Armelle Chabot

Liedi Bernucci

Ferhat Hammoum

Jean-Michel Simonin

Jamilla Teixeira

Amélie Thiriet

Rodrigo Siroma

Natasha Bahrani

Domenico Vizzari

Brahim Mazhoud

Paulina Leiva-Padilla

Mario Castañeda López

Laura Mazzoni

Zila Mascarenhas

Fernanda Carvalho

Iuri Bessa

Lucas Andrade

Marcia Takahashi

João André Kazuo

Paulo Carvalho

Paulo Moraes

Guilherme Barbosa

Deise Dias

Guilherme Pereira

Larissa Zipoli

Camila Christine

Leidy Espinosa

Fernanda Gadler

Ingrid Camargo

Edson Robson Costa

Diomaria Moura

Santos

and LTP and LIM, in Brazil, for always maintaining a friendly and warm working environment. I would like to

Keywords: Electrified roads, Viscoelasticity, Finite Elements Method, Digital Image Correlation

Babadopulos). A special thanks goes to my colleagues Ibishola Santos for passing on the knowledge on the DIC tools (EyeMotion

ACKNOWLEDGEMENTS

Throughout my educational journey I have crossed paths with passionate professors who have recognized in me the potential I did not know I had. They have shared with me their knowledge, pushed me towards being more disciplined and shaped my critical personality to do research, both in the laboratory and in the field. It is not a surprise that these first advisors were and still are my parentsprofessional teachersto whom I dedicate this work and all of my achievements during my postgraduating studies.

Complementary to the strong foundation I have received at home, it is no coincidence that my other leading educational examples were in the majority female engineers, professors and researchers. I am truly grateful to have encountered and learned from women who have outstood STEM career challenges, and overcame challenges our male colleagues have never ever thought about facing. I would like to express here my sincere gratitude to some of those professors who gave special contributions to my academic path and who continue to inspire me: Suelly Barroso, Liedi Bernucci, Kamilla Vasconcelos and my co-advisor Rosângela Motta.

I would like to acknowledge the Department of Materials and Structures of Université Gustave Eiffel (ex-Ifsttar), in the name of my co-advisor Thomas Gabet, for giving me the opportunity of developing the biggest part of my doctorate studies in their facilities and for providing me financial and technical support throughout this research.

I also thank the team of technicians who have helped me to fabricate and to saw specimens (Emile Etourneau, Jean-Philippe Gourdon, Jérôme Demoncheaux and Oliver Burban), and to the ones who helped in the development of the experimental protocol (Cédric Petiteau, Christophe Ropert, Jean-Philippe Terrier, Nadège Buisson and Stéphane Bouron). I would like to express my gratitude to Alstom and edilon)(sedra for providing the elastomeric materials used in this study. I would like to thank Yasmine Filali for welcoming me in the facilities of Université de Nantes and for kindly lending one of her calorimeters to us. I would like to acknowledge the researchers who have given significant contributions to the development of my work and accepted to be part of my final defense jury (Romain Balieu, Eshan Dave and Michel Coret); of my Comités de Suivi RESUMO Em geral, quatro fatores devem ser considerados com precisão e simplicidade em projetos de pavimentos flexíveis: tráfego e carga, condições ambientais, propriedades dos materiais e critérios de falha [START_REF] Huang | Pavement analysis and design[END_REF]. A inclusão de tecnologias de carregamento dinâmico de veículos na infraestrutura rodoviária altera não apenas o perfil tradicional em camadas dos pavimentos flexíveis, mas também sua resposta estrutural às solicitações térmicas e mecânicas. Para quantificar o impacto dessas inclusões no desempenho do pavimento, este estudo propõe metodologias numéricas e experimentais para medir a evolução dos campos de temperatura, tensões e deformações em rodovias eletrificadas (eRoads). Por meio de simulações termoviscoelásticas transientes em 2D usando Método de Elementos Finitos (MEF), perfis de rodovias tradicionais e eletrificadas foram submetidos a flutuações diárias de temperatura e ao tráfego. A eRoad estudada contém trilhos eletrificados embutidos na camada superficial betuminosa, um caso particularmente interessante devido à sua exposição direta ao tráfego e ao clima. A resposta das estruturas foi analisada e comparada com valores admissíveis comumente utilisados para prever danos: a tensão de compressão vertical no topo do solo de fundação (deformação permanente) e a tensão de tração horizontal na fibra inferior da camada betuminosa (vida de fadiga). As inserções rígidas afetaram a distribuição de temperatura dentro das camadas. As repetidas variações volumétricas de cada componente devido a flutuações de temperatura geraram deformações na camada betuminosa, de uma ordem de grandeza que pode levar a falhas prematuras e fissuras. Em laboratório, foi proposto um teste térmico para avaliar corpos de prova de eRoad submetidas a ciclos de calor e de frio usando a técnica da Correlação Digital de Imagens (DIC). A aplicação da técnica DIC para obter os coeficientes térmicos de contração/expansão dos materiais é considerada precisa e confiável, embora algumas condições de contorno do ensaio precisem de melhorias para minimizar fontes externas de deformação e ruído de fundo. Os campos de deformação medidos numericamente e experimentalmente levaram à mesma conclusão: as inserções rígidas geram deformações adicionais ao longo da interface entre a unidade de carregamento e a camada betuminosa devido apenas às flutuações diárias de temperatura. O modelo termoviscoelástico e a configuração experimental propostos têm grande potencial para avaliar perfis de pavimentos inovadores (eRoads indutivos e condutivos).

Palavras-chave:

Rodovias eletrificadas; Misturas betuminosas;

Viscoelasticidade; Método de Elementos Finitos; Correlação Digital de Imagens.

RÉSUMÉ

En général, quatre facteurs doivent être pris en compte avec précision et simplicité lors de la conception des chaussées souples : le trafic et la charge, les conditions environnementales, les propriétés des matériaux et les critères de défaillance [START_REF] Huang | Pavement analysis and design[END_REF]. L'inclusion de technologies de charge de véhicules en mouvement à l'intérieur des infrastructures routières modifie non seulement la disposition commune des couches, mais également la réponse globale de la structure aux sollicitations thermiques et mécaniques. Afin de quantifier l'impact de ces inclusions sur les performances des chaussées, cette étude propose des méthodologies à la fois numériques et expérimentales pour mesurer les évolutions de température, de contraintes et de déformations au sein des routes électrifiées (eRoads). Au moyen de simulations thermo-viscoélastiques transitoires en 2D en utilisant la Méthode des Éléments Finis (MEF), des profils routiers traditionnels et électrifiés ont été soumis aux fluctuations de température quotidiennes et au trafic.

LIST OF TABLES

INTRODUCTION AND MOTIVATION

Introduction

In the last decades, as a consequence of more restrictive rules to control greenhouse gas (GHG) emissions, electromobility has gained growing attention by public and private organizations, automobile industry and stakeholders. Significant fiscal incentives have stimulated the market and have contributed to expand the production of electric vehicles (EV)i.e. vehicles that use electricity for propulsion or rely on a battery to store energy. Despite this promising scenario, to effectively reduce the carbon footprint of the transport sector, electromobility needs to fulfil the demands of long haulage transportation (road freight) and to assure that the main source of the electricity used to charge the vehicles is renewable, among other concerns. Batteries are currently the bottleneck of electric medium-and heavy-duty vehicle segments.

They are costly, heavy and limited in terms of energy density, not to mention the lack of efficient management alternatives in dismantling and end-of-life recycling procedures. In this context, Electric Road Systems (ERS) arise as a solution to overcome the constrains of the existing batteries, while maximize environmental gains, raise the asset value of road infrastructure and contribute to the development of smart cities [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF][START_REF] Chen | Structural performance of electrified roads: A computational analysis[END_REF][START_REF] Gustavsson | Overview of ERS concepts and complementary technologies[END_REF][START_REF] Gustavsson | Overview of ERS concepts and complementary technologies[END_REF][START_REF] Gustavsson | Overview of ERS concepts and complementary technologies[END_REF].

ERS include different sorts of charge-while-drive technologies and are subdivided into five subsystems, from which the road infrastructure constitutes the focus of this study. In the framework of electrified road infrastructure, the term eRoad is used to refer to a transportation infrastructure that delivers electrical power to vehicles, by means of conduction or induction. An eRoad can consist of either a new road specially designed for that purpose or of a traditional road (tRoad) which is modified in order to receive the components that transfer power to the vehicles. The term charging unit (CU) is commonly used to address the inserts embedded in the pavement as part of charge-while-drive technologies. This term comprises the power delivery components (e.g. cables, coils and rails), as well as the components that support, enclose and protect the eRoad power delivery components (e.g. cement concrete boxes, elastomeric bedding and bonding materials). In general, the process of adaptation of a tRoad into an eRoad comprises two distinct construction technologies: the in situ construction method and the prefabrication-based construction method [START_REF] Chen | Sustainable Implementation of Electrified Roads: Structural and Material Analyses[END_REF][START_REF] Chen | Electrification of roads: opportunities and challenges[END_REF][START_REF] Chen | Electrification of roads: opportunities and challenges[END_REF]PIARC, 2018). For both technologies, discontinuities need to be created in the pavement wearing course to accommodate the system, generally in the centre of the driving lane.

Typical pavement structures are constituted by bituminous layers (flexible pavements). Bituminous mixtures are inherently heterogeneous materials, with the behaviour dependent on factors such as the temperature, the type and frequency of the load applied, the aging of the binder, the physicochemical interactions of the various mixture components, the material state of stress, and also on small-scale variables like binder, moisture and air voids content [START_REF] Kim | Modeling of asphalt concrete[END_REF]. Despite its local adaptations, most flexible pavement design methods assess the performance of a structure using models to predict stresses and strains in predefined locations. Iterative calculation procedures compare two primarily strain-based failure criteria with admissible values as to avoid distresses: the vertical compressive stress reaching the top of the subgrade as a parameter to control permanent deformation, and the horizontal tensile strain at the bottom of the bituminous layer to estimate fatigue life. In order to calculate those parameters, the environmental conditions and the loading characteristic to which the pavement will be exposed to needs to be drawn, alongside with the determination of the materials mechanical properties and layers thicknesses.

Temperatures in the surface level of a road tend to increase during daytime, and to decrease during night-time. The structural response of bituminous layers to loading is strongly linked to temperature: at high temperatures the mixture is more viscous and more susceptible to permanent deformation under repeated load stress, while at low temperatures it is more brittle and more susceptible to thermal cracking. In flexible The structural analysis and the design of eRoad pavements constitute a recent field of study in road engineering and has received relatively little attention. A possible reason for that is the fact that, after the inclusion of a charging unit, the newly constructed eRoad can no longer be assessed using purely linear-elastic layered theories that are used to assess tRoads. In this way, analytical approaches and nonlinear finite element (FE) techniques become an alternative to predict stress, strain and displacements within the structure. These techniques generally require sound theoretical and practical experience from users; increase the computational effort demand; and/or are conditioned to costly commercial licences as they get more sophisticated. Equally important and yet under industrial property rights, the adequate characterization of the charging unit components in order to provide parameters for the models, and the bonding performance of the unit with the pavement are lacking standardized and unified laboratory testing procedures.

The few numerical studies addressing the mechanical performance of eRoad pavements focused primarily on the response of the structure to traffic-induced loadings [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF]CHABOT;[START_REF] Chabot | 2D multilayer solution for an electrified road with a built-in charging box[END_REF][START_REF] Chen | Towards an understanding of the structural performance of future electrified roads: a finite element simulation study[END_REF][START_REF] Chen | Structural performance of electrified roads: A computational analysis[END_REF]].

Despite giving a significant contribution to this innovative branch of pavement engineering, these studies displayed the properties of the bituminous layers according

Objective

The main objective of this research is to propose numerical and experimental approaches for the investigation of the impact of rigid inclusions from charge-whiledrive technologies on the behaviour of flexible pavements.

Dissertation outline

The present dissertation is divided into seven chapters: "The pen is the tongue of the soul; as are the thoughts engendered there, so will be the things written. [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF][START_REF] Chen | Structural performance of electrified roads: A computational analysis[END_REF]. A common statement is that electricity constitutes an excellent alternative to power the transport sector at large scale, and at a relatively fast pace so to achieve the Paris Agreement pledge of zero emission mobility by 2050as long as the generation of energy is resulted from renewable sources. Nevertheless, the substantial investments required to equip the existing infrastructure and the lack of regulations on performance criteria of these new roads remain a hurdle to the wide implementation of ERS.


The road infrastructure subsystem consists of pavements, barriers and auxiliary components, like signalization. In this context, an eRoad (electrified or electric road) is defined as the transportation infrastructure that delivers electrical power to vehicles.

