# Data-Driven Prediction of Binder Rheological Performance in RAP/RAS-Containing Asphalt Mixtures
## 3 Results and Discussion
### Correlations Between Rheology and Other Parameters
#### 3.3.3 Block Cracking Correlations  
Figure 14 presents a heatmap showing the correlation matrix for the G-R and other parameters being tested, which consist of the thermal residue, chemical indices (\(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\)), ABR by RAP or RAS, total AC, and mix's age. There were strong, significant positive and negative correlations between G-R and \(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\), respectively. The aged material from RAP/RAS increased the aging indices, and the aliphatic components were transformed into aromatics, which created binders that were more susceptible to block cracking. A moderate, significant negative correlation was observed between G-R and total AC. Additionally, moderately significant positive correlations were observed between G-R and thermal residue and ABR by RAS. Reduced total AC and increased ABR by RAS affect the aging components and increase the aliphatic to aromatic transformers, which are reflected in the increased thermal residue and worsened binder-block-cracking resistance of the extracted binder.  
Equation (11) is a linear model of the G-R and other factors, as shown in Figure 15, which shows the regression linear model generated from Equation (11) to show the relationship between the measured and predicted G-R values from the 37 binder samples. The measured and predicted pairs of data were clustered around the ideal fit slope line with a slope of 1:1. The R\({}^{2}\) was 0.84 and R was 0.92, indicating a strong linear correlation. The prediction error based on the variation in the sample was moderate, as indicated by the standard error ratio (Se/Sy = 0.40). The strongest predictors of the linear model were the chemical indices interactions (\(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\)), followed by the thermal  
Figure 14: Heatmap of block cracking parameter.  
residue. This indicates the value of chemical and thermal analyses, which provide valuable information for predicting the binder block cracking parameter.  
The following equation demonstrates the linear relationship between G-R and the additional parameters:  
\[\begin{split}\text{G}-\text{R}=-29,195.90-101.54\times\text{A}-35.28\times\text{B}-1319.28\times\text{C}-287.85\times\text{D}+\\ 67,875.74\times\text{E}+27,939.39\times\text{F}+314.38\times\text{G}-2,071.307.73\times\left[\left(\text{E}-16.73\times\ 10^{-2}\right)\right.\\ \times\left.\left(\text{F}-86.65\times\ 10^{-2}\right)\right]+89.53 \times\left[\left(\text{D}-8.16\right)\times\ \left(\text{G}-18.67\right)\right]+3.40\times\left[\left(\text{A}-16.03 \right)\times\\ \left.\text{(B}-5.59\right)\right],\end{split} \tag{11}\]  
where  
A is the ABR by RAP (%);  
B is ABR by RAS (%);  
C is the total AC (%);  
D is the age of the mix (years);  
E is the \(I_{\text{CO}}+I_{\text{SO}}\);  
F is the \(I_{\text{CC}}+I_{\text{CH}}\);  
G is the residue (%).  
An RF regression model was built to predict G-R using 29 samples for training and 8 samples for prediction. A comparison of the measured and predicted results for the G-R model is shown in Figure 16. The model possessed high predictive capability, with an R\({}^{2}\) of 0.81, an Se/Sy ratio of 0.44, and an R value of 1.00 for the test sample size. The observed data points were very close to the ideal-fit line, showing little spread between the measured and predicted values of the two. The relative importance of the features in the model is shown in Figure 17. The features rated the highest were \(I_{\text{CO}}+I_{\text{SO}}\), \(I_{\text{CC}}+I_{\text{CH}}\), total AC, and thermal residue. This further demonstrates the value of chemical and thermal analyses in predicting the binder block-cracking parameters.  
Figure 15: Measured versus predicted block cracking parameters based on a linear model.