Magnetite-Modified Asphalt Pavements in Wireless Power Transfer: Enhancing Efficiency and Minimizing Power Loss Through Material Optimization

Abstract

Wireless power transfer (WPT) is recognized as a critical technology to advance carbon neutrality in transportation by alleviating charging challenges for electric vehicles and accelerating their adoption to replace fossil fuel. To ensure durability under traffic loads and harsh environments while avoiding vehicle obstructions, WPT primary circuits should be embedded within pavement structures rather than surface-mounted. This study systematically investigated the optimization of magnetite-modified asphalt material composition and thickness for enhancing electromagnetic coupling in WPT systems through integrated numerical and experimental approaches. A 3D finite element model (FEM) and a WPT platform with primary-side inductor–capacitor–capacitor (LCC) and secondary-side series (S) compensation were developed to assess the electromagnetic performance of magnetite content ranging from 0 to 25% and pavement thickness ranging from 30 to 70 mm. Results indicate that magnetite incorporation increased efficiency from 80.3 to 84.7% and coupling coefficients from 0.236 to 0.242, with power loss increasing by only 0.25 W. This enhancement is driven by improved equivalent permeability, which directly enhances magnetic coupling efficiency. A critical pavement thickness of 50 mm was identified, beyond which the reduction in transmission efficiency increased significantly due to magnetic flux dispersion. Additionally, the nonlinear increase in power loss is partially attributed to the significant rise in hysteresis and eddy current losses at elevated magnetite content levels. The proposed design framework, which focuses on 10% magnetite content and a total pavement thickness of 50 mm, achieves an optimal energy transfer efficiency. This approach contributes to sustainable infrastructure development for wireless charging applications.

1. Introduction

The global energy transition and the “Carbon Peaking and Carbon Neutrality” strategy have accelerated electrification in transportation. The rapid adoption of electric vehicles (EVs) has created an urgent demand for efficient and sustainable charging infrastructure. Wireless power transfer (WPT) technology, enabling dynamic charging during vehicle motion, offers an innovative solution to alleviate range anxiety and charging station scarcity [1,2,3]. To ensure the long-term stability of WPT systems under continuous traffic loads and harsh environmental conditions while avoiding physical obstructions, primary circuits should be embedded within pavement structures rather than surface-mounted. However, integrating WPT systems into pavements introduces complex challenges. Pavement materials such as asphalt and cement concrete replace air as transmission media, significantly altering electromagnetic field propagation [4,5].

Current studies on WPT integration into road infrastructure focus on electromagnetic losses, structural damage, and environmental impacts. Systematic conclusions exist regarding the dielectric loss properties of pavement materials. For asphalt mixtures, dielectric loss in low-frequency ranges (0–100 kHz) is dominated by ionic conductivity, with humidity exerting significant influence [6]. When aggregate size exceeds 2.36 mm, its impact on dielectric performance diminishes markedly due to reduced interfacial effects between coarse aggregates and asphalt, as well as air void formation [7]. In magnetic pavement materials, the main research findings originate from the work of Li et al. and Venugopal et al. Studies [5] demonstrated that conventional pavement materials reduced transmission efficiency and increased power loss, primarily caused by their heterogeneous composition and interfacial scattering effects. The same research group subsequently confirmed that the addition of Mn-Zn and Ni-Zn ferrite powders to cement-based materials significantly improved transmission efficiency [8]. Venugopal et al. [9] investigated the effects of transfer distance on coupling coefficients and transmission efficiency under fully aligned coil conditions. Regarding structural damage, embedded primary coils compromise pavement layer integrity. Vehicle loads near interface zones increase rutting susceptibility [10]. Additionally, ensuring electromagnetic safety for biological organisms and minimizing environmental impacts remain critical challenges for WPT systems [11].

