From Conventional to Electrified Pavements: A Structural Modeling Approach for Spanish Roads

Comments 1: The study relies entirely on numerical simulations. Provide at least some form of experimental validation or calibration, or clearly discuss the limitations and future work needed to validate the model (e.g., field deflection data, strain gauge measurements).

Response 1: We appreciate the reviewer’s comment. The authors fully agree that experimental validation is essential to ensure the reliability of simulation-based findings. Although the present manuscript focuses on a first-stage structural assessment using standardized elastic assumptions, validation efforts are currently in progress.

Specifically, Falling Weight Deflectometer (FWD) measurements are being carried out on the CARDHIN pilot section, which replicates the electrified pavement configuration modeled in this study. These tests are part of an ongoing campaign, and the resulting data will be used to calibrate and refine the FEM models in future work. This limitation and the planned validation strategy have been described in the newly added Section 4.4 of the revised manuscript from line 573 to 615.

Comments 2: All pavement layers are modeled as purely elastic, which may oversimplify actual behavior under repeated or thermal loading. Include a discussion on the limitations of elastic modeling and, ideally, preliminary viscoelastic results or plans for future implementation.

Response 2: Thank you for this insightful comment. The authors recognize that assuming purely elastic behavior for all pavement layers may not fully capture time-dependent effects such as viscoelastic relaxation and thermal-induced deformation.

In the present study, the elastic modeling approach was selected to align with the Spanish Pavement Design Standard 6.1-IC, which adopts linear-elastic behavior for mechanistic-empirical analysis. This allowed for a standardized comparison of conventional and electrified configurations under controlled conditions. Nonetheless, we agree that incorporating viscoelasticity would enhance the model's fidelity.

To address this, parallel studies are currently underway to characterize the viscoelastic properties of SMA8 and AC16 asphalt mixtures. The resulting parameters (e.g., Prony series) will be implemented in future simulations to enhance the accuracy of predicted stress and strain responses, particularly for fatigue assessment under repeated loading. This limitation and future development pathway are now discussed in Section 4.4 of the revised manuscript from lines 573 to 615.

Comments 3: Fatigue life estimates (Nf) and damage progression are presented as fixed values, without confidence intervals or sensitivity tests. Add sensitivity analysis for fatigue predictions, especially with respect to material stiffness, layer thickness, or bonding conditions.

Response 3: We appreciate the reviewer's important observation. We agree that fatigue life predictions can be sensitive to variations in input parameters such as layer stiffness, thickness, and interface conditions.

The present study was conceived as a comparative structural assessment based on standard pavement sections defined by the Spanish Catalogue (6.1-IC), with fixed material properties and geometries. This enabled the identification of critical structural locations and stress concentration patterns under various electrification scenarios.

These findings will serve as the basis for a comprehensive sensitivity analysis in future work, in which the number of structural configurations will be reduced to a set of representative or worst-case sections. The upcoming study will explore the impact of material variability, bonding conditions, and viscoelastic behavior on fatigue performance.

This methodological limitation and the planned extension of the analysis have been acknowledged in Section 4.4 of the revised manuscript from lines 573 to 615.

Comments 4: The CU–asphalt interface is modeled as fully bonded based on lab results, but in practice, bonding quality can vary. Add simulations with partially bonded or debonded interfaces, or at least discuss the impact of interface degradation over time.

Response 4: Thank you for this relevant comment. The interface between the Charging Unit (CU) housing and the asphalt mixture is indeed critical to the long-term performance of electrified pavements. In the current model, a fully bonded interface was assumed based on the results of laboratory adhesion tests conducted by the authors, which showed strong initial bonding under optimized conditions.

To clarify this assumption, the manuscript has been updated to include a technical justification and additional references supporting the use of bonded contact conditions when interlayer shear strengths exceed accepted thresholds. These additions reflect standard practice in FEM simulations of asphalt pavements, particularly when adhesives are used under controlled conditions.

Nonetheless, we agree that real-world conditions may lead to interface degradation over time due to factors such as moisture, thermal cycling, or construction variability. To address this, a cohesive interface model is currently under development, calibrated from previously published adhesion tests, and will be incorporated into future pavement simulations to account for partial bonding and debonding scenarios.

