## 1 Introduction  
Snow and ice on highways have become a major cause of car accidents during the winter. To address this issue, numerous efforts have been made to melt snow and ice on roadways, the most common of which are chemical de-icing [1, 2], geothermal de-icing [3, 4], and electric de-icing [5, 6]. The spraying of de-icing chemicals on the road to melt snow and ice is a chemical de-icing method that not only demands a lot of people and material resources, but also causes traffic congestion and traffic safety hazards. De-icing chemicals left on roads can cause corrosion damage to pavement structures when they seep into the road [7] and damage soil ecology when they seep into the soil [8, 9]. In order to convey heat from underground heat sources to the road surface, the geothermal de-icing method entails laying circulation pipes on the road's surface. These pipes use gas or liquid as the circulation medium. However, this technology has more severe circulating media requirements, and the selection and installation of circulating pipes and subsurface heat exchange tubes is more difficult. Electrothermal de-icing technology melts snow and ice by putting conductive material on road, bridge, and airport pavement and activating that material to generate heat by utilizing the conductive material's electrical resistance [10]. Because of the benefits of its easy building process, low cost, environmental protection, high efficiency, and stability, the technology is extensively employed in actual projects. Carbon fiber heating wire is becoming increasingly extensively employed as a conductive material for snow and ice melting as technology advances. The investigation of road surface temperature stress is separated into two parts: temperature distribution and mechanical properties. In terms of temperature distribution, [PERSON] [11] meticulously examined the impact of previous de-icing technologies on both the road and environment, establishing the long-term viability of electric heating as an environmentally beneficial de-icing technology. [PERSON] [12] investigated the de-icing impact of carbon fiber electric heating wire on concrete pavement using model testing and numerical experiments, establishing the feasibility of de-icing concrete pavement using carbon fiber electric heating wire as well as the benefits of cleanliness and environmental protection. Real-time de-icing is faster than previous procedures and demonstrates the advantages of carbon fiber over other heating wire materials, including it being lightweight and possessing high flexibility and high tensile strength. [PERSON] [13] investigated the effect of heat flux on the ice melting effect of concrete pavement through model tests and suggested that the increase in heat flux can effectively reduce the total energy consumption of ice melting. [PERSON] [14] established a full-scale model in the field for assessing the performance of the carbon fiber heating wire approach for snow melting on airport pavement, proposing that a nonlinear temperature gradient is formed inside the pavement during the heating process. [PERSON] [15] proposed an electric heat pipe ice and snow melting pavement thermal field prediction model based on line heat source theory, considering the effects of burial spacing, burial depth, heating power, heating time, and ambient temperature on pavement temperature. [PERSON] [16] developed a one-dimensional heat transfer model for pavement temperature distribution and evaluated the influence of air temperature on stiff paving slab temperature distribution along the depth direction. [PERSON] [17] presented a three-dimensional finite element model for effectively forecasting the thermal behavior of fire-exposed RC beams. [PERSON] [18] used thermal modeling to evaluate the impacts of electric heating pipe burial spacing and depth, heating power, and wind speed on the energy consumption and energy utilization of an electric heating pipe automated snow melting system.