Characterizing Pavement Material Properties for Thermal Modeling of Embedded Wireless Power Transfer Systems

Abstract

Pavements with wireless power transfer (WPT) for charging electric vehicles represent a significant technology shift from the current fossil fuel-based system to a cleaner transportation system with reduced emissions and impact on our climate. Electrified roadways equipped with WPT will incorporate charging units embedded in the upper layer of the pavement, enabling electric vehicles to charge their batteries via electromagnetic induction. Components of these units generate waste heat that must be dissipated through the pavement. To reduce the temperature sensitivity of flexible pavements for durable electrified roadways, there is a need to understand the impact of additional heat on the temperature and performance of the asphalt pavement layers. This study focuses on the thermal implications of embedding WPT systems in flexible pavements, considering the additional heat generated by WPT components and their impact on pavement temperature profiles. Experimental and validation work, consisting of developing a testing protocol for laboratory compacted specimens and finite element modeling, was conducted to assess temperature distributions within asphalt pavement layers under various conditions. The results indicate significant temperature increases in pavements with embedded WPT systems and temperature profiles that are different from those expected in conventional pavements. The increased temperatures should be taken into account for the selection of appropriate materials and structural design of pavements with WPT.

Electric vehicles (EVs) are advantageous in shifting toward more sustainable transportation systems by decreasing emissions from fossil fuels. Alongside their environmental benefits, more affordable prices and an expanded range of options are rapidly increasing the adoption of and consumer demand for EVs. In 2022, approximately 810,000 EVs were sold in the U.S.A., making up 5.9% of new vehicle sales. The following year marked a notable rise in EV sales, with an additional 380,000 units sold, reaching 7.6% of new vehicle purchases ( 1 ).

Some major concerns with EVs include range anxiety ( 2 ), high initial costs, and lengthy charging times. One potential solution to address these concerns without integrating large-capacity batteries into vehicles is the implementation of in-road wireless power transfer (WPT) systems (Figure 1) ( 3 ). This technology is much needed to boost the adoption of EVs, and therefore to make a significant shift toward sustainable transportation ( 2 , 4 ). By utilizing high-frequency inductive power transfer between transmitter ground coils and receiver vehicle coils, WPT can occur across an air gap between the underside of the car and the road surface. It has been demonstrated that embedding WPT systems in flexible pavements does not hinder the functionality of induction ( 4 ).

Figure 1.

Schematic of electrified roads with wireless power transfer (WPT) systems.

Currently, plug-in charging operates at an efficiency of 86%, but WPT technology has achieved efficiencies of up to 93%, providing opportunities for charging in a wide range of use cases. These include stationary charging in parking lots and semi-dynamic opportunity charging at signal-controlled intersections, bus stops, and taxi ranks, as well as dynamic charge-on-the-move on arterial roads and major highways ( 5 – 7 ).

The design of pavement-embedded WPT systems requires navigating significant tradeoffs in thermal, structural, and electromagnetic performance. There are challenges with respect to the long-term reliability and maintainability of the pavement structure and the embedded electrical components. Asphalt pavements are widely used worldwide because they offer several advantages, including easy maintenance, quick construction, smooth driving experience, and lower construction costs ( 5 ). However, one of the main challenges associated with asphalt pavements is managing the potential impact of temperature on the asphalt. The stresses and strains caused by traffic loads depend on the temperature profile within the asphalt layer, mainly because of the viscoelastic nature of the asphalt material ( 8 ).

Hot mix asphalt (HMA) pavements, because of their dark color, absorption of solar radiation, and low thermal conductivity, may experience substantial temperature elevation during the summer ( 5 ). For instance, in a region with a maximum ambient temperature of 30°C, the pavement temperature can reach or exceed 60°C. This issue becomes more critical with the implementation of wireless charging systems in asphalt pavements, as additional heat is generated by energy losses in the WPT components, primarily from the induction coil located within the asphalt pavement layer ( 9 ). Electrified asphalt pavements are expected to experience localized heat spots around the wireless charging unit to varying degrees and frequencies, depending on the charging on/off duty cycles.

