## 10 Verification of Thermal Simulation Model Validity by Laboratory Test  
In order to verify the validity of simulation models, laboratory tests were carried out to observe the temperature variation of asphalt mixture specimens during the cooling and heating process. During the cooling process, asphalt mixture specimens of four different aggregate gradations (AC-13, AC-20, AC-25 and PAC-13) were put into the 100 \({}^{\circ}\)C oven for more than four hours; then the specimens were taken out and quickly transferred into thermal insulation cabinet with 20 \({}^{\circ}\)C.  
Through the automatic infrared temperature sensor set in the thermal insulation cabinet, the surface temperature data of the specimens were collected, and the temperature variation curves of specimens were drawn. The data collection processes were all set to be 90 min. Because it is a non-destructive test, the same batch of specimens was tested twice in this study to reduce the error and random variability.  
During the laboratory heating process, the initial temperatures of specimens were set to 20 \({}^{\circ}\)C by the same method mentioned above, and the temperature variations of specimens were recorded under 100 \({}^{\circ}\)C ambient temperature.  
Figure 8: Thermal conductivity variations with the temperature of asphalt mortar.  
Figure 7: Volume contents of components in asphalt mortar.  
In the simulation processes, the same conditions as laboratory tests were set. The temperature fields of these four kinds of mixtures were calculated by meso-structure thermal simulation models in ABAQUS software. The specimen temperature data was extracted, and the temperature curves during cooling and heating processes were drawn, respectively, as shown in Figure 9. Exp1_1 represents the first experimental test data during the cooling process, Exp2_2 represents the second experimental test data during the heating process, Sim1 and Sim2 represent the simulation data during the cooling and heating process, respectively, and so on.  
Figure 9: _Cont._  
It can be found that the simulation results of various asphalt mixtures are in good agreement with the laboratory test results. In order to evaluate the consistency between the results of simulations and laboratory tests, the Pearson correlation coefficient (PCC) was introduced in this paper. The calculation formula of PCC is as follows:  
\[\rho(X,Y)=\frac{\mathrm{cov}(X,Y)}{\sigma_{X}\sigma_{Y}}=\frac{\sum\limits_{i=1 }^{n}\left(X_{i}-\overline{X}\right)\left(Y_{i}-\overline{Y}\right)}{\sqrt{ \sum\limits_{i=1}^{n}\left(X_{i}-\overline{X}\right)^{2}}\sqrt{\sum\limits_{i =1}^{n}\left(Y_{i}-\overline{Y}\right)^{2}}} \tag{10}\]  
in this formula, \(X\) and \(Y\) are two columns of n-dimensional vectors. Because the specimen data recording frequencies in laboratory tests were not consistent with the simulation analysis, the results of the experiment and simulation were interpolated by MATLAB software first, and then the PCC values between them were calculated directly by corrcoef command in MATLAB.  
The average PCC values between the experimental and simulation results during cooling and heating processes are shown in Figure 7 as \(\rho(\mathrm{Exp},\mathrm{Sim})\). It can be seen from the figures that the PCC values of all mixtures were above 0.997, showing high degrees of consistency. Therefore, the simulation model and analysis parameters adopted in this paper were proved to be effective and reliable in temperature field analysis.  
Figure 9: Temperature variations during experimental and simulation processes of (**a**) AC-13, (**b**) AC-20, (**c**) AC-25, (**d**) PAC-13 mixtures.