They consist of either new roads specially designed for that purpose or rehabilitated conventional roads. The adaptation of an ordinary road into an electrified road is made by the inclusion of special components in-road and/or on-roadsides, whose goal is to detect and to transfer power from the dispositive to a pick-up unit connected to the vehicle. The different types of eRoads are categorized according to the method used to transfer power between the source and the vehicle: by physical contact (conductive)

or wirelessly (inductive). In accordance to what is found in literature, the term eRoad will be used throughout the text to address the electrified roads, and the term tRoad to address traditional roads.

In terms of dynamic power transfer, the most mature conductive eRoad technology is the overhead lines, which requires a pantograph current collector on top of vehicles and overhead cables (or catenaries) above the road. This technology can be found on modern-day trolleys and streetcars in many cities, as well as on roadway sections in Sweden, Germany and the USA, as part of pilot test tracks built to evaluate its efficiency for applications on freight transportation (GUSTAVSSON; HACKER; HELMS, 2019; KANE, 2014; SUUL; GUIDI, 2018) (Figure 1). The catenary system used for overhead lines has more similarities with the systems used for trains other than to the ones used for trolley buses, due to this latter's relatively lower operating speed and tension (SUUL; GUIDI, 2018). The in-road live rail (or rail embedded in the pavement) is another eRoad conductive solution undergoing trial tests. This technology relies on the direct contact of a pick-up unit installed on the vehicle with segmented electrified rails embedded longitudinally on the roadway infrastructure (Figure 2). The pick-up unit consists on a mechanical arm or on an inverted pantograph coupled to the vehicle's engine. This dispositive extends and retracts to get in contact with a ground module containing the rails once they become aligned, and only the sections that the vehicle is travelling above are electrified to assure safety (OLSSON, 2014a;[START_REF] Suul | Technology for dynamic on-road power transfer to electric vehicles[END_REF][START_REF] Suul | Technology for dynamic on-road power transfer to electric vehicles[END_REF]. This technology is based on successful similar applications on subways, tramways and tram installations, where a "third rail" located between the traction rails provides power supply, playing a similar role as the catenary on overhead lines. Some adaptations are yet under development, such as the addition of a ground return of the power supply, due to the fact that there are no rails to perform this task and that the presence of rubber wheels isolates the vehicle from the ground (SUUL; GUIDI, 2018). Even though the concept of sliding contacts for guided transportation constitutes an already well established domain, the adaptation for roads is mostly developed by industry and little information is public in terms of practical, safety and technical reliability of the devices for both the vehicle and the road infrastructure (SUUL; GUIDI, 2018). Consortiums like Elways (eRoadArlanda/Elways AB), ElonRoad (Elon Road Inc./Lund University) and Slide-In/APS for Roads (Alstom/Volvo) hold the three most mature technologies in terms of development and large-scale testing. These technologies differ slightly in some aspects: number of rails, disposal, power transfer capacity, power take-off and system integration on the road surface (ASPLUND; [START_REF] Asplund | Conductive feeding of electric vehicles from the road while driving[END_REF][START_REF] Emre | Review of existing power transfer solution[END_REF][START_REF] Suul | Technology for dynamic on-road power transfer to electric vehicles[END_REF][START_REF] Suul | Technology for dynamic on-road power transfer to electric vehicles[END_REF]. With a different approach, Honda R&D is testing a conductive solution in which a lateral pantograph is connected to rails fixed on a fence alongside the road. Contrarily to the first mentioned three inroad live rail systems, Honda R&D technology has initially no impact on the pavement infrastructure as the rails are not embedded in its layers (PIARC, 2018;[START_REF] Suul | Technology for dynamic on-road power transfer to electric vehicles[END_REF][START_REF] Suul | Technology for dynamic on-road power transfer to electric vehicles[END_REF]. [START_REF] Ledesma | Analysis of effects and consequences of constructing Inductive Power Transfer Systems in road infrastructure[END_REF]. Amongst those, the use of magnetic field (IPT) to provide energy to vehicles is the most studied technology for inductive dynamic charging. When compared to the second most mature wireless technology for road applications (i.e. CPT), IPT shows as main advantages the possibility of longer mechanical distancing between the transmitters and receiving sides, and higher capacity levels [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF][START_REF] Suul | Technology for dynamic on-road power transfer to electric vehicles[END_REF][START_REF] Suul | Technology for dynamic on-road power transfer to electric vehicles[END_REF].

The basic condition for an IPT system to satisfactorily work is the existence of a magnetic coupling between a primary coil installed in the road and a secondary coil installed under the vehicle's chassis (Figure 3). The main challenge relies on the optimal balance between the energy transfer distance (air gap) and the efficiency of the system. In other words, the goal is to minimize the dielectric loss while assuring the protection of the conductive coils, ferrite cores and backing plate embedded in the roadway. 2018). This pilot test demonstrated a functional dynamic IPT charging solution that was later implemented on some local bus linesa significant innovation at the time despite its further overlook due to technical constrains. During that decade and the ones that followed, several optimizations of equivalent solutions became recurrent. Considerable public and private investments were made to assess the possibility of deploying these technologies on a commercial basis. As an example, the On-line Electrical Vehicle (OLEV) concept developed by the Korean Advanced Institute of Science and Technology (KAIST) reached an advanced Technology Readiness Level 1 (TRL). The OLEV solution is currently on its fifth generation and it has been successfully

1 The maturity of different technologies can be classified on a scale from 1 to 9 though a method named Technology Readiness Levels (TRL). Each technology is assigned a scale after being evaluated in terms of concept, technology requirements, and demonstrated technology capabilities.

demonstrated at test tracks and in an operational environment. The technology consists of a minimal invasive wireless device suitable for modular and large-scale production, which is capable of charging heavy vehicles like buses (Figure 3) despite air-gaps and vehicle misalignment [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF].

A summary of projects with real-scale test track demonstrations for eRoad technologies is depicted in

Design of flexible pavements

A flexible pavement is composed of multiple layers, which vary in terms of thickness, function, material composition and properties (Figure 4). The wearing surface is the element visible to users and, in general, the most expensive on the system (BADELI, 2018; PEREIRA; PAIS, 2017), but several other subjacent layers are bonded together with the main purpose of supporting and transferring loads in acceptable levels to underlying layers, especially to the subgrade. It is in the external layers that critical mechanical, thermal and physicochemical stresses take place [START_REF] Vu | Etude expérimentale et numérique du comportement au gel et au dégel des enrobes bitumineux partiellement satures[END_REF]. On an eRoad configuration, it is mostly on the wearing surface that the power delivery components are embedded. The design of an eRoad needs hence to follow accurate methods, as to attend the high quality standards also adopted for tRoads, at the same time as it needs to integrate the effects of traffic and environmental loads on the response of the new components of the pavement. As observed in Figure 4, the wearing surface constitutes the layer in direct contact with traffic and climatic conditions (e.g. rain, snow, heat and radiation). On flexible pavements, the wearing course is composed of bituminous mixtures, while on rigid pavements it is constituted by slabs or continuous reinforced concrete. Flexible pavements have two variants: pavements with granular base and full-depth bituminous pavements. In both cases, the bituminous wearing surface must meet particular requirements in terms of rolling comfort, safety, drainage and durability. Typical structural damages on flexible pavements are fatigue cracking, rutting due to permanent deformation, and thermal cracking in regions with either significant temperature variations or very cold temperatures [START_REF] Huang | Pavement analysis and design[END_REF]. Understanding the causes and mechanisms of such distresses is the purpose of many laboratory tests, field experimental programmes and numerical models.

In the process of adapting a tRoad into an eRoad, two construction technologies are tested for the inclusion of the charging devices into the pavement: the in situ construction method and the prefabrication-based construction method (CHEN; TAYLOR; [START_REF] Chen | Electrification of roads: opportunities and challenges[END_REF]PIARC, 2018). In both technologies, a trench (also referred as a trough or a ditch) is created on the pavement wearing surface to accommodate the system, generally in the centre of the driving lane. The installation is commonly followed by the compaction of a thin coat layer above the unit in the case of an inductive system, or even by the replacement of the full lane. Depending on the thickness of the existing road wearing surface and of the ERS technology to be used, the trench depth can reach base and subbase layers of the pavement. [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF] recommend the use of polymer materials (or their blends) to constitute the charging assembly, as these do not interfere with electromagnetic fields and are stiff enough to protect the coils and ferrite cores from traffic and environmental loads. In this study, the term charging unit (CU) is going to be used to address the inserts embedded in the pavement. The term comprises the power delivery components (e.g. cables, coils, rails) and also the support, enclosure and protection components (e.g. cement concrete, elastomers).

Below the wearing surface there is an aggregate base, commonly granular. This base is responsible for providing the thickness to ensure the quality of the pavement throughout its service life, and to support significant loads during the construction period. Depending on the traffic level, the aggregate base combines more or less layers, treated or not with hydraulic binders (in that case, it is named composite pavement instead of flexible). Traditionally, the aggregate base is designed with coarse aggregates on the bottom layers and smaller particles on the top granular layers. The composition and thicknesses of the layers, however, are chosen according to many variables, e.g. hardness of the aggregates, cleanness of the sand and gravel, and angularity of the particles. It is also important to remind that base and subbase layers can differ significantly from the wearing course in terms of permeability, being more susceptible to damage originated from freeze-thaw cycles, for example.

The subgrade, also referred as the foundation soil, is the one that varies the most within the extension of a road in terms of composition and mechanical performance of the soils. The main role of the subgrade is to support the loads without developing excessive settlements, which is in conformity with an essential objective of a pavement structure above it: to reduce the magnitude of the vertical stress that reaches the top of the subgrade so that permanent deformations do not occur [START_REF] Huang | Pavement analysis and design[END_REF]. If it becomes necessary to enhance the overall bearing capacity of the system, the subgrade, initially an untreated granular layer, can be reinforced by a compacted coat of selected or treated soil. The bearing capacity of the subgrade is an important input on the definition of overlaying layers materials and thicknesses.

Designing durable flexible pavements is hence a difficult task. PEREIRA and PAIS (2017) present an historical overview of the most used design methodologies, which were initially based on empirical methods and field pavement performance observations. Nowadays, field observations are complementary to measurements of pavement structural response (stresses, strains and deflections) through laboratory testing and in situ data acquisition. These mechanistic-empirical (M-E) design approaches are carried out by estimating traffic volumes and specific weather conditions for the pre-defined lifespan of the pavement, as well as by considering the bearing capacity of the subgrade above which the road is going to be constructed. The Mechanistic-Empirical Pavement Design Guide (MEPDG) developed in the USA [START_REF] Inc | Guide for mechanistic empirical design of new and rehabilitated pavement structures[END_REF], the Shell pavement design procedure [START_REF] Claessen | Asphalt pavement design -the shell method[END_REF], the French pavement design method (CORTÉ; [START_REF] Corté | Design of pavement structures: the French technical guide[END_REF], and the National Design Method (MeDiNa) currently in implementation phase in Brazil [START_REF] Franco | Método de dimensionamento mecanísticoempírico de pavimentos asfálticos -SisPav[END_REF] are some examples of methodologies used to design flexible pavements.

Consideration of traffic-induced loads

M-E methodologies based on elastic layered theories use the concept of equivalent single-axle load with a circular contact area as a parameter to account for both traffic volume and load levels. Directly below the axis of the wheel, traffic and loading are responsible for developing vertical compressive stresses that are transmitted throughout the layers until reaching the subgrade. Due to deflection, tensile and compressive stresses are also developed under and in the surroundings of the loading application area (Figure 5). In front of and behind the wheel load, in the bottom of the layer, compressive stresses are generated, while under the wheel the stresses are strongly tensile. The number of repetitions and the velocity of traffic and loading are important parameters, especially when viscoelastic theories are used, as they determine the duration and severity of loading and unloading processes that lead to cumulative damage. Bituminous mixtures behave as viscoelastic materials, whose mechanical response depends on the time of loading. At higher frequencies, the material displays mostly an elastic behaviour, while at lower frequencies the viscous component is more significant than the elastic component, and the material behaves more like a fluid. As an example of traffic and loading consideration in pavement design, the French method uses the estimated number of heavy goods vehicles (HGV) per day to choose pavement layers materials. The total number of HGV estimated for the service life of the road is used to choose the layers thicknesses. Daily and total HGV passages are expressed by a converted equivalent number of passages of a reference axle (in that case, single axles with dual wheels with a total load of 130 kN), which is expected to cause the same structural damage to the pavement as the real composite traffic [START_REF] Balay | Adaptation of the French pavement design to countries in South America[END_REF]. The cumulative traffic is defined by the upper limit of the interval in which the number of HGV is located per direction of traffic, on the busiest lane [START_REF] Pedraza | Propriétés thermomécaniques d'enrobés multi-recyclés[END_REF].