These elevated temperatures are expected to accelerate rutting and cracking because of the aging oxidation of the binder in the HMA layer surrounding the charging system. An accurate determination of the temperature distribution in electrified pavements is vital for their successful design.

Considerable research has been conducted on the design and modeling of coils and power electronic circuits; however, limited research has been published on asphalt pavements containing embedded wireless charging systems, especially the thermal analyses of WPT-pavement systems ( 4 , 5 , 8 , 9 ). This is a major knowledge gap in the design and construction of WPT systems, since thermal impacts could be particularly problematic during continuous stationary charging and when using high power levels for rapid charging. This paper focuses on the thermal aspects of embedding WPT systems in asphalt pavements.

Objective and Scope

The objectives and scope of work presented in this paper are summarized as follows:

1. developing a testing protocol to estimate the impact of the embedded WPT system on the temperature of asphalt pavements utilizing laboratory compacted HMA specimens with conventional performance grade (PG) and modified asphalt binder;

2. developing numerical and analytical models to predict time–temperature data at different placement depths of charging units under various ambient conditions and validating with experimental results.

Experimental Design

Thermal Test

The recently developed mechanistic-empirical pavement design guide (MEPDG) has integrated the effects of pavement temperature on material properties, structure responses, and pavement performance prediction. While WPT systems can charge light-duty EVs with power levels ranging from 3 to 11 kW for static and semi-dynamic charging, heavy-duty vehicles and dynamic charging applications utilize higher power levels within the range of 20–300 kW ( 4 ). This wide range of induced power and power loss in WPT systems poses challenges in estimating temperature fluctuations in electrified pavements. When investigating the thermal behavior of electrified pavements, this extensive range of power losses becomes a substantial obstacle in accurately predicting or quantifying the precise temperature increases experienced by these pavements. To ensure the effective integration of WPT into the pavement infrastructure, it is necessary to study the diverse temperature increase scenarios and evaluate the impact of these temperature variations on the thermal distributions and temperature of the asphalt pavements. Four ambient temperatures of 10°C, 25°C, 30°C, and 40°C were simulated in an environmental chamber. To reproduce the heating effect of the WPT system, temperature-controlled silicone rubber fiberglass flexible heating pads with a diameter of 75 mm and a power density of 0.0155 W/mm² were utilized in a diverse temperature range from 50°C to 100°C (Figure 2). The heating pad could be programmed to maintain a specific temperature for a specific time.

Figure 2.

The study experiment design.

For the experimental simulation of WPT in pavements, laboratory-scale Superpave gyratory compacted HMA specimens of conventional and polymer-modified mixes were utilized. Polymer-modified asphalt has been extensively utilized in asphalt pavement because of its favorable performance across various temperatures ( 10 ). The polymer-modified binder, with its network and interlinking properties, enables the HMA to resist permanent deformation and recover elastically. The 150-mm-diameter and 115-mm-thick specimens were compacted to a density of 93% of the theoretical maximum density using the Superpave gyratory compactor. A PG 64-22 binder was used to produce a laboratory-prepared conventional HMA, whereas a plant-produced PG 82-22 (polymer-modified) loose mix was used to compact the polymer-modified HMA samples.

The heating pads were placed at different depths (measured from the surface of the specimens). For a depth of 115 mm, the pad was placed at the bottom of the specimen, above another HMA specimen, with a tack coat in between. To place the pads at shallower depths, the compacted HMA specimens were sliced into different thicknesses, and the pads were inserted at the desired levels, in between two thinner specimens. The specimens were then insulated on all sides using Styrofoam materials. Thermocouples were placed at different levels through holes drilled at different points along the thickness of the specimens. The entire specimen assembly was kept inside an environmental chamber that was maintained at a constant (ambient) temperature (Figure 3). The heating pad power was controlled to produce the desired temperature. The pads were kept heated for 4 h and then switched off. The corresponding temperature data were obtained from the thermocouples (see the example in Figure 4).

Figure 3.

(a) Heating pad with tack coat placed and specimens drilled for thermocouple installation. (b) Insulating the specimens. (c) Installing thermocouples in the environmental chamber. (d) Schematic of the upper hot mix asphalt specimen of (c) and thermocouple locations.

