Optimization and Analysis of Electrical Heating Ice-Melting Asphalt Pavement Models

Abstract

Electrical heating ice removal pavement represents a promising technology for pavement ice melting. Existing studies primarily focus on optimizing cable-heated asphalt pavement through indoor model tests or finite element results. To obtain more accurate and reasonable temperature rise processes and heat transfer results, we propose a new evaluation metric for heat transfer capability and optimization in electric heating asphalt pavement. Firstly, a three-dimensional heat transfer model considering environmental heat exchange is established, and the accuracy of the model is verified by outdoor measured data. A dual-variable control experiment was carried out between the cable buried depth and insulation layer configuration to specifically analyze their influence on the temperature field of the asphalt layer. We further investigated heat transfer performance metrics (entransy dissipation and entransy dissipation thermal resistance), with results indicating that shallower cable burial depths reduce environmental interference on pavement heat transfer; the thermal insulation layer most significantly enhances pavement surface temperature (35.66% improvement) when cables are embedded in the lower asphalt layer. Placing cables within corresponding pavement layers according to burial depth reduces heat transfer loss capacity and thermal resistance, and positioning cables in the lower asphalt layer with a thermal insulation layer significantly decreases thermal resistance in both concrete and lower asphalt layers while reducing heat transfer capacity loss, demonstrating that installing thermal insulation layers under this structure improves heat transfer efficiency. The combined experimental and simulation verification method and fire dissipation evaluation system proposed in this study provide a new theoretical tool and design criterion for the optimization of electric heating road systems.

1. Introduction

Winter blizzards, freezing rain, and other severe weather conditions can result in road icing or snow accumulation. Once snow and ice on roads are not promptly removed, the anti-slip performance of roads will be significantly reduced, which can lead to vehicle skidding or brake failure, and exacerbate traffic congestion, delays, and transportation costs. To address this issue, numerous efforts have been made, including traditional mechanical de-icing and chemical de-icing [1,2,3], as well as the rapidly developing active ice-melting pavement technologies, such as geothermal de-icing pavements [4,5,6] and electric heating de-icing pavements [7,8,9,10,11].

Traditional mechanical and chemical de-icing requires a lot of time and labor costs, which is inefficient and costly. More importantly, chemical de-icing can corrode infrastructure, cause severe water pollution, and have significant environmental impacts [12,13]. Therefore, some efficient and environmentally friendly “active” snow-melting technologies are increasingly favored by people. Along with electric heating technology’s continuous development and maturation, its application in active snow and ice removal fields is becoming increasingly widespread [9,14,15,16,17]. Electrical heating snow and ice removal technology converts electrical energy into thermal energy to heat the road surface, thereby achieving the melting of ice layers. Compared to other active de-icing road surfaces (such as anti-freezing pavement, phase change material pavement, geothermal energy, solar energy, etc.), it has the advantages of being simple to operate, easy to control, and fast acting. As a new type of heating material, carbon fiber heating elements have the advantages of good electrical conductivity, high strength, good thermal stability, and high energy conversion efficiency [10,18]. Therefore, the heating cables used on the road surface are mainly carbon fiber cables.

In recent years, extensive research has been conducted on the impact of design parameters of electric heating snow-melting pavements on snow-melting performance. For instance, to achieve optimal pavement structure, Jiao et al. [8] recommended the best system parameters based on snow-melting efficiency, energy costs, and mechanical durability of the pavement. Mohammed et al. [19] embedded three different forms of carbon fibers into concrete specimens to investigate the effects of thermal power density, ambient temperature, installation depth, concrete water content, and carbon fiber morphology on temperature variations. Moreover, Zhu et al. [9] explored the comprehensive energy-efficient design strategies for cable heating systems, employing the finite element method to study the effects of different parameters on snow melting, energy consumption, and mechanical responses of cable heating systems. The recommended optimal pavement structure involves a cable power of p = 32 W/m, spacing of s = 100 mm, burial depth of d = 30 mm, and the inclusion of an insulating layer. To improve snow melting efficiency, Fu et al. [14] investigated a directional heat transfer electric heating bridge system with an insulation layer and determined the optimal mixing ratio using fuzzy mathematics. They evaluated the heating and snow-melting performance of the model. Studies have shown that a heat-conductive functional layer with a water-to-cement ratio of 0.53 and an iron powder-to-cement ratio of 2, composed of reduced iron powder, achieves the best thermal conductivity, flexural strength, and compressive strength. Zheng et al. [10] used extruded polystyrene foam board (XPS) and polyethylene foam cotton (PEF) as insulation materials under carbon fiber heating cables. Results demonstrated that compared to road structures without insulation layers, the ice melting rate increased by 25% to 50%. Jiao et al. [15] incorporated steel slag as heat-conductive fillers in pavement structures and applied them to the upper layer of the pavement to enhance the heat transfer efficiency of the electric heating system. Wang et al. [20] developed a new method for calculating snow-free ratios based on pavement temperature distribution, incorporating pavement average temperature and pavement temperature uniformity coefficient. Through finite element simulation, the effects of heating tube spacing, burial depth, heating power, and wind speed on average temperature and temperature uniformity coefficient were analyzed, and prediction models for average temperature and temperature uniformity coefficient were established.

