## 4 Results and Discussion
### Comparative Analysis of Adsorbed Asphalt Film Thickness Based on Different Micromechanical Models  
The adsorbed asphalt film thickness was calculated using three micromechanical models to enable a comparative evaluation. The calculations were derived from Dynamic Shear Rheometer (DSR) test data. For consistency in the analysis, the film thickness was determined under controlled conditions at a temperature of 28 \({}^{\circ}\)C and a frequency of 5 Hz, while the effects of temperature and frequency variations were excluded. The results are presented in Figure 7.  
As illustrated in Figure 7, the thickness of the adsorbed asphalt film between the asphalt and mineral filler ranges from 0.01 to 0.45 \(\upmu\)m. The film thickness, calculated using the three micromechanical models, exhibits a similar trend with the filler-to-binder (F/B) ratio: initially decreasing and then increasing as the F/B ratio increases. This behavior is attributed to the reduction in asphalt content as the volume fraction of mineral filler  
Figure 6: Complex shear modulus of asphalt mastic and base asphalt: (**a**) LAM; (**b**) FAM; (**c**) CAM. rises, resulting in a thinner adsorbed film. When the mineral filler volume fraction exceeds the critical value, particle interactions become significant, resulting in a rapid increase in the shear modulus of the asphalt mastic and, consequently, an increase in the calculated film thickness. As shown in Figure 7b, the GSC model predicts a negative film thickness for FAM when the F/B ratio is 0.8. To investigate the cause of this discrepancy, the experimental \(G_{\rm c}/G_{\rm m}\) values for various asphalt mastics were compared with the predictions of micromechanical models, as illustrated in Figure 8.  
Figure 8 indicates that for FAM with a mineral filler volume fraction of 29.73%, the experimental \(G_{\rm c}/G_{\rm m}\) value is lower than the GSC model's prediction. At this stage, the effective volume fraction (\(\phi_{\rm eff}\)) calculated using the GSC model is lower than the filler volume fraction (\(\phi_{\rm f}\)), resulting in the negative value observed in Figure 7b. Therefore, within a certain range of mineral filler content, the accuracy of the adsorbed asphalt film thickness predicted by the GSC model requires further validation. The micromechanical models employed in this study--namely, the Hashin model, Mori-Tanaka model, and generalized self-consistent (GSC) model--provide valuable insights into the interaction between asphalt and mineral fillers. However, these models are based on certain assumptions that may not fully account for the complexities of the actual internal structure of asphalt mastic. For instance, asphalt mastic may contain internal voids, and the interface between the mineral filler and asphalt may not always be  
Figure 7: Adsorbed asphalt film thickness based on different micromechanical models: (**a**) LAM; (**b**) FAM; (**c**) CAM. perfectly bonded [24; 25]. These factors are not explicitly considered in the models, leading to potential discrepancies between the model predictions and the actual internal structure of asphalt mastic. It should be noted that this limitation is not unique to these models; experimental methods for measuring the adsorbed asphalt film thickness also have inherent sources of error [15; 17]. Achieving a completely accurate measurement of the adsorbed asphalt film thickness remains a challenge at the current stage of technology and requires further in-depth research. The trends in the adsorbed asphalt film thickness are analyzed through the application of these micromechanical models, rather than focusing on the absolute accuracy of the predictions. This approach enables meaningful conclusions to be drawn regarding relative interaction strengths, which are crucial for understanding the performance of asphalt mastics. Figure 9 presents a comparison of film thickness predictions from three micromechanical models.