# Hybrid ML/FWI method using GPR data to evaluate the tack coat characteristics in pavements: Experimental validation

Grégory Andreoli, Amine Ihamouten, Franziska Schmidt, Mai Lan Nguyen, David Souriou, Xavier Dérobert

► To cite this version:

Grégory Andreoli, Amine Ihamouten, Franziska Schmidt, Mai Lan Nguyen, David Souriou, et al. Hy-brid ML/FWI method using GPR data to evaluate the tack coat characteristics in pavements: Exper-imental validation. Transportation Engineering, 2025, 20, pp.100339. 10.1016/j.treng.2025.100339 . hal-05070894

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# Hybrid ML/FWI method using GPR data to evaluate the tack coat characteristics in pavements: Experimental validation

Grégory Andreoli<sup>a,●,*</sup>, Amine Ihamouten<sup>b</sup>, Franziska Schmidt<sup>c</sup>, Mai Lan Nguyen<sup>b</sup>, David Souriou<sup>d</sup>, Xavier Dérobert<sup>e</sup>

## ARTICLE INFO

### Keywords:

Tack coat

GPR

Machine learning

FWI

Hybridization

## ABSTRACT

Time resolution is one of the limiting factors when using Ground Penetrating Radar (GPR) techniques to characterize thin layers in the subsurface, such as the tack coat in pavements. To evaluate this residual bituminous emulsion at the interface between the wearing course and the binder course, we have developed an inverse method based on a hybrid data processing approach that combines machine learning (ML) algorithms with Full-Waveform Inversion (FWI). Adding the dielectric permittivity of the wearing course (extracted via FWI) as a structural *a priori* input into the SVM/SVR models has demonstrated the strong potential of this methodology on synthetic time domain signals. This research proposes extending such a methodology through experimental campaigns. To carry out this study, three distinct campaigns have been planned, namely on: Hot-Mix Asphalt (HMA)-controlled slabs manufactured in the laboratory; a controlled full-scale structure using the Gustave Eiffel University fatigue rollover (Nantes, France); and a new, yet-to-be-used, road in France. These experiments serve to validate the performance improvements of various classification and regression SVM/SVR algorithms when adding the dielectric permittivity of the wearing course. Herein will be compared the results of the global approach, without preprocessing raw time domain signals, with the developed hybrid model.

## 1. Introduction

The lifespan of transportation infrastructure is decreasing due to climate variations (freeze-thaw cycles, extreme temperatures), increased traffic density and construction quality (compliance with standards, environmental conditions). Surface defects like potholes, peeling, and slippage often result from subsurface issues. To enable bonding and consequently restrict deterioration, a tack coat should be applied between the wearing and binder courses of the pavement. This addition enhances adhesion, increasing the structure's rigidity and durability while reducing mechanical stresses and deformations [1]. A good tack coat helps diffuse surface stresses to lower layers [2]. Delamination typically occurs at high temperatures, high loads (especially horizontal loads) or a combination of both, specifically in the presence of a weak interface bond. This weakness is often due to a low-quality tack coat material or improper application. These conditions are therefore critical throughout the infrastructure's lifespan [3]. The tack coat is a key requirement according to standards [4], serving as a reference

for diagnosing civil engineering structures. Evaluating *in situ* tack coat application requires an understanding of the impact of dosage in terms of weight per unit area (in g/m²). Under-dosing tack coat leads to peeling and layer separation [5], while over-dosing can increase the risk of slippage. Nowadays, identifying and estimating a subsurface layer thinner than a millimeter without damaging the medium is challenging.

Various research works have characterized the tack coat through investigations into its mechanical behavior [6], chemical properties [7] and rheology [8]. However, these methods remain destructive or need to be conducted before pavement installation, in some cases using ionizing devices like a gamma-ray densitometer. Efforts to employ Non-Destructive and more environmentally-friendly methods have explored various approaches, such as hyper-frequency electromagnetic techniques. Recent studies have concluded using the Full-Waveform Inversion (FWI) method along with Stepped-Frequency Radar (SFR) shows the polarization capacity of bituminous emulsion (dielectric susceptibility) to be correlated with its dosage [9].

<footnote><sup>a</sup>MAST/MIT Research Group, Gustave Eiffel University, Nantes, France</footnote>

<footnote><sup>b</sup>MAST/LAMES Research Group, Gustave Eiffel University, Nantes, France</footnote>

<footnote><sup>c</sup>MAST/EMGCU, Research Group, Gustave Eiffel University, Marne-la-Vallée, France</footnote>

<footnote><sup>d</sup>FI-NDT, Nantes, France</footnote>

<footnote><sup>e</sup>GERS/GeoEND Research Group, Gustave Eiffel University - FI-NDT, Nantes, France</footnote>

<footnote>* Corresponding author.
E-mail address: gregory.andreoli@univ-eiffel.fr (G. Andreoli).</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1. Flowchart illustrating the data acquisition and processing method (experimental adaptation of numerical validation flowchart) [10].</figcaption></figure>

Nevertheless, due to the limited resolution of commercial radar devices, it remains quite challenging to discriminate the tack coat dosage from experimental signals. To address this issue, we have explored various solutions, including machine learning methods. These algorithms have recently been introduced into civil engineering applications, particularly within the GPR community [11–14]. Such methods enable the construction of models from large datasets, whether they be synthetic or experimental. Among the various algorithms, the Support Vector Machine (SVM) method has allowed for both the detection of subsurface debonding [15] and the classification of different types of pavement bonding [16]. Our previous research has demonstrated the possibility of detecting thin interfaces in the subsurface using machine learning (ML) methods [17,18]. However, despite their good performance, these methods often overlook the physical behavior of the environment under study, which in turn limits their ability to provide significant physical interpretations of the results. By integrating parameters that account for both physical behavior (such as dielectric permittivity) and data morphology (SVM/SVR), we have demonstrated the relevance of a hybrid ML/FWI approach for estimating tack coat characteristics in pavements using Non-Destructive Techniques. We have achieved greater accuracy than with conventional methods through controlled synthetic data [10].