Based on the aforementioned research, it can be observed that existing studies have mainly focused on optimizing cable-heated asphalt pavements based on test results or finite element analysis results, such as optimizing power, insulation materials, and structural design according to surface temperature or snowmelt rates. However, research based on outdoor asphalt pavements’ heat transfer capabilities or characteristics for optimization purposes is relatively limited. To more scientifically determine pavement structure and reduce energy waste, studying the heat transfer capabilities and characteristics of asphalt pavements is necessary. To overcome the limitations of conventional heat transfer analysis methods, Guo et al. [21,22] introduced the concept of entransy to address optimization challenges in heat transfer processes. Entransy describes an object’s capacity to transfer thermal energy, with entransy-based theoretical research having successfully guided multi-objective optimization of heat exchanger networks, enhanced convective heat transfer in microchannels, gradient thermal conductivity pavement cooling designs, and asphalt pavement heat transfer characteristics. Notable applications include Xu et al.’s [23] optimization analysis of cascade latent heat storage systems, Wang et al.’s [24] derivation of optimal melting temperatures through entransy dissipation in dual-stage latent heat storage units [22], Liu et al.’s [25] calculation of equivalent thermal conductivity and resistance in composite materials [23], and Zhao et al.’s [26,27] establishment of entransy as a quantitative indicator for asphalt pavement heat transfer capacity, enabling systematic evaluation of pavement temperature and thermal effects using entransy dissipation. In summary, entransy exhibits independence from system geometry or material homogeneity/heterogeneity, establishing it as an essential physical quantity for investigating system-level heat transfer capacity and characteristics.

This study establishes and conducts small-scale outdoor field experiments to obtain more accurate and rational temperature rise processes and heat transfer results while proposing novel evaluation metrics for investigating heat transfer characteristics and optimization of electrothermal asphalt pavements. Firstly, a three-dimensional heat transfer finite element model of electrically heated pavement was developed using ANSYS 2021 R1 software and validated through outdoor ice-melting experiments. Subsequently, the effects of design parameters (embedment depth, insulation layer) on surface temperature and subsurface asphalt layer temperature were systematically analyzed. Furthermore, heat transfer performance metrics including entransy dissipation and entransy dissipation thermal resistance were quantitatively evaluated. The study reveals key contributing factors to heat transfer capacity loss in electrically heated ice-melting pavements, establishing a theoretical framework for analyzing thermal performance characteristics of snow-melting pavement systems in cold regions.

2. Methods

2.1. Numerical Model

The longitudinal (y-axis direction) and horizontal (x-axis direction) dimensions of the model are 3.5 m and 1.75 m, respectively. The model composition is shown in Figure 1. S1 is the distance of the carbon fiber heating cable from the left side of the pavement, S2 is the distance of the carbon fiber heating cable from the right side of the pavement, d is the burial depth of the cable, and S is the spacing of the cables. The structural and thermal parameter performances of the pavement model are given in

Table 1. Material and thermophysical parameter characteristics of pavement layer [9,14,27].

Material/Layer	Thickness/mm	Density/kg/m3	Thermal Conductivity (W/(m·K))	Specific Heat Capacity (J/(kg·K))	Poisson’s Ratio (-)
cable	Diameter 9 mm	7930	24.5	510	0.3
SMA-13	40	2300	0.833	1000	0.35
AC-20	60	2400	1.583	970	0.35
C30	100	2380	1.74	925	0.24
ice	5	917	2.2	2050	0.33
insulation layer	2	400	0.18	400	0.26

.

Table 2. Design parameters of finite element and test model.

Parameters	d/mm	Thermal Insulation Layer/mm	Ice Thickness/mm
Test model	115	With/Without	0/5
Numerical model (Scheme 1)	115	With	5
Numerical model (Scheme 2)	115	Without	5
Numerical model (Scheme 3)	85	With	5
Numerical model (Scheme 4)	85	Without	5
Numerical model (Scheme 5)	32	With	5
Numerical model (Scheme 6)	32	Without	5

gives the parameters of the experimental and numerical models for designing different burial depths, where S1 is 500 mm, S2 is 500 mm, and cable spacing S is 10 cm.

