# The Law and Mechanism of the Effect of Surface Roughness on Microwave-Assisted Rock Breaking
## 4 Analysis and Discussion  
Microwave-assisted rock breaking is the process of applying microwave irradiation to rock: The rock temperature rises to produce thermal stress, and when the stress is greater than the strength limit, the rock is damaged. This is an electromagnetic-thermal-solid multi-field coupling process. In this section, the mechanisms of the influence of rough surfaces on the effect of microwave irradiation are discussed. When an electromagnetic wave is incident at the interface of the medium, reflection, diffraction, and refraction occur. The power flow density results indicate that the direction of the power flow density of rough surfaces changes when it reaches the surface of the sample, and the direction of the power flow density is consistent with the propagation direction of the electromagnetic wave. Thus, the incident angle of the electromagnetic wave is changed by the rough surface, and the refractive angle and the reflection angle are also altered. Table 2 presents the average results of the microwave incidence angle calculations for the whole rough surface performed in MATLAB. Calculating the reflection coefficient R through [PERSON]'s formula, the reflection coefficient of the flat surface was approximately 0.250, and the reflection coefficient of the specimen with a roughness of 1.5 was approximately 0.179, i.e., the electric field strength of the specimen with a flat surface and that of the sample with a roughness value of 1.5 were approximately 50% and 42.3%, respectively, indicating that the rough surface can reduce the energy loss caused by a certain electromagnetic wave reflection. When an incident wave passes through the surface of a medium, a reflected wave and a refracted wave are formed with frequencies that are the same as the incident wave; thus, reflection of the electromagnetic wave can easily cause interference between the incident wave and the reflected wave, weakening the electric field strength of the microwave. The incident wave and the reflected wave on a flat surface have the same frequency but contrasting directions and phase differences; as such, interference occurs, thereby weakening \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Roughness**} & **Average Incident** & **Reflection** & **Reflection Loss Rate** \\  & **Angle (°)** & **Coefficient, R** & **(\%)** \\ \hline
1 & 0 & 0.250 & 50.0 \\
1.1 & 25 & 0.227 & 47.6 \\
1.2 & 34 & 0.209 & 45.7 \\
1.3 & 40 & 0.196 & 44.2 \\
1.4 & 44 & 0.187 & 43.2 \\
1.5 & 48 & 0.179 & 42.3 \\
1.6 & 51 & 0.175 & 41.8 \\
1.7 & 54 & 0.172 & 41.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Reflection coefficient and reflection loss for samples of each roughness value. Figure 16: The total volume of the plastic zone of the samples with different roughness values after microwave irradiation. the intensity of the incident wave. The incident wave approached the rough surface in different directions from the reflected wave, and thus, the influence of the reflected wave on the incident wave was reduced. Therefore, the loss of electric field strength was further reduced by the rough surface specimen relative to the flat surface specimen. Solid heat transfer methods include heat conduction, convective heat transfer, and heat radiation: Convective heat transfer and heat radiation are the transfers of heat between the sample and the air, although the amount of heat transferred is small, and the influence of the two is basically negligible in microwave-irradiated rock; heat conduction is the main influencing factor.