## 3 Experimental Methods and Model Parameters  
### Experimental Methods  
The asphalt used in this study is Liaohe 90# base asphalt, sourced from Panjin, Liaoning Province, China. The basic properties of the asphalt are summarized in Table 1.  
Three types of mineral fillers were selected for this study: limestone filler, fly ash, and coal gangue filler. Natural limestone was sourced from Zhengzhou, Henan, China, while fly ash was obtained from the Zhengzhou Power Plant, and coal gangue filler was derived from crushed unburned coal gangue from the Zhengzhou Coal Mine. The appearance of these fillers is shown in Figure 4. The specific surface area of the three fillers was measured using the Brunauer-Emmett-Teller Surface Area Analyzer (Autosorb-iQ, Quantachrome Instruments, Boynton Beach, FL, USA). The basic properties of the fillers are presented in Table 2.  
A laser particle size analyzer was employed to sequentially test the three types of mineral powders. The average of three measurements was taken to plot the particle size distribution curves, as shown in Figure 5. The results indicate that among the three types of mineral powders, the fly ash powder exhibits the finest particle size, with 90% of the particles having a diameter below 26.942 \(\upmu\)m. The particle sizes of the three mineral powders, in ascending order, are as follows: fly ash \(<\) limestone filler \(<\) coal gangue filler.  
Three types of fillers were selected and mixed with 90# base asphalt to prepare the asphalt mastics. The filler-to-binder (F/B) ratios were set at 0.4, 0.8, 1.2, 1.6, and 2.0. The resulting mastics were designated as limestone asphalt mastic (LAM), fly ash asphalt mastic  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Index** & **Penetration at** & **Softening** & **Ductility at** & **Flash Point (\({}^{\circ}\)C)** & **Density at** \\
**25 \({}^{\circ}\)C (0.1 mm)** & **Point (\({}^{\circ}\)C)** & 5 \({}^{\circ}\)C (cm)** & **15 \({}^{\circ}\)C (g/cm\({}^{3}\))** \\ \hline Test results & 80 & 48 & 8.6 & 254 & 1.003 \\ Specification requirements & & & & & \\
[1] & 80–100 & \(\geq\)44 & / & \(\geq\)254 & As-measured record \\ (JTG F40-2004) 1  & & & & \\ \end{tabular}
\end{table}
Table 1: Basic properties of asphalt.  
Figure 4: Pile appearance of different fillers: (**a**) limestone filler; (**b**) fly ash; (**c**) coal gangue filler.  
(FAM), and coal gangue asphalt mastic (CAM). The preparation process of the asphalt mastic was as follows: The fillers were first dried in an oven at 165 \({}^{\circ}\)C for 2 h to remove any residual moisture. Subsequently, the dried fillers were cooled to room temperature in a desiccator to ensure thermal stability prior to mixing. Meanwhile, the base asphalt was heated to 140 \({}^{\circ}\)C to achieve optimal fluidity for uniform mixing. After weighing the fillers and asphalt according to the predetermined filler-to-binder ratios, the components were mixed in a preheated iron pan to ensure thorough dispersion and adhesion between the fillers and asphalt binder. The mixture was then stirred with an electric stirrer at a speed of 300 RPM and a temperature of 150 \({}^{\circ}\)C for 15 min, until homogeneity was achieved and no air bubbles were present on the surface of the asphalt mastic.  
A Bohlin Gemini rheometer was utilized to conduct temperature-frequency scanning tests on the asphalt and asphalt mastic samples to measure their complex shear modulus values. An 8 mm diameter parallel plate was used, with a sample thickness of 2 mm. The loading rate ranged from 0.628 to 125.7 rad/s, corresponding to frequencies from 0.1 to 20 Hz. The tests were performed at temperatures of 28 \({}^{\circ}\)C, 40 \({}^{\circ}\)C, and 52 \({}^{\circ}\)C, with a loading strain of 0.1%.