## 4 Discussion
### Correlation between the Dynamic and Mechanical Properties of Concrete  
#### 4.3.1 Correlation between Ultrasonic Pulse Velocity and the Compressive Strength of Concrete  
Figure 14 denotes the correlation between UPV and the compressive strength of PPFRC for the direct, semi-direct, and indirect methods. The values of UPV_dir = 4281.30 m/s (B-1.2%-60), UPV_sem = 3275.00 m/s (B-Pattern) and UPV_ind = 6049.10 m/s (B-1.2%-60) were eliminated because the calculated DFFITS parameters were 1.40, 1.87 and 3.78, respectively (all greater than 0.89). The regressions resulted in correlation coefficients of +0.065, \(-0.125\), and \(-0.642\) for the direct, semi-direct, and indirect methods, respectively, thus evidencing a very poor relation in the direct and semi-direct method and a significant relation in the indirect method. The \(p\) values were 0.869, 0.748 and 0.062, respectively. As only the indirect method reported a \(p\) value under 0.100, the null hypothesis that there is no correlation between variables in the indirect method is therefore rejected. Still, our null hypothesis is accepted for the direct and semi-direct methods. The indirect method exhibits a higher value for the Pearson correlation coefficient, and its slope is more marked. For every 1000-unit increase in the UPV, there is a decrease of 4.1 MPa in compressive strength. This trend differs from what was found in the literature review. [PERSON] et al. (2015) [19], [PERSON] et al. (2017) [12], and [PERSON] (2013) [43] report that the higher the UPV, the greater the compressive strength of concrete with steel fibers. Figure 14: Correlation between ultrasonic pulse velocity and compressive strength. Figure 13: Correlation between the reinforcement index and the dynamic elasticity modulus. 4.3.2 Correlation between Ultrasonic Pulse Velocity and the Static Modulus of Elasticity of Concrete  
Figure 15 illustrates the correlation between UPV and the Static Modulus of Elasticity of PPFRC for the direct, semi-direct, and indirect methods. The values of UPV_dir = 3897.55 m/s (B-Pattern), UPV_sem = 3275.00 m/s (B-Pattern) and UPV_ind = 6049.10 m/s (B-1.2%-60) were eliminated because the calculated DFFITS parameters were 1.18, 1.81 and 2.77, respectively (all greater than 0.89). The regressions resulted in correlation coefficients of +0.01, \(-\)0.24, and +0.68 for the direct, semi-direct, and indirect methods, respectively, showing a non-existent relation in the direct method, a poor relation in the semi-direct method and a significant relation in the indirect method. The \(p\) values were 0.978, 0.531 and 0.044, respectively. As only the indirect method had a \(p\) value below 0.100, the null hypothesis that there is no correlation between variables in the indirect method is therefore rejected. However, our null hypothesis is accepted for the direct and semi-direct methods. The indirect method reports the highest value for the Pearson correlation coefficient. For every 1000-unit increase in UPV, there is an increase of 4.9 GPa in the Static Modulus of Elasticity. This result is consistent with the results reported by [PERSON] et al. (2015) [19], who reported a similar correlation using steel fibers. 4.3.3 Correlation between the Dynamic Modulus of Elasticity and the Compressive Strength of Concrete  
Figure 16 denotes the correlation between the Dynamic Modulus of Elasticity and the compressive strength of PPFRC for the direct, semi-direct, and indirect methods. The values of \(E_{d\_}\)dir = 27.98 GPa (B-0.8%-50), \(E_{d\_}\)sem = 22.17 GPa (B-Pattern), \(E_{d\_}\)ind = 78.78 GPa (B-1.2%-60) and \(E_{d\_}\)ind = 41.95 GPa (B-0.8%-50) were eliminated because the calculated DFFITS parameters were 1.25, 1.07, 3.32 and 0.91, respectively (all greater than 0.89). The regressions resulted in correlation coefficients of \(-\)0.48, \(-\)0.16, and \(-\)0.83 for the direct, semi-direct, and indirect methods, respectively, showing an average relation in the direct method, a very poor relation in the semi-direct method and strong relation in the indirect method.