Figure 4.

Example plots of variations in temperature with time (heat pad at 115 mm depth, with a temperature of 80°C and an ambient temperature of 25°C).

Theoretical Considerations and Finite Element Modeling

Fluctuations in pavement temperature can be explained by the principles of heat transfer theory. The relevant heat transfer modes consist of conduction, radiation, and convection ( 11 ). As demonstrated in Figure 5, the predominant mode of heat transfer within the pavement structure is thermal conduction. Conversely, at the pavement surface, heat is exchanged with the external environment through radiation and convection. Essentially, the prediction of the variation of temperature within a pavement layer entails the solution of the heat equation while considering the appropriate boundary conditions. The three-dimensional heat transfer equation for pavement structures with constant thermal conductivity is shown in Equation 1:

$$\frac{\partial T(r,t)}{\partial t}=\frac{k}{\rho c}{\nabla }^{2}T(r,t)+\frac{Q(r,t)}{\rho c}$$

(1)

where T(r,t) is temperature (°C); r is a three-dimensional position vector with coordinates (x, y, z) (m); t is time (s); k is thermal conductivity (W m⁻¹ K⁻¹); ρ is density (kg/m¹); c is the specific heat capacity (J kg⁻¹ K⁻¹); ∇¹ is the three-dimensional Laplacian operator (∂¹/∂x¹+∂¹/∂y¹+∂¹/∂z¹) (m⁻¹); and Q is the volumetric heat source (W/m¹).

Figure 5.

Schematic of heat transfer mechanisms in a pavement.

Convective heat transfer refers to the transfer of thermal energy between a surface and a moving fluid. It is classified as forced convection when flow is driven by external means, such as fans. In this study, airflow from a chamber fan creates forced convection over the top surface of the asphalt specimen. The convective heat transfer coefficient h is calculated using the dimensionless Nusselt number Nu, which relates convective and conductive heat transfer ( 12 ):

$$h=\frac{\mathrm{Nu}·k}{D}$$

(2)

where Nu is the Nusselt number; k is air thermal conductivity (W m⁻¹ K⁻¹); and D is the diameter of the cylindrical sample (m).

For forced convection over a circular disk, the Nusselt number correlation is given by the following:

$$\mathrm{Nu}=0.612\times \mathrm{R}{\mathrm{e}}^{0.5}\times \mathrm{P}{\mathrm{r}}^{0.33}$$

(3)

where Re is the Reynolds number and Pr is the Prandtl number. The Reynolds number is a dimensionless quantity expressing the ratio of inertial forces to viscous forces in the fluid, calculated as follows:

$$\mathrm{Re}=\frac{V\rho D}{\mu }$$

(4)

where V is the air velocity (m/s); ρ is the density of air (kg/m¹); D is the diameter of the cylindrical sample (m); and μ is the dynamic viscosity of air (Pa·s). The Prandtl number is a dimensionless parameter representing the ratio of momentum diffusivity to thermal diffusivity:

$$\mathrm{Pr}=\frac{\mu c}{k}$$

(5)

where μ is dynamic viscosity (Pa·s); c is the specific heat of air (J kg⁻¹ K⁻¹); and k is the thermal conductivity of air (W m⁻¹ K⁻¹). Surface radiation was not applied during the experiments.

To fully understand the thermal state of an embedded system, it is essential to know the thermal properties of the material in which the system is embedded. Key thermal properties of pavement materials include thermal conductivity, specific heat capacity, and thermal diffusivity. Thermal conductivity measures a material's ability to conduct heat, and higher thermal conductivity enables more efficient heat transfer to the layers beneath. Specific heat capacity is the amount of energy required to increase the temperature of a unit mass of a substance by one degree, meaning that a lower specific heat capacity can result in higher pavement temperatures for the same amount of heat input. Thermal diffusivity is the ratio of heat conducted through the material to the heat stored per unit volume, and a higher thermal diffusivity leads to faster heat propagation within the material. Table 1 presents the range of thermal properties for HMA as obtained from a literature review ( 11 , 13 ).

Table 1.