Previous studies primarily focused on ferrites and cement-based materials for magnetic pavements. However, Mn-Zn and Ni-Zn ferrites require high-temperature sintering processes for fabrication. These processes elevate costs and carbon emissions, thus limiting their large-scale applications. In contrast, magnetite is a naturally occurring mineral with low cost. It is used for pavement materials, while ferrites are used for specialized applications such as magnetic cores. Although Guo et al. [12] conducted numerical simulations of WPT efficiency with 20% magnetite content, experimental validation has not been provided. In this study, natural magnetite was substituted for basalt coarse aggregates to fabricate magnetite-modified asphalt mixtures, and WPT experiments were subsequently performed. All tests were conducted under dry conditions with 4.75 mm nominal magnetite particles, at room temperature and approximately 85 kHz, in compliance with SAE J2954 standards. Previous studies [6,7] have confirmed that dielectric losses are negligible under these operating conditions. In terms of numerical simulations, existing COMSOL Multiphysics 6.3-based studies rarely quantify the effects of magnetite content on asphalt mixtures’ electromagnetic properties. To address this gap, a 3D COMSOL model was proposed in this study to simulate magnetic field distributions in magnetite-modified asphalt mixtures. The effective permeability model was utilized to quantify the influence of magnetite content. Furthermore, series–series (SS) compensation topologies currently dominate pavement-embedded WPT research [13]. In contrast, LCC-S topologies achieve zero phase angle (ZPA) over wide operational ranges through primary-side LCC compensation, demonstrating superior robustness against coupling coefficient variations. The application of LCC-S topologies in pavement-embedded WPT systems remains unexplored [14]. This study addresses this unexplored application scenario through a combined numerical and experimental approach.

The environmental and economic implications of this research are profound. By reducing power loss through optimized magnetite content, the proposed pavement design decreases grid dependency and operational costs. For instance, a 15% improvement in transmission efficiency (from 80% to 95%) translates to an annual energy saving of approximately 1.2 MWh per kilometer of roadway, significantly lowering the carbon footprint [15,16,17]. Moreover, the integration of magnetite (a byproduct of iron ore processing) into pavements aligns with circular economy principles. This strategy repurposes industrial waste into high-value infrastructure components [18].

Material characterization techniques, including X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), and vibrating sample magnetometry (VSM), were employed to investigate the magnetite crystal structure, morphological characteristics, elemental composition, and magnetic hysteresis, thereby elucidating the mechanisms underlying the impact of magnetite on WPT transmission performance.

This paper is structured as follows: Section 2 details material preparation and permeability modeling techniques. Section 3 describes theoretical models, finite element modeling, and WPT system design. Section 4 presents experimental results on magnetite morphology characterization, coupling coefficient dynamics, efficiency trends, and power loss interactions. Section 5 integrates key findings, highlighting optimal magnetite content thresholds (10%) and a critical pavement thickness of 50 mm, beyond which the coupling coefficient decay stabilizes. It underscores the dominance of eddy current and hysteresis losses at elevated contents and proposes design guidelines for balancing energy transfer efficiency with mechanical durability. Future research directions emphasize refining magnetic material dispersion, exploring dynamic coupling adaptability, and advancing lifecycle assessments to accelerate the sustainable integration of magnetite-modified pavements in wireless charging infrastructure.

2. Materials and Methods

2.1. Raw Materials

The raw materials include SBS-modified asphalt, aggregates, and magnetite. The SBS-modified asphalt was provided by a manufacturer in Yunnan Province, China, with a density of 1.024 g/cm³, penetration of 55 (0.1 mm), and softening point of 72 °C, according to the standard “Test Methods for Asphalt and Asphalt Mixtures in Highway Engineering” (JTG E20–2011). The basalt coarse aggregates, limestone fine aggregates, and mineral filler were provided by Yunnan Province, China. The magnetite was supplied by Hebei Province. AC-13 asphalt mixtures were used in this research, and the particle size distribution is shown in

Table 1. Particle size distribution of aggregates.

Sieve Size (mm)	Passing Rate (%)
13.2	97.8
9.5	74.7
4.75	47.4
2.36	33.9
1.18	25.9
0.6	19.1
0.3	11.8
0.15	8.2
0.075	6.7

.

2.2. Sample Preparation

The properties of the aggregates are shown in

Table 2. Basic characteristics of aggregates used.