This article aims to address the feasibility of applying the hybridization methodology developed for synthetic GPR signals to experimental ones. For this purpose, we introduce electromagnetic wave propagation with a GSSI central frequency device of $f_c = 2.6$ GHz (offering a good compromise between subsurface temporal resolution and backscattering) with a quasi-monostatic ground-coupled antenna for maximizing energy propagation in the multilayer structure. The aggregates used in wearing and binder course can reach sizes of 10 to 14 mm. A frequency exceeding 2.7–3 GHz leads to A-scans being affected by backscattering, increasing signal interpretation difficulties and potentially misleading SVM/SVR detection algorithms. Conversely, a lower frequency would reduce temporal resolution, limiting the ability to detect subtle variations in dielectric contrast at interfaces. The challenge here is to achieve better data separation with SVM/SVR models despite the resolution, low echo amplitude at the interface, and presence of constructive interferences due to geometry and the coupling effect. In addition, an ultra-wideband (UWB) device with a calibrated antenna and an SFR is used to collect frequency data and extract the complex dielectric permittivity through FWI, as required for hybridization.

To address, such challenges we have structured this article as follows: Section 2 reviews the methodology applied to synthetic data and examines how it can be extended to experimental data. Section 3 details three experimental campaigns: controlled test slabs in the laboratory, partially controlled experiments on a test site at Gustave Eiffel University in Nantes (France) and actual conditions on a new road in western France's Vendée Department. Results obtained are then presented and discussed in Section 4. A conclusion is provided in Section 5, followed by the acknowledgments.

## 2. Methods

During work performed on hybrid ML/FWI GPR synthetic data processing, we modeled a two-layer pavement and its interface using gprMax [19], with a grid whose length and width corresponded to the positioning of radar emission and reception sources at the nodes [10]. Here, we adapt the methodology used for numerical validation in order to conduct an initial experimental validation (Fig. 1). The first goal is to build a comprehensive database composed of various subsurface time domain signals (A-scans) representative of realistic configurations, as part of a global approach (without preprocessing). Next, the database is reduced using a time window around the targeted area (interface echo). During a second phase, the SFR device (including a Vivaldi antenna and a vector network analyzer) enables data acquisition in the frequency domain over an ultra-wideband. These data are necessary as input for FWI to extract the dielectric permittivity of the wearing course following the computational steps (Fig. 2). Lastly, an extracted dielectric permittivity is added to provide an *a priori* information that facilitates the SVM/SVR machine learning model process. To evaluate model prediction and prevent overfitting when the dataset is imbalanced, the *stratified k-fold* method (a variant of *k-fold* cross-validation) is implemented with $k = 5$ [20]. The results obtained then allow us to map the thickness/dosage of the tack coat with excellent performance (see Table 1).¹² Performance evaluation is conducted using standard metrics such as the Dice Score (DSC, also known as the F1-Score) (Eq. (1)) for

<footnote n="1">¹ Computer specifications: Dell Precision 7750, Intel® Core™ i7-10875H CPU 2.30 GHz, 32 GB RAM, GPU NVIDIA Quadro RTX 3000.</footnote>

<footnote n="2">² TCSVM: Two-Class SVM; MCSVM: Multi-Class SVM and SVR: Support Vector Machine for Regression.</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 2. ML/FWI Flowchart principle.</figcaption></figure>

classification, the Root Mean Square Error (RMSE) (Eq. (2)), and the Coefficient of Determination ($R^2$) (Eq. (3)) for the regression.

$$DSC = \frac{2 \times TP}{2 \times TP + FP + FN} \qquad (1)$$

where TP is the True Positive, FP the False Positive and FN the False Negative.

$$RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (\hat{y}_i - y_i)^2} \qquad (2)$$

$$R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i - \bar{y})^2} \qquad (3)$$

where $y_i$ is the real output value, $\bar{y}$ the mean value and $\hat{y}_i$ the estimated output value.

<table><caption>Table 1 Methods and performance according to various approaches [10].</caption><thead><tr><th>Method</th><th>Approach</th><th>DSC (%)</th><th>RMSE</th><th>R<sup>2</sup> (%)</th><th>Average computational processing time (s)</th></tr></thead><tbody><tr><td rowspan="2">TCSVM</td><td>Global</td><td>83</td><td>-</td><td>-</td><td>138</td></tr><tr><td>Hybrid</td><td><b>96</b></td><td>-</td><td>-</td><td><b>26.9</b></td></tr><tr><td rowspan="2">MCSVM</td><td>Global</td><td>78</td><td>-</td><td>-</td><td>221.5</td></tr><tr><td>Hybrid</td><td><b>88</b></td><td>-</td><td>-</td><td><b>51</b></td></tr><tr><td rowspan="2">SVR</td><td>Global</td><td>-</td><td>0.42</td><td>93</td><td>199.6</td></tr><tr><td>Hybrid</td><td>-</td><td><b>0.35</b></td><td>93</td><td><b>70.5</b></td></tr></tbody></table>

The results on synthetic signals show improved performance achieved through the use of this hybrid model. To address issues faced by road managers regarding the identification of areas with tack coat defects, this same methodology is to be applied on experimental data as model input to classify and estimate tack coat dosage through various experiments.

The following section presents the equipment used to carry out these experiments and their study sites. The objective of these three experiments can be described as follows:

* **Hot-Mix Asphalt (HMA) controlled test slabs:** With its three degrees of freedom (tack coat dosage, compactness, geometry), this experiment serves to validate binary and multiclass classification hybrid methods, in addition to estimating tack coat dosage, using samples manufactured in the laboratory, with a controlled formulation;

* **The fatigue carousel platform in Nantes (France) [21]:** With its two degrees of freedom (presence or absence of tack coat, geometry), this full-scale structure, built using standard civil engineering design methods, also offers a known mix design. Due to a single dosage at the interface on 3 of the 5 sections, only the two-class SVM is to be validated here. Moreover, two measurement campaigns have yielded two distinct datasets: one at the initial state of the structure, $T_0$, the other after controlled aging, $T_1$ (aging method detailed in Section 3.3);

* **New experimental road in Vendée (western France):** With a single degree of freedom (tack coat dosage), this new roadway has been constructed with three distinct dosages at the interface on three sections specifically for this experiment. The output allows validating the multiclass classification (MCSVM) and estimation via SVR regression on a road with known formulation yet an uncontrolled implementation.

The entirety of this campaign, through a progressive increase in the complexity of the surveyed environments, enables validating our methodology step-by-step. The following section will present all the equipment used for the A-scans collection and as well as the extraction of the dielectric permittivity of the wearing course. A detailed overview of the three experiments will then be provided.

