# Data-Driven Prediction of Binder Rheological Performance in RAP/RAS-Containing Asphalt Mixtures
## 3 Results and Discussion
### Correlations Between Rheology and Other Parameters
#### 3.3.2 Fatigue Cracking Correlations  
Figure 10 shows a heatmap of the correlation matrix of \(G^{*}\)-sin\(\delta\) and other parameters, including thermal residue, chemical indices (\(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\)), ABR by RAP or RAS, total AC, and mix's age. The absolute value of Pearson's critical correlation (0.33) was calculated using a sample size of 37 and a significance level of 0.05. With a sample size of 37, the Pearson correlation coefficient was statistically significant at the 0.05 level (\(1\,\mathrm{r}\,\mathrm{l}\,\mathrm{>}\,0.33\)). A strong, significant negative correlation was observed between the \(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\) indices. Binders with increased aging have higher aging indices (\(I_{CO}+I_{SO}\)) and lower total aliphatic than aromatic compounds (lower \(I_{CC}+I_{CH}\)). Moderate, significant positive and negative correlations were observed for \(G^{*}\)-sin\(\delta\), \(I_{CO}+I_{SO}\), and \(I_{CC}+I_{CH}\). The incorporation of aged materials from RAP/RAS boosted the aging indices and facilitated the transformation of aliphatic compounds into aromatics, indicating that the binders had  
Figure 8: Measured versus predicted rutting parameters based on an RF model. a higher susceptibility to fatigue cracking. Additionally, moderately significant positive and negative correlations were observed for \(G^{*}\).sin\(\delta\), thermal residue, and total AC. Thus, as discussed in previous studies [12; 52], the contributions of aging from RAP/RAS led to an increase in the transformation of maltenes into asphaltenes, increasing the thermal residue and reducing the binder's resistance to fatigue cracking. A parallel observation was made in which the total AC was lowered and negatively impacted the binder resistance to fatigue cracking. Moderate, significant positive and negative correlations were extrapolated between the thermal residue and \(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\), respectively. Augmenting the aging components resulted in heightened aging indices (\(I_{CO}+I_{SO}\)), diminished \(I_{CC}+I_{CH}\), and increased thermal residues. Moreover, the total AC exhibited moderately significant positive and negative correlations with \(I_{CC}+I_{CH}\) and \(I_{CO}+I_{SO}\), respectively. A higher total AC resulted in slower aging conditions in asphalt mixes, leading to increased \(I_{CC}+I_{CH}\) and decreased \(I_{CO}+I_{SO}\) indices. The ABR by RAS and \(G^{*}\).sin\(\delta\) exhibited a weak correlation. However, the ABR using RAS showed moderately significant positive and negative correlations with \(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\). An increase in the aging components detected by the ABR using RAS raised the \(I_{CO}+I_{SO}\) and decreased the \(I_{CC}+I_{CH}\). Equation (10) presents a linear model of \(G^{*}\).sin\(\delta\) and other parameters. Using the linear regression model produced in Equation (10), Figure 11 depicts the correlation between the measured and predicted \(G^{*}\).sin\(\delta\) values from 35 extracted binders. The data pairs were clustered around the ideal fit line with a slope of 1:1. The R\({}^{2}\) value was 0.67, and the R value was 0.82, indicating a strong linear correlation. The prediction error based on the variation in the sample only was moderate, as indicated by the standard error ratio (Se/Sy = 0.57). The most significant factors of the linear model were thermal residue, total AC, the interaction between ABR by RAP, ABR by RAS, and the age of the mix, followed by the interaction between the chemical indices (\(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\)); therefore, this highlights the importance of chemical and thermal analyses as useful tools for predicting the binder fatigue cracking parameter. Figure 9: Feature importance in the rutting parameter RF model. The following equation represents the linear relationship between \(G^{*}\)sin\(\delta\) and other parameters:  
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