Property	Size (mm)	Bulk Density (g/cm3)	Los Angeles Abrasion Value (%)	Water Absorption (%)
Basalt	4.75–13.2	2.757	22.7	1.61
Magnetite	4.75	4.331	20.792	0.863
Limestone	0.075–2.36	2.718	-	1.32

, according to the “Test Methods of Aggregate for Highway Engineering” (JTG E42–2005). The bitumen content of all mixtures was 4.7% by mass of aggregates based on the Marshall test results. Due to the higher density of magnetite, it was used as a substitution (0%, 5%, 10%, 12.5%, and 25%) for basalt aggregates by volume with the particle size of 4.75 mm based on the results of the mix design (as detailed in

Table 3. Mix proportion for Marshall specimens.

Mixture Type	Bitumen (by Mass)	% of Addition 4.75 mm Particle Size (by Volume)
		Basalt	Magnetite
1	4.7%	100	0
2		95	5
3		90	10
4		87.5	12.5
5		75	25

). Referencing previous studies on functional material-modified asphalt mixtures [19], the Marshall specimens were prepared using a stepwise mixing procedure. Through preliminary tests to ensure uniform magnetite distribution in the asphalt mixture, the mixing procedure was standardized as follows: initially, magnetite and aggregates were mixed for 100 s (100 s), followed by the addition of bitumen and filler with an additional mixing duration of 100 s. Finally, the entire mixture was homogenized for another 100 s. The experimental design followed the principle of repeatability verification, with three independent parallel specimens prepared for each magnetite content level.

2.3. Material Testing and Characterization Methods

The microscopic morphology and elemental composition of the magnetite sample were analyzed using a Jeol JSM-IT700HR scanning electron microscope coupled with JED-2300 energy dispersive X-ray spectroscopy (JEOL Ltd., Tokyo, Japan). The analysis was performed at an acceleration voltage of 5.0 kV, a working distance of 11.1 mm, and a magnification of 5000×. The magnetic hysteresis loop of the magnetite sample was measured using a LakeShore-7404 vibrating sample magnetometer (Lake Shore Cryotronics Inc., Westerville, OH, USA); the instrument has a sensitivity of 5 × 10⁻⁷ emu and an accuracy of 2%. During the test, the maximum applied magnetic field was set to 2.17 T. Self-inductance, mutual inductance, and coil resistance were measured using a Keysight E4980A Inductance Capacitance and Resistance (LCR) meter device (Keysight Technologies, Santa Rosa, CA, USA).

2.4. Effective Permeability Model

Numerous theoretical models exist for predicting the effective permeability of composite materials when analyzing their magnetic properties [20,21]. This study employs the classical Maxwell–Garnett model to estimate the effective permeability of asphalt mixtures incorporating magnetite particles at varying volume fractions [22]. The Maxwell–Garnett model assumes that the distance between magnetic particles significantly exceeds their radius, making it suitable for composites with low magnetic filler content. As defined in Equation (1), μ_i represents the relative permeability of the nonmagnetic matrix, μ_m denotes the relative permeability of magnetic particles obtained from VSM measurements, ϕ corresponds to the volume fraction of magnetic particles, and μ_e defines the effective relative permeability of the composite material.

$${\mu }_{\mathrm{e}}={\mu }_{\mathrm{i}}+3 \varphi {\mu }_{\mathrm{i}}{\displaystyle \frac{{\mu }_{\mathrm{m}}-{\mu }_{\mathrm{i}}}{{\mu }_{\mathrm{m}}+2{\mu }_{\mathrm{i}}-\varphi \left({\mu }_{\mathrm{m}}-{\mu }_{\mathrm{i}}\right)}}$$

(1)

3. WPT System for LCC-S Topology

3.1. Theoretical Analysis of the WPT System

Figure 1 shows the LCC-S resonance compensation topology, respectively. The ac source U_s is generally an equivalent voltage generated from a full-bridge inverter that operates at an angular frequency ω. L_p and R_p are the equivalent inductance and resistance of transmitting coil, and L_s and R_s are the equivalent inductance and resistance of receiving coil. C_p and C_s are the resonance compensation capacitances at the primary side and secondary side for enhancing the energy transfer capacity and reducing the VA rating of the ac grid. L_in and C_f are additional resonance devices in LCC-S. R_L is the ac output load resistance.