## 3. Experimental study

### 3.1. Experimental set-up

Of widespread use throughout the operational radar community, the GSSI device has been chosen herein. It comprises an SIR®4000 acquisition system and a ground-coupled antenna operating at 2.6 GHz, a frequency that corresponds to our needs (Fig. 3).

The first part of the experimental protocol involves acquiring time domain signals that describe the surveyed pavement. Given the fixed parameters (Table 2), the A-obtained scans enable the construction
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** Measurement GPR device SIR®4000 acquisition unit, with 2.6 GHz GSSI antenna.</figcaption></figure>

<table><caption>**Table 2**
Data acquisition parameters.</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>Resolution</td><td>2045 pts</td></tr><tr><td>Time window</td><td>5 ns</td></tr><tr><td>Step</td><td>2 mm for the slabs experiment<br>2 cm for the other two experiments</td></tr><tr><td>Transmission rate</td><td>200 kHz</td></tr><tr><td>Filter FIR</td><td>Low pass : off<br>High pass : off</td></tr><tr><td>Filter IIR<br>(For reading use only)</td><td>Low pass : 5 GHz<br>High pass : 400 MHz</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Device propagating the EM wave through the surveyed medium, in enabling FWI.</figcaption></figure>

of a comprehensive database, which can be labeled based on our ground-truth knowledge of the tack coat dosage.

Once the time domain signals have been acquired, the second part of the protocol entails obtaining the dielectric permittivity of the wearing course using FWI. Let us apply the methodology developed in the works of [22–25], which address: calibrating the antenna, generalizing the antenna model for near-field conditions (whereby the field distribution over the antenna aperture varies), using the multiple-offset Green’s function, and processing the amplitude-weighted objective function [9]. Given that the bituminous medium can be considered weakly dispersive and the tack coat as a dielectric material, the use of a 2p Jonscher model [26] is well-suited for the problem across the entire frequency band and moreover is less computationally intensive than the 4p model.

<table><caption>**Table 3**
Data acquisition parameters.</caption><thead><tr><td>Parameter</td><td>Value</td></tr></thead><tbody><tr><td>Starting Frequency</td><td>400 MHz</td></tr><tr><td>Stopping Frequency</td><td>8 GHz</td></tr><tr><td>Frequency resolution</td><td>401 pts</td></tr><tr><td>Antenna height</td><td>50 mm</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Manufacturing of HMA slabs: (a) MLPC slab compactor; (b) Set of manufactured two-layered HMA slabs.</figcaption></figure>

The acquisition chain (Fig. 4) consists of: an N9928 A FieldFox Handheld VNA (Vector Network Analyzer), an acquisition station, and a Vivaldi UWB400-D ultra-wideband (UWB) antenna (Applied EM Innovations). Its characteristics are described in [27]. The parameters used for this measurement procedure are defined in Table 3.

After introducing the device to be used, the series of campaigns conducted will be presented, along with their objectives and scientific and technical challenges.

## 3.2. HMA controlled test slabs

In this experiment, 32 two-layered HMA slabs (600 × 400 mm were manufactured using the MLPC slab compactor (Fig. 5a), which replicates road texture in the laboratory also known as the RETEX disposable [28]).

The compactor is equipped with a metal mold measuring 600 × 400 mm with an adjustable depth (90 mm in this case) to produce a surface layer (wearing course + binder course) that closely replicates real conditions. A twin-wheel system performs longitudinal and transverse movements following the European standard EN 12697-33 [29] to achieve the desired compaction level. First, the binder course is manufactured. Once it reaches ambient temperature, the tack coat is applied to each slab at the target dosage. Finally, after emulsion breaking, the wearing course is stacked and compacted (Fig. 5b).

The nomenclature for each layer is as follows:

* **BBTM** (French acronym for *Béton Bitumineux Très Mince* corresponding to Very Thin Bituminous Concrete): used for the wearing course. The targeted average thickness ranges from 25 to
<figure><img src="image_7.png" /><figcaption>Fig. 6. Example of a B-scan along diagonal D2 of slab P16 dosed with 600 g/m² tack coat dosage (100 mm was removed from each corner to avoid edge effects).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. Location of the GPR profiles on the HMA samples.</figcaption></figure>

30 mm with a binder content of 5%. The particle size distribution of the stone aggregate fractions is 0/10 mm, with a discontinuity of between 2 and 6.3 mm.

* BBSG (French acronym for Béton Bitumineux Semi-Grenu corresponding to Semi-Coarse Bituminous Concrete): used for the binder course (as well as the wearing course). The targeted average thickness ranges between 55 and 60 mm with a binder content of 5%. The particle size distribution of the stone aggregate fractions is continuous at 0/10 mm.

The three degrees of freedom in this experimental design are thus tack coat dosage: i.e. absence (0 g/m²); under-dosage (200 g/m²); standard dosage (400 g/m²); over-dosage (600 g/m²), compactness of the BBTM layers at 75% and 90%, and the BBSG layers at 91% and 96% and lastly the geometry of the wearing course (BBTM or BBSG). The selected aggregates originate from Carrières et Travaux de la Côte Vendéenne (CTCV) located in La Roche Guillaume (France). Their mineralogical nature is a mixture of rhyolite (volcanic rock with a microlithic structure) whose dielectric permittivity ranges between 4.8 < ε<sub>rhyolite</sub> < 5.7 and gneiss (metamorphic rock) whose dielectric permittivity ranges between 4.9 < ε<sub>gneiss</sub> < 5.5 [30,31]. The bituminous emulsion used is Emulpropre® with 60% pure bitumen; this is a cationic fast breaking emulsion for application of a tack coat that quickly becomes exposed to traffic.

Fig. 6, shows an example of a radargram (B-scan) from slab P16 (a BBTM layer compacted at 90% on a BBSG layer compacted at 96%) with a tack coat dosage of 600 g/m². The surface echo is initially identified as mixed with the direct wave (at 0.8 ns) and the PEC (at 2 ns). The B-was truncated by 100 mm on each side in order to retain only ose signals from the core of the slab, thereby eliminating edge effects (due to our limited size). It became overly difficult to visually distinguish the interface using only GPR on the B-scan, despite the high dosage applied in this case.

By following the protocol outlined in the data paper and combined with an accurate description of the samples [32], we where able to gather a representative volume of data for each sample by making multiple profiles (Fig. 7) with the device set-up described in Section 3.1. Each slab was initially placed on a Perfect Electric Conductor (PEC), such as a metallic plate, to identify the bottom of the binder course (which yields an estimate of the maximum time window relevant for subsequent experiments under actual conditions). The measurement parameters used for acquisition are those described in Table 2 with a measurement step of 2 mm.

