## 2 Materials and Methods
### Test Methods
#### 2.3.3 High Temperature Rheological and Fatigue Properties Tests  
The Smart Pave 102 type DSR produced by Anton Paar Company of Austria (as shown in Figure 3) was adopted in this study. The high temperature rheological properties of MFAM after microwave heating were investigated via temperature sweep tests and frequency sweep tests. The parallel-plate with a diameter of 25 mm and a gap of 1 mm was selected in the tests. The temperature sweep tests were conducted between 46 \({}^{\circ}\)C and 82 \({}^{\circ}\)C at the constant stress of 0.12 Pa. The frequency sweep tests were performed from 0.1 Hz to 10 Hz at 40 \({}^{\circ}\)C, 50 \({}^{\circ}\)C, 60 \({}^{\circ}\)C, and 70 \({}^{\circ}\)C, respectively. The complex shear modulus (G*), phase angle (\(\delta\)), and rutting factor (G* \(\times\) (sin \(\delta\))\({}^{-1}\)) based on temperature sweep tests and frequency sweep tests are three important parameters quantifying rheological properties of materials. G* reflects the ability to resist deformation of asphalt materials. The larger the G*, the better the deformation resistance of the material. \(\delta\) is an index assessing the components of viscosity and elasticity of asphalt materials. The smaller the \(\delta\) is, the more elasticity and the less viscosity the material has. G* \(\times\) (sin \(\delta\))\({}^{-1}\) is an indicator reflecting the resistance to rutting of asphalt materials. The larger the G* \(\times\) (sin \(\delta\))\({}^{-1}\), the better resistance of the material. Figure 3: Smart Pave 102 type DSR. Figure 2: FCMCR-3C type microwave reactor. The fatigue properties of MFAM after microwave heating were evaluated via LAS tests. The parallel-plate with a diameter of 8 mm and a gap of 2 mm was selected in the tests. The test included two steps: (1) the frequency sweep performed from 0.2 Hz to 30 Hz at a strain of 0.1% and a temperature of 20 \({}^{\circ}\)C, and (2) the strain amplitude sweep conducted from 0.1% to 30% at a frequency of 10 Hz and a loading time of 10 s under each strain. According to LAS test results, non-destructive parameter \(\alpha\) can be calculated by Equations (6) and (7), and cumulative damage \(D(t)\) can be calculated by Equation (8). \[\log{G^{\prime}(\omega)}=m(\log{\omega})+b \tag{6}\]  
\[\alpha=1+\frac{1}{m} \tag{7}\]  
\[D(t)\cong\sum_{i=1}^{N}{[\pi I_{D}\gamma_{0}^{2}(|G^{*}|\sin{\delta_{i-1}}-G^{ *}|\sin{\delta_{i}}|)]^{\frac{\alpha}{1+\alpha}}(t_{i}-t_{i-1})^{\frac{1}{1+ \alpha}}} \tag{8}\]  
where \(G^{\prime}(\omega)\) is storage modulus, MPa; \(\omega\) is frequency, Hz; \(m\) is fitting parameter; \(I_{D}\) is complex shear modulus at a strain level of 1%, MPa; \(\gamma_{0}\) is strain level, %; \(|G^{*}|\) is complex shear modulus, MPa; and \(t\) is test time, s.  
According to viscoelastic continuum damage (VED) theory, the relationship between \(|G^{*}|\sin{\delta(\omega)}\) and \(D(t)\) can be described by Equation (9). \[\left|G^{*}\right|\sin{\delta}=C(t)=C_{0}-C_{1}(D)^{C_{2}} \tag{9}\]  
where \(C_{0}\) equals 1, and \(C_{1}\) and \(C_{2}\) are fitting parameters. Fatigue failure criterion \(D_{f}\) is defined as Equation (10). Fatigue life \(N_{f}\) can be calculated by Equations (10)-(14). \[D_{f}=0.35(\frac{C_{0}}{C_{1}})^{\frac{1}{C_{2}}} \tag{10}\]  
\[A_{35}=\frac{f(D_{f})^{k}}{k(\pi I_{D}C_{1}C_{2})^{\alpha}} \tag{11}\]  
\[k=1+(1-C_{2})\alpha \tag{12}\]  
\[B=-2\alpha \tag{13}\]  
\[N_{f}=A_{35}(\gamma_{\max})^{B}\at low frequencies, while the opposite is true when the frequency is greater than 4.8 GHz. As can be seen from Figure 4d, the value of \(\mu^{\prime\prime}\) for the magnetite filler is between 0 and 0.29 and larger than that of the limestone filler in general, indicating that the magnetite filler has a higher magnetic loss than limestone filler. Moreover, with the increase in frequency, both \(\mu^{\prime}\) and \(\mu^{\prime\prime}\) of the magnetite filler show a wavelike decrease.