The most common traffic-induced damages are rutting (or permanent deformation) and fatigue cracking. Rutting is measured by the difference in the downward depression along the wheel paths and the upward deformation beside the wheel paths due to repeated loading. This surface upheaval occurs as a consequence of single or combined complex modes of mechanisms: loss of materials, densification, dilation and lateral plastic flow. In M-E methodologies, an important parameter to predict rutting is the traffic-induced compressive stress that reaches the subgrade.

However, more recent rutting models compute the total rutting depth as the sum of the deformation of each individual layer composing the pavement. In this scenario, the composition and cohesion of the bituminous mixtures and the bearing capacity of granular layers play a crucial role, and consequently climatic factors such as temperature and moisture as they affect directly the properties of these materials. In

Consideration of environmental-induced loads

Pavements undergo environmental-induced stresses. These stresses are a direct consequence of effects related to solar radiation, temperature, precipitation (moisture), freeze-thaw cycles, air pressure and wind (Figure 6) [START_REF] Badeli | Evaluation of the Damage of an Asphalt Mix under Repeated Freeze-Thaw Cycles[END_REF][START_REF] Ongel | Analysis of 30 years of pavement temperatures using the enhanced integrated climate model[END_REF]HARVEY, 2004). In composite pavements, cyclic thermal variation is responsible for the opening and closing processes of shrinkage cracks. In rigid pavements, thermal gradients produced by temperature over time and depth causes bending stresses in the concrete slabs. In flexible pavements, the temperature affects the viscoelastic response of bituminous mixtures and generates stresses within the material due to the prevention of thermal expansion and contraction (BAYAT; KNIGHT; SOLEYMANI, 2012; ISLAM; TAREFDER, 2015; PEREIRA; PAIS, 2017).

Figure 6. Environmental phenomena experienced by pavement structures [START_REF] Herb | Simulation and Characterization of Asphalt Pavement Temperatures[END_REF].

In most M-E methodologies, damage resulted from environmental loading is addressed as a consequence of two parameters: temperature variation in bituminous layers and moisture variation in unbound granular layers. Usually, the temperature variation over a full year is divided into a number of periods (seasonal variation) and,

for each period, a set of materials properties is displayed according to a reference temperature value defined as representative of the period/season. In summary, temperature is considered on the design of the pavement by defining an equivalent constant temperature, which produces the same annual damage as seasonal temperature variations under the same level of traffic. As an example: in mainland France this equivalent temperature is set to 15°C, while for overseas territories higher equivalent temperatures are adopted (25°Cexcept for Guyana, where 28°C is considered) [START_REF] Ktari | Consideration of Seasonal Temperature Changes in the French Pavement Design Method[END_REF]. Similarly, the stiffness and shear strength of the granular layers are displayed according to a the seasonal variability of moisture content and suction, mostly as a consequence of rainfall (ONGEL; HARVEY, 2004).

Temperatures in the surface level tend to increase during daytime, and to decrease during night-time, and the temperature at any given time is dependent on previous temperatures (thermal loading history) and on the position in which the measurement is done (surface to subsurface thermal gradient practical issues as the use of controlled temperature chambers at constant temperatures limit the accurate representation of the temperature gradient along the depth of the pavement. In terms of M-E design methodologies, rutting and fatigue models mostly fail in considering the effect of hourly, daily and seasonal temperature fluctuations on the short and long pavement service life prediction.

Overview of the mechanical behaviour of bituminous mixtures

Bituminous mixtures have been used for road construction and maintenance since the end of the 19th century [START_REF] Vu | Experimental study and modeling of the behavior of partially saturated asphalt concrete under freezing condition[END_REF]. They are inherently heterogeneous materials, composed by aggregates in a variety of particle sizes, bituminous binder, air voids and, if necessary, additives to improve the workability and the performance of the mix. A typical bituminous mixture is composed of around 5% binder and 95%

aggregate by mass (80-85% in volume) [START_REF] Badeli | Evaluation of the Damage of an Asphalt Mix under Repeated Freeze-Thaw Cycles[END_REF][START_REF] Vu | Etude expérimentale et numérique du comportement au gel et au dégel des enrobes bitumineux partiellement satures[END_REF]. The mineral skeleton (aggregates distribution) provides rigidity to the mixture, due to the granular arrangement and accommodation of the grains. The binder is responsible for the cohesion of the mixture and its impermeable properties. Bitumen behaves mechanically as a viscoelastic material (i.e. thermo-susceptible and time and rate-dependent in response) and it affects directly and significantly the properties of the mixture, despite constituting a smaller percentage of its total volume.

Simplified models characterize the bituminous mixture response by assuming it behaves as an isotropic linear elastic material under stationary loading conditions.

However, the overall structural performance of bituminous mixtures is highly dependent on factors such as the aging of the binder, the physicochemical interactions of the various mixture components, the material state of stress, the type and frequency of the load applied, and also on small-scale variables like binder, moisture and air voids content [START_REF] Kim | Modeling of asphalt concrete[END_REF]. In this context, rheology is used to bridge the wide gap between idealized classical theories of pure elasticity (Hookean spring) and perfect viscosity (Newtonian fluid) in characterizing viscoelastic materials. The behaviour of bituminous mixtures may encompass solid and viscous types of behaviour, as well as intermediate types of response, depending on the test conditions and on the factors aforementioned. In Figure 7, four different domains of behaviour for bituminous mixtures at a constant temperature are depicted, where ε represents the strain amplitude and N is the number of load cycles applied. The indicated limits for each domain are illustrative, and vary considerably in orders of magnitude depending on the material composition, the temperature and the direction of the stress path.

Generalized Maxwell Model (GMM)

The Generalized Maxwell model (Figure 9), also known as Maxwell-Wiechert model, is constituted by the association, in parallel, of a single spring and several

Maxwell branches. In this model, σ is the stress applied in order to keep the system under constant strain ε ; 𝐸 𝑖 and η 𝑖 represent, respectively, the constants of each elastic and viscous element of the Maxwell branches; and 𝐸 0 represents the instantaneous elastic response of the system, also responsible for preventing the complete stress release (relaxation function). The relaxation function characterizes the mechanical behaviour of a body that displays a progressive decrease in stress, when subjected to a constant strain at a given temperature. The GMM considers that the relaxation does not occur at a single time, but at a distribution of times, which are represented by all the Maxwell branches. The nonlinearity of viscoelastic materials can be characterized by both stress relaxation and a phenomenon known as creep, which describes the mechanical behaviour of a body that displays a progressive increase in strain when subjected to a constant stress at a given temperature. Figure 9 depicts the asymptotic representation of viscoelastic materials in terms of creep and stress relaxation. From the plot in Figure 9, it is observed that a purely elastic material displays a response in terms of strain immediately after the stress application. Contrarily, a purely viscous material displays a strain trajectory out of phase with the stress application.

For viscoelastic materials, however, a combination of elastic and viscous timedependent responses occurs. In other words, there is a relative lag (phase angle φ)

between the imposed stress and the obtained strain. Most rheological models are adequate to characterize the behaviour of viscoelastic materials in terms of stiffness and phase angle within limited frequency and temperature ranges, when the material exhibit a linear viscoelastic state. However, the linearity range decreases as temperature increases and frequency decreases (NILSSON; HOPMAN; [START_REF] Nilsson | Influence of different rheological models on predicted pavement responses in flexible pavements[END_REF].

The GMM model is composed of a spring of elastic modulus 𝐸 0 in parallel with 𝑛 Maxwell branches, with the 𝑛 𝑡ℎ branch having a relaxation time constant 𝜏 𝑛 and a spring of elastic modulus 𝐸 𝑛 . Considering that all of the components of the GMM have the same strain 𝜀(𝑡) at all times 𝑡, and that the total stress of the system is the sum of the stresses in each branch, the constitutive law of the model can be described by Equation 1, and its relaxation function by Equation 2. In both equations, 𝐸 𝑖 and η 𝑖 represent, respectively, the constants of each elastic and viscous element of the Maxwell branches; and 𝐸 0 represents the instantaneous elastic response of the system, also responsible for preventing the complete stress release. The finite Prony series is the mathematical description of the GMM mostly used in numerical models. It is characterized by pairs of terms: an elastic constant Young's modulus (shear modulus or bulk modulus) and the characteristic time associated to it.

These decaying exponentials make it possible to solve the viscoelastic constitutive relations in a recursive manner, and can be obtained through curve fitting from experimental data (relaxation test or complex modulus tests). Its representation in the time domain is defined by:

𝐸(𝑡) = 𝐸 ∞ + ∑ 𝐸 𝑖 𝑒 - 𝑡 𝜏 𝑖 𝑛 𝑖=1 Equation 3
Where 𝑡 is the loading time, in seconds; 𝐸(𝑡) is the relaxation modulus, in MPa;

𝐸 ∞ is the long-term equilibrium modulus, in MPa; 𝐸 𝑖 is the relaxation strength of each Maxwell branch, in MPa; and 𝜏 𝑖 is the relaxation time, in seconds. More on the determination of the frequency-domain expressions of the GMM for the transient linear viscoelastic analysis of bituminous mixtures can be found in the literature [START_REF] Jalocha | Revisiting the identification of generalized Maxwell models from experimental results[END_REF][START_REF] Jalocha | Revisiting the identification of generalized Maxwell models from experimental results[END_REF][START_REF] Jalocha | Revisiting the identification of generalized Maxwell models from experimental results[END_REF][START_REF] Lv | An extended search method for identifying optimal parameters of the generalized Maxwell model[END_REF][START_REF] Park | Methods of interconversion between linear viscoelastic material functions. Part I-a numerical method based on Prony series[END_REF][START_REF] Park | Methods of interconversion between linear viscoelastic material functions. Part I-a numerical method based on Prony series[END_REF][START_REF] Zhao | Analysis of transient viscoelastic response of asphalt concrete using frequency domain approach[END_REF][START_REF] Zhao | Analysis of transient viscoelastic response of asphalt concrete using frequency domain approach[END_REF]CHEN, 2015)].

Time-Temperature Superposition Principle (TTSP)

The TTSP is a concept that relates temperature variation to changes in the mechanical properties of materials, more precisely on its response in global time scale.

It is adopted to characterize rheologically simple viscoelastic materials along an extrapolated frequency range that could not be reached by means of an experiment, due to limited measurable analytical instrumentation (high frequencies) or to impracticable long testing durations (low frequencies). The theory of the TTSP relies on the assumption that the same viscoelastic function (e.g. 𝐸 ′the elastic modulusand 𝐸 ′′the viscous modulus) can be obtained either by changing the frequency (time)

or the physical state of the material (solid-like/liquid-like) (IONITA; CRISTEA; GAINA, 2020). In the case of bituminous mixtures, here assumed as a linear viscoelastic and thermo-rheologically simple materials, the state of the material is modified through temperature.

The methodology used to obtain master curves of the magnitude (|𝐸 [START_REF] Williams | The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids[END_REF]:

𝑎 𝑇 = 𝑒 - 𝐶 1 (𝑇-𝑇𝑟𝑒𝑓) 𝐶 2 +𝑇-𝑇𝑟𝑒𝑓 or 𝑙𝑛 (𝑎 𝑇 ) = - 𝐶 1 (𝑇-𝑇𝑟𝑒𝑓) 𝐶 2 +𝑇-𝑇𝑟𝑒𝑓 Equation 4
Where 𝛼 𝑇 is the shift factor that controls the horizontal position of each isotherm by multiplying its frequency until they become superimposed; 𝑇 is the test temperature for each isotherm; and 𝐶 1 and 𝐶 2 are the values of the viscoelastic coefficients that depend on the bituminous mixture and on the chosen reference temperature 𝑇 𝑟𝑒𝑓 . The coefficients 𝐶 1 and 𝐶 2 are commonly found in order of magnitude of 10 and 100, respectively (LIU; LUO, 2017; WILLIAMS; LANDEL; FERRY, 1955).