<figure><img src="image_9.png" /><figcaption>Fig. 8. Example A-scans for each dosage.</figcaption></figure>

Let us now examine the signals in the time domain (Fig. 8). A-scans have been plotted from four different slabs (P04, P08, P12, P16) with BBTM on BBSG. These slabs all have the same compactness for both the BBTM (91%) and BBSG (96%) layers, each with a different tack coat dosage (0, 200, 400 and 600 g/m², respectively). A total of 10 A-scans were averaged for this plot; they were taken at the core along the Longitudinally-Centered (LC) profile and Transversally-Centered (TC) profile (Fig. 7) for each scan. Note that slab P08 (corresponding to a bituminous dosage of 200 g/m²) shows an echo at the PEC ahead of the others. This slab (red curve) has a binder course (BBSG) thickness approximately 5 mm less than intended after manufacturing. Unlike on the B-scan, the presence of dielectric contrast can be identified at around 1.15 ns, which confirms the link between the capability of a bituminous emulsion to be polarized (dielectric susceptibility) and consequently, the tack coat dosage [9]. While the junction between wearing course and binder course can be identified, its impossible to detect and estimate directly the tack coat, but rather a variation in the theoretical reflection coefficients associated with FWI, which reflect a dielectric contrast at this interface. Indeed, during its application (before breaking), the emulsion fills the asperities (with an air-filled zone with a permittivity ε<sub>air</sub> = 1) with tack coat (ε<sub>TC</sub> ≈ 2.41 [33]). This variation in permittivity, governed by a mixing law, provides the relevant information for the detection. However, the difficulty in distinguishing among the various dosages affirms the relevance of using advanced processing methods. We therefore propose applying the hybrid ML/FWI method developed on synthetic signals.

### 3.3. The fatigue carousel platform

The Gustave Eiffel University in Nantes (France) has been using a full-scale road traffic simulator since 1984; this device, known as the “fatigue carousel” (Fig. 9), replicates the structural aging of a pavement in an accelerated manner for experimental purposes. Fitted with four arms around a central hub, the device allows for testing on real structures and varying moving loads representative of traffic (65 kN on single or dual-wheel axles, in tandem or tridem) at different rotational speeds of up to 90 km/h [5]. The circular track measures 120 m in length (at 19 m from the center) and 6 m in width.

As part of these experiments, a BBM (French acronym for Thin Bituminous Concrete) on a BBSG road structure was manufactured for the needs of the French ANR Agency's BINARY project [34], with a track measuring 60 m long and 3.5 m wide. Let us note that for this experiment, the old surface layer was partially removed in order to implement the new structure across various sections (Fig. 10). Five sections span the entire test area (with the last two, S2b and S2c, being identical) with a different surface layer (wearing + binder courses) geometries, comprising two states of tack coat dosage.
<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Picture of the fatigue carousel platform at the Gustave Eiffel University in Nantes (France).</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Fig. 10.** Diagram of the carousel representing the various sections [18].</figcaption></figure>

The selected aggregates originate from the *Carrières et Matériaux du Grand Ouest* (CMGO) facility located in Rouans (France); they are mineralogically based on gneiss (metamorphic rock), with a dielectric permittivity ranging from $4.9 < \epsilon_{gneiss} < 5.5$. Moreover, Sections S1a, S2b, and S2c, contain a tack coat dosage of 300 g/m² applied between the wearing and binder courses. The first two sections feature: a BBM with a targeted 50 mm thickness of wearing course on a BBM with a targeted 50 mm thickness of binder course, a particle size distribution of stone aggregate fractions 0/10 mm, a 5.48% binder content and a Mean Texture Depth (MTD) of 1.25 mm. The three other sections are composed of: a BBSG with a targeted 60 mm thickness of wearing course on a BBM with a targeted 40 mm thickness of binder course, the same particle size distribution of stone aggregate fractions, a 5.63% binder content, and an MTD of 0.83 mm.

In addition to the rotation of thekarousel's axes, the wheels move
transversely along a Gaussian pattern [35], which makes it possible to
guide our choice of inspection profiles on the test track. By perform-
ing several passes according to a defined protocol, a volume of data
representative of each section could be compiled. Over the of 3.5 m
width, four longitudinal profiles and two transverse profiles were thus
considered per section (Fig. 11). This part of the experiment targets a
comparative study before T₀ and after pavement aging at T₁.

*   **Longitudinal Profile P1:** located 17.9m from the center of the
carousel (0.86 m from the inner edge). When the carouse wheels
are in operation, this profile is at the start of the wheel path.
Pavement degradation is considered to be low.

<figure><img src="image_12.png" /><figcaption>**Fig. 11.** Experimental protocol and measurement profiles.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 12.** Example A-scans from various BBM and BBSG sections, both with and without a tack coat.</figcaption></figure>

*   **Longitudinal Profile P2:** located 18.6m from the center of the
carousel (1.5 m from the inner edge). When the carouse wheels
are in operation, this profile is on the ascending slope of the
Gaussian wheel path. Pavement degradation is considered to be
moderate.

*   **Longitudinal Profile P3:** located 19m from the center of the
carousel (1.9m from the inner edge). When the carouse wheels
are in operation, this profile is at the peak of the Gaussian path.
Pavement degradation is considered to be maximum.

*   **Longitudinal Profile P4:** located 19.75m from the center of the
carousel (2.65m from the inner edge). This profile lies out-
side the wheel path and therefore not subject to any pavement
degradation.

*   **Transverse Profiles P5:** located 3m after the beginning of each
section.

*   **Transverse Profiles P6:** located 3m before the end of each
section.

The starting point for measuring each longitudinal profile is located
1 m before the beginning of the section and ending 1 m after the
section. This protocol serves to include each section for evaluation and
balance of any potential shifts between theoretical and practical begin-
nings/ends of tack coat spreading. The measurement parameters used
for acquisition are those described in Table 2 with a 2 cm measurement
step.