To calculate the temperature field, in the finite element model, the cable model is simplified as a solid cylinder, whose body heat source density is represented by $q_c$ (W/m³)—that is, the power of the 1 m³ cable entity, which can be calculated as follows:

$$q_c={\displaystyle \frac{4p}{\pi D^2}}$$

(1)

Here, D is the cable diameter (m) and p is the heating power of 1 m cable (W/m).

2.2. Boundary Conditions

In thermal analysis, boundary conditions need to be applied, assuming that the upper boundary is convective heat transfer. In this research, the surrounding and lower boundaries are adiabatic, and the heat convection boundary conditions are applied to the top, which satisfies the equation as follows:

$$h(T-T_{\mathrm{e}})+\lambda {\displaystyle \frac{\partial T}{\partial \overrightarrow{n}}}=0$$

(2)

Here, T is the road temperature and $T_e$ is the ambient temperature; in this research, the ambient temperature is a constant (−3 °C), $\lambda$ is the thermal conductivity, and $h$ is the convective heat transfer coefficient, determined by Equation (3):

$$h=5.678[a+b{\left({\displaystyle \frac{v}{0.304}}\right)}^n]$$

(3)

where $v$ is the ambient wind speed (m/s); when 0 ≤ $v$ ≤ 4.88, $a$ = 1.09, $b$ = 0.23, $n$ = 1, when 4.88 ≤ $v$ ≤ 30.48, $a$ = 0, $b$ = 0.53, $n$ = 0.78.

In thermal analysis, it is assumed that the heat generated by the cable is mainly transferred to the road surface through thermal conduction. The temperature function $T(x,y,z,t)$ of asphalt pavement is not only related to the spatial position but also to the change in time. The heat conduction temperature field of asphalt pavement can be described as follows:

$$\rho c{\displaystyle \frac{\partial T_1}{\partial t}}+q_{c\left(t\right)}={\displaystyle \frac{\partial }{\partial x}}(\lambda {\displaystyle \frac{\partial T_1}{\partial x}})+{\displaystyle \frac{\partial }{\partial y}}(\lambda {\displaystyle \frac{\partial T_1}{\partial y}})+{\displaystyle \frac{\partial }{\partial z}}(\lambda {\displaystyle \frac{\partial T_1}{\partial z}})$$

(4)

$\rho$ is the density of asphalt pavement; λ is the thermal conductivity; $c$ is the specific heat capacity of the pavement layer; $T$ is the temperature of the pavement layer; and $q_{c\left(t\right)}$ is the heat source of the cable.

2.3. Optimization Index

In winter, the main external factors affecting the effect of snow melting on the road surface are wind speed, ambient temperature, ice or snow layer thickness, and the internal factors are cable heating power, buried depth, and spacing. To improve the snow melting efficiency of road surfaces and reduce energy consumption, it is necessary to analyze the structure and heat transfer characteristics of road cable systems. In this research, the buried depth and heat insulation layer are selected as the design factors, the finite element model is established and the numerical analysis is carried out, and the pavement temperature, entransy dissipation, and entransy dissipation thermal resistance are taken as the heat transfer performance indexes of the pavement structure to analyze the optimal pavement heat transfer structure.

2.3.1. Pavement Temperature

The surface temperature of the road directly affects the melting speed of snow and ice, which in turn affects the safety of the road. Specifically, road surface temperature is closely related to snow melting and ice formation. When ambient temperatures approach or fall below freezing, the system should be activated to maintain a safe road surface temperature. During periods of slightly elevated temperatures, the system can be deactivated due to the distinct thermal responses of different pavement materials. Notably, asphalt concrete exhibits superior heat storage capacity compared to conventional concrete, enabling natural ice melting through its retained thermal energy without requiring external heating intervention. Therefore, understanding and monitoring the road temperature can help determine whether it is necessary to turn on the heating system to maintain a certain temperature of the road and ensure the safety of the road [28].

2.3.2. Entransy Dissipation and Entransy Dissipation Thermal Resistance

Analogous to the current in the conductor medium transmission, due to resistance caused by the loss of electrical energy, is fluid in the medium transfer process due to resistance caused by the dissipation of mechanical energy, and heat in the transfer process due to the role of thermal resistance will also exist in the dissipation phenomenon, except that the transmission process of heat is conservative, causing the dissipation of the fire volume. The lower the transfer efficiency of the fire product, the greater the dissipation of the entransy dissipation, indicating that the deeper pavement layer, the greater the loss of heat transfer capacity. The definition of the entransy dissipation is the following formula [7,21,26,27,29]:

$$E_g=\iiint k|\nabla T{|}^{2}dV$$

(5)

Here $k$ is the thermal conductivity W/(m·°C); $\nabla T$ is the temperature gradient of the pavement layer °C m⁻¹.

