## 4 Results and Discussion
### Comparative Analysis of Adsorbed Asphalt Film Thickness Based on Different Micromechanical Models
It illustrates the relationship between the effective volume fraction of the mineral filler and the experimental \(G_{\rm c}/G_{\rm m}\) value. To eliminate the influence of factors such as mineral filler type, volume fraction, and temperature, the experimental \(G_{\rm c}/G_{\rm m}\) value for LAM with a mineral filler volume fraction of 11.89% at 28 \({}^{\circ}\)C was selected. In Figure 9, \(\phi_{1}\), \(\phi_{2}\), and \(\phi_{3}\) denote the differences between the effective volume fraction (\(\phi_{\rm eff}\)) and the filler volume fraction (\(\phi_{\rm f}\)) as predicted by the Hashin model, Mori-Tanaka model, and GSC model, respectively, for arbitrary experimental \(G_{\rm c}/G_{\rm m}\) values. According to Equation (4), for asphalt mastics with the same filler volume fraction, film thickness is determined by the difference between \(\phi_{\rm eff}\) and \(\phi_{\rm f}\). Thus, \(\phi_{1}\), \(\phi_{2}\), and \(\phi_{3}\) serve as indicators of film thickness trends predicted by the three micromechanical models. Within the critical volume fraction range of mineral filler defined in Section 3.3, before particles establish a contact network, their reinforcement effect on asphalt primarily results from volumetric filling and physicochemical interactions, without direct particle contact. The Hashin model captures the volumetric filling effect, whereas the Mori-Tanaka and GSC models incorporate inter-particle interactions to varying extents. The Mori-Tanaka model accounts for inter-particle interactions less comprehensively. In Figure 9, shaded areas of varying intensity represent the magnitudes of volumetric filling enhancement and inter-particle interaction enhancement. The physicochemical interaction capability between mineral filler and asphalt is reflected in the thickness of the adsorbed asphalt film, which depends on the difference between \(\phi_{\rm eff}\) and \(\phi_{\rm f}\). The lower shaded area (marked in the figure) represents the enhancement due to physicochemical interactions. The enlarged view of the Hashin and Mori-Tanaka model curves in Figure 9b shows that, compared to the Hashin model, the Mori-Tanaka model's consideration of inter  
Figure 8: Comparison between measured value and calculated value of \(G_{\rm c}/G_{\rm m}\) for different mastics. particle interactions results in a slight underestimation of physicochemical interactions between the asphalt and mineral filler. Consequently, the Mori-Tanaka model predicts a slightly smaller film thickness than the Hashin model. A comparison of Figure 9a,c reveals that the GSC model significantly underestimates the physicochemical interactions between the asphalt and mineral filler due to its consideration of inter-particle interactions. As a result, the GSC model predicts a significantly smaller film thickness than the other two methods and may even yield negative values. Based on this analysis, the Hashin model is chosen to determine the adsorbed asphalt film thickness for evaluating asphalt-mineral filler interaction capability. Improvement in Evaluation Indicators for the Interaction Between Asphalt and Mineral Filler Based on Hashin Model  
As discussed in Section 4.2, while the Hashin model provides a more accurate representation of the physicochemical interactions between asphalt and mineral filler, the adsorbed asphalt film thickness remains influenced by the mineral filler volume fraction. Eliminating this dependency is essential to ensure a more reliable evaluation. To achieve this, further refinement of the calculation method for adsorbed asphalt film thickness is required to establish a more accurate and representative interaction evaluation indicator. This section introduces a nonlinear fitting method for calculating adsorbed asphalt film thickness, transforming it into an independent interaction evaluation indicator while removing its dependency on the mineral filler volume fraction.