Fig. 12 shows 4 random A-scans (one per section on the P3 profile). While the presence of the interface caused by the dielectric contrast can be identified, yet visually confirming its correspondence to the tack coat proves to be impossible. Once again, the utility of ML methods has been confirmed, especially hybrid processing to help identify this thin bituminous layer.
<figure><img src="image_14.png" /><figcaption>Fig. 13. Study area for the new road in Vendée (France).</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 14. Targeted pavement structure on the new road.</figcaption></figure>

## 3.4. Experimental new road in Vendée (France)

In the Vendée department, ML/FWI methods have been evaluated on a new, yet-to-be-used road (Fig. 13). More specifically, this road features: two lanes of traffic in each direction, a width of 5 m, a traffic speed limitation of 90 km/h, low traffic volumes, and an urban bypass function.

The aggregates chosen to build of this new road originate from the Sainte-Florence Enrobés company, located in Les Lombardières (France); they consist of microdiorite (a rock similar to diorite but micro-granular in its structure), with a dielectric permittivity of $\epsilon_{microdiorite} \approx 5.3$ [30]. The wearing course is a BBSG with a continuous particle size distribution of stone aggregate fractions 0/10, containing 5.1% of residual binder with a grade of 35/50. Its targeted thickness is 50 mm, with compactness varying by around 85%. The binder course is a GB (French acronym for Bituminous Gravel), with: a particle size distribution of stone aggregate fractions 0/14 (using the same aggregates), a 4.5% of binder content, and a compactness exceeding 93%. Its estimated thickness is 60 mm, while the base layer is a GB with granular fraction 0/14 (Fig. 14).

Lastly, the emulsion used for the tack coat consists of 69% pure bitumen: it is a cationic emulsion with rapid breaking comprising 50% Atlantiques Émulsions from Montoir-de-Bretagne and the other 50% from Liants Routiers Vendéens (LRV85). For purposes of this research work, we spread different dosages of tack coat across three sections, each 40 m long yielding 450 g/m² on the first section, followed by 250 g/m² on the second and 300 g/m² on the last one. It should be noted that beyond the test area (i.e. before Section 1 and after Section 3), the project manager applied a tack coat dosage of 300 g/m².

By using the same acquisition protocol and device parameters as for the fatigue carouse l experiment, we could compile a volume of data representative of each section. Three longitudinal profiles (P1 located 1.2 m from the right side of the road, P2 at 2.5 m, P3 at 3.8 m and two transverse profiles, at 3 m respectively from the beginning and end of each section (Fig. 15), were thus considered herein. The starting point for measuring each longitudinal profile is located 1 m before the beginning of the section ends 1 m after.

Fig. 16, which depicts 3 A-scans (one per section on the P3 profile), indicates that the interface is visible due to the dielectric contrast;

<figure><img src="image_16.png" /><figcaption>Fig. 15. Experimental protocol and measurement profiles.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Fig. 16. Example A-scans from sections with differing tack coat dosage.</figcaption></figure>

however, a precise identification of the tack coat remains impossible visually. Once again, the usefulness of hybrid ML/FWI model methods for tack coat characterization can be confirmed.

With the three experimental sites now introduced, let us present the results obtained for each case in the following section of the paper.

## 3.5. Database construction

To validate our method, a dataset has been built for each experimental site. Each of the three datasets was then split into a training set and a test set specific to the SVM/SVR model. The A-scans composing the different datasets are raw and have not undergone any preprocessing such as filtering, background removal, or averaging. However, to adjust the values of the A-scans used as input for the SVM/SVR model, signal normalization was applied. Normalization helps, among other things, to compare the performance metrics (such as the Dice Score and RMSE) returned by the model.

To prevent overlap between the two datasets, the following approach was adopted:

* **HMA controlled test slabs:** 20 A-scans were randomly selected on each slab from a full database of 33,824 A-scans in order to solely obtain a new 320 A-scans new dataset and avoid overfitting. This new dataset was then divided into a balanced ratio of 70% (224 A-scans including 56 A-scans of each four classes) for training and 30% (96 A-scans including 24 A-scans of each four classes) for testing.

* **The fatigue carouse l platform:** A-scans were selected from the transverse profiles (representing approximately 11.9% of the dataset), taken at sufficient distances from intersections (3 m) so as to eliminate uncertainties regarding tack coat implementation. This A-scans sample represents the training dataset, with 36.5% of the A-scans corresponding to areas without tack coat and 63.5% corresponding to areas with tack coat. The use of stratified K-fold cross-validation helps mitigate the imbalance in the dataset. Next, testing was conducted on the entire structure, with longitudinal profiles serving as the test set (approximately 88.1% of the dataset).
<figure><img src="image_18.png" /><figcaption>Fig. 17. Results of radar data FWI on P16 bi-layers made of bituminous concrete (antenna height: 50 mm): (a) Real part of the effective permittivity in the frequency domain (BBTM in red, BBSG in blue); (b) Imaginary part of the effective permittivity in the frequency domain (BBTM in red, BBSG in blue).</figcaption></figure>

* **Experimental new road in Vendée:** The same method applied for the fatigue Carousel was used, with A-scans selected from the transverse profiles (representing approximately 9.2% of the dataset), taken at sufficient distances from intersections again to eliminate uncertainties over tack coat implementation. Similarly to the fatigue Carousel, this A-scans sample represents the training dataset, with 33.33% of the A-scans for each dosage. Testing was subsequently conducted on the entire structure, with longitudinal profiles serving as the test set (approximately 90.8% of the dataset).

With the data now processed, the following section will present the results obtained for each experimental site.

# 4. Results

## 4.1. FWI on the P16 bi-layer slab

Using the set-up shown in Fig. 4 on the P16 bi-layer, Fig. 17 reveals high-frequency stability around the central frequency of the GSSI device, i.e. $f_c = 2.6$ GHz, which is beneficial for data collection.

The measured real parts of the effective permittivity are: for BBTM $\epsilon'_{BBTM} \approx 4.2$ and for BBSG $\epsilon'_{BBSG} \approx 4.34$ (Fig. 17a). These values are of the same order of magnitude since materials have an identical mineralogical composition and binder content. Their differences arise from compaction levels and the continuity or discontinuity of aggregate gradation, which explains such a noticeable difference.

By analyzing the imaginary part of effective permittivity, the non-dispersive nature of the bi-layers at $f_c = 2.6$ GHz can be confirmed, with: for BBTM $\epsilon''_{BBTM} \approx 0.32$ and for BBSG $\epsilon''_{BBSG} \approx 0.34$ (Fig. 17b).

Using FWI, thus inverts the radar data with an SFR Ultra-Wideband device and yield the dielectric permittivity necessary for hybridization.