In LCC-S topology, the resonance conditions are as shown in Equation (2) when the system operates at ω₀. The output power and system efficiency of LCC-S can be given by Equations (3) and (4).

Among the equations, Z_in is the input impedance, Z_r is the reflection resistance, and Z_s is the equivalent impedance of the secondary side. When ω = ω₀, they can be given by Equation (5).

$${\mathsf{\omega }}_0{\mathrm{L}}_{\mathrm{in}}={\displaystyle \frac{1}{{\mathsf{\omega }}_0{\mathrm{C}}_{\mathrm{p}}}},{\mathsf{\omega }}_0{\mathrm{L}}_{\mathrm{p}}-{\displaystyle \frac{1}{{\mathsf{\omega }}_0{\mathrm{C}}_{\mathrm{f}}}}={\mathsf{\omega }}_0{\mathrm{L}}_{\mathrm{i}\mathrm{n}} \mathrm{a}\mathrm{n}\mathrm{d} {\mathsf{\omega }}_0{\mathrm{L}}_{\mathrm{s}}={\displaystyle \frac{1}{{\mathsf{\omega }}_0{\mathrm{C}}_{\mathrm{s}}}}$$

(2)

$${\mathrm{P}}_{\mathrm{O}}={\displaystyle \frac{{\left({{\mathsf{\omega }}_0}^2{\mathrm{L}}_{\mathrm{i}\mathrm{n}}\mathrm{M}\right)}^2{{\mathrm{U}}_{\mathrm{s}}}^2{\mathrm{R}}_{\mathrm{L}}}{{\left[{\mathrm{Z}}_{\mathrm{i}\mathrm{n}}{\mathrm{Z}}_{\mathrm{s}}\left({\mathrm{R}}_{\mathrm{p}}+{\mathrm{Z}}_{\mathrm{r}}\right)\right]}^2}}$$

(3)

$$\eta ={\displaystyle \frac{{\left({\mathsf{\omega }}^2{\mathrm{L}}_{\mathrm{in}}\mathrm{M}\right)}^2{\mathrm{R}}_{\mathrm{L}}}{{\mathrm{Z}}_{\mathrm{in}}{{\mathrm{Z}}_{\mathrm{s}}}^2{\left({\mathrm{R}}_{\mathrm{P}}+{\mathrm{Z}}_{\mathrm{r}}\right)}^2}}$$

(4)

$${\mathrm{Z}}_{\mathrm{s}}={\mathrm{R}}_{\mathrm{s}}+{\mathrm{R}}_{\mathrm{L}},{\mathrm{Z}}_{\mathrm{r}}={\displaystyle \frac{{\left(\mathsf{\omega }\mathrm{M}\right)}^2}{{\mathrm{R}}_{\mathrm{s}}+{\mathrm{R}}_{\mathrm{L}}}}\mathrm{and}{\mathrm{Z}}_{\mathrm{in}}={\displaystyle \frac{{\left(\mathsf{\omega }{\mathrm{L}}_{\mathrm{in}}\right)}^2\left({\mathrm{R}}_{\mathrm{s}}+{\mathrm{R}}_{\mathrm{L}}\right)}{{\mathrm{R}}_{\mathrm{p}}\left({\mathrm{R}}_{\mathrm{s}}+{\mathrm{R}}_{\mathrm{L}}\right)+{\left(\mathsf{\omega }\mathrm{M}\right)}^2}}$$

(5)

