# Predicting Putting Development Using Machine Learning Methods Based on RIOCHTrack Data
## 3 Results and Discussion
### Comparison with a Mechanistic-Empirical Model  
Currently, the M-E rutting prediction models integrated into the pavement are widely utilized by pavement practitioners. Chinese specifications for the design of Highway Asphalt Pavement provide a calculation formula for rutting,  
\[R_{a}=\sum_{i=1}^{n}R_{ai} \tag{11}\]  
\[R_{ai}=2.31\times 10^{-8}k_{Ri}T_{pef}^{2.93}p_{i}^{1.80}N_{e3}^{0.48}\bigg{(} \frac{h_{i}}{h_{0}}\bigg{)}R_{0i} \tag{12}\]  
Among them, Ra represents the permanent deformation of the surface layer of the asphalt mixture, Rai represents the deformation of the i-th layer of the asphalt mixture, n represents the number of layers, and T\({}_{\text{pef}}\) represents the equivalent temperature of permanent deformation of the asphalt mixture. N\({}_{\text{e}}\)\({}^{0.48}\) represents the cumulative number of equivalent axle loads on a lane since the initiation of traffic. It is also referred to as the equivalent single axle loads (ESALs) in this study. Further, hi is the thickness of the i-th layer (mm), and h0 is the thickness of the specimen. R is the permanent deformation of the i-th layer of asphalt concrete during the rutting test at a temperature of 60 \({}^{\circ}\)C, a pressure of 0.7 MPa, and 2520 loading cycles. K is the correction coefficient, and the calculation formula is as follows:  
\[k_{Ri}=(d_{1}+d_{2}\cdot Z_{i})\cdot 0.9731^{Z_{i}} \tag{13}\]  
\[d_{1}=-1.35\times 10^{-4}h_{a}^{2}+8.18\times 10^{-2}h_{a}-14.50 \tag{14}\]  
\[d_{2}=8.78\times 10^{-7}h_{a}^{2}-1.50\times 10^{-3}h_{a}+0.90 \tag{15}\]  
This section utilizes the aforementioned calculation formula to calculate the rut depth of STR1, STR5, and STR9 under different axle loads, which are compared to the rut depths  
Figure 10: Predicted vs. measured rutting depth for different methods. (**a**) RF; (**b**) GBDT; (**c**) Extra Trees; (**d**) ANN; (**e**) SVR. predicted by RF, as shown in Figure 11. The figure shows that the detected rutting depth increases with the increasing ESALs in both prediction models. However, the observed rut depths exhibited an oscillatory increasing trend, but the M-E predicted rutting depth exhibited a monotonic increasing trend, which is not reflective of the actual behavior. The developed GBDT model can achieve higher performance without requiring any local calibration efforts. The detected rutting tends to peak during the summer months. As winter approaches and ambient temperature decreases, the ruts significantly decrease. This phenomenon can be explained by the density of the asphalt mixture at the rut depressions and bumps being different, which leads to a significant variation in temperature shrinkage performance. In winter, the rutting depressions have a higher density, smaller temperature shrinkage coefficient, and smaller deformation, whereas the bumps have a lower density, larger temperature shrinkage coefficient, and greater deformation. This decreases the difference in deformation between the rut depressions and bumps, resulting in rutting recovery in winter. Tree-based machine learning models, especially RF prediction models, can effectively predict the change patterns of rutting depth, which comprise both linear and fluctuating trends. The developed GBDT rutting prediction model was compared with other models in terms of generalizability and accuracy. The M-E model is the most widely used in the field of engineering. Before using the M-E model, it is necessary to conduct advanced laboratory testing to obtain the material properties of various asphalt pavement layers. It also needs to carry out locally calibrated work before using. [PERSON]. [35] proposed a variable-order fractional Burgers rutting model by fitting the test data of RIOHTrack. In the paper, rutting can be quantitatively described as the time-varying mechanical deformation, considering the mechanical rheological properties of asphalt mixtures. [PERSON]. [36] proposed a local correction  
Figure 11: Rutting depth predicted by RF and the M-E prediction model and the observations for STR1, STR5, and STR19 vs. ESALs.