Typical Values for Thermal Properties of Hot Mix Asphalt ( 11 , 12 )

Property	Range
Thermal conductivity (W m−1 K−1)	0.5–2.5
Specific heat capacity (J kg−1 K−1)	900–2100
Thermal diffusivity (10−7 m2 s−1)	1.2–16.8

Conventional HMA has relatively low thermal conductivity. However, the thermal properties are not constant because HMA is a composite material consisting of aggregates and binder. The thermal properties of an asphalt pavement layer depend on the thermal properties of each material component, mass and volumetric composition, air voids, gradations, and even microstructures, and can be obtained from experiments or simulations ( 8 , 14 ). As shown in Table 2, a wide range of thermal property values can cause inappropriate estimation and may lead to unexpected errors in the prediction results of pavement temperature. Therefore, because of the wide range of HMAs, any model must be validated for the specific asphalt before it can be used.

Table 2.

Analysis of Six Cases to Determine Thermal Conductivity and Specific Heat Capacity

Case number	Heat pad location	Heat pad temperature (°C)	Thermocouple location (mm)	Ambient temperature (°C)
1	Middle (57 mm)	60	30	25
2	Two-thirds (75 mm)	60	115	40
3	Middle (57 mm)	60	80	40
4	Bottom (115 mm)	60	75	30
5	Two-thirds (75 mm)	60	50	10
6	Two-thirds (75 mm)	60	0	10

A transient thermal analysis was carried out to simulate the laboratory conditions using the finite element (FE) software MECWAY ( 15 ), as depicted in Figure 6. A three-dimensional FE model was developed to simulate each test setup, including the asphalt mix specimens, the heat source (heating pad), and the insulation material (Styrofoam), along with their thermal properties. Thermal properties for all materials were assigned to the FE model. The top surface of the cylindrical specimen was configured to account for the convection caused by the chamber air velocity. The thermal properties, specifically thermal conductivity, were optimized (within the suggested range as noted in Table 1) to improve the accuracy of the FE predictions.

Figure 6.

Finite element model of the experimental setup.

Results and Discussion

The results were analyzed to estimate the most appropriate thermal properties, develop analytical models to predict the temperatures, evaluate the effect of different asphalt binder grades on the pavement temperatures, and estimate the temperature profiles along the depth of a pavement.

Estimation of Thermal Properties from Backcalculation

The method for estimating the thermal conductivity and specific heat capacity of HMAs in this study involved a backcalculation process to match the FE predicted temperatures with the experimental data. An iterative process was used to adjust the thermal conductivity and specific heat capacity by matching the temperatures at different conditions and points in the FE model to those measured at the same conditions and points in the experiment. Six cases with different ambient temperatures, heat pad locations, and thermocouple locations were considered (Table 2). The thermal conductivity and specific heat capacity were estimated by minimizing the root mean square error (RMSE) between the experimental data and corresponding numerical value using Equation 6:

$$\mathrm{RMSE}\left(\mathrm{\%}\right)=\sqrt{\frac{1}{n_d}\sum _{i=1}^n{\left(\frac{T_{\mathrm{fe}}-T_{\exp }}{T_{\exp }}\right)}^2}100$$

(6)

where T_fe denotes the FE model temperatures and T_exp denotes the experimental temperatures. For this purpose, the seven time periods ranging from 5 min to 4 h shown in Table 3 were considered.

Table 3.

Example of the Backcalculation Process using Case 1

Time (h)	Experimental values (°C)	Predicted values (°C)	RMSE (%)
0.08	26	25.3	5.46
0.25	28.6	28.7
0.5	32.1	33.5
1	36.3	39
2	39.8	42.7
3	41.2	44.2
4	42	44.9

Note: RMSE = root mean square error.

The variations of RMSE with thermal conductivity and specific heat capacity within the range reported in Table 1 are shown in Figure 7 for Case 1, as an example. The change in specific heat capacity does not significantly affect the RMSE. In contrast, the RMSE is very sensitive to changes in thermal conductivity. This has also been confirmed by a similar study in which asphalt samples were retrofitted with embedded IPT (Inductive Power Transfer) pads ( 5 ). The study showed that changes in specific heat had minor effects on thermal response, while thermal conductivity was identified as the most important parameter for design. To maximize the stability of the backcalculation process, a constant specific heat capacity of 1100 Wm⁻¹°K⁻¹ that yielded the lowest RMSE was selected for all six cases and the RMSE error was minimized by varying the thermal conductivity for those six cases.