The thermal resistance in heat transfer is usually defined in the one-dimensional case. In two or three dimensions, the thermal resistance in general heat transfer can only be described by dividing the difference between the highest temperature and the lowest temperature by the heat transfer. Therefore, quantifying thermal resistance by temperature difference at non-isothermal boundaries becomes arbitrary and inaccurate. To avoid these problems, the thermal resistance is redefined using the theory of entransy dissipation, as shown in Equation (6) [21,26,30]:

$$R_g={\displaystyle \frac{E_g}{Q^2}}={\displaystyle \frac{\iiint k|\nabla T{|}^{2}dV}{({\iint \dot{q}·\mathit{n}dS)}^2}}$$

(6)

Here, $E_g$ is the entransy dissipation, W·K, $k$ is the thermal conductivity of the road layer, the unit is W/(m·K); $\nabla T$ is the temperature gradient K/m, $\dot{q}$ is the heat flux vector W/m², $n$ is the unit normal vector, and $Q$ is the heat transfer W.

To enhance the heat transfer performance, the principle of minimum dissipative thermal resistance was implemented during structural optimization [20,28]. In the context of road surface heat transfer processes, inevitable thermal dissipation leads to a reduction in heat transfer efficiency. Therefore, the heat transfer capacity and heat transfer effect of ice and snow melting pavement in the heat transfer process is evaluated and the optimal structure is selected by using entransy dissipation and entransy dissipation thermal resistance as measurement indexes and referring to the surface temperature of the road surface.

3. Experimentation and Validation

3.1. Outdoor Model

The size of the outdoor model is 350 cm in the longitudinal direction (Y-direction) and 350 cm in the transverse direction (X-direction). There is a 4 cm asphalt upper layer, 6 cm asphalt lower layer, and 10 cm concrete layer, respectively, from top to bottom. Figure 2 shows the process of outdoor modelingl. The depth of the grooves carved in the concrete pavement to place the heat-generating cables is 2 cm, and then the insulation layer, internal thermocouples, and installation of the cables are arranged, and finally, two layers of asphalt are paved on top and compacted.

As shown in Figure 3, three layers of thermocouples are arranged, all of which are located in the center of the road—that is, 1.75 m. The first layer’s surface thermocouple serial numbers are #14, #15, #16, #17, #18, and #19, while the second layer is 11.5 cm away from the surface and the serial numbers are #1~#5, #6, #8, #9, #10 and #12. The third layer is 11.7 cm from the surface and the serial numbers are #7, #11, and #13.

3.2. Experimental Results and Verification

When the road temperature is low in winter, the ambient temperature is also low, which may cause the road to freeze due to frost, freezing rain, and snow. To prevent the road from freezing, when the temperature is low in winter, the electric heating system is turned on (from 12:00 a.m. to 5:00 a.m.), and the pictures of the initial and melted ice layer are shown in Figure 4.

Figure 5 shows the comparison between the measured road temperature and the simulated data. There are some differences between the simulated results and the measured temperatures. This is because the heat transfer of the actual road surface is more complex than that of the simulation, and the influence of the surrounding environment and the heat transfer inside the road surface make the results slightly different. However, it can be seen that the temperature field simulation results of asphalt pavement have a strong agreement with the measured results. Therefore, the heat transfer model can be used to analyze the heat transfer process of asphalt snow-melting pavement.

4. Results and Discussion

4.1. Pavement Temperature Variation

In practical engineering, the fusion of vehicle-mounted/fixed cameras and infrared sensors can be used to determine the switch-on time of the system by obtaining real-time visual characteristics of the road surface temperature field, cracks, and snow and ice cover [29]. Figure 6 shows the rise in pavement surface temperature and asphalt sublayer surface temperature during ice melting when the cable is located in the concrete layer. It can be seen that within five hours, the surface temperature of Scheme 2 (without the insulation model) reaches 1.61 °C, and Scheme 1 (with the insulation model) reaches 1.98 °C. The surface temperature of the asphalt underlayer in the insulated model reaches 9.05 °C, and the surface temperature of the asphalt underlayer in the uninsulated model reaches 8.11 °C. At the same time, in the overall temperature rise trend of the surface and asphalt upper surface, different from the temperature rise of the asphalt upper surface, the temperature of the pavement surface does not rise after the system has been opened for some time, but there is a period of decline. As can be seen from the figure, in the 1876s, the surface temperature of the non-insulated model pavement reaches −1.03 °C, and then the temperature begins to rise gradually. However, the rise is smaller than the asphalt surface, and the asphalt surface temperature is greater than the road surface; for example, the temperature of the uninsulated asphalt surface is 0.33 °C.

