# Evaluation of Low-Temperature Performance of Recycled
## 3 Results and Discussion
### Prediction of Low-Temperature Cracking Temperature
The temperature deviations for the original mixture, the RAM with UVRAP, and the RAM with THRAP were found to be \(-4.68\%\), \(4.40\%\), and \(11.46\%\), respectively. Notably, the deviation in prediction for the first two mixtures is relatively small, while the accuracy of the prediction for the RAM with THRAP is lower. To evaluate the accuracy of predicting the LTP of RAMs using the Burgers model, in this paper, residual analysis is employed to assess the prediction model. The residual, defined as the difference between the experimental value and the model's estimated value, is calculated using the formula presented in Equation (16). Figure 14: Comparison of fracture temperature and estimated cracking temperature. The standardized residual is determined by dividing each residual by its standard deviation, as calculated using Equation (17). \[\mu_{i}=y_{i}-\hat{y}_{i} \tag{16}\]  
\[r_{i}=\frac{\mu_{i}}{\sigma_{e}}=\frac{y_{i}-\hat{y}_{i}}{\sigma_{e}} \tag{17}\]  
Figure 15 presents the residual absolute value color gradient and standard residual values for seven pairs of data. The figure indicates that the standard residual values for the original asphalt mixture and an RAM with UVRAP added are relatively small, with differences ranging from \(-2\) to \(+2\), suggesting that the model predictions are fairly accurate. In contrast, the standard residuals for the RAM with THRAP are generally excessive. Notably, when the addition amount reaches 40%, the standard residuals exceed acceptable limits, indicating the presence of outlier data. This analysis reveals that the [PERSON] model is more suitable for predicting the performance of the original asphalt mixtures and an RAM with UVRAP, while it exhibits reduced accuracy in forecasting the LTP of an RAM with THRAP. This discrepancy can be attributed to two main factors. Firstly, the calculation of the bending strain energy density at \(-30\)\({}^{\circ}\)C relies on a three-point temperature fitting curve, leading to a relatively constant value due to the elastic properties of asphalt mixtures at low temperatures. Secondly, the assumption of a local cooling rate of 10 \({}^{\circ}\)C/h when calculating the temperature strain energy density does not align with the actual cooling rate experienced by those mixtures at low temperatures. Studies [23] have shown that the greater the cooling rate, the greater the temperature strain energy density. Resulting in a lower actual temperature strain energy density than the calculated value. These factors contribute to a more conservative estimate of the cracking temperature, particularly manifest in the case of the RAM with THRAP. Notably, for RAM with the same thermal history RAP, the predicted temperature and fracture temperature exhibit a similar trend, indicating a gradual decrease in LTP as the RAP content increases. It can be seen that the above model is not suitable for the comparative evaluation of the LTP of an RAM with RAPs from different sources, but it demonstrates predictive capabilities for evaluating the LTP of an RAM with RAPs from the same source or with a similar thermal history.