## 4 Discussion  
The analysis and findings of this study indicated that the novel approach of establishing \"master curves\" in maturity modeling proposed by this research for the first time is feasible and with excellent results. The selected NDTs included in the study can be successfully used in concrete maturity. Since the relationship between concrete quality measures (e.g., compressive strength, UPV, or modulus of elasticity from RFT) and maturity index are mixture-specific, this study explored the development of a representative maturity function, identified herein as a \"master curve.\" The analysis indicated that NDT-based maturity models provided good fit and were of the same model form (i.e., logarithmic). Specifically:  
* The best fit model relating NDT response and the maturity temperature-time product is of logarithmic form, providing a coefficient of determination in almost all cases above 0.9 and \(p<0.05\), thus resulting in a very good fit for these two parameters and consistent model form for all concrete mixtures that were included in this study.  
This led to the development of a \"master curve\" for maturity. The methodology for defining the shift for each mixture maturity curve to the generalized form (i.e., master curve) was obtained through the definition of a transfer function in relation to key concrete properties, according to the following:  
* The \"master curve\" shift factors were successfully related to concrete mixture properties. These properties were selected based on Pearson's correlation analysis. Based on alternative model fitting, this led to the inclusion of compressive strength, air content,  
Figure 5: Compressive strength prediction model, (**a**) actual vs. predicted values, and (**b**) model residuals.  
and average concrete temperature for \(\delta_{\rm UPV}\) and compressive strength, unit weight, and average concrete temperature for \(\delta_{\rm DM}\), respectively. In terms of prediction accuracy, as it was observed from the results, the prediction accuracies for the selected models were 91% and 94% for the UPV and the dynamic modulus shift factor cases (Tables 6 and 7).
* The shift factor equations were successfully defined using linear regression multivariate analysis, and the \"master curves\" for pulse velocity and dynamic modulus were defined providing an excellent fit (R\({}^{2}\) = 1, Figure 3). A compressive strength prediction model was successfully developed in relation to the maturity index and NDT response, providing a high coefficient of determination (R\({}^{2}\) = 0.93, Equation (8)). In terms of prediction accuracy, Figure 5a presents a comparison between observed and predicted compressive strength values from Equation (8) using the data from the mixtures included in this study. Overall, there is very good agreement between observed and predicted strength values, and most of them are within the 95% prediction interval. In terms of limitations of the study findings, since MI is mixture-specific, the applicability of this modeling works well for a group of concrete mixtures in which similar ingredients and compositions are used. This reflects the fact that chemistry kinetics during hydration follow similar trends. In fact, this research has proven that when mixtures of similar content and ingredients are used, the \"master curves\" concept in maturity works very well. Thus, the development of \"master curves\" for different types of concretes (such as self-consolidating and fiber-reinforced concrete or when use of alternative cementitious materials like fly ash and slag cements are used) should be further validated since chemistry kinetics may be significantly altered.