## 3 Research Methods  
### Finite Element Simulation Model  
(1) Two-dimensional Thermoelectric Coupling Model  
The thermoelectric coupling model of microwave heating asphalt concrete involves electromagnetic field control equations and heat transfer control equations. Theoretically, the heat transfer performance, dielectric properties, and magnetic permeability of asphalt concrete depend on the temperature. It is not realistic to accurately measure the relationship between all attribute parameters of asphalt concrete with temperature. Additionally, only the main attribute parameters can be selected, while the rest of the parameters are considered constant. The two-dimensional non-linear thermo-electric coupling model was established by selecting the asphalt (cement) concrete dielectric constant and the specific heat capacity, \(C_{P}\), as the temperature change parameters and the rest of the property parameters being constants. (2) Assumptions in Simulating Microwave De-icing  
The melting of ice and snow is a very complicated process, which involves the conversion of microwave energy into heat energy, which then conducts heat energy to the surface. To simplify the entire process of melting snow, some assumptions are made during the simulation. The ice cover on the pavement layer is uniform; asphalt concrete characteristics of the pavement layer are uniform. Ignore the change in volume when water is formed into ice. It is considered that \begin{table}
\begin{tabular}{c c c} \hline
**Material** & **Relative Dielectric Constant** & **Loss Angle Constant** \\ \hline Water & 76.7 & 0.157 \\ Ice & 3.2 & 0.0009 \\ Asphalt concrete & 4.5–6.5 & 0.015–0.036 \\ Cement concrete & 8 & 0.048 \\ \hline \end{tabular}
\end{table} 
Table 1: Relative dielectric constant and loss angle constant of materials. the whole analytical region is adiabatic on all four sides, that is, there is no heat loss. Loss of heat inside the concrete is used to heat the junction of the ice layer and the surface layer. Under microwave radiation, the sum of the absorbed microwave heat is a constant. The propagation of the microwave is propagated in the form of a plane wave. (3) Selection of Related Parameters  
According to the mechanism of microwave icing and the references related, the two-dimensional non-linear thermo-electric coupling model was established considering the asphalt (cement) concrete dielectric constant, loss angle constant, density, conductivity coefficient, and the specific heat capacity, \(C_{p}\), as the temperature change parameters. When using software to simulate the process of microwave melting snow, set the ambient temperature, ice temperature, and the initial temperature of the asphalt concrete to \(-10\)\({}^{\circ}\)C, microwave emission power of 1000 W, frequency of 2.45 GHz, 5.8 GHz, and air convection of 12.5 W/m\({}^{3}\). The relative dielectric constant and the loss angle constant of the material are shown in Table 1, and other relevant parameters that need to be used are shown in Table 2.  
(4) The Establishment of the Heat Transfer Model for Melting Snow  
The finite element simulation software, Abaqus (Abaqus6.14, SIMULIA, Providence, RI, USA), is used to simulate the heat conduction in the snow melting process. The simulation used a two-dimensional model and meshed the area, ABCD, of the simulation, as shown in Figure 2.  
Heat transfer in asphalt concrete: In heat transfer analysis, only the heat conduction is considered, the regular of the temperature distribution, T, of the asphalt concrete changing with time is determined by the heat conduction equation, i.e.,  
\[\rho C_{P}(T)\frac{\partial T(x,y,t)}{\partial t}=k_{\mathrm{eff}}\left[\frac {\partial^{2}T(x,y,t)}{\partial^{2}x}+\frac{\partial^{2}T(x,y,t)}{\partial^{2 }y}\right]+P^{*}(x,y) \tag{2}\]