\)\(RI\)) \(\times\) (fc)\({}^{*}\)0.5 & Direct & Steel/PP & Various & Equation (19) \\ \({}^{[24]}\) & Ed\_sem = (4170 \(-\) 1.7 \(\times\)\(RI\)) \(\times\) (fc)\({}^{*}\)0.5 & Semi-direct & Steel/PP & Various & Equation (20) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Dynamic modulus of elasticity prediction equations based on reinforcement index and compressive strength. strength. On the other hand, from the results, the non-existent correlation between IR and the Static Modulus of Elasticity cannot be ruled out, even when the correlation coefficient is 0.47. The average ratio for the modulus of elasticity between the root of compressive strength is 4690, a value that is very close to that of 4700 given by the ACI Committee 318; therefore, it can be concluded that the Static Modulus of Elasticity is not significantly affected by PP fibers, and its value can be calculated with the traditional concrete formulas without reinforcing fibers for PP fiber volume fractions of 0, 0.4, 0.8 and 1.2%. * From the relation between the Reinforcement Index and Ultrasonic Pulse Velocity, it is concluded that there is a correlation using the three prospecting methods. The higher the _RI_, the higher the UPV. However, a significant correlation was found only through the indirect method regarding the relationship between the Dynamic Modulus of Elasticity and _RI_. * The relation between dynamic and mechanical properties shows a significant correlation between UPV and compressive strength and between UPV and the Static Modulus of Elasticity. In both cases, the indirect prospecting method was the only method that had significant correlations. Therefore, empirical equations of these relations have been developed. In the first case, the higher the UPV, the lower the compressive strength, with a correlation coefficient of 0.64. In the second case, the higher the UPV, the greater the Static Modulus of Elasticity, with a correlation coefficient of 0.68.