Figure 7 shows the comparison between the surface temperature of the model when the cable is located in the lower layer of asphalt and the surface temperature of the lower layer of asphalt. It can be seen that the temperature rise trend is the same as that when the cable is located in the concrete layer. The surface temperature of Scheme 4 (without the insulation model) reaches 2.63 °C after five hours, and Scheme 3 (with the insulation model) reaches 2.85 °C. The surface temperature of the asphalt underlayer in the non-insulated model reaches 11.37 °C, and the surface temperature of the asphalt underlayer in the insulated model reaches 11.75 °C. Different from when the cable is embedded in the concrete layer, the surface temperature of the asphalt layer has a more obvious rising trend; there is basically no transition section, and the heat transfer efficiency is greater than that when the cable is embedded in the concrete layer, but the surface temperature of the road still has a certain degree of decline at the beginning, which means that when the cable is embedded in the concrete layer or the asphalt layer, the influence of the external environment temperature on the surface temperature of the road is greater than the internal heat transfer of the road.

Figure 8 shows the temperature variation of the pavement surface and asphalt subsurface when the cable is located on the upper layer of asphalt. Compared with the cable when the concrete layer and asphalt sublayer are different, the pavement surface temperature and asphalt subsurface temperature are significantly higher than the first two. The surface temperature of Scheme 6 (without the insulation model) reached 4.29 °C after five hours, and Scheme 5 (with the insulation model) reaches 5.82 °C after five hours. The surface temperature of the asphalt underlayer is 15.46 °C for the insulated model and 14.17 °C for the uninsulated model. At the same time, it is obvious that after the system is opened, the surface temperature of the road surface and the surface temperature of the asphalt layer change in the same way—that is, the temperature of the two rapidly rises, and there is no falling section of the surface temperature of the road surface, which means that when the cable is located on the upper layer of the asphalt, the heat transferred by the cable is the main factor affecting the heat transfer of the road surface.

Figure 9, Figure 10 and Figure 11 present temperature contour maps of the pavement surface when cables are embedded in the concrete layer, lower asphalt layer, and upper asphalt layer, respectively. Analysis of pavement surface temperature reveals distinct thermal patterns under varying embedment depths. When there is no insulation layer, compared with the concrete layer when the cable is located in the asphalt layer, the surface temperature of the cable is increased by 63.35% and the surface temperature of the asphalt layer is increased by 40.19%. When the cable is located in the upper layer of asphalt, the surface temperature increases by 166.46%, and the surface temperature of the lower layer of asphalt increases by 74.72%. When the insulation layer is arranged, the surface temperature of the cable under asphalt is increased by 43.94% and the surface temperature of the asphalt under asphalt is increased by 29.83% compared with that of the cable under the concrete layer. When the cable is located in the upper layer of asphalt, the surface temperature is increased by 193.94%, and the surface temperature of the lower layer of asphalt is increased by 70.83%.

Based on the analysis of the data, it can be observed that the installation of insulation layers increased both the surface temperature of the road and the surface temperature of the asphalt lower layer. Specifically, when the cable is located in the concrete layer, the installation of the insulation layer results in an increase of 22.98% in the surface temperature of the road and an increase of 11.59% in the surface temperature of the asphalt lower layer. When the cable is located in the asphalt lower layer, the installation of the insulation layer leads to an increase of 8.36% in the surface temperature of the road and an increase of 33.34% in the surface temperature of the asphalt lower layer. When the cable is located in the asphalt upper layer, the installation of the insulation layer causes an increase of 35.66% in the surface temperature of the road and an increase of 9.10% in the surface temperature of the asphalt lower layer. Considering the distribution of temperature fields alone, the structure where the cable is placed in the asphalt lower layer with an insulation layer (Scheme 3) represents the optimal pavement structure.

4.2. Entransy Dissipation of Pavement Layer

Asphalt pavements have a high heat absorption capacity. When the system is activated, heat is transferred from the interior of the pavement to the surface of the asphalt pavement, resulting in an increase in pavement temperature and heat accumulation within the different structural layers. However, due to differences in the thermal parameters of the structural layers, the heat transfer capacity between different structural layers varies. To determine the variation in heat transfer capacity between different structural layers, the entransy dissipation of each structural layer after system activation was calculated.