## 4.2. Classification and regression on HMA controlled slabs

As shown in [10], the double inverse method improves the decision-making process by integrating dielectric permittivity while reducing computational processing time.

Using the Bayesian approach [36], the optimal parameters for minimizing the cost function (Table 4) were identified for each method.

Let us now compare the TCSVM confusion matrices (Fig. 18a) for both the global approach (Fig. 18c) and hybrid model. The output values were chosen as follows: -1 for signals without a tack coat and +1 for signals with a tack coat.

A notable improvement is observed in the detection of tack coat absence (i.e. True Negatives), with 26 A-scans correctly classified as

<table><caption>**Table 4**

Hyperparameters tuning for HMA controlled slabs experiment.</caption><thead><tr><th>Parameter</th><th>Value (TCSVM)</th><th>Value (MCSVM)</th><th>Value (SVR)</th></tr></thead><tbody><tr><td>Kernel</td><td>Gaussian (RBF)</td><td>Gaussian (RBF)</td><td>Gaussian (RBF)</td></tr><tr><td>C</td><td>500.98</td><td>502.21</td><td>498.51</td></tr><tr><td>γ</td><td>6.01 · 10<sup>-4</sup></td><td>7.3 · 10<sup>-4</sup></td><td>5.12 · 10<sup>-4</sup></td></tr><tr><td>ε</td><td>-</td><td>-</td><td>0.074</td></tr></tbody></table>

<figure><img src="image_19.png" /><figcaption>Fig. 18. Confusion matrices for the test slab data: (a) TCSVM global approach; (b) MCSVM global approach; (c) Hybrid TCSVM model; (d) Hybrid MCSVM model.</figcaption></figure>

<table><caption>**Table 5**

Methods and performance using different approaches.</caption><thead><tr><th>Method</th><th>Approach</th><th>DSC (%)</th><th>RMSE</th><th>R<sup>2</sup> (%)</th><th>Average computational processing time (s)</th></tr></thead><tbody><tr><td rowspan="2">TCSVM</td><td>Global</td><td>85</td><td>-</td><td>-</td><td>6.75</td></tr><tr><td>Hybrid</td><td><b>100</b></td><td>-</td><td>-</td><td><b>6.73</b></td></tr><tr><td rowspan="2">MCSVM</td><td>Global</td><td>87</td><td>-</td><td>-</td><td>7.7</td></tr><tr><td>Hybrid</td><td><b>99</b></td><td>-</td><td>-</td><td><b>6.38</b></td></tr><tr><td rowspan="2">SVR</td><td>Global</td><td>-</td><td>159</td><td>80</td><td>5.85</td></tr><tr><td>Hybrid</td><td>-</td><td><b>88.8</b></td><td><b>91</b></td><td><b>4.55</b></td></tr></tbody></table>

True Negatives (hybrid model) vs. 18 A-scans (global approach). In addition, 70 A-scans are classified as True Positives (hybrid model) vs. 69 (global approach). Five A-scans previously classified as False Positives are now seen as being correctly classified as True Negatives. Similarly, 4 A-scans previously classified as False Negatives are now classified as True Positives. The results on the MCSVM confusion matrices (Fig. 18b for the global approach, Fig. 18d for the hybrid model) also show improved discrimination of tack coat dosages through a better rate of True Positives. A significant reduction in classification errors across all dosages is noted, with just one A-scan being misclassified when applying the hybrid model, compared to 12 previously.

Let us now compare performance in the HMA-controlled slab experiment (Table 5). Here, the performance of the global approach is assessed vs. the hybrid model, as well as across methods (Two-Class SVM, Multi-Class SVM, Regression SVR) on the experimental data. Improvements are observed in both accuracy and average computational processing time. The choice of hybrid model underscores the benefit of adding the dielectric permittivity of the wearing course as a structural a priori in the ML model input.

## 4.3. Binary classification on fatigue Carousel

As stated in Section 2, only two states of tack coat dosage are present in the fatigue Carousel experiment (0 and 300 g/m²). Consequently, the hybrid TCSVM/FWI method has been employed. Furthermore, the structural change between Sections S1b and S2a serves to validate the
<figure><img src="image_20.png" /><figcaption>**Fig. 19.** TCSVM mapping applied to GPR data showing the tack coat presence in yellow and its absence in blue: (a) Ground truth; (b) Initial state (0 cycle); (c) After 50,000 cycles.</figcaption></figure>

algorithm's robustness against two different pavement layer thicknesses and formulations. Lastly, since the primary principle of the fatigue
carousel is to accelerate road aging, two measurement campaigns were
conducted: the first, at $T_0 = 0$ cycle of rotation (with a cycle denoting a
complete rotation of thekarousel), thus indicating a new surface; and
the second after $T_1 = 50 \times 10^3$ cycles of rotation (i.e. during a 5 month
span). As a complementary objective, the robustness of the algorithmic
model can thus be validated by training on data from $T_0$ and then
testing on $T_1$.

Using FWI methods (presented in Section 3.1) yields the dielectric permittivity values of the wearing course for both BBM sections (S1a and S1b), and BBSG sections (S2a, S2b, and S2c) as $\epsilon_{BBM} \approx \epsilon_{BBSG} \approx 4.4$. Consequently, this observable is incorporated into the training matrix for hybridization.

The mapping presented (Fig. 19) shows the impact of the hybrid
model on the fatiguekarousel experimental data. Fig. 19a indicates the
ground truth for estimating the classifier's potential error. The EM map-
ping projected onto a half-circle, accurately representing the surveyed
track, identifies the spatial distribution of the tack coat characteristics.
From Fig. 19b, at the initial state ($T_0$), the representation of radar data
inversion in terms of TCSVM classification proves to be excellent. Let us
note the presence of transition zones at intersections with overlapping
phenomena, thus causing systemic errors in hyperparameter optimiza-
tion and, consequently, aberrations in the results. Fig. 19c shows the
mapping of the experimentation conducted after $50 \times 10^3$ cycles using
the training set collected at the 0 cycle. It is observed that certain
misclassified areas at $T_0$ are correctly classified at $T_1$, particularly in the

<table><caption>**Table 6**
Hyperparameters tuning for fatiguekarousel experi-
ment.</caption>
  <thead>
    <tr>
      <th>Parameter</th>
      <th>Value (TCSVM)</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>Kernel</td>
      <td>Gaussian (RBF)</td>
    </tr>
    <tr>
      <td>C</td>
      <td>450</td>
    </tr>
    <tr>
      <td>γ</td>
      <td>5.72 &middot; 10<sup>-4</sup></td>
    </tr>
  </tbody>
</table>

<figure><img src="image_21.png" /><figcaption>**Fig. 20.** TCSVM fatiguekar confusion matrix: (a) $T_0 = 0$ cycle (global approach); (b) $T_1 = 50 \times 10^3$ cycles (global approach); (c) $T_0 = 0$ cycle (hybrid model); (d) $T_1 = 50 \times 10^3$ cycles (hybrid model).</figcaption></figure>

transition zones. An improvement is noted on the confusion matrices,
first between the global approach and the hybrid model and then
between $T_0$ and $T_1$.