3.2. Modeling of Coils and Pavement

To investigate the variations in self-inductance, mutual inductance, and magnetic field distribution of primary and secondary coils with pavement material integration, a 3D FEM comprising primary and secondary coils and pavement material media was established using COMSOL Multiphysics 6.3, as illustrated in Figure 2. The coil models were developed based on structural parameters from prior experimental configurations. Both primary and secondary coils adopted a circular geometry with an inner diameter of 30 mm and outer diameter of 106 mm. The coils were fabricated using Litz wire, featuring a strand diameter of 1.5 mm and 22 turns, with identical configurations for primary and secondary coils. The misalignment between secondary and primary coils significantly impacts wireless power transfer efficiency [23]. In the FEM, geometric configurations ensured full alignment of the primary and secondary coils, with a focus on analyzing the influence of pavement materials as transmission media on the resonant induction system, with the material thickness defined as the transmission distance between the two coils. The pavement material was modeled as an idealized homogeneous medium in the FEM [24,25]. The permeability of the pavement material was derived from the equivalent permeability model in Section 2.4, while its electrical conductivity and relative permittivity were derived from previous studies [24,26].

The FEM yielded a primary coil self-inductance of 31.017 μH, compared to a measured value of 31.225 μH for the physical primary coil, resulting in a 0.65% deviation. Similarly, the secondary coil self-inductance derived from the FEM was 31.013 μH, versus a measured value of 31.235 μH (0.71% error). The minimal discrepancies between the FEM predictions and experimental measurements validate the efficacy of the coil models.

The pavement material medium was modeled as a cylindrical specimen with a diameter of 152.5 mm, replicating the large-scale Marshall specimen geometry used in experiments. The material thickness was varied from 30 mm to 70 mm in 10 mm increments. Within the FEM framework, an alternating voltage frequency of 83.9 kHz was applied, with excitation currents of 1.0 A in both primary and secondary coils. Self-inductance and mutual inductance values were numerically simulated across different pavement material thicknesses, and the inductive coupling coefficient was calculated using Equation (6).

$$\mathrm{k}={\displaystyle \frac{\mathrm{M}}{\sqrt{{\mathrm{L}}_{\mathrm{p}}{\mathrm{L}}_{\mathrm{s}}}}}$$

(6)

3.3. WPT System Test

To verify the effect of pavement materials on the transmission performance of the wireless power transfer system, a prototype WPT system was constructed based on the coupling structure defined in the FEM and the circuit parameters specified in

Table 4. Parameters of the WPT system.

Udc (V)	ω (kHz)	Lin (μH)	Cf (nF)	Cp (nF)	Cs (nF)	RL (Ω)
48	83.9	11.98	199.23	299.63	199.66	3.8

, as shown in Figure 3. The system employed an LCC-S topology configuration, where the primary-side circuit comprised a DC power supply and a full-bridge inverter, while the secondary side incorporated a full-bridge rectifier and a rheostat to regulate output power. A Tektronix MDO3014 digital oscilloscope was connected in parallel to monitor output waveforms. Digital multimeters and clamp meters were utilized to measure voltage and current values. Vernier calipers were employed to position the primary and secondary coils, ensuring precise alignment with the geometric center of the large-scale Marshall specimen and strict spatial alignment between the two coils. The transmission distance between the primary and secondary coils was set to the thickness of the large-scale Marshall specimen. All experiments were conducted at room temperature (25 °C). To address thermal accumulation in the primary-side inverter circuit and secondary-side rheostat during operation, an intermittent cooling protocol was implemented. Following each experimental run, the WPT system underwent a 10 min power-off cooling procedure, ensuring temperature stabilization back to initial ambient conditions. To mitigate interference from spatial heterogeneity in magnetite-modified asphalt mixtures on electromagnetic parameter measurements, all specimens were tested using a dual-side alternating measurement protocol. Accurate characterization of wireless power transfer parameters was achieved, by calculating the arithmetic mean of measurements obtained from both front and reverse surfaces. The coil resistance was measured at 150 mΩ, and the coupling coefficient was derived from self-inductance and mutual inductance measurements, both obtained using an LCR meter.