Overview of the mechanical behaviour of elastomeric materials

Most traditional elastomers display extremely large strain capacities and nonlinear stress-strain relationships. They are commonly made from natural rubber or synthetic compounds that went through vulcanization. Vulcanization can be defined as a curing process, where substances like sulphur are incorporated to rubbery or elastomeric materials at high temperature mixing procedures. This induces a chemical rearrangement of polymer chains inside the material due to the formation of a crosslinked molecular network and an increase in the number of junctures (MARK; 10). The classical configuration into which these materials are found is between alternated layers of more rigid materials and with lateral spreading restrained (reinforced elastomers), being subjected mostly to compression and shear forces. Elastomers properties and their consequent instabilities are not only dependent on the intrinsic material behaviour, but also on the specimen geometry, which is expressed by means of a shape effect. Typically, when an elastomeric specimen is compressed in the vertical direction, the sides of the material tend to spread out laterally, changing the initial shape of the sample. The parameter that accounts for such effect is the shape factor (𝑆), defined as the ratio between the loaded area and the area free to bulge out when compressed. Several experimental and numerical studies on rubber and elastomeric bearings have shown that a low shape factor (thick rubber layers) provides an isolation effect in both horizontal and vertical directions, whereas high shape factors (thin rubber layers) provide isolation only in the horizontal direction (IMBIMBO; [START_REF] Imbimbo | stress analysis of rubber bearings under axial loads[END_REF][START_REF] Poulain | Determination of the intrinsic behavior of polymers using digital image correlation combined with video-monitored testing[END_REF][START_REF] Swarner | Material Evaluation of an Elastomer, Epoxy and Lightweight Concrete Rail Attachment System for Direct Fixation Light Rail Applications[END_REF]. The compression modulus of the elastomer and the vertical stiffness of the system are directly proportional to the shape factor, i.e. they tend to increase as the shape factor increases. In this way, it is customary to determine mechanical parameters such as modulus, stiffness, or hardness of elastomeric materials at prescribed size and shape, and under loading configurations as similar as possible to field conditions.

Elastomeric materials behave differently when in tension, compression or shear.

Moreover, the mechanical response of the material depends highly on the strain range and temperature, displaying a composite of viscous and elastic behaviour due to their polymeric composition. The complexity of framing and modelling the behaviour of elastomers has long been addressed by dividing it into phases and by setting specific limits for the transition from one phase to another (e.g. strain energy, glass temperature, melting temperature) [START_REF] Antunes | Hyperelastic modelling of cork-polyurethane gel composites: non-linear FEA implementation in 3D foot model[END_REF][START_REF] Imbimbo | stress analysis of rubber bearings under axial loads[END_REF][START_REF] Imbimbo | stress analysis of rubber bearings under axial loads[END_REF][START_REF] Mark | Science and technology of rubber[END_REF][START_REF] Mark | Science and technology of rubber[END_REF][START_REF] Swarner | Material Evaluation of an Elastomer, Epoxy and Lightweight Concrete Rail Attachment System for Direct Fixation Light Rail Applications[END_REF]. As an example, in terms of strain range, it is considered that once the elastomer is under small deformations it behaves as linear elastic solids and, in large strain range, it behaves as a nonlinear hyper-elastic material. This is explained by the fact that bulk modulus in compression is about 400 to 10,000 times higher than shear modulus, which reassures the incompressible character of elastomers. In this way, the elastic behaviour under small strains can be described with good approximation by a single elastic constant (shear modulus 𝐺), the Poisson's ratio (𝑣 equal to 0.5) and the Young's modulus (𝐸 = 3𝐺).

Nevertheless, slight changes in the magnitude of these parameters influence the stress distributions within the material.

Besides the aforementioned complex stress-strain response, elastomers are viscoelastic materials with inhomogeneous deformations, and, as a result, temperature constitutes an important material parameter. The glass temperature 𝑇 𝑔 is defined as the transition limit from rubbery (𝑇 > 𝑇 𝑔 ) to glassy (𝑇 < 𝑇 𝑔 ) behaviour of polymers in a molecular level, and it varies significantly in terms of polymers composition, curing process, on the strain rate and cooling or heating rate. Researches focusing on plastic instabilities of polymers have shown that, as temperature varies, the strain limit in which deformation will occur is reduced, and a decrease in shear modulus 𝐺 as temperature increases is noticed (Figure 11) (FARGE; ANDRÉ; BOISSE, 2018).

Similarly to the methodology used to characterize the viscoelastic response of bituminous mixtures, plots in the form of isotherms are used to correspond elastomers dynamic moduli and compliances as a function of frequency, or shear and tensile moduli and compliances as a function of time (MARK; [START_REF] Mark | Science and technology of rubber[END_REF]. The thermoviscoelastic behaviour of elastomers is also associated to the level of freedom is provided for volume rearrangement of the sample (reinforced or unreinforced elastomers). In this way, it is sorely through experimental testing of the complete system into which the elastomer is applied that properties and parameters can be assessed, both for design and structural analysis.

Numerical assessment of eRoad pavements

The road infrastructure subsystem is affected by embedding charging units in the pavement. Despite the good knowledge and some experience from stakeholders in conceiving and maintaining similar systems, the impact linked to the concentration of stress in the proximity of the units is still unclear, as well as issues linked to possible hazard to people and animals (ALDAMMAD; ANANIEV; KALAYKOV, 2014; [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF]PIARC, 2018). As one of the main objectives of this study, the structural analysis of pavements constituting an eRoad has received relatively little attention [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF]CHABOT;[START_REF] Chabot | 2D multilayer solution for an electrified road with a built-in charging box[END_REF][START_REF] Chen | Sustainable Implementation of Electrified Roads: Structural and Material Analyses[END_REF][START_REF] Chen | Electrification of roads: opportunities and challenges[END_REF][START_REF] Chen | Electrification of roads: opportunities and challenges[END_REF]. One possible reason is the fact that, after the inclusion of the power delivery system, the new road can no longer be assessed using purely linear-elastic layered theories commonly adopted to predict the stresses, strains and displacements in pavement systems. In this way, analytical approaches and nonlinear finite element techniques become an alternative, which generally increase the computational effort demand, require sound theoretical and practical experience from users and/or are conditioned to costly commercial licences as they get more sophisticated.

Nevertheless, the detailed evaluation of the short and long resistance to damage is crucial to better design and estimate the lifespan of the pavement and of the power delivery dispositive, without ignoring all of the thermal, mechanical and chemical variables that influence the response of eRoads to loadings.

The few studies that addressed the mechanical behaviour of eRoad pavements focused primarily on the response of the structure to traffic-induced loadings. From the first block of analyses, the authors highlight the importance of using contact elements to describe the vicinities of the CU. The levels of horizontal transverse stress calculated in the structures with and without contact elements differs in more than 10 times for some predefined locations in the bituminous layer (near the CU). The eRoad containing non-contact elements displayed the higher magnitudes of stress, which was expected due to the accounting of the tensile stress between the two bonded components in the calculations. In terms of response to dynamic excitations (vibration and passage of a heavy vehicle at 70 km/h), tRoad and eRoad did not exhibit differences in the response. From these observations the authors conclude that by using linear elastic models in ideal conditions of use (no wheel wander) the comparative analysis of tRoad and eRoad tend to give very similar results.

On the other hand, in the results of the viscoelastic 3-D time-dependent simulations the authors emphasize the need of well characterizing the load intensity in eRoads to predict more realistic cumulative vertical deformation. The vertical displacement in the surface of the pavement varied non-uniformly when the probability of passage of a heavy vehicle varied. In addition, an important remark is done concerning the differential settlement of bituminous layers and the materials composing the CU. As observed in Figure 12, the generation of a gap between the pavement and the CU is noticed in eRoads, which can lead to drivability issues and new modes of rutting damage.

Despite the careful validation and detailing of each step of the numerical model, the results of the computational procedure developed by [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF] aimed at predicting the horizontal tensile strain evolution at the bottom of the bituminous layer and the vertical displacements in the surface of the pavements to estimate rutting and fatigue life through deterministic models. In the fatigue analysis, for example, the eRoad displayed a better performance than the tRoad, mainly because the sole parameter used in the empirical law was the horizontal strain at the bottom of the bituminous layer under the wheel axis and far from the influence of the CU. From these results the authors bring to light the need of construction and monitoring of experimental eRoad sites in order to better understand the distribution of strain and stress within the CU and the pavement layers. The authors also acknowledge that using traditional design data, simplified elastic hypotheses and fully bonded assumptions may lead to inaccurate lifetime estimation of eRoads, and that deeper investigations concerning the effects of temperature, drainage and spalling are necessary for a more realistic design of these new infrastructures. Results in terms of interfacial normal stress between layers 1 and 2 for the two eRoad profiles studied displayed significant higher magnitudes in the scenario of a flexible road (layer 1 is above the CU and layer 2 is the layer that can be considered as the extension of the upper half of the CU in the transverse direction). The attenuation of stress in the composite profile scenario was nothing more than expected, once the properties of the cement layers were assumed equal to the properties of the unit (Young modulus=30GPa) and 30 times more stiff than the bituminous layer (Young modulus=1000MPa). Hence, no differential mechanical behaviour between the CU and the pavement layers would lead to the generation of additional stress in the composite case, except for the local discontinuity near the vertical debonding interface (existing macro-crack). Attention must be given also to the fact that the lane-changing analysis replicated the misleading assumption adopted in the work of [START_REF] Chen | Towards an understanding of the structural performance of future electrified roads: a finite element simulation study[END_REF], which possibly overestimates the levels of stress endured by the road by the reduction of the wheel axis.

In a more practical study, [START_REF] Hornych | Evaluation of a solution for electric supply of vehicles by the road, at laboratory and full scale[END_REF] addressed the performance of flexible eRoad pavements through laboratory testing and APT facilities. This investigation evaluated an ERS conductive technology, in which feeding rails are embedded in the pavement surface and in direct contact with traffic and climatic loadings. Bituminous mixtures slabs were compacted and swan to receive a rubber block that simulated the bedding of the electrified rails, which were bonded to the mixture by an elastomeric resin. The main goal of the tests performed was to compare the behaviour of different interface materials in order to size an attachment for the rubber assembly to the wearing surface in real scale tests. In this way, the authors recreated traffic and temperature solicitations using wheel tracking tests at three controlled temperatures (20, 40 and 60°C). Rut depths in the wheel path were measured on each specimen at different positions after 30,000 load cycles. For some specimen the wheel circulated with the centre over the rubber block and for others it circulated over the interface between the mixture and the rubber. In addition to wheel tracking tests, the eRoad samples were also tested under temperature variations of 40°C in a climatic chamber (from 20 to -20°C). These tests followed elastic FE thermal simulations of the samples, and served to qualitatively investigate the differential thermomechanical behaviour of the eRoad components to severe temperature fluctuations.

From the wheel tracking tests, the rut depths for all of the samples did not exceed the maximum limit according to French standards (10 mm). From the thermal tests, the samples with the elastomeric resin as bonding material did not present visible cracks unlike the other materials samples. It was then decided to use the elastomeric resin in the pavement section of the full-scale test. HORNYCH et al. (2020) described the profile of the flexible eRoad and the loading that simulated the traffic condition of lane changing (wheel passing above the power delivery system). The loading campaign consisted in applying 500,000 load cycles: dual wheels loaded at 65 kN with a velocity of 3.6 km/h. The temperature in the surface of the pavement during the tests varied from 5 to 26°C, and from 7 to 21°C at a depth of 5 cm. The transversal profile measurement at the mid-length of the feeding rails after the load cycles was compared to the initial profile (Figure 15). Deflections were also measured at two longitudinal positions by means of a Benkelman beam. From the transverse profile measurements in Figure 15, an important remark is the clear distinction between the surface of the metallic rails and the rubber block. A careful observation also allows the visualization of the transition between the CU and the wearing course. The authors reported no visible cracking and emphasised the fact that a real conductive eRoad would endure much less traffic in terms of wheel passage, as the centre of the vehicle is supposed to be aligned to the CU to be activated.

Nevertheless, the inclined deformation of the CU may indicate a non-uniform block settlement that is dependent on the stiffness of the underlying layers. Finally, the qualitative analyses of the thermal tests and thermal simulations brought to light the importance of evaluating the compatibility of the eRoad components in terms of thermomechanical behaviour as a design step.

Digital Image Correlation

Digital Image Correlation (DIC) is a high precision and non-contact method used to measure shape, deformation and/or motion of materials from acquired and stored images in digital form (SUTTON; ORTEU; SCHREIER, 2009). Since its early development focused on aerial photographs in the 1960s, DIC has been successfully optimized to attend a wide range of research and industrial sectors, alongside with several other optical methodse.g. laser speckle photography, grid method, geometric Moiré, holographic or shearing interferometry and photoelasticity (GRÉDIAC; SUR; [START_REF] Grédiac | The grid method for in-plane displacement and strain measurement: A review and analysis[END_REF][START_REF] Sirkis | Displacement and strain-measurement with automated grid methods[END_REF][START_REF] Sirkis | Displacement and strain-measurement with automated grid methods[END_REF][START_REF] Sjödahl | Dilation behavior of hot mix asphalt under triaxial loading[END_REF][START_REF] Sutton | Determination of displacements using an improved digital correlation method[END_REF]. In experimental solid mechanics, the use of image processing techniques can substitute or be complementary to the classic conventional contact methods used to measure deformation, such as LVDTs displacement sensors, extensometers and strain gauges. In the study of anisotropic and heterogeneous materials, the use of DIC has become increasingly popular for measuring full-field displacement and strain evolution before, during and after loading of specimens [START_REF] Buttlar | Digital image correlation techniques to investigate strain fields and cracking phenomena in asphalt materials[END_REF][START_REF] Haddadi | Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique[END_REF][START_REF] Haddadi | Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique[END_REF]HILD;[START_REF] Hild | Digital Image Correlation: from displacement measurement to identification of elastic properties -a Review[END_REF][START_REF] Romeo | Two-dimensional digital image correlation for asphalt mixture characterisation: interest and limitations[END_REF].