Figure 12 presents the entransy dissipation distribution of different pavement layers without thermal insulation. When cables are placed in the concrete layer, the entransy dissipation values are 11,198.13 W·K for the concrete layer, 9759.17 W·K for the lower asphalt layer, and 6094.83 W·K for the upper asphalt layer. The concrete layer’s entransy dissipation is 1.84 times higher than the upper asphalt layer and 1.15 times higher than the lower asphalt layer. This indicates that when cables are positioned in the concrete layer, entransy dissipation during heat transfer primarily occurs in the concrete and lower asphalt layers, meaning heat transfer capacity loss mainly concentrates in these two layers. Consequently, the lower surface temperature of the upper asphalt layer is observed under this structure.

When cables are positioned in the lower asphalt layer, the entransy dissipation values are 15,147.69 W·K for the concrete layer, 3615.41 W·K for the lower asphalt layer, and 10,741.01 W·K for the upper asphalt layer. The concrete layer’s entransy dissipation is 1.41 times higher than the upper asphalt layer and 4.19 times higher than the lower asphalt layer. Changing the cable position results in altered entransy dissipation distribution among pavement layers. When cables are placed in the lower asphalt layer, their entransy dissipation becomes the smallest compared to the upper asphalt and concrete layers. This indicates that heat transfer capacity loss in the model mainly occurs in the concrete and upper asphalt layers, with entransy dissipation loss in the concrete layer exceeding that in the upper asphalt layer.

When cables are positioned in the upper asphalt layer, the entransy dissipation values are 2423.47 W·K for the concrete layer, 5025.27 W·K for the lower asphalt layer, and 8257.55 W·K for the upper asphalt layer. The entransy dissipation distribution in pavement layers under this structure is in direct contrast to the scheme when cables are placed in the concrete layer, following this order: upper asphalt layer > lower asphalt layer > concrete layer. Specifically, the upper asphalt layer’s entransy dissipation is 3.52 times higher than the concrete layer and 1.69 times higher than the lower asphalt layer. Compared to structures with cables in the concrete or lower asphalt layers, significant changes occur in entransy dissipation distribution when cables are located in the upper asphalt layer. Here, the concrete layer exhibits the lowest entransy dissipation, indicating that heat transfer capacity loss in the model primarily occurs in the upper and lower asphalt layers, with the loss magnitude in the upper asphalt layer exceeding that in the lower asphalt layer. This phenomenon results in the highest surface temperature of the upper asphalt layer under this structure compared to the other two cable positions.

Figure 13 presents the entransy dissipation distribution of different pavement layers with thermal insulation installed. When cables are placed in the concrete layer, the entransy dissipation values are 16,125.3 W·K for the concrete layer, 12,730.08 W·K for the lower asphalt layer, and 7392.5 W·K for the upper asphalt layer. The concrete layer’s entransy dissipation is 2.18 times higher than the upper asphalt layer and 1.27 times higher than the lower asphalt layer. This indicates that similar to the scheme without thermal insulation, when cables are positioned in the concrete layer, entransy dissipation during heat transfer primarily occurs in the concrete and lower asphalt layers, meaning heat transfer capacity loss still mainly concentrates in these two layers. The installation of thermal insulation does not alter the heat transfer characteristics of the model. However, in terms of entransy dissipation magnitudes, compared to the structure without thermal insulation, the concrete layer’s entransy dissipation increases by 44%, the lower asphalt layer’s by 30.4%, and the upper asphalt layer’s by 21.29%. This demonstrates that thermal insulation installation enhances entransy dissipation in all pavement layers.

When cables are positioned in the lower asphalt layer, similar to the scheme without thermal insulation, the heat transfer capacity loss in the model with thermal insulation mainly occurs in the concrete and upper asphalt layers, with entransy dissipation loss in the concrete layer exceeding that in the upper asphalt layer. However, compared to the structure without thermal insulation, entransy dissipation in pavement layers decreases: concrete layer entransy dissipation decreases by 18.95%, lower asphalt layer by 60.04%, while upper asphalt layer entransy dissipation remains nearly unchanged. When cables are located in the upper asphalt layer, consistent with the non-insulated structure, the concrete layer exhibits the lowest entransy dissipation, and heat transfer capacity loss primarily occurs in the upper and lower asphalt layers with the loss magnitude in the upper asphalt layer exceeding that in the lower asphalt layer. Compared to the non-insulated structure, entransy dissipation increases by 30.84% in the upper asphalt layer, 75.26% in the lower asphalt layer, and 47.48% the concrete layer.

Figure 14, Figure 15 and Figure 16 present the overall temperature contour plots for both non-insulated and insulated structures when cables are positioned in the concrete layer, lower asphalt layer, and upper asphalt layer, respectively. These figures demonstrate that as the burial depth of cables decreases, their surface temperatures become more pronounced. Notably, when cables are placed in the upper asphalt layer, significantly higher temperatures are visually evident at the cable installation locations compared to other areas.