Figure 7.

Root mean square error (RMSE) values for different values of (a) thermal conductivity and (b) specific heat capacity of hot mix asphalts.

Table 4 exhibits the variation in the RMSE with the thermal conductivity of the HMA layer for all cases using a constant specific heat capacity of 1100 Wm⁻¹°K⁻¹ over the typical range of thermal conductivities suggested in previous studies. The goal was to maintain the RMSE below 5% as an acceptable threshold. Although cases 1 and 5 had RMSE values slightly above 5%, a thermal conductivity of 1.1 Wm⁻¹°K⁻¹ consistently produced the lowest RMSE (<5%) across all six cases. The thermal conductivity value was also validated through six additional cases with different heat pad locations, thermocouple positions, ambient conditions, and heat pad temperatures, as shown in Table 5. This second validation showed that, in all six cases, the RMSE was below or close to 5%.

Table 4.

Root Mean Square Error (RMSE) Percentages for Different Thermal Conductivity Values for all Six Cases

Thermal conductivity (Wm−1°K−1)	RMSE (%)
	Case 1	Case 2	Case 3	Case 4	Case 5	Case 6
0.7	3.57	5.18	3.38	10.38	14.68	21.14
0.8	2.58	4.17	2.49	8.63	10.35	13.67
0.9	3.01	3.29	1.80	7.11	7.72	9.27
1.0	4.16	2.48	1.37	5.80	6.23	6.11
1.1	5.46	1.80	1.31	4.66	6.71	4.56
1.2	6.72	1.25	1.58	3.73	9.27	6.46
1.3	7.91	0.93	1.93	3.03	11.9	8.76
1.4	9.02	1.06	2.43	2.64	13.13	11.21
1.5	10.06	1.41	2.89	2.59	13.97	11.92
1.6	11.03	1.85	3.33	2.85	15.77	13.49
1.7	11.93	2.30	3.75	3.29	17.46	15.64
1.8	12.78	2.75	4.16	3.82	19.05	17.65

Note: 1.1 W m^–1 K^–1 (in bold) gave the lowest RMSE (< 5%) across all cases.

Table 5.

Additional Six Cases for Second Validation of Thermal Conductivity Values

Case number	Heat pad location	Heat pad temperature (°C)	Thermocouple location (mm)	Ambient temperature (°C)	RMSE (%)
7	One-third (40 mm)	60	0	25	3.67
8	Middle (57 mm)	80	80	40	4.31
9	Two-thirds (75 mm)	80	50	25	6.69
10	Bottom (115 mm)	60	75	10	5.78
11	Middle (57 mm)	60	30	30	4.01
12	Bottom (115 mm)	80	0	30	3.47

Note: RMSE = root mean square error.

Figure 8 compares the experimental and FE model predicted temperature data. With an R ² of 0.95 and a standard error of estimate of 0.73, the two sets of data match well, confirming the validity of the FE model.

Figure 8.

Comparisons of experimental and finite element model predicted temperature for Case 3 (heat pad at 57 mm depth, with a temperature of 60°C and an ambient temperature of 40°C).

Analytical Models

The experimental results were analyzed to develop analytical models for predicting time–temperature data under different conditions. As shown in Figure 4, the temperature profiles within the HMA specimens during the heating phase resemble a sigmoidal function. A sigmoid curve is an S-shaped curve characterized by a slow start, rapid growth in the middle, and a slow end, in the form of the following:

$$T(t)=\frac{L}{1+e^{-K(t-x0)}}$$

(7)

where T(t) is the temperature in °C at a given time t in hours; L is the asymptotic maximum, representing the maximum value that the function approaches; and K is the steepness parameter, determining how quickly the curve transitions from the lower to the upper asymptote, which can indicate the thermal properties of HMAs. As such, the experimental data can be characterized by three parameters: L, K, and x₀. Table 6 presents these three calculated values for all six cases. As depicted in Figure 9, the predicted results from the developed analytical model matched well with those from the FE model.