4. Results and Discussions

4.1. Morphological Characteristics of Magnetite

Microstructural images of the magnetite sample were obtained from SEM test. Figure 4a–f display the elemental distribution of the magnetite sample, while Figure 4g–i reveal polyhedral morphology, irregular cracks in the magnetite, and chain-like particle agglomerations, attributed to internal stress release during mechanical crushing and indicating magnetic interactions. The larger particle size and non-uniform distribution lead to increased magnetic domain boundary density, which impedes the free rotation of magnetic domains under external magnetic fields, thereby enhancing coercivity. Additionally, the surface displays an uneven topography with concave and convex structures, influenced by oxide overlays. The chain-like particle agglomeration regions may induce localized eddy currents, resulting in minor power losses.

Table 5. The chemical composition of the magnetite sample.

Elements	Mg	Al	Si	Fe	Ni	Zn
Quality percentage (%)	20.93	18.92	24.23	33.77	0.49	1.66
Atomic number percentage (%)	28.1	22.89	28.16	19.74	0.28	0.83

summarizes the chemical composition of the magnetite sample. Fe dominated the composition, with a mass fraction of 33.77%.

Figure 5a illustrates the magnetic properties of the magnetite sample. The X-axis represents the external magnetic field H, and the Y-axis represents magnetization M. The narrow S-shaped hysteresis loop demonstrates soft magnetic behavior. The maximum magnetic susceptibility, represented by the steepest slope of the hysteresis loop, is a dimensionless parameter. This value directly correlates with the maximum relative permeability of the sample, enabling its calculation from the measured magnetic susceptibility. Compared to magnetite, the remaining components of the asphalt mixture exhibit paramagnetic behavior with negligible hysteresis losses. Figure 6 presents the XRD pattern of the magnetite sample. The main diffraction peaks of magnetite are observed at 2θ angles of 35.5° and 30.1°, which are characteristic of magnetite. Magnetite exhibits an inverse spinel structure, while the secondary mineral phase corresponds to chlorite group minerals.

4.2. Coupling Coefficient and Transmission Efficiency

Experimental measurements reveal that the self-inductance of both primary and secondary coils positively correlates with the permeability of magnetite-modified asphalt mixtures (Figure 7). As the magnetite dosage rises from 0% to 25%, primary coil self-inductance increases progressively from 31.415 μH to 32.378 μH, while secondary coil self-inductance grows from 31.368 μH to 32.385 μH. Mutual inductance exhibits nonlinear behavior: it initially declines from 7.410 μH at 0% to 6.985 μH at 5% magnetite content, then peaks at 7.682 μH at 10% before stabilizing at 7.766 μH for 25%. This trend demonstrates a positive correlation between mutual inductance and permeability at a magnetite content below 10% [27]. The coupling coefficient k follows a similar nonlinear trajectory, rising from 0.236 at 0% to 0.242 at 10% magnetite content, then marginally decreasing to 0.240 at 25%. When the magnetite content increases to 12.5% and 25%, the reduction in coupling coefficient indicates a negative correlation between magnetic coupling efficiency and additive concentration. The incorporation of magnetite leads to contrasting trends in coil self-inductance and mutual inductance: self-inductance continuously rises with increasing magnetite content, while mutual inductance significantly decreases at 0–5% content, sharply increases at 5–10%, and gradually declines beyond 10%. According to Equation (6), the competing mechanisms between these parameters lead to the nonlinear variation in the coupling coefficient with magnetite content.

Figure 8 presents the wireless power transfer system’s transmission efficiency and coupling coefficient across magnetite content variations. A significant correlation is evident between these parameters. The system achieves a peak efficiency of 84.67% at 10% magnetite content, surpassing the baseline efficiency of 80.38% observed under 0% magnetite content conditions. Beyond this concentration, efficiency progressively declines to 78.64% at 25% magnetite content. This trend directly aligns with the coupling coefficient’s variation pattern. According to Equation (3), the system output power exhibits a linear proportionality to the ac voltage source, where increasing the ac source effectively enhances output power. Equation (4) further demonstrates that system transmission efficiency remains stable during output power amplification through voltage source regulation. Therefore, to prioritize energy conservation and emission reduction, the primary research objective for magnetite-modified asphalt pavement systems should be optimizing transmission efficiency.

