# Data-Driven Prediction of Binder Rheological Performance in RAP/RAS-Containing Asphalt Mixtures
## 3 Results and Discussion
### Correlations Between Rheology and Other Parameters
#### 3.3.4 Thermal Cracking Correlations  
The heatmap in Figure 18 provides the correlation matrix for \(\Delta T_{c}\) and other parameters being tested [e.g., thermal residue and chemical indices (\(I_{CO}+I_{SO}\) and \(I_{CC}+I_{CH}\))] and mixes' information (e.g., ABR by RAP or RAS, total AC, and the age of the mix). There were moderate, significant positive correlations between \(\Delta T_{c}\) and \(I_{CC}+I_{CH}\) and the total AC. \(\Delta T_{c}\) had moderately significant negative correlations with the other features, including \(I_{CO}+I_{SO}\) and ABR by RAS. In addition to the total AC, the aged material from RAP/RAS played a crucial role in altering the binder chemical indices, which led to binders being more thermally susceptible to cracking.  
Equation (12) is the linear model of \(\Delta T_{c}\) and other factors. Figure 19 shows the linear regression model generated using Equation (12) to show the relationship between the measured and predicted \(\Delta T_{c}\) values of the 37 binder samples. The measured and predicted data pairs were clustered around an ideal fit slope line with a slope ratio of 1:1. The R\({}^{2}\) was 0.89 and R was 0.94, indicating a strong linear relationship. The prediction error based on sample variation alone was moderate, with a standard error of 0.34 (Se/Sy). The age of  
Figure 16: Measured versus predicted block cracking parameters based on an RF model.  
Figure 17: Feature importance in the block cracking parameter RF model.  
the mixture, total AC, ABR by RAP, and \(I_{CC}+I_{CH}\) were the most robust predictors in the linear model.  
The following equation illustrates the linear relationship between \(\Delta T_{c}\) and the additional parameters:  
Figure 19: Measured versus predicted thermal cracking parameters based on a linear model.  
Figure 18: Heatmap of the thermal cracking parameter.  
\[\begin{array}{l}\Delta T_{c}=-274.32+0.32\ \times\ \mathrm{A}+6.10\ \times 10^{-3}\times\ \mathrm{B}+3.80\ \times\ \mathrm{C}+1.59\ \times\ \mathrm{D}+119.75\ \times\ \mathrm{E}+\\ 237.85\ \times\ \mathrm{F}+0.28\ \times\ \mathrm{G}+0.15\times\left[(\mathrm{D}-8.16)\ \times\ (\mathrm{G}-18.67)\right]+9.73\ \times\ 10^{-3}\times\left[(\mathrm{A}-\\ 16.03)\ \times\ (\mathrm{B}-5.60)\ \times\ (\mathrm{C}-5.40)\right]\end{array} \tag{12}\]  
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 \(I_{CO}+I_{SO}\);  
F is the \(I_{CC}+I_{CH}\);  
G is the residue (%).  
An RF regression model was constructed to predict \(\Delta T_{c}\) using 29 training and eight prediction samples. Figure 20 shows a comparison of \(\Delta T_{c}\) between the measured and predicted values. The ratio of Se to Sy of 0.36, R value of 0.95 for the test sample, and R\({}^{2}\) value of 0.87 all showed that the model had high predictive power. The observed data showed minimal variation between the measured and predicted values and were extremely close to the ideal-fit line. Figure 21 shows the relative importance of the model's features. The features with the highest ratings were total AC, thermal residue, ABR by RAP, and ABR by RAS. The aged RAP/RAS components with the total AC changed the binder components and affected the thermal residue, which in turn affected the binder resistance to thermal cracking.