## 4 Results and Discussion
### Microwave Frequency
#### 4.1.1 Simulation Research  
When the initial temperature of the ice layer and asphalt concrete surface layer is \(-10\)\({}^{\circ}\)C, the output power of the microwave is 1000 W, the ice layer thickness is 50 mm, and the emitter is 50 mm away from the ice surface. The model is used to analyze the de-icing process with microwave emission frequencies of 2.45 GHz and 5.8 GHz. The simulation of the temperature field under different frequencies is shown in Figure 5.  
As shown in Figure 6, when the microwave emission frequencies are 2.45 GHz and 5.8 GHz, respectively, the temperature at the center point, G, changes with time. It can be seen from Figure 6 that the temperature at the center point, G, rises continuously as time increases under the influence of the microwave energy. At different transmission frequencies, the time for point G to reach 0 \({}^{\circ}\)C is different, and its time is 280 s and 65 s, respectively. It can be concluded that the 5.8 GHz ice-melting efficiency is 4.31 times more than that of 2.45 GHz. Under the same conditions,  
Figure 5: Distribution of the temperature field at different microwave frequencies. Figure 6: Comparison of temperature changes at different frequencies at point G.  
the deicing efficiency at the frequency of 5.8 GHz was greatly improved, and the ice-melting time only required 65 s. From a molecular point of view, microwaves polarize molecules and cause regular and intense movements of the molecules. This movement causes molecules to rub against each other and produce a lot of heat, which causes the material to be heated. When the frequency is changed from 2.45 GHz to 5.8 GHz, the speed and amplitude of polar molecules will increase accordingly, and the motion will become even stronger. The more heat the friction generates, the faster the ice at the interface will melt into water. Water can absorb a large amount of microwave energy and accelerate the melting of ice on the junction between the road surface and the ice layer. Therefore, the ice melting time is reduced and the efficiency is improved at high frequencies. Therefore, increasing the microwave frequency can improve the deicing efficiency. The temperature field distribution of asphalt concrete is shown in Figures 5 and 7. When the surface temperature of asphalt concrete specimen reaches 0 \({}^{\circ}\)C, the temperature of the ice surface is the lowest, and the concrete specimen first rises with the depth, and reaches the peak value of 12 mm. After that, the temperature decreases as the depth increases. Under 2.45 GHz microwave radiation, the depth of the temperature rise is even higher. The reason for this phenomenon may be that on the one hand, the microwave heating time of 2.45 GHz (280 s) is longer than the microwave heating time of 5.8 GHz (65 s), and the sample under 2.45 GHz absorbs more heat. On the other hand, from the perspective of energetics, when the microwaves heat the road surface, the microwave energy absorbed by the surface of the road is the most. As the depth of the road surface increases, the transformed microwave energy absorbed by the deeper position of the pavement layer is gradually reduced, and this process appears as an exponential decay. Therefore, there is a heating depth indicator when heating the road surface by microwaves. Heating depth refers to the depth of the node from the surface when the microwave power decays from the surface of the material to an initial value, \(\frac{1}{\epsilon}\), or 0.3679 times. The heating depth, \(D\), is calculated as follows:  
\[D=\frac{\lambda_{0}}{\pi\sqrt{2\epsilon^{\prime}\Big{(}\sqrt{1+\tan^{2}\delta }-1\Big{)}}} \tag{6}\]  
The formula for calculating the wavelength and frequency is:  
\[f=\frac{c}{\lambda}\Leftrightarrow\lambda=\frac{c}{f} \tag{7}\]  
where \(\lambda_{0}\) is the free space wavelength of the microwave; \(\epsilon^{\prime}_{r}\) is the relative dielectric constant; \(\tan\delta\) is the loss angle constant; and \(c=3\times 10^{8}\) m/s.