Based on the aforementioned analysis, when cables are positioned in the lower asphalt layer, the entransy dissipation of the lower asphalt layer is minimized. This indicates that cable placement in the lower asphalt layer is more favorable for pavement heat transfer. Therefore, according to the entransy dissipation distribution results, the structure without thermal insulation with cables located in the lower asphalt layer (Scheme 3) is determined to be the optimal heat transfer structure.

4.3. Pavement Layer Entransy Dissipation Thermal Resistance

The entransy dissipation thermal resistance can be used as an index to evaluate the heat transfer capacity of asphalt pavement. To further explore the heat transfer behavior of ice-melting pavements under different schemes and the selection of optimization schemes, the entransy dissipation thermal resistance of the pavement layer under different schemes was analyzed.

Figure 17 presents the entransy dissipation thermal resistance distribution of different pavement layers without thermal insulation when cables are located in various positions. When cables are placed in the concrete layer, the entransy dissipation thermal resistance values are 0.59 × 10⁻⁴ K/W for the concrete layer, 6.37 × 10⁻⁴ K/W for the lower asphalt layer, and 75.63 × 10⁻⁴ K/W for the upper asphalt layer. According to the distribution pattern, the upper asphalt layer exhibits the highest entransy dissipation thermal resistance, while the concrete layer has the lowest. This indicates that when cables are embedded in the concrete layer, heat transfer resistance primarily occurs in the upper asphalt layer, whereas the concrete layer containing the cables experiences relatively low resistance. The heat generated by the cables reduces the entransy dissipation thermal resistance within the concrete layer. As heat transfer distance increases towards the pavement surface, the heat flux conducted by the cables decreases, leading to gradual thermal resistance augmentation under ambient environmental influence. This mechanism results in a lower surface temperature of the upper asphalt layer when cables are positioned in the concrete layer.

When cables are positioned in the lower asphalt layer, the entransy dissipation thermal resistance of the lower asphalt layer reaches its minimum value. Altering the cable location results in a redistribution of entransy dissipation thermal resistance across pavement layers. When cables are placed in the lower asphalt layer, their entransy dissipation thermal resistance becomes the smallest compared to the upper asphalt and concrete layers. This indicates that heat transfer resistance in the model primarily occurs in the concrete and upper asphalt layers, with the resistance magnitude in the upper asphalt layer exceeding that in the concrete layer.

When cables are located in the upper asphalt layer, the minimum entransy dissipation thermal resistance occurs in the upper asphalt layer, while the maximum occurs in the concrete layer. This represents a significant change in entransy dissipation thermal resistance distribution compared to structures with cables in the concrete or lower asphalt layers. Here, the upper asphalt layer exhibits the lowest entransy dissipation thermal resistance, indicating minimal ambient environmental influence on pavement layers. The primary factor determining pavement surface heat transfer becomes the heat generated by the cables. Additionally, the entransy dissipation thermal resistance distribution pattern under this structure is inversed compared to the scheme with cables in the concrete layer, signifying better heat transfer performance of cables embedded in the upper asphalt layer. Consequently, the highest surface temperature of the upper asphalt layer is observed under this structure compared to the other two cable positions.

Figure 18 presents the entransy dissipation thermal resistance distribution of different pavement layers with thermal insulation installed when cables are located in various positions. When cables are placed in the concrete layer, compared to the non-insulated structure, entransy dissipation thermal resistance decreases by 59.32% in the concrete layer, 21.98% in the lower asphalt layer, and 3.13% in the upper asphalt layer. This indicates that thermal insulation installation reduces entransy dissipation thermal resistance in all pavement layers, with the most significant reduction occurring in the concrete layer. The decreased resistance in the concrete layer improves its heat transfer performance, while reductions in the lower and upper asphalt layers also enhance overall heat transfer efficiency. From a heat transfer effectiveness perspective, thermal insulation installation results in increased pavement surface temperatures, as the reduced entransy dissipation thermal resistance in the lower asphalt and concrete layers facilitates more efficient heat transfer through these structural layers.