The main advantages of using DIC are at the same time the weak points of using classic conventional contact methods. Both have the same overall goal, but differ in terms of set up, equipment and costs [START_REF] Ghani | Digital Image Correlation (DIC) technique in measuring strain using opensource platform[END_REF]. For the successful use of strain gauges, for example, it is important to have an idea of the expected strain magnitudes to be measured before the experiment, in order to use sensors with compatible gauge factors. Similarly, the zone of investigation must be decided prior to the test for the installation of the sensor. A strain gauge is limited to provide local readings, which means that a certain quantity of gauges are necessary if the objective is to measure strain fields [START_REF] Hoult | Experimental accuracy of two dimensional strain measurements using Digital Image Correlation[END_REF]. As a resistive elastic unit which operates on the basis of resistance change, prior to data interpretation, the signals acquired during the experiment need to be corrected in order to eliminate additional sources of deformation not linked to the applied strain. Temperature variations in the strain gauges and in the wires/cables that connect the system to a data logger are amongst the most common causes of error in strain measurements. Last but not least, depending on the properties of the material studied, a bad attachment of a strain gauge to its support can create discontinuities or local concentrations of stress, leading to errors in the strain calculation [START_REF] Poulain | Determination of the intrinsic behavior of polymers using digital image correlation combined with video-monitored testing[END_REF].

The use of DIC eliminates partially the high costs related to equipment acquisition and the exhaustive calibration and preparation of specimens in experimental mechanics. One of the greatest features of the DIC technique relies on its flexibility.

Amongst several applications reported in the literature, the DIC method has been used in the fields of knowledge comprised in this research to: quantify deformation fields of various materials under mechanical and/or thermal loadings (FARGE; ANDRÉ; [START_REF] Farge | Use of Digital Image Correlation to study the effect of temperature on the development of plastic instabilities in a semi-crystalline polymer[END_REF][START_REF] Poulain | Determination of the intrinsic behavior of polymers using digital image correlation combined with video-monitored testing[END_REF][START_REF] Teguedi | Towards the local expansion and contraction measurement of asphalt exposed to freeze-thaw cycles[END_REF]; identify constitutive parameters of materials [START_REF] Promma | Application of the virtual fields method to mechanical characterization of elastomeric materials[END_REF]WANG;[START_REF] Wang | A high resolution DIC technique for measuring small thermal expansion of film specimens[END_REF]; characterize damage and debonding mechanisms [START_REF] Buttlar | Digital image correlation techniques to investigate strain fields and cracking phenomena in asphalt materials[END_REF][START_REF] Gharbi | Caractérisation du collage des interfaces de chaussées par essais de rupture en mode I[END_REF][START_REF] Santos | Modélisation intrinsèque de la fissuration par fatigue des enrobés bitumineux à partir de mesures de champs: Application à la correspondance entre différents types d'essais de fatigue[END_REF], and calibrate and validate models in FEM or theoretical analyses (CHEHAB; SEO; [START_REF] Chehab | Viscoelastoplastic damage characterization of asphalt-aggregate mixtures using Digital Image Correlation[END_REF][START_REF] Masad | Modeling and experimental measurement of strain distribution in asphalt mixes[END_REF].

Fundamentals of DIC

The DIC method consists in matching two images of a studied area to two different mechanical configurations: a reference undeformed configuration (unloaded)

and a deformed one (during and/or after loading). Simply put, for the set of images depicted in Figure 16, a point M is associated to a pair of coordinates (𝑋, 𝑌) in the reference image. On the image to be correlated (deformed configuration), the DIC algorithm searches for the same point M and saves its new coordinates (𝑥, 𝑦). The deformation is parametrized by the derivatives of the displacements of point M, which are calculated as the difference between the final and the initial coordinates. In order to uniquely identify point M in the reference image and to follow it up throughout the studied test, several prerequisites need to be fulfilled. Initially, the specimen surface must display a speckle granulometry. A speckle consists in a homogeneous randomly oriented texture, which allows the creation of a virtual stochastic grid of pixels (sensing elements) by the DIC algorithm. A speckle pattern can be the natural aspect of the material or can be artificially created in order to distinguish one group of pixels from the others. Generally, a speckle pattern is created by applying a thin film of black paint overprinted by white dots, or vice versa (white film and black dots). In the presence of a speckle pattern and based on the hypothesis of luminance conservation, the light reflected by each pixel and captured by the camera is converted into a set of numbers or grey scale levels (0 to 255 for an 8-bit file, in which 0 corresponds to a zero light intensity representation). In this way, it becomes possible to relate the intensity pattern stored on the reference image to the ones of the deformed image. Observing the scheme in Figure 16, the matching between the initial and final location of point M is obtained by means of the statistical comparison of the grey values of a small window of pixels in the reference image to an equally sized window of pixels in the deformed image. These windows are named subsets or subwindows, and the deformation inside each subset is assumed to be homogenous.

As it can be observed in Figure 16, point M is in the centre of both windows.

Different approaches can be adopted to evaluate the similarities between reference and deformed images. The two most used are the Cross-Correlation technique and the Least Squares Matching (LSM) [START_REF] Buttlar | Digital image correlation techniques to investigate strain fields and cracking phenomena in asphalt materials[END_REF][START_REF] Romeo | Two-dimensional digital image correlation for asphalt mixture characterisation: interest and limitations[END_REF]. The cross-correlation technique consists in searching for the subset defined in the reference image by shifting it along horizontal and/or vertical axes of a predefined area in the deformed image (keypoint matching). For each shifted position, a cross-correlation coefficient is calculated and the best-matched subset is determined when the minimum coefficient value is obtained (ideally, close to zero). The crosscorrelation coefficient is calculated as a discrete function of the displacement (∆𝑥, ∆𝑦):

𝜌 = ∑ ∑ (𝑓(𝑥, 𝑦) -𝑓 ̅ ) 𝑦 𝑥 × (𝑔(𝑥 + ∆𝑥, 𝑦 + ∆𝑦) -𝑔̅ ) (∑ ∑ (𝑓(𝑥, 𝑦) -𝑓 ̅ ) 2 𝑦 𝑥 × ∑ ∑ (𝑔(𝑥 + ∆𝑥, 𝑦 + ∆𝑦) -𝑔̅ ) 2 ) 𝑦 𝑥 1/2 Equation 5
Where 𝑓 ̅ and 𝑔̅ are the mean values of the grey levels of the subsets in reference and deformed images, respectively. These mean values are dependent on the number of data points in the subset.

The LSM technique is a differential method. It is an area-based matching approach and it combines affine transformation model and linear model to describe the geometric position of the subset and the grey level intensity, respectively (Equation 6).

In the LSM technique, Taylor expansion are used to transfer the nonlinear model into the linear one in order to find the final solution. In general, the optimum matching is obtained through iterations by minimising the grey value difference between two subsets by least squares estimation:

𝑔 1 (𝑥 1 , 𝑦 1 ) = ℎ 0 + ℎ 1 𝑔 2 (𝑎 0 + 𝑎 1 𝑥 1 + 𝑎 2 𝑦 1 , 𝑏 0 + 𝑏 1 𝑥 1 + 𝑏 2 𝑦 1 ) Equation 6
Where 𝑔 1 and 𝑔 2 are the grey levels of the pixels in the reference and deformed images, respectively (dependent on the pixels coordinates); 𝑎 𝑖 and 𝑏 𝑖 are the unknown parameters in the affine transformation model; and, ℎ 0 and ℎ 1 are the unknown parameters in the linear model of grey level intensity.

The quality of the DIC method application is mainly dependent on two types of factors: the ones linked to the quality of the experimental conditions, and the ones linked to the correlation principle itself. Included in the first group of factors, one can list aspects related to the measurement devices and working environment such as lightening, vibration and noise (air movement), characteristics of the camera used (optical lens and CCD sensor) and the overall arrangement of all devices in the workspace. For the second type of factors, one can cite the quality of the speckle pattern, the size of the subset and the definition of equations governing the DIC correlation algorithm. Find more complete studies on the uncertainty assessment of the DIC method in [START_REF] Bornert | Assessment of Digital Image Correlation measurement errors: methodology and results[END_REF][START_REF] Haddadi | Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique[END_REF][START_REF] Haddadi | Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique[END_REF][START_REF] Pan | Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review[END_REF][START_REF] Reu | DIC Challenge: Developing images and guidelines for evaluating accuracy and resolution of 2D analyses[END_REF]SCHREIER;[START_REF] Schreier | Systematic errors in digital image correlation due to undermatched subset shape functions[END_REF][START_REF] Zappa | Uncertainty assessment of digital image correlation method in dynamic applications[END_REF][START_REF] Zappa | Uncertainty assessment of digital image correlation method in dynamic applications[END_REF][START_REF] Zappa | Uncertainty assessment of digital image correlation method in dynamic applications[END_REF].

Summary

In this chapter, important definitions were given concerning the existing chargewhile-drive technologies, and the main advantages and disadvantages of their implementations from the road infrastructure point of view. The challenges linked to the design of traditional flexible pavements were also discussed, with an overview of how traffic and environmental conditions are commonly considered in mechanisticempirical design methodologies. It is highlighted that an eRoad, characterized by the presence of a power delivery system, can no longer be assessed using the numerical and experimental approaches adopted to predict stresses, strains and displacements in pavement systems. In addition to the evident geometric divergences between an eRoad and a tRoad, the complexity of framing the behaviour of bituminous mixtures and of elastomeric materials (dependent on the strain range and temperature) suggests the use of nonlinear finite-element models. In order to obtain useful insights into the structural performance of eRoads, experimental verifications are also required. and unbound granular layers are considered as linear elastic, with elastic properties kept constant and independent from the temperature, contrarily to the bituminous materials. Neither fatigue, damage nor moisture is considered.

Geometries

Charging unit

The eRoad configuration analysed in this study was based on the APS for Roads, developed by the French multinational Alstom (OLSSON, 2014a). The basic principle of the APS for Roads is the integration of segmented conductive charging units into the pavement, in the centre of the driving lane, to which a sliding shoe coupled to the vehicle extends to get in contact with (Figure 17(a)). The APS for Roads unit is composed by three distinct rails (return current, live polarity and voltage barrier) laid on a rubber-based material, which works both as support and as insulator. This assembly was mainly an adaptation from well-established subway and tramway technologies, where a "third rail" located between the traction rails provides power supply, playing a similar role as the catenary on overhead lines. In this study, the eRoads were assumed to be renovated tRoads with the CU integrated in the wearing surface, inside a trench excavated in the centre of the driving lane. In Figure 19, due to symmetry, only half of the eRoad geometries are depicted side by side for comparison.

Constitutive models in Cast3M®

Cast3M® is an open source finite element software developed by the French Alternative Energies and Atomic Energy Commission (CEA). It is generally used for solving both linear and nonlinear mechanical and heat transfer problems. The architecture of Cast3M® platform is modular, in which the independent system modules are compatible in terms of mesh generation and post-processing [START_REF] Brebbia | Finite element systems: a handbook[END_REF]. The combination of several systems provides a wide database of formulations which can be solved using partial differential equations in the static and dynamic domains (with step by step integration), and in one, two and three dimensions.

The code is written by means of an object-oriented language, denoted Gibiane scripting language, with no predefined hierarchy between the various operators.

Simply put, the modularity of Cast3M® allows coupling problems of different disciplines and to solve them without the need of compiling subroutines. All implementations discussed in this study were carried out using Cast3M® finite element code.

Modes of heat transfer

In thermodynamics, heat is the energy that flows from hotter to colder systems when there exists both a suitable path and a gradient between them (temperature difference). Heat conduction is amongst the mechanisms of energy transfer, and it is characterized by the diffusive transport of thermal energy through the contact of bodies. The transient heat conduction problem for an isotropic material is described by Fourier's law:

𝑞 𝜆 ̇= -𝜆 𝑛 ⋅ 𝜕𝑇 𝜕𝑛 Equation 7
Where 𝑞 𝜆 ̇ is the conductive heat flux in direction 𝑛, in W/m 2 ; 𝜆 𝑛 is the thermal conductivity in direction 𝑛, in W/(m⋅°C); 𝑇 is the temperature, in °C; and 𝜕𝑇 𝜕𝑛 is the thermal gradient in direction 𝑛, in °C/m.