Figure 9 presents numerical simulations of magnetic field distributions in pavement materials with magnetite contents of 0%, 5%, 10%, 12.5%, and 25%. For conventional asphalt mixtures (0% magnetite), the magnetic field distribution aligns with air-core system characteristics [28], exhibiting flux lines concentrated near the primary coil. The low permeability of air-dominated media disperses flux transmission paths, resulting in significantly reduced coupling efficiency compared to air-core systems. At 5% and 10% magnetite content, the magnetic flux density modulus in the secondary coil gap markedly increases, confirming enhanced coupling efficiency driven by permeability improvement. Further increasing magnetite to 12.5% and 25%, however, causes magnetic field contraction toward the secondary coil, reducing flux density uniformity between coils and degrading coupling efficiency. Experimental data and numerical simulations were subjected to integrated analysis. The results demonstrate that 10% magnetite content represents the optimal dosage. This finding provides vital technical support for developing energy-efficient wireless power transfer pavement, thus advancing carbon peaking and neutrality goals in transportation infrastructure.

4.3. Thicknesses of Pavement Materials

Figure 10 presents numerical simulations of coupling coefficients across varying pavement material thicknesses (10% magnetite content). The coupling coefficient exhibits stepwise reduction with increasing material thickness. Within the 30–50 mm thickness range, the coupling coefficient undergoes rapid reduction, reaching a 50.8% reduction rate. Within the 50–70 mm thickness range, the reduction rate decreases to 44.6%, with the coupling coefficient stabilizing progressively. This behavior aligns with magnetic field attenuation theory [3]. The red polyline in Figure 10 illustrates the variation trend of coupling coefficient gain values for magnetite-doped asphalt mixtures, compared to non-magnetite asphalt mixtures, under identical transmission distances. The enhancement trend aligns with the coupling coefficient variation observed at 10% magnetite content. This alignment indicates that the enhancement effects of magnetite incorporation in asphalt mixtures on coupling coefficients are significantly weakened when material thickness exceeds 50 mm. Figure 11 presents numerical simulations of wireless power transfer efficiency across pavement material thicknesses (10% magnetite content). Within the 30–50 mm range, transmission efficiency exhibits reduction rates of 1.35% and 2.26%. Within the 50–70 mm range, the reduction rates increase markedly to 4.58% and 7.023%. These findings conclusively identify 50 mm as the critical thickness threshold for pavement materials. Figure 12 presents numerical simulations of magnetic field distributions across varying pavement material thicknesses. Increasing material thickness progressively reduces the system’s magnetic field coupling strength, evidenced by gradient attenuation in the magnetic flux density modulus between primary and secondary coils. Maximum and minimum magnetic field intensities exhibit strong negative correlations with thicknesses below 50 mm. At 60 mm, however, the peak intensity shows an anomalous rebound, while the minimum continues declining. This nonlinear behavior confirms the intensified non-uniformity of the magnetic field distribution in the coil near-field region beyond the critical thickness, inducing significant magnetic energy dispersion. These findings validate 50 mm as the critical thickness threshold.

Finite element simulations (Air core-FEM) exhibit < 2% error across the 30–70 mm transmission distance range, as presented in Figure 13, validating the model’s accuracy [27]. Minor deviations in pavement material simulations may stem from unmodeled interfacial scattering effects caused by permeability discontinuities [9]. Based on prior studies [24], the FEM assumes magnetite-modified asphalt mixtures as idealized homogeneous media. However, as a typical multiphase porous composite material, its heterogeneous microstructure induces unstable electromagnetic responses [25]. Future research may develop three-dimensional multiphase composite material models, enabling a refined distribution of magnetic materials within asphalt mixtures. This work is currently in progress.

