## Mechanism Analysis
### Microwave Ice Melting Mechanism  
According to the theory and practice of microwave heating, it can be known that microwave heating is actually a process of consuming power, and the formula for the microwave power to be consumed for heating a unit volume of a substance is:  
\[P=0.556f\varepsilon_{r}^{\prime}\tan\delta\cdot E^{2}\times 10^{-12} \tag{1}\]  
where \(P\) is the power consumed on a per unit volume basis; \(f\) is the microwave frequency; \(E\) is the electric field intensity; \(\varepsilon_{r}^{\prime}\) is the relative dielectric constant; and \(\tan\delta\) is the loss angle constant.  
From formula (1), the main performance parameters that affect the absorption of microwave energy by the material are the relative dielectric constant and the loss angle constant. The smaller the relative dielectric constant and the loss angle constant are, the worse the absorbing ability of the material is. Table 1 shows the relative dielectric constant and the loss angle constant of various materials.  
Figure 1: Diagram showing dielectric polarization.  
It can be seen from Table 1 that the relative dielectric constant of ice at \(-12\)\({}^{\circ}\)C is 3.2, and the value of the loss angle constant is 0.0009, which is relatively small. It can be known from formula (1) that the power loss of microwaves in ice is extremely small when \(\tan\delta=0.0009\). Therefore, when microwave heating is applied to the icing of road pavements, the microwave energy is minimally depleted in the ice layer, the ice layer on the road surface hardly absorbs microwave energy, and the ice layer is equivalent to \"transparent\" for microwaves. Microwave energy can penetrate the ice directly, just as light can penetrate transparent glass. After the microwave penetrates the ice layer, it directly acts on the road surface. The surface materials, such as asphalt concrete and cement concrete, can absorb part of the microwave energy and convert the microwave energy into heat energy, thereby melting the ice at the junction between the road surface layer and the ice layer. When the ice at the junction is melted into water, the liquid water can also absorb microwave energy in a large amount, which will greatly accelerate the melting of the ice formed at the junction between the road surface layer and the ice layer, thereby reducing the bond stress between the ice and the surface layer. When the bond stress is zero, it will make the road deicing easier. Only by adding machinery or manpower can it be easy to remove ice from the road and achieve ice melting on the road. In actual projects, the thickness of the asphalt concrete surface layer on highways and urban roads is generally between 12-20 cm. For supporting load pavement, the thickness may be as high as 30 cm or more. When heating the asphalt concrete pavement with microwaves, the effective heating depth is generally between 0 to 15 cm. Therefore, in the simulation of asphalt concrete pavement, to simplify the simulation, when microwave heating the pavement, only the road surface layer, which is the asphalt concrete surface layer, is heated. In the two-dimensional simulation, the length and width of the simulated area are all 15 cm, and the upper layer covered 5 cm of ice.