Convection constitutes another mode of heat transfer. In conduction, the heat is transferred by the stochastic motion of atoms and molecules within and through a solid;

in convection, the internal energy is transferred by the actual motion of the medium (liquids or gases) in contact with an adjoining wall. For the cases proposed in this study, the medium is the air. The convective heat transfer from the surface of a body to the external environment and vice versa is written as follow:

𝑞 ℎ ̇= ℎ ⋅ (𝑇 𝑆 -𝑇 𝑎𝑖𝑟 ) Equation 8
Where 𝑞 ℎ ̇ is the convective heat flux, in W/m 2 ; ℎ is the convection heat transfer coefficient, in W/(m⋅°C); 𝑇 𝑆 is the temperature in the surface where the convective heat flux occurs, in °C; and 𝑇 𝑎𝑖𝑟 is the temperature of the air relatively far from the surface of the body, in °C.

The convection heat transfer coefficient, or simply Newton coefficient, is dependent on the wind flow type (laminar or turbulent) and velocity, as well as on the temperature of the surrounding atmosphere. In this research, the determination of ℎ was made using the empirical relationship (PILATE, 2007): Where 𝜈 𝑤𝑖𝑛𝑑 is the wind flow velocity, in m/s; and 𝑇 𝑎𝑖𝑟 is the temperature of the air relatively far from the body surface, in °C. Assuming that there is no heat sources and sinks, the net heat fluxes must be equal to the storage rate of thermal energy:

𝐻 ̇𝑠𝑡 = 𝜌𝐶 𝑃 𝜕𝑇 𝜕𝑡 𝑑𝑉 Equation 11
Where 𝜌 is the density of the material, in kg/m 3 ; 𝐶 𝑃 is the specific heat capacity, in J/(kg⋅°C); and 𝜕𝑇 𝜕𝑡 is the partial derivative of the temperature with respect to time.

Finally, the Fourier's partial differential equation is the simple balance of 𝑄 ̇𝑛𝑒𝑡 and 𝐻 ̇𝑠𝑡 , that must be satisfied in every point x = (𝑥, 𝑦, 𝑧) for every moment 𝑡:

div(𝜆∇𝑇) = 𝜌𝐶 𝑃 𝜕𝑇 𝜕𝑡 Equation 12

Thermal expansion

In general, when a solid is heated, the energy absorbed by the material is dissipated through heat transfer and also used for thermal expansion. The thermal expansion is characterized by the increase in volume of the solid (dilation). In an opposite way, when the energy is released by the material, there is a decrease in

(𝑙 𝑓 -𝑙 0 ) 𝑙 0 = 𝛼 (𝑇 𝑓 -𝑇 0 ) Equation 13
Where 𝑙 0 and 𝑙 𝑓 represent, respectively, the original and final lengths associated to the temperature change from 𝑇 0 to 𝑇 𝑓 . The coefficient 𝛼 is conventionally described with units of reciprocal temperature (°C -1 ). If the coefficient of linear expansion is the same in all directions for a given material, the coefficient of superficial expansion is approximately two times the coefficient 𝛼 (𝛽 = 2𝛼) and the coefficient of volumetric expansion is approximately three times the coefficient 𝛼 (𝛾 = 3𝛼).

For polymeric materials, when temperature reaches a specific range, the behaviour of the solid changes from rigid glassy to soft rubbery (not melted). This temperature is defined as the glass transition temperature (𝑇 𝑔 ). The materials properties can be dramatically different above and below 𝑇 𝑔 , also affecting the thermal expansion coefficient. In this research, all of the elastomeric components were considered to be used in temperatures far below their 𝑇 𝑔 . In this way, the thermal expansion was defined by the linear thermal coefficient 𝛼, which was assumed to be independent of temperature, time nor direction of analysis for all of the tRoad and eRoad components.

Linear elasticity

In general, when a force is applied on a solid body, it can change the body's state of movement and/or its shape or size. To be considered as a linear elastic material, the relation between the force applied and the response in terms of deformation of a solid needs to be proportional and linear. In other words, the material must obey the generalization of Hooke's law for a spring (Equation 14). Also, the resulting deformations have to be small compared to the total possible deformation of the solid, and, once the loading is ceased, the material naturally returns to its original undeformed shape.

𝐹 = 𝐾 𝑢

Equation 14

Where 𝐹 denotes the force needed to extend or compress the spring; 𝑢 is the resulting elongation or contraction of the spring; and 𝐾 is a constant factor characteristic of the spring (i.e. its stiffness).

Many materials are considered as linear elastic materials for a certain range of For a multiaxial tension state, the general constitutive relationship in an elastic model is written by the expression: 𝜎 𝑖𝑗 = 𝐶 𝑖𝑗𝑘𝑙 𝜀 𝑘𝑙 . Where 𝜎 𝑖𝑗 and 𝜀 𝑘𝑙 are the tensors of stress and strain, respectively, and 𝐶 𝑖𝑗𝑘𝑙 is a fourth-order tensor that couples the two second-order tensors of 3-D stress and 3-D strain (Figure 22). The linear relationship between stress and strain applies for 0 ≤ 𝜎 𝑖𝑗 ≤ 𝜎 𝑦𝑖𝑒𝑙𝑑 . In the case of symmetry of stress and strain tensors and of isotropy, in which the behaviour of the medium is independent of the direction analysed, the constitutive law for linearly elastic materials is known as the Generalized Hooke's law. When solved for strain, it is expressed as in Equation 15. Where 𝜎 is the stress, 𝐾 is the bulk modulus, 𝜀 is the strain, 𝛿 is the Kronecker delta (equal to 1 if 𝑖 = 𝑗 and equal to 0 otherwise), and 𝐺 is the shear modulus. In the above derivation, the subscripts 𝑖, 𝑗 and 𝑘 refer to the orthogonal directions 𝑥, 𝑦 and 𝑧

(1, 2 and 3 in the schematic of Figure 22). In matrix form, the constitutive relation (Equation 15) can be written in terms of the elastic constants 𝐾 and 𝐺 as: Using simple relationships that correlate 𝐾 and 𝐺 with the Young's modulus 𝐸 and Poisson's ratio 𝜈 (Equation 17and Equation 18) in Equation 15, the Generalized Hooke's law that relates strain to stress in inverse form is expressed by Equation 19.

{
𝐾 = 1 3 ⁄ 𝐸/(1 -2𝜈) Equation 17 𝐺 = 1 2 ⁄ 𝐸/(1 + 𝜈)
Equation 18

𝜀 𝑖𝑗 = 1 + 𝜈 𝐸 𝜎 𝑖𝑗 - 𝜈 𝐸 𝜎 𝑘𝑘 𝛿 𝑖𝑗 Equation 19
In this research, the charging unit components (rails, EPDM and elastomer-epoxy system) and the unbound granular layers were defined in Cast3M® as linear elastic materials under uniaxial stress state (𝜀 𝑖𝑗 = 1 𝐸 𝜎 𝑖𝑗 ). The elastic parameters (Young's modulus 𝐸 and Poisson's ratio 𝜈) were considered constant with respect to position and orientation, and were not affected by temperature variation.

Linear viscoelasticity

The Generalized Maxwell Model (GMM) is a rheological model often used in FEM simulations to describe the constitutive viscoelastic behaviour of materials. The GMM is an association of a single spring and several Maxwell branches (Figure 23 There are two similar, yet distinct, mechanisms that a rheological model must cover to satisfactorily represent the constitutive response of viscoelastic materials:

creep and stress relaxation. The creep phenomenon is defined by an increase in strain with increasing time under constant stress. The trajectories plotted in Figure 24 describe the evolution of the strain 𝜀 for a homogeneous uniaxial loading, when a stress 𝜎 0 is applied to the material at time 𝑡 0 , and kept constant. As for the stress relaxation phenomenon, the material experiences a stress attenuation with increasing time under constant strain 𝜀 0 (Figure 25). In this study, the bituminous mixtures were defined in Cast3M® by a Generalized Maxwell Model using the Prony series with respect to the relaxation modulus (eight Maxwell units and a standalone spring). Concerning the tri-dimensional aspects, the Poisson's ratio was considered as constant. The TTSP was assumed to describe the viscoelastic behaviour of the bituminous mixtures, the GMM internal variables were dependent on the temperature of the material. This comes to consider the viscosity 𝜂 𝑖 of the fluid in the dashpot as the parameter affected by temperature variations, and therefore changing the relaxation time of each Maxwell branch (𝜏 𝑖 ). Equation 22and Equation 23 describe how the thermal sensitivity of the bituminous mixtures was accounted using the WLF equation:

𝜏(𝑇) = 𝜏(𝑇 𝑟𝑒𝑓 ) * 𝛼 𝑇 (𝑇)

Thermomechanical coupling

In order to characterize the thermal and mechanical response of a material, the physics driving both responses need to be considered, as well as the interactions between them. Thermomechanical coupling effects play a crucial role in the assessment of multi-components structural performance. In this research, the coupling between the heat conduction and solid mechanics equations (linear elasticity) relies in the following assumption: the temperatures obtained from the heat conduction equations cause thermally-induced strains, which result in mechanical displacement.

Hence, the Generalized Hooke's Law (Equation 19) for linear elastic materials was modified by the addition of the thermal expansion effect:

𝜀 𝑡𝑜𝑡𝑎𝑙 = 𝜀 𝑚𝑒𝑐 + 𝜀 𝑡ℎ𝑒
Equation 24

𝜀 𝑖𝑗 = 1 + 𝜈 𝐸 𝜎 𝑖𝑗 - 𝜈 𝐸 𝜎 𝑘𝑘 𝛿 𝑖𝑗 + 𝛼ΔT𝛿 𝑖𝑗 Equation 25
In summary, the thermomechanical coupling in Cast3M® was defined as a oneway coupling, in which only one of the two physics fields affected the other. The internal heat generation caused by mechanical deformations from mechanical loadings was not considered. Due to the time dependency of heat conduction, the changes of thermal strain fields were transient processes. It is important to remind, however, that for the specific case of the bituminous materials (linear viscoelasticity), the mechanical properties of the material varied in relation to temperature, which corresponds to a second level of dependency to heat conduction. 2,3) 0.3 (1,3) 7800 (2) 12 * 10 -6 ( 4) 46 (3) 450 (3, 5) (1) Values used in FEM simulations of embedded rail structures in the scope of ERIA project in the Netherlands (HUURMAN; MARKINE; DE MAN, 2003). (2) Values used in Dynavoie simulations of high-speed train/track systems, and validated with an extensive database from experimental measurements in real high-speed tracks in France [START_REF] Paixão | Numerical simulations to improve the use of under sleeper pads at transition zones to railway bridges[END_REF]. (3) Same orders of magnitude of the parameters of the rail in the 3-D thermo-mechanical coupling model of wheel/rail contact system, at 25°C (WEI; WU; DUAN, 2018). (4) Coefficients of linear expansion of solids -Copper = 16.7 * 10 -6 m/(m⋅°C); Cast iron = 10.2 to 11 * 10 -6 m/(m⋅°C); Steel = 10.5 to 12.5 * 10 -6 m/(m⋅°C) (ENGINEERING TOOLBOX, 2003; HAGART-ALEXANDER, 2009). (5) Specific heat capacity for metals at constant pressure (1 atm) and 25°C -Copper = 385 J/(kg⋅°C); Iron = 450 J/(kg⋅°C); Steel = 466 J/(kg⋅°C) (UNIVERSITY OF TEXAS, 2022).

Materials

Elastomeric components

Ethylene-propene-diene terpolymer blend

For this study, the material used as base for the electrified rails was an ethylenepropene-diene-monomer blend (EPDM). Commercial EPDM terpolymers are elastomeric materials resulted from a combination of a saturated polymer backbone with residual unsaturations as side groups [START_REF] Martin | Viscoelasticity of randomly crosslinked EPDM networks[END_REF]. As a consequence of its particular molar mass distribution of network chains (i.e. unsaturation sites are in the side chain and not in the backbone), these synthetic rubbers are characterized by good resistance to oxidation, ozone, ultraviolet radiation and heat (overall good aging resistance). In terms of mechanical performance, however, most EPDM applications require a crosslink agent to be mixed during formulation in order to increase strength and tracking resistance.