For starters, the confusion matrices for the global approach (Figs.
20a and 20b) at $T_0$ and $T_1$, respectively, show a slight decrease in
the identification of zones without a tack coat, with 4,035 A-scans
(True Negatives) at $T_1$ vs. 4,046 at $T_0$. Conversely, an improvement
is observed in the detection of the bonding state, with 7,191 A-scans
(True Positives) at $T_1$ vs. 7,041 at $T_0$, once again for the global ap-
proach. This outcome can be explained by an increase in the surface
structure compactness after $50 \times 10^3$ cycles, thereby reducing potential
air gaps both at the interfaces and within the layers. This mechanical
consolidation of the pavement was empirically evaluated at around
$10 \times 10^3$ cycles, in estimating the normalized amplitude averages of
the reflected wave at $f_c = 2.6$ GHz, as well as in terms of Young's
modulus [35,37]. This structural phenomenon helps understand the
improvement in the classification model between $T_0$ and $T_1$ by better
identifying dielectric contrasts.

The optimal parameters for minimizing the cost function (Table 6)
were identified for the TCSVM method.

Figs. 20c and 20d reveal better TCSVM results with the hybrid
model compared to Figs. 20a and 20b, with a reduced number of
False Positives, i.e. 346 A-scans at $T_1$ (hybrid model) vs. 403 A-scans
at $T_1$ (global approach): 57 A-scans previously classified as False
Positives are now correctly classified as True Negatives. For the False
Positives, 353 A-scans are found at $T_1$ (hybrid model) vs. 548 at $T_1$
(global approach): 195 A-scans previously classified as False Negatives
are now correctly classified as True Positives. The same distribution
of misclassified A-scans can be observed for the case $T_0$. This better
balance in the distribution of classification errors indicates an optimal
positioning of the decision boundary due to the addition of the wearing
course dielectric permittivity.

Let us now compare the performance indicators (Table 7) derived
from the fatiguekarousel experiment. These results demonstrate the
advantages of using a hybrid model over a global approach when
employing the binary classification TCSVM method, in terms of both
performance and computational processing time. This outcome vali-
dates the methodology applied to a full-scale experiment, both during
the initial degradation state of a pavement with variable geometry and
<table><caption>**Table 7**
Methods and performance using various approaches.</caption><thead><tr><th>Method</th><th>Nbr</th><th>Cycle</th><th>Approach</th><th>DSC (%)</th><th>Average computational processing time (s)</th></tr></thead><tbody><tr><td rowspan="4">TCSVM</td><td>0</td><td></td><td>Global</td><td>91</td><td>169.62</td></tr><tr><td>0</td><td></td><td>Hybrid</td><td><b>93</b></td><td><b>71.58</b></td></tr><tr><td>50,000</td><td></td><td>Global</td><td>92</td><td>149.14</td></tr><tr><td>50,000</td><td></td><td>Hybrid</td><td><b>94</b></td><td><b>73.06</b></td></tr></tbody></table>

<figure><img src="image_22.png" /><figcaption>**Fig. 21.** Actual MCSVM road in the Vendée confusion matrix: (a) Global approach; (b) Hybrid model.</figcaption></figure>

<table><caption>**Table 8**
Hyperparameters tuning for new road experiment.</caption><thead><tr><th>Parameter</th><th>Value (MCSVM)</th><th>Value (SVR)</th></tr></thead><tbody><tr><td>Kernel</td><td>Gaussian (RBF)</td><td>Gaussian (RBF)</td></tr><tr><td>C</td><td>529.5</td><td>529.5</td></tr><tr><td>γ</td><td>6.27 · 10<sup>-4</sup></td><td>6.27 · 10<sup>-4</sup></td></tr><tr><td>ε</td><td>–</td><td>14.83</td></tr></tbody></table>

after aging. The two bonding states (i.e. with and without tack coat) are clearly identified and enhanced by the hybrid TCSVM/FWI method. Furthermore, using the dataset from the initial campaign at $T_0$ as the training set and the dataset at $T_1 = 50 \times 10^3$ cycles of rotation as the test set, the model's robustness is confirmed for application in degradation monitoring.

## 4.4. Multi classification and regression on an experimental new road in Vendée (France)

As discussed in Section 2, this experiment includes three tack coat dosages: under-dosed (250 g/m²), normally dosed (300 g/m²), and overdosed (450 g/m²). Consequently, the use of hybrid MCSVM/FWI and SVR/FWI methods to classify and estimate the dosage of each section proves to be more suitable. As discussed in Section 3.4, this experiment is characterized by a uniform geometry, mineral composition, and construction method across the entire structure. The tack coat dosage constitutes the only theoretical variable parameter for this pavement.

By applying FWI methods (presented in Section 3.1), the dielectric permittivity value of wearing course $\epsilon_{BBSG} \approx 4.1$ can be obtained. Consequently, this observable has been incorporated into the training matrix for hybridization.

Given the results obtained from the methodology applied for the fatigue caramel experiment, the principle of training on cross-sectional profiles and testing on longitudinal profiles was to be reiterated.

The optimal parameters for minimizing the cost function (Table 8) were identified for each method.