4.4. Output Power and Power Loss

Experimental data revealed a nonlinear dependence of both output power and power loss on magnetite content in the wireless power transfer system, as shown in Figure 14. When the magnetite content increased from 0% to 10%, the output power rose from 110.07 W to 149.79 W. As the magnetite content increased from 12.5% to 25%, output power elevated from 145.85 W to 162.98 W. Notably, the most rapid power gain of 25.58 W was observed at 10% magnetite content. A transient power reduction of 3.94 W occurred at 12.5% magnetite content. As the magnetite content increased from 12.5% to 25%, the output power displayed a secondary increase, albeit with decelerated growth rates. Concurrently, power loss escalated nonlinearly from 30.62 W to 44.28 W. Beyond 10% magnetite content, loss growth accelerated markedly, showing a 38.78% surge between 10% and 25% magnetite content.

The equivalent permeability of magnetite-modified asphalt mixtures increased with magnetite content, thereby enhancing the magnetic field intensity and output power in wireless power transfer. At 0%, 5%, and 12.5% magnetite content, power loss and output power exhibited an approximately proportional relationship. At 10% magnetite content, output power increased significantly while power loss decreased substantially. This phenomenon is attributed to nonlinear variations in mutual inductance and transmission efficiency with increasing magnetite content (Figure 7). Figure 9c demonstrates uniform and concentrated magnetic field distributions on both primary and secondary sides at 10% magnetite content. At 25% magnetite content, however, output power and power loss increased markedly, coupled with a significant decline in transmission efficiency. Figure 9e further reveals reduced magnetic flux within the effective coupling region at 25% magnetite content [6]. Concurrently, the minimum magnetic flux density modulus increased significantly, indicating magnetic flux dispersion into non-effective coupling regions. Additionally, hysteresis and eddy current losses escalated substantially at 25% magnetite content.

5. Conclusions

This study systematically investigated the electromagnetic performance of magnetite-modified asphalt mixtures in wireless power transfer systems through integrated numerical simulations and experimental validations. Key findings and implications are summarized as follows:

• Magnetite incorporation significantly improved magnetic coupling properties, with the coupling coefficient peaking at 0.242 at 10% content and efficiency reaching 84.67%. Beyond this threshold, efficiency declined due to escalating eddy current and hysteresis losses, defining 5–10% as the optimal magnetite dosage range. Incorporating magnetite significantly enhances coupling efficiency by improving permeability, evidenced by an increased magnetic flux density modulus in secondary coil gaps. In contrast, conventional asphalt (0% magnetite) exhibits air-core system characteristics with dispersed flux paths and poor coupling due to low-permeability media. These findings demonstrate that strategic magnetite integration effectively concentrates magnetic flux transmission, overcoming the limitations of air-dominated systems. The research prioritizes permeability enhancement through material modification as the key pathway for sustainable electromagnetic pavement system development.
• The critical thickness threshold for magnetite-modified asphalt pavements is identified as 50 mm. Below 50 mm, maximum and minimum magnetic field intensities exhibit strong negative correlations with thickness, while exceeding this threshold intensifies magnetic field non-uniformity in the coil near-field region, leading to significant energy dissipation. The coupling coefficient gain of magnetite-modified mixtures weakens markedly beyond 50 mm. Finite element simulations (error < 2%) validate the model accuracy. These findings provide critical guidance for balancing electromagnetic performance and structural feasibility in wireless charging pavements. Future work will refine multiphase composite models to optimize magnetic material distribution.
• The output power and power loss in the WPT system exhibited a nonlinear dependence on magnetite content. Output power increased with magnetite content, with the most rapid power gain at 10% content. The equivalent permeability of magnetite-modified asphalt mixtures increases with magnetite content, enhancing magnetic field intensity and output power in wireless power transfer systems. However, at 25% magnetite content, magnetic flux within the effective coupling region decreases, while the minimum flux density modulus rises significantly, indicating flux dispersion into non-effective regions. Concurrently, hysteresis and eddy current losses escalate substantially. These results identify 10% as the critical magnetite content threshold, highlighting the need for optimized material composition to balance electromagnetic efficiency and energy dissipation.

In summary, this study demonstrates that optimizing magnetite content and pavement thickness can achieve a balance between wireless power transfer system transmission performance and road performance, offering a sustainable solution for energy-efficient wireless charging infrastructure.