Due to confidentiality regarding its industrial development, the formulation of the EPDM mixture used was not provided. Nevertheless, a set of physical and mechanical parameters of this material was determined in laboratory. The traditional method to analyse rubber networks is through equilibrium swelling experiments and viscoelastic or mechanical testing. For the sake of simplicity, throughout this research the EPDM mixture was considered as homogeneous and isotropic. The Young's modulus at 100% elongation was obtained after a tensile strength and elongation at break test carried out using a Dynamometer ZWICK (NF ISO 37 Standard) at room temperature (23 ± 2°C) (FERCHAUD; RODRIGUES, 2014). For hyperelastic materials like EPDM rubber, Poisson's ratio approaches the physically maximum value of 0.5, which means that the material is nearly-incompressible. In order to minimize divergence problems in the nonlinear FEM analysis, a constant elastic value of 0.49 was arbitrarily chosen to numerically model the EPDM blend. The density of the blend was determined in laboratory from hydrostatic weighing.

Elastomer epoxy-system

The bonding between the EPDM base and the wearing surface was made by an Similarly to the application reported by SWARNER ( 2016), the elastomer-epoxy system in the studied CU is technically unreinforced, but disposed in layers separated byand bonded toother materials that resist to lateral spreading of the elastomer when in compression (EPDM blend and bituminous mixture). elastomeric materials that they remain below the glass transition temperature for the particular use in eRoads, so as to be considered as glassy or "rigid". For the numerical analysis performed, the thermomechanical properties of the elastomeric materials composing the charging unit are depicted in Table 3: Table 3. Thermomechanical properties of the elastomeric materials. Coeff. of linear thermal expansion α (m/(m⋅°C)) EPDM 5 * 10 6 (1) 0.49 (2) 1060 (3) 0.5 (3) 2160 (3) 165 * 10 -6 (4) Corkelast VA-60® 4.34 * 10 6 (5) 0.4657 (5) 1080 (3) 0.32 (3) 1804 (3) 115 * 10 -6 (4)

(1) Young's modulus at 100% elongation (NF ISO 37 Standard) at room temperature (23 ± 2°C) (FERCHAUD; RODRIGUES, 2014). (2) Value adopted in conventional near-incompressible numerical analysis of hyperelastic rubbers to avoid divergence problems [START_REF] Kwon | A finite element procedure with Poisson iteration method adopting pattern approach technique for nearincompressible rubber problems[END_REF]. (3) Values obtained through laboratory testing and/or experimental data fitting performed by the author. (4) Arbitrarily chosen parameter values. (5) Average elastic constants 𝐸 and 𝜈 calculated based on the 𝐾 and 𝐺 measured from compression and shear full scale test results (SWARNER, 2016).

Complex modulus tests

Dynamic modulus tests (also referred as complex modulus tests) are amongst the most used laboratory procedures to assess the viscoelastic behaviour of materials.

In these tests, the complex modulus (𝐺* or 𝐸*) is measured across a wide range of temperatures and/or frequencies, in sinusoidal mode of loading. For the mixtures composing the French structure (BBSG and GB), the complex modulus was obtained from trapezoidal specimens subjected to small constant strain (NF EN 12697-26

Standard)to guarantee that the materials were tested on their linear viscoelastic domain. The mixtures were manufactured at 160°C according to the NF EN 12697-35

Standard, and then compacted into slabs by means of the French wheel compactor (NF EN 12697-33+A1). The trapezoidal specimens were sawed, dried and fixed to a metallic base that is part of the embedding apparatus of the 3MC device (Figure 30).

Four specimens of each mixture were tested with a temperature sweep of -10 to 40°C

(intervals of 10°C) and a frequency sweep of 1 to 40 Hz. The test consisted in applying cyclic alternate loads in two points of the specimen, and to measure two important parameters: the stress response to deformation and the lag between the applied load and the resulting strain. From complex modulus test results, and assuming that the Time-Temperature Superposition Principle (TTSP) is applicable, complex modulus (|𝐸 * |) and phase angle (𝛿) master curves were obtained at a reference temperature of 20°C for the three mixtures (Figure 32). The parameters of the Huet-Sayegh model and the Prony series terms were determined using the software Viscoanalyse (CHAILLEUX; DE LA ROCHE; PIAU, 2010), also for a reference temperature of 20°C (Table 5, Table 6 andTable 7). A summary of the thermomechanical properties of the bituminous mixtures is found in Table 8. Coeff. of linear thermal expansion α (m/(m⋅°C)) BBSG 1.37E+10 (1) 0.35 (3) 2480 (4) 2.0 (5) 869 (7) 27 * 10 -6 (8) CBUQ 9.14E+09 (2) 0.35 (3) 2450 (4) 1.212 (6) 920 (6) 27 * 10 -6 (8) GB 1.22E+10 (1) 0.35 (3) 2350 (4) 1.9 (5) 869 (7) 27 * 10 -6 (8)

(1) Equivalent Young's modulus obtained at 15°C for an average speed of 72 km/h (10 Hz).

(2) Equivalent Young's modulus obtained at 25°C for an average speed of 72 km/h (10 Hz). (3) Coefficient of Poisson's ratio conventionally chosen equal to 0.35 for all of the three bituminous layers. (4) Round values for bulk specific gravity obtained through laboratory testing (Table 4). (5) Characteristics adopted for pavement materials when calculating frost front propagation in a pavement structure (LCPC-SETRA, 1998). (6) Properties of a Brazilian bituminous concrete used in a finite elements model of flexible pavements undergoing thermal gradients (VASSOLER; CHONG; SPECHT, 2011). (7) Specific heat capacity of pavement materials (MINISTÈRE DE LA TRANSITION ÉCOLOGIQUE, 2005). 9): 120 (1) 0.35 (1) 2200 (1) 1.8 (1) 964 (5) 13 * 10 -6 (6) BGS 350 (2) 0.32 (2) 1700 (4) 0.695 (2) 800 (2) 13 * 10 -6 (6) Brazilian roadbed 120 (3) 0.35 (2) 2200 (3,4) 1.5 (2) 800 (2) 13 * 10 -6 ( 6)

(1) Thermomechanical properties of the platform type PF3 conventionally used in the design and conception of French pavement layers (LCPC-SETRA, 1998). (2) Thermomechanical properties of granular base and subgrade layers of a Brazilian profile used in a FE-model of flexible pavements undergoing thermal gradients (VASSOLER; CHONG; SPECHT, 2011). (3) In order to minimize the impact of variations in the properties of the roadbeds on the structural analysis of the pavements, these values were assumed to be equal to the ones of the French platform type PF3. (4) Values considered as representative of sublayers of typical Brazilian pavements in a finite element incremental algorithm for dynamic viscoelastic analysis [START_REF] De Araújo | Dynamic viscoelastic analysis of asphalt pavements using a Finite Element formulation[END_REF]. (5) Specific heat capacity of non-treated soil (MINISTÈRE DE LA TRANSITION ÉCOLOGIQUE, 2005). (6) Coefficient of linear thermal expansion arbitrarily chosen: equal to half of the coefficient adopted for the bituminous mixtures (Table 8).

Simplification and boundary conditions

In order to simplify the thermomechanical coupling simulations, the structures were solved as a 2-D plain strain problem. Due to the symmetry condition, only half of the sections were considered. The assumed thermal and mechanical boundary conditions are depicted in Figure 34. In this research, the rail, elastomeric materials and unbound granular layers were considered as homogeneous and isotropic. The thermal and mechanical properties of these components did not vary with temperature, time nor direction of analysis. On the contrary, for the bituminous mixtures, the mechanical properties were temperaturedependent. In this study, the hydric state of the materials was kept relatively constant in the optimum content, thus the focus of the analysis remained solely on the influence of temperature on the structural pavement response.

The different modes of heat transfer that act on pavements were simplified by imposing temperature variations on the surface. For the transient thermal analysis, the initial steady-state condition of the pavement was defined as a constant 𝑇 0 (Dirichlet boundary condition). There was no internal heat generation and, for a given point in time (𝑡 𝑖 > 𝑡 0 ), thermal exchanges were possible only from imposed temperatures at the upper surface of the structure 𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 (Neumann boundary condition). Within the structure, the heat flowed by conduction, within and through the components (Figure 34 schematic on the left).

As observed in Figure 34 (schematic on the right), the left boundary of the structure was assumed to be symmetric with constrained degree of freedom in stretching direction (𝑢 𝑥 = 0). The same condition was adopted for the right boundary of the subgrade layer, as an attempt to numerically represent the lateral confining condition of real pavements. Clamped boundary conditions were assumed at the bottom of the subgrade (𝑢 𝑥 = 𝑢 𝑦 = 0). The interfaces between different layers/components were assumed to be fully bonded, so as to reduce the complexity of the analysis (tied without sliding). No cracking models were implemented in the FEM simulations.

Time-dependent structural performance assessment

Two different types of structural simulations were performed, using the aforementioned models and boundary conditions. The first one was a simulation of an environmental loading, which mainly considered the effect of hourly temperature variations on the thermomechanical response of the structures. Transient simulations lasting 2 virtual days (48 hours) were performed. The main objective of these simulations was to exhibit the influence of daily temperature fluctuations on the evolution of heat inside flexible pavements, highlighting the non-uniform temperature distribution inside the layers and the possible impact of the charging unit in this distribution.

The second type of simulation aimed at evaluating the impact of a passing wheel on the road section, giving orders of magnitude of stress and strains levels reached under traffic. These simulations lasted several milliseconds, and could be performed at any given hour of the days simulated in the previous thermal loading case. Here, the main idea was to compare stress and strain fields in both tRoad and eRoad structures due to combined environmental and mechanical loading. The other purpose was to investigate the impact of the charging unit on the two primarily strain-based failure criteria used in pavement design methodologies: the vertical compressive strain on the top of the subgrade as a parameter to control permanent deformation, and the horizontal tensile strain at the bottom of the bituminous layer to control fatigue cracking. It is a common consideration that the air temperature daily peak occurs after midday, and the minimum air temperature peak occurs after midnight. In this way, the absolute difference of temperature for the interval of 12 hours was defined as a reasonable parameter to select the days from the available field data which would be simulated as "thermal loading" on the FE analysis (∆𝑇 12ℎ ). In Figure 37, the curves represent the temperature evolution acquired by the thermocouples installed in the French pavement for the days with the greatest diurnal-temperature variation (maximum |∆𝑇 12ℎ | of 24.9°C in the surface). In the same way, Figure 38

Traffic simulation using Cast3M®

The methodology used to fit the strain obtained with the 2-D loading simulations in Cast3M® with the results from the 3-D model in ViscoRoute© was based on an equivalence of loading magnitudes per areas. It is important to highlight that, since world-space (x,y,z) coordinates in ViscoRoute© were transformed to screen-space (x,y) coordinates in Cast3M®, the final convention adopted in this study considers that: the x-component refers to the tire width direction and the y-component refers to the depth of the structure. The z-component exists only when referring to the solution in ViscoRoute©, and it represents the driving direction.

To begin with, the equivalence methodology starts by plotting ViscoRoute© results of vertical stress (𝜎 𝑦𝑦 ) in the surface of the pavement (y = 0) for several zcoordinates against the x-axis (Figure 41(a)). The constant 𝑧 0 was defined as the first z-coordinate to present a vertical stress different than zero, and it was associated to a length 𝑙 𝑤0 of loading pressure, in metres, and to a mean vertical stress 𝜎 𝑦0 , in Pascal.

The number of z-constants in the case studied (𝑖 = 6) refers to the number of coordinates in which the length 𝑙 𝑤 of the loading pressure varied significantly from the previous one, since the mean vertical stress magnitudes did not show significant variations. The distances between the chosen z-coordinates were denoted as ℎ 𝑤 , in metres, and in Figure 41(b) a graphical scheme on how they were obtained is shown.

As expected, the maximum length 𝑙 𝑤 and the maximum compressive stress in the ydirection occurred in the central z-axis of the ellipse-shaped wheel area, while 𝑧 0 displayed a tensile stress, as a consequence of the dynamic component of the moving wheel, and with its coordinate located immediately further/before the wheel area in the longitudinal direction. Knowing that pressure is defined as the force exerted on a surface divided by the area over which that force is applied, from the plots in Figure 41 the loading areas 𝐴 𝑤 in ViscoRoute© were calculated as well as the mean vertical stress (𝜎 𝑦𝑦 in Pa) associated to it.

Mesh characteristics

Similarly to what is found in every FEM based software, a numerical simulation in Cast3M® is composed of four equally important steps: 1. Definition of the geometry and mesh; 2. Definition of the mathematical model to be used; 3. Discretization of the problem; and, 4. Solving and post-treatment. Important factors that validate the use of a numerical model are: the precision of results with the mesh refinement, the speed of the convergence, the computational cost and the easiness of implementation and continuous use. In this section, a mesh convergence analysis was performed comparing the impact of different sizes of elements and mesh densities on the calculation of mechanical parameters (displacement, deformation and stress).