Table 6.

Sigmoid Curve Values for Six Cases (Refer to Table 2)

Case number	L	K	x 0
1	41.61	1.51	−0.27
2	51.00	1.45	−0.078
3	50.86	2.07	−0.60
4	46.43	1.51	−0.38
5	27.29	1.60	0.4
6	20.99	1.27	0.19

Figure 9.

Plots of predicted temperatures from the analytical and the finite element models for Case 3 (heat pad at 57 mm depth, with a temperature of 60°C and an ambient temperature of 40°C).

Effect of Asphalt Grade

Up to this point, the data presented were for a mix with a PG 64-22 asphalt. As shown in Figure 10, changing the binder to PG 82-22 does not significantly affect the temperature profile at different locations within the samples. For example, when the heating pad is located 40 mm from the surface, the temperature profiles at the surface, the bottom of the upper samples, and at two additional locations (90 and 65 mm from the surface) are similar for both asphalts. This consistency in temperature profiles across all four thermocouple locations supports the findings of previous studies, which report that asphalt has low thermal conductivity—approximately 0.24–0.28 Wm⁻¹°K⁻¹—with minimal variation across PGs. This finding indicates that asphalt viscosity has little effect on the overall thermal performance of the mixture ( 16 ).

Figure 10.

Plots for the logistic curve of temperature versus time for heating pad depth of 40 mm for performance grade (PG) 64-22 and PG 82-22 asphalt mixes.

Temperature Profiles along the Depth under Steady-State Conditions

To investigate the difference in thermal profiles under steady-state conditions, three cases are considered, each with a heating pad located at the middle of the specimen (57 mm) and a constant heating pad temperature of 80°C, but with different ambient temperatures. Figure 11 illustrates the temperature versus depth under steady-state conditions for all three cases. The temperature profile under similar ambient conditions without any heating pad is also included for each case as a reference. For the surface temperature and temperature at other depths without the heat pad, Equations 8 and 9 are used ( 17 ), respectively:

Figure 11.

Plots of temperature versus depth at ambient temperatures of (a) 25°C, (b) 30°C, and (c) 40°C.

$$T_{\mathrm{surface}}=T_{\mathrm{airmax}}-0.00618\mathrm{la}{t}^2+0.2289*\mathrm{lat}+24.4$$

(8)

$$T_{\mathrm{depth}}=T_{\mathrm{surface}}*(1-0.063*d+0.007*d^2-0.0004*d^3)$$

(9)

where T_airmax is the maximum air temperature (°F), lat is the latitude in degrees (32° for El Paso), T_surface is the surface temperature calculated from Equation 8, and d is the depth (in.).

As shown in Figure 11, there are significant differences in the temperature profiles between the cases with and without the heat pad. Activating the heating pad to 80°C significantly affects the temperature profiles. As expected, the maximum temperature difference occurs in the location of the heat pad. Therefore, the hottest spots are expected to be near the WPT system. The shape of the temperature profile and the points for all cases are consistent, which can lead to strong predictive models under different ambient and charging temperatures.

The design of electrified pavement needs to consider the increased temperature because of the WPT. The models developed in this study could be used for the selection of appropriate materials and the prediction of structural response under vehicular loading.

Conclusions and Recommendations

Based on this study, the following conclusions and recommendations are made.

1. The increase in temperature along the depth of the HMA layer is a function of the depth of placement of the unit, the elevation of temperature caused by the generation of the waste heat, and the ambient temperature.

2. The numerical model developed in this study could be used to estimate the temperature profile of an asphalt pavement layer at different ambient temperatures because of the heat generation from the charging units.

3. An increase in temperature because of the generation of waste heat from charging units is expected to be similar in asphalt mixes with unmodified and modified binders.

4. Accelerated loading and testing of simulated electrified pavements should be carried out with a range of appropriate parameters (such as charging unit depths, temperatures, and ambient conditions) to evaluate and compare the performance lives of layers with different types of materials and mixes.