When cables are positioned in the lower asphalt layer with thermal insulation installed, the entransy dissipation thermal resistance distribution in pavement layers remains fundamentally consistent with the non-insulated structure, i.e., the lower asphalt layer exhibits the smallest entransy dissipation thermal resistance compared to the upper asphalt and concrete layers. Compared to the non-insulated structure, entransy dissipation thermal resistance decreases by 28.28% in the concrete layer, 80% in the lower asphalt layer, and increases by 1.55% in the upper asphalt layer. This indicates that thermal insulation installation reduces heat transfer resistance in both the concrete and lower asphalt layers, with a more significant reduction occurring in the lower asphalt layer. These reductions facilitate improved heat transfer performance in pavement layers. Although heat transfer resistance in the upper asphalt layer remains primarily influenced by ambient environmental factors, the overall heat transfer effectiveness under this structure exceeds that when cables are placed in the concrete layer.

When cables are positioned in the upper asphalt layer, the entransy dissipation thermal resistance distribution in pavement layers remains identical to the non-insulated structure, following this order: upper asphalt layer < lower asphalt layer < concrete layer. Specifically, the concrete layer’s entransy dissipation thermal resistance is 323.05 times higher than the upper asphalt layer, and the lower asphalt layer’s is 23.67 times higher. Compared to the non-insulated structure, entransy dissipation thermal resistance decreases by 22.64% in the concrete layer, 30.39% in the lower asphalt layer, and increases by 360% in the upper asphalt layer. In reality, when cables are placed in the upper asphalt layer, the temperature difference between the pavement surface and the concrete layer bottom reaches its maximum value. After thermal insulation installation, under the combined influence of the ambient environment and cable-generated heat, the temperature gradient in the upper asphalt layer intensifies, resulting in increased heat transfer resistance. This phenomenon indicates that thermal insulation may not be required when cables are installed in the upper asphalt layer.

Based on the aforementioned analysis, when cables are positioned in different pavement layers, their corresponding entransy dissipation thermal resistance decreases accordingly. When cables are placed in the lower asphalt layer, compared to structures with cables in the concrete or upper asphalt layers, entransy dissipation thermal resistance in both the concrete and lower asphalt layers is significantly reduced. This indicates that installing thermal insulation in the lower asphalt layer is more favorable for pavement heat transfer. Therefore, according to the entransy dissipation thermal resistance distribution results, the structure with cables located in the lower asphalt layer and thermal insulation installed (Scheme 3) is determined to be the optimal structure.

5. Conclusions

In this research, a three-dimensional finite element model of ice-melting asphalt pavement with different input parameters was developed. Small-scale outdoor ice-melting tests were carried out for verification. By taking pavement temperature, entransy dissipation, and entransy dissipation thermal resistance as the heat transfer performance indicators of the pavement structure, the ice-melting performance and heat transfer characteristics of different pavement structures were analyzed. The main conclusions of this study are as follows:

(1)

Cable burial depth has a significant impact on pavement temperature field distribution and heat transfer efficiency. When cables are located in the upper asphalt layer, heat generated by the cables becomes the primary factor influencing heat transfer. Conversely, when cables are positioned in the concrete layer or lower asphalt layer, heat transfer is mainly dominated by ambient environmental conditions. Thermal insulation installation can effectively elevate both pavement surface and lower asphalt layer surface temperatures. Notably, when cables are placed in the upper asphalt layer, thermal insulation demonstrates the most pronounced enhancement effect on pavement surface temperature (35.66%).

(2)

The greater the entransy dissipation, the greater the heat transfer capacity loss in pavement layers. When cables are located in the concrete layer, entransy dissipation primarily concentrates in the concrete and lower asphalt layers. When cables are positioned in the lower asphalt layer, entransy dissipation is mainly distributed in the concrete and upper asphalt layers. Conversely, when cables are placed in the upper asphalt layer, entransy dissipation primarily accumulates in the upper and lower asphalt layers, with the highest value observed in the upper asphalt layer. This indicates that heat transfer capacity loss mainly occurs in the asphalt layers, demonstrating that the cable heat source reduces heat transfer capacity loss in the corresponding pavement layer.

(3)

When cables are located in the concrete layer and upper asphalt layer, thermal insulation increases entransy dissipation in all pavement layers. Conversely, when cables are positioned in the lower asphalt layer, thermal insulation significantly reduces entransy dissipation in all pavement layers, indicating that thermal insulation installation under this structure is more favorable for enhancing heat transfer efficiency.

(4)

The value of entransy dissipation thermal resistance reflects the level of heat transfer resistance in the pavement layers. When the cables are in the concrete layer, the heat transfer resistance is highest in the upper asphalt layer. Conversely, when cables are placed in the upper asphalt layer, the entransy dissipation thermal resistance of the upper asphalt layer reaches its minimum value. When the cables are placed in the lower asphalt layer, thermal insulation significantly reduces the entransy dissipation thermal resistance of both the concrete and lower asphalt layers (28.28% and 80%, respectively), indicating that thermal insulation improves heat transfer efficiency in this structure.