<table><caption>**Table 9**
Methods and performance using various approaches.</caption><thead><tr><th>Method</th><th>Approach</th><th>DSC (%)</th><th>RMSE</th><th>R<sup>2</sup> (%)</th><th>Average computational processing time (s)</th></tr></thead><tbody><tr><td rowspan="2">MCSVM</td><td>Global</td><td>88</td><td>–</td><td>–</td><td>504.53</td></tr><tr><td>Hybrid</td><td><b>91</b></td><td>–</td><td>–</td><td><b>433.22</b></td></tr><tr><td rowspan="2">SVR</td><td>Global</td><td>–</td><td>62.3</td><td>97</td><td>470.78</td></tr><tr><td>Hybrid</td><td>–</td><td><b>42.5</b></td><td><b>99</b></td><td><b>159.3</b></td></tr></tbody></table>

Let us compare the MCSVM confusion matrices (Figs. 21a and 21b) corresponding to the global approach and the hybrid model, respectively. A reduced number of misclassified signals is observed, with: 588 A-scans (hybrid model) vs. 829 A-scans (global approach) for the true class 250 g/m², 629 A-scans (hybrid model) vs. 859 A-scans (global approach) for true class 300 g/m², and 381 A-scans (hybrid model) vs. 416 (global approach) for true class 450 g/m². Similar misclassified values are observed with 505 A-scans (hybrid model) vs. 499 (global approach) and 111 A-scans (hybrid model) vs. 109 A-scans (global approach). These values correspond to data too close to the decision boundary to be correctly classified.

Let us now compare the performance indicators (Table 9) derived from the experiment on the new, yet-to-be-used road. The multiple bonding states are identified and do confirm the advantages of using a hybrid model when implementing the MCSVM and SVR methods, in terms of both performance and computational processing time. This finding validates the methodology applied to a full-scale experiment on a pavement constructed under actual conditions with a fixed geometry throughout the project site.

Fig. 22a display the theoretical ground truth in order to estimate the classifier's potential error. Through an analysis of the EM mapping resulting from the radar data inversion, it becomes possible to distinguish areas with different tack coat dosage (Figs. 22b and 22c) for MCSVM classification and estimation SVR, respectively. Once again, please note the presence of transition zones at 40 m and 80 m with overlapping phenomena leading to systemic errors in the optimization process for hyperparameter estimation and thus aberrations in the results at intersections. By comparing the results from the confusion matrices and the EM mapping, a likely spatial mismatch in tack coat spreading and the given labels in the training matrix can be confirmed. This difference inevitably increases the number of classification errors. Nevertheless, EM mapping demonstrates excellent correspondence between the ground truth and results obtained from the hybrid MCSVM/FWI and SVR/FWI methods. It should also be noted that the use of SVR regression enables an EM mapping rendering close to that of the MCSVM classification, with the added benefit of being three times faster (Table 9).

## 5. Conclusion and outlook

In conclusion, radar technology offers the advantage of eliminating the need for ionizing techniques, which are still in use today, by leveraging a detailed study of sensitivity to variations in dielectric permittivity. Methods such as gamma densitometry have demonstrated the ability to detect the presence or absence of tack coat in laboratory [9]. However, French regulations mandate the removal of radioactive sources and the development of high efficiency NDT solutions that can be widely applied across infrastructure surfaces. The choice of radar technology, combined with advanced data processing techniques (such as machine learning), enables efficient handling of large datasets, providing a non-ionizing, automated, and high efficiency methodology. This approach significantly enhances field performance for both research teams and road infrastructure professionals.

It has been demonstrated herein that hybrid ML/FWI methods can effectively characterize the tack coat in pavements through various experiments using high-frequency electromagnetic data. A survey frequency was selected to provide sufficient time-domain resolution in the subsurface while minimizing disturbances from factors
<figure><img src="image_23.png" /><figcaption>**Fig. 22.** (a) Ground truth discriminating 3 distinct zones, (450 g/m²) in yellow, (250 g/m²) in dark blue and (300 g/m²) in light blue (b) MCSVM mapping applied to GPR data (c) SVR mapping applied to GPR data.</figcaption></figure>

like backscattering. By incorporating a priori knowledge of the wearing course's dielectric permittivity, both classification and regression performance were improved using Support Vector Machine (SVM/SVR) and computational processing time could be reduced.

To validate this methodology, three distinct experimental campaigns were conducted: controlled test slabs of Hot-Mix Asphalt (HMA), pavement on a fatigue carousel, and a newly constructed road. The objective was to incrementally increase the complexity of the surveyed medium while following the same protocol. First, A-scans with a commercial 2.6 GHz impulse GPR; next, an SFR device equipped with a near-field, ultra-wideband antenna was used to extract the dielectric permittivity of the wearing course by means of the FWI method.

The initial experiment on HMA-controlled test slabs demonstrated the feasibility of characterizing tack coat dosage using materials of known formulation under controlled laboratory application. Despite variations in the geometry and compaction of both the wearing and binder courses, hybrid ML/FWI processing enabled a classification of both the bonding states and dosage estimation of the tack coat. The second experiment, conducted on the fatigue carousel (a full-scale pavement aging device in Nantes, France), showed that the hybrid TCSVM/FWI model could distinguish between two bonding states (presence or absence of tack coat) even with changes in the wearing course geometry, even after pavement aging. The last experiment, conducted on a newly constructed road in France's Vendée Department, involved dividing the pavement into three sections with identical structural layers but different tack coat dosages. This experiment validated the feasibility of estimation even with small differences in dosage (250 and 300 g/m²).

To build on this work, additional observable quantities can be incorporated to describe the surveyed medium using complementary methods. Full-Waveform Inversion (FWI) can yield additional geometric and physical properties, such as layer thickness and conductivity, that had previously been neglected. Furthermore, indicators derived from mechanical, thermal and physicochemical methods can be integrated into a multiphysics description of pavements. These new observable quantities would not only provide for a more precise understanding of the medium's behavior but also reduce computational processing times by enhancing the learning database. This approach supports predictive maintenance by enabling continuous monitoring of pavement conditions and an early detection of potential issues.

### CRediT authorship contribution statement

**Grégory Andreoli:** Writing – original draft, Validation, Software, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation. **Amine Ihamouten:** Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization. **Franziska Schmidt:** Writing – review & editing, Validation.

**Mai Lan Nguyen:** Resources. **David Souriou:** Resources. **Xavier Dérobert:** Writing – review & editing, Supervision, Resources, Project administration, Investigation.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

The authors would like to thank the French National Research Agency (ANR), France, which through its BINARY project [34], allowed us to conduct this study on the fatigue carousel at Gustave Eiffel University (Nantes, France). Gratitude is also expressed to the Pays-de-la-Loire Region for its support in funding equipment for the DEMOFIT regional project. Our appreciation extends to Dominique Pineau for his help in carrying out the experiments at the Vendée site.

### Data availability

Data will be made available on request.

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