You may find the following clarification now included in the manuscript (Line 354):

“considered indicative of effective interlayer bonding in asphalt pavements [28,29]. Such values are commonly accepted in literature to justify bonded contact conditions in FEM modeling of asphalt layers [18,21,23], mainly when adhesive agents are used under controlled construction conditions. These considerations support the assumption of a bonded interface in this study”

This limitation, along with the ongoing development of a more advanced interface model, is now discussed in Section 4.4 of the revised manuscript from lines 573 to 615.

Comments 5: The study is specific to Spanish standards (Norma 6.1-IC), limiting international relevance. Include a section discussing the applicability of the methodology and findings to other countries or pavement standards (e.g., AASHTO, Eurocodes).

Response 5: We appreciate this important observation. While the structural configurations and fatigue criteria applied in the study are based on the Spanish Pavement Design Catalogue (Standard 6.1-IC), the overall simulation methodology—combining mechanistic-empirical multilayer modeling and 3D FEM analysis—is broadly applicable to other international design frameworks.

To clarify this, a paragraph has been added to Section 4.4 of the revised manuscript from lines 573 to 615.

Comments 6: Some material parameters are taken from guidelines without detailing testing conditions or statistical variation. Include a summary table of mechanical properties, test methods, and standard deviations for asphalt, base, subgrade, and CU materials.

Response 6: We thank the reviewer for this valuable suggestion. While the elastic modulus and Poisson’s ratio for each material were already included in Table 4 of the original manuscript, the revised version now clarifies the source of each property value through footnotes directly associated with each material.

For the asphalt mixtures (SMA8 and AC16), mechanical properties were obtained experimentally in accordance with EN 12697-26, using four specimens per mixture. As requested, Table 2 has been updated to report the corresponding standard deviations, which are now also reflected in the asphalt entries in Table 4.

For the other layers (granular base, cement-treated materials, subgrade, and CU housing), values were drawn from design catalogues or technical datasheets. Because these are typical reference values, no statistical variation is reported, and this is now explicitly noted in the table via footnotes.

Comments 1: The authors should explain why two layers of the pavement have the same name MB.

Response 1: Thank you for your observation. In accordance with the Spanish Pavement Design Catalogue (Standard 6.1-IC), the acronym "MB" (Mezcla Bituminosa) is commonly used to refer to all asphalt layers, regardless of their specific structural function. However, to improve clarity and avoid confusion, we have updated the nomenclature throughout the manuscript to distinguish between the different asphalt layers: MB-S for the surface course (SMA8) and MB-B for the binder course (AC16).

Additionally, in electrified pavement configurations, where the Charging Unit (CU) is embedded within the binder course, we have further subdivided MB-B into two segments: an upper binder layer (MB-BU) and a lower binder layer (MB-BL), corresponding to the material located above and below the CU, respectively. This clarification has been incorporated into a new paragraph inserted just before line 173, and the updated terminology is now used consistently in the text, figures 4 and 5, and Tables 1 and 4.

Comments 2: The location of the charging units (CUs) should be marked in Fig.2a.

Response 2: Thank you for your suggestion. Figure 2a has been revised to clearly indicate the position of the embedded Charging Unit (CU). A labeled marker has been added at the corresponding depth within the asphalt layers, using the phrase “CU at 9 cm depth” to denote its installation level from the pavement surface. This correction enhances the clarity of the pavement layout and aligns with the actual configuration used in the CARDHIN pilot section.

Comments 3: The authors wrote that the CU is 3 cm thick, which means that the MB (binder course) layer has been reduced to 4 cm. The effect of this on the pavement load-bearing capacity should be written (line 173).

Response 3: Thank you for your comment. To clarify this point, we have inserted a new paragraph immediately after line 173 (From lines 176 to 184), explaining in detail how the geometry of the binder course was adapted to incorporate the 3 cm thick Charging Unit (CU). Specifically, the CU was embedded at a depth of 9 cm from the surface, and the upper portion of the binder course was adjusted to include a 6 cm upper binder layer (MB-BU) above the CU. The remaining binder material below the CU (MB-BL) varied in thickness depending on the pavement section analysed, with the total MB-B thickness ranging from 12 cm to 32 cm.

Comments 4: The thicknesses of the successive layers and the depth of the CU location should be given in Fig.4 (Fig.4 and Fig.5).

Response 4: Thank you for your suggestion. Figures 4 and 5 have been revised to indicate the thicknesses of all pavement layers, as well as the exact location of the Charging Unit (CU). The CU is now clearly shown embedded at a depth of 9 cm from the pavement surface, consistent with the CARDHIN pilot section configuration. In addition, the asphalt layers are labeled using the updated nomenclature and mixture types: MB-S (surface course, SMA asphalt mixture), MB-BU (upper binder layer, AC16 asphalt mixture), and MB-BL (lower binder layer, AC16 asphalt mixture). These modifications improve the clarity of the cross-sectional diagrams and ensure consistency with the materials and terminology used throughout the manuscript.

Comments 5: On what basis was it assumed that the deflection depths caused by road traffic become negligible? In addition, it should be written in the manuscript why this particular depth of the CU location was chosen (line 188).

Response 5: Thank you for your comment. We have expanded the explanation near line 188 (New line 206) to clarify the basis for the boundary condition assumptions. The assumption that traffic-induced deflections become negligible beyond a certain depth is based on multilayer elastic theory, which shows that vertical stress and deformation decay rapidly with depth—particularly below the asphalt-bound layers. This modeling approach is widely accepted in pavement analysis and has been supported with references now included in the manuscript. Additionally, the selected depth of 9 cm for CU installation reflects the design adopted in the CARDHIN pilot section, providing a balance between mechanical protection and inductive efficiency.

Comments 6: The dimensions should be given in Fig.6 and it should be written how the CUs differ specifically.

Response 6: Thank you for your observation. Figure 6 has been updated to include the main dimensions of the Charging Unit (CU). Subfigures (a) and (b) show the real external geometry of the CU housing (90 × 50 × 3 cm), including the upper and lower views. Subfigure (c) displays the simplified version of the CU used in the FEM simulations, where curved features and geometric undulations around the coil area were removed to improve mesh generation and reduce computational cost. The figure caption has been revised accordingly to clarify these differences and additionally improved manuscript from new lines 220 to 231.

Comments 7: It should be written in the manuscript what ZA, SC, GC mean (Table 4).

Response 7: Thank you for your observation. We have included a clarification in the manuscript explaining the acronyms used in Table 4. ZA, SC, and GC refer to Crushed Aggregate, Cement-Soil, and Cement-Treated Gravel, respectively. This information has been added at the end of the paragraph describing the pavement layer configurations.

New Line 189: The base layer materials included Crushed Aggregate (ZA), Cement-Soil (SC), and Cement-Treated Gravel (GC), as defined in the Spanish road pavement catalogue.

Comments 8: An incredibly high modulus of elasticity for 100 MPa rubber?? (271 lines).

Response 8: Thank you for your observation. We acknowledge that the modulus of elasticity of typical natural rubber is generally much lower (1–10 MPa). However, in this study, the assigned value of 100 MPa was not intended to represent actual tire rubber. Instead, it was applied to the circular plates used to simulate the contact area between the tire and the pavement in the FEM model.

To clarify this point, we have updated the manuscript with the following sentence:

New line 307: “To simulate a stiff, nearly incompressible interface, the plates were assigned a Young’s modulus of 100 MPa and a Poisson’s ratio of 0.499. This enabled stable contact modeling and realistic vertical stress distribution without requiring explicit modeling of the tire structure.”

Comments 9: Must be written in English (445 - 448 lines).

Response 9: We apologize for this oversight. The sentence originally written in Spanish in lines 445–448 (New lines 489-494) has been translated into English in the revised version of the manuscript. The corrected sentence now reads:

“The results revealed concerning strain concentrations commonly observed across most models under the misaligned path configuration, which could potentially affect the pavement's service life. Figure 16 illustrates these critical points, which are distributed along the upper fiber of the surface course between the dual tires and at the interface between the asphalt mixture and the CUs.”

Comments 10: 223 line, Tab.2: Please explain in the manuscript E_B1 - E_B3.

Response 10: Thank you for your observation. We have added a sentence to the manuscript clarifying that EB1 to EB4 correspond to the individual specimens tested for each asphalt mixture, as specified in EN 12697-26. This clarification now appears immediately before Table 2 (New Lines 244 to 250):

“The asphalt mixtures were characterized using resilient modulus values (EBi) obtained in accordance with European Standard EN 12697-26. Four samples, labeled EB1 to EB4, were tested for each type of asphalt mixture. For the surface course (MB-S), a gap-graded SMA8 mixture was used, with a maximum aggregate size of 8 mm, designed to provide high wear resistance and good rutting stability. For the intermediate layers (MB-B), a semi-dense AC16 mixture with a maximum aggregate size of 16 mm was selected, as it is suitable for providing structural support and facilitating the transition between layers”.

Comments 11: Please write more about the PBT/PET polymer blend.

Response 11: Thank you for your comment. We have expanded the description of the PBT/PET polymer blend in line 237 to provide more specific technical information about its mechanical and thermal properties. The revised text now includes the following sentence (New Lines 267 to 270):

“This blend is a thermoplastic with a tensile modulus of 2500 MPa, tensile strength and elongation at break of 70%, and low moisture absorption (0.2%). It remains dimensionally stable up to 170 °C and offers high surface hardness (Brinell 145 MPa), making it suitable for structural housings in DWPT systems subjected to mechanical and thermal cycling.”

These values are based on the technical data sheet of the selected material and support its suitability for long-term structural use in pavement-embedded charging units.

Comments 1: Ad.3 The authors did not write what effect the reduction of the MB (binder course) layer had on the pavement's load-bearing capacity.

Response 1: We appreciate the reviewer’s observation regarding the impact of the reduced upper binder layer (MB-BU) on pavement performance. To address this point, we introduced two modifications in the revised manuscript.

First, in the Geometry Definitions subsection (lines 182–185), we added a clarifying sentence to acknowledge this potential effect early in the text:

“The remaining binder course, located below the CU (MB-BL), varied by section, with total MB-B thicknesses ranging from 12 cm to 32 cm. Although the overall thickness was maintained, reducing the upper binder layer (MB-BU) to 6 cm may affect the surface response. This is discussed in the Results and Discussion section.”

Second, in Section 4.2 (lines 492–502), we added a new paragraph and restructured the closing of the subsection to provide a technically grounded analysis based on FEM results:

“Among the structural parameters analyzed, the reduction of the upper binder layer (MB-BU) from 9 cm to 6 cm—required to embed the 3 cm thick Charging Unit (CU)—emerged as a key factor affecting near-surface mechanical performance. Although the total binder course (MB‑B) thickness was preserved by increasing the lower binder layer (MB‑BL), FEM simulations showed elevated tensile and tangential strain concentrations in the MB‑BU and MB‑S layers, particularly under misaligned loading when the tire overlapped the CU. These localized peaks, observed along the surface course and at the CU–asphalt interface (Figure 16), increase the risk of microcracking and interfacial debonding, reducing pavement service life. Similar effects have been reported in other FEM studies, where thinner asphalt layers resulted in up to 2-fold increases in critical strains under comparable conditions [30–32].”

We also added the following sentence to connect the observed structural effect to the modeling framework (lines 503–508):

“These strain concentrations, especially in the upper layers, underscore a key limitation of the current elastic multilayer modeling approach. While effective for comparative analysis, it does not capture time-dependent effects such as viscoelastic relaxation, plastic deformation, or thermal sensitivity, which are relevant in asphalt materials. A more comprehensive discussion of these limitations and the proposed shift toward viscoelastic and viscoplastic modeling is provided in Section 4.4.”

Finally, references [30–32] have been included to strengthen the academic foundation of the analysis.

Comments 2: Ad.8 The authors should absolutely explain what material the slabs were made of. For asphalt surface layers, the modulus of elasticity is several times greater than 100 MPa.

Response 2: We appreciate the reviewer’s observation. The circular plates with a modulus of 100 MPa used in the FEM simulations do not correspond to actual pavement layers. Instead, they were introduced as numerical elements placed directly on the pavement surface to simulate the tire–pavement contact interface. Their assigned mechanical properties (E = 100 MPa, ν = 0.499) represent a stiff, rubber-like material and are intended to enable stable and realistic load transfer without explicitly modeling the full tire structure.

To avoid misinterpretation, the paragraph in lines 307-314 has been revised to clarify this modeling assumption and distinguish the plates from the actual asphalt layers.

“In the finite element model, vertical pressure was applied to two circular plates (1 mm thick) placed directly on the pavement surface, representing the tire–pavement contact areas. These plates were not physical components of the pavement, but numerical tools to simulate the mechanical footprint of the tires. To replicate the load transfer behavior of pneumatic tires without modeling their geometry, the plates were defined with a Young’s modulus of 100 MPa and a Poisson’s ratio of 0.499, simulating a stiff yet nearly incompressible rubber-like interface. This approach enabled stable contact modeling and a realistic vertical stress distribution at the loading points.”