Additionally, a parametric study on the total length and width of the 2-D geometrical model is presented, to obtain optimal accuracy in the calculated horizontal tensile strain at the bottom of the bituminous layer without the influence of the extremities boundary conditions.

As there is no graphical user interface in Cast3M®, just a command line written in Gibiane language, it becomes a hard task to create, manipulate and optimize complicated geometries and meshes solely with Cast3M®. In this way, an alternative was to use a mesh generator software named Gmsh. Gmsh is an interactive program that uses parametric inputs to create 3-D finite element geometries and meshes, with built-in post-processing tools and advanced visualizations capabilities (GEUZAINE; [START_REF] Geuzaine | Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities: THE GMSH PAPER[END_REF]. The compatibility between the two software was possible by exporting the Gmsh mesh in a readable extension in Cast3M® (.unv), in which the numerical simulation proceeded normally (steps 2, 3 and 4 aforementioned). Finally, the operator can opt to extract the calculation results in other formats to ease its treatment (Excel, Abaqus, Paraview, etc.), or to continue with Cast3M® to plot graphs and create images (FICHOUX, 2011).

Mesh refinement

The structured mesh was prescribed in Gmsh by specifying the size of the elements in relation to the distance of the areas of interest (vicinities of the charging unit and under the wheel load). The French eRoad geometry served as reference for this study, and two scenarios were evaluated: i) a mechanical calculation with the sequence of rectangular pulse loads that simulate the moving vehicle as described in The cases studied are illustrated in descendent order of density in Figure 43, from Case A to Case D. Case A was the mesh with finer elements in the charging unit (element size 𝑙 𝑚𝑎𝑥 equal to 0.007 m), while Case D constituted the less dense case (element size 𝑙 𝑚𝑎𝑥 equal to 0.025 m). For all the cases, the mesh in the region below the wheel remained the same, in order to avoid the laborious creation of lines with nodes that converge to the new mesh and the recalculation of forces. Particularly in Case E, the mesh in the charging unit was the finer one (similar to Case A), and the areas between the zones of interest had elements sizes increasing according to a positive geometric progression. and the wearing surface. For the comparative analysis, point PC had the same coordinates in all of the meshes studied (x = 0.195m; y = -0.085m). The results in this corresponding Gauss point in terms of temperature, displacement, stress and strain evolutions were used as a parameter to evaluate the impact of the mesh density in the calculations. Additionally, as an important parameter to quantify the fatigue life of flexible pavements, the maximum tensile strain at the bottom of the bituminous layers was analysed, more precisely in line 𝐿𝐵 y = -0.34m . A detailed summary of all simulated cases is shown in Figure 44, which also depicts the total number of elements per geometric entity (physical group) and the durations of calculations for each scenario evaluated. The calculations were launched on a four cores processor (2.50 GHz total). As a result from the mechanical simulation of a passing wheel, Figure 46 depicts the evolution of displacement, strain and stress for point PC. In terms of displacement, no significant divergence was observed. From stress and strain plots, Cases A and E displayed noticeable differences in terms of magnitude, yet following the same trend in time of the other cases studied. Case D was considered to provide the less accurate result in terms of strain and stress evolution, since it was constituted by the less dense mesh. In Figure 47, the maximum tensile strain in line 𝐿𝐵 y = -0.34m is depicted. The curve tendency and the orders of magnitude obtained were in good accordance with the maximum tensile strain in the bottom of the bituminous layer of the ViscoRoute© simulation (Figure 40). However, the overlapping of the curves indicated that the mesh density in this zone was satisfying for all of the mesh densities studied, thus not contributing to the definition of one over the others. The choice of mesh was done for Case E. This decision was made based on the stress and strain evolutions in point PC and on the fact that Case E simulations required less computational effort to complete (Figure 44).

Mesh dimensionality

The study of mesh densities described in the previous section was performed in The width of the charging unit was kept constant for the dimensionality study, while x and y were equally increased. It is important to highlight that the roadbed is the single layer that contributes to the dimension increase in the y-axis, as for the x-axis all of the pavement layers were enlarged. A summary of the factors simulated and the variation in the maximum tensile strain obtained at the bottom of the bituminous layer is comprised in Table 11. The graphical visualization of the results for French tRoad and eRoad is depicted in Epigraph chosen by Kilvia de Freitas Alves It is important to highlight that several other tests were performed in order to accurately manipulate the software used in the procedures; and to overcome the constraints in terms of timing and availability of laboratory equipment and personnel.

Finally, the main objective of this laboratory campaign was to explore appropriate experimental protocols for the direct examination of eRoad specimens subjected to thermal loadings. Afar from setting a definitive guideline, the content of this chapter constitutes the first attempt to develop a repeatable thermal loading test for roads containing rigid inserts, making use of an innovate and flexible system of measurement.

Specimens fabrication

Bituminous mixture

The semi-dense bituminous concrete composing the specimens was constituted by diorite aggregate, lime fines and a neat 35/50 penetration grade bitumen, designed in accordance with the French methodology [START_REF] Lcpc-Setra | LCPC-SETRA. Construction des chaussées neuves sur le réseau routier national (Spécifications des variantes)[END_REF]. This type of mixture is denoted as BBSG 0/10 Classe 2 in the NF EN 13108-1 Standard. The aggregate gradation for the mixture was depicted in Figure 28(a) and its overall properties were presented in Table 4 (Section 3.3.2.1.1 Bituminous mixtures design).

The mixture was manufactured at 160°C according to the NF EN 12697-35 Standard, and compacted into slabs by means of the French wheel compactor (NF EN 12697-33+A1). In this experimental campaign, a total of five slabs (600 x 400 x 120 mm) were fabricated using the slab compactor MLPC (Matériel des Laboratoires des Ponts et Chaussées). For the tRoad specimens, two slabs were initially trimmed to eliminate the areas near the edges where the mixture was not densified according to the design criteria (borders effect). The schematic of the edges elimination of the tRoad slabs is depicted in Figure 51. Some technical limitations determined the geometry of the specimens: the maximum size of slabs produced with the compactor MLPC, the dimensions of the climatic chamber and the saw blade characteristics. The handling of large sized specimens required the use of a larger diameter blade, meaning that the thickness of the blade could not be neglected, and that the cuts were less precise than when sawing small samples. In Figure 51, the rolling direction indication refers to the wheel compactor rolling direction. For the eRoad specimens, two slabs were initially sawn in the centre of the longest slab dimension (x axis direction: 540 mm), but not in the complete depth of the slabs. The goal was to create a trench in the bituminous slab, inside which the EPDM and the bonding elastomer-epoxy system would be further included. The method used to excavate the trench aimed at recreating field conditions as realistic as possible.

Generally, in road intervention works, the pavement is neatly cut using an asphalt rotary saw and squared off, with no acute angles. Using the same approach, the sides of the trench were cut to neat straight lines (perpendicular to the wheel rolling direction)

and right edged angles were adopted for the corners of the trench. The schematic of the trench saw cutting and of the elimination of the edges in the eRoad slabs are depicted in Figure 52. The method used to excavate the trench consisted in cutting several straight lines parallel to the laterals of the trench (approximately 10 mm distant one from the other, along the x axis), and in lapidating these smaller bituminous subsections manually one by one. Traditionally, in field conditions, trench excavation is performed with the use of a milling machine and a backhoe, after the saw-cut of the trench limits. This comes to consider that, in a real road configuration, the bottom of the excavated trench rarely results on a smooth surface. For the specimens in this study, the bottom of the slab trench was treated as to create a texture, which would also provide an adequate bonding of the bituminous mixture to the elastomer-epoxy system. In Figure 53

Elastomer-epoxy system

The mixing and application of Corkelast VA-60® followed the guidelines of the Product Data Sheet provided by edilon)(sedra (Annexe A). The two components were mixed for at least 60 seconds using a mixing paddle attached to a drill, in a ratio of 2:1 -"Component 1" and "Component 2", respectively (Figure 56 The external surfaces of the bituminous mixture and the EPDM were covered with duct tape to avoid leaking and running of Corkelast VA-60® on the surface of the final eRoad specimens. The volume of Corkelast VA-60® produced was precisely calculated as to fill in the whole bonding volume of each pre-assembled eRoad slab (desired thickness of 20 mm in every interfacebottom and laterals). In the sequence, the two Corkelast VA-60® components were mixed and quickly poured. Another alternative for the assembly relies on placing the EPDM atop a layer of fresh bonding material and then proceed to filling the lateral interfaces. Both alternatives require attention not to create air bubbles below the EPDM, which would not be noticed and thus not eliminated, possibly affecting the mechanical performance of the eRoad in the tests. Additional care was taken in order to avoid misalignments during the pouring of the elastomer-epoxy system, using weights above the EPDM support to limit its movement in the vertical direction. After pouring the elastomer-epoxy system, the specimens were left to stabilize for a week.

Speckle pattern

In order to create a homogeneous randomly oriented texture on the front surface of the specimens, two techniques were tested: spray paint patterns and water transfer printing (WTP). For the first technique, the pattern was applied on a tRoad specimen surface with white spray paint. The tRoad specimen was previously coated with a thin film of black paint. The challenge was to get the grains of the pattern to have a similar diameter, which is a time consuming and very operator-dependent procedure, especially when manipulating large sized specimens. The second technique used was based on the work of CHEN et al. (2015), which proposed a repeatable way to create speckle patterns using computer-generated patterns and portable transfer paper. The WTP technology relies on the use of waterslide decal paper, which is commonly used to transfer images onto 3-D objects and flexible substrate in the fields of graphic arts, tattooing and electronics, among others. The decal paper is composed of several layers: a protective sheet layer, an adhesive layer, a printed speckle pattern part, a transparent elastic layer, a water soluble slip layer and a base layer. The WTP application began by inkjet printing the speckle pattern on the decal paper. After the paint has dried, a coat of acrylic clear matte was evenly sprayed onto the decal paper.

While the paint protective layer dried, the surface of a tRoad specimen was cleaned and received a thin white coat of spray paint. Once all of the materials were dry, the decal paper was sipped into a recipient with water so the water soluble layer could dissolve and the part with the ink could be slipped away from its base. Delicately, the adhesive transparent layer containing the ink was pulled from the water recipient and glued to the specimen surface, with attention not to create air bubbles between the thin film and the surface of the specimen. In Figure 60 The two tRoad specimens used for the speckle pattern study were left to dry for 24 hours before being tested inside the climatic chamber. A warm cycle (20 to 50°C)

was applied in both of the specimens for feasibility studies. A visual analysis of the specimens after the test showed that the WTP technique was not suitable for the objective of this work. The airflow inside the chamber dried out the adhesive coat and the extremities of the speckle pattern started to peel off. In this way, it was decided to continue with the spray paint patterns for this study. The paint used in all of the tested specimens was a water based ("Luxens mat deco paint" by Leroy Merlin). The two tRoad specimens that went through the aforementioned feasibility studies were not reused in the final experimental program.

Experimental set-up

The aerial schematic of the experimental set-up is shown in Figure 61. It consisted of a climatic chamber, a digital image capturing system and two LED white light sources. In a typical experiment, a specimen with its front surface decorated with fine paint speckles is placed on a horizontal support inside the chamber. The horizontal support is constituted by the original plate of the chamber, above which an additional metallic plate was set to obtain a more stable support. Between the metallic base and the specimen, a 15 mm thick layer of polytetrafluoroethylene (PTFE) or Teflon® was added. The main goal of using Teflon® was to avoid the heat from the base from reaching the specimen. Similarly, the laterals of the specimens were not in contact with the metallic walls of the chamber. In order to reduce the friction between the bottom of the specimen and the Teflon® layer, a thin coat of lubricant oil was spread over the base before placing the specimens. Once the specimen is inside the chamber, the thermocouples are installed and connected to an acquisition equipment outside the chamber. For the ideal use of 2-D DIC it is necessary that the optical axis of the acquisition camera remains normal to the surface of the specimen and that the out-of-plane displacements are minimal or non-existent. In this way, based on the experimental protocol reported by [START_REF] Teguedi | Towards the local expansion and contraction measurement of asphalt exposed to freeze-thaw cycles[END_REF], the front surface of the specimen was wedged against a Teflon® isolated frame using an alternative support system.

However, the lateral space between the specimen and the chamber was limited for the direct encircling of the specimen by a rubber band as the referred authors did. In addition, that configuration would make the rubber band cross the visible surface area of the specimen, affecting the final images acquired for the DIC analyses. Hence, the solution was to use a wooden timber in the gap between the specimen and the back surface of the chamber, which was pressed against the back of the specimen with the aid of elastic rubber bands, with hooks at the end. The elastic bands held the wooden joists connected to the timber against the specimen and were stretched and attached to the plate of the chamber. In summary, this system worked as a spring that returned the specimen to its frontal frame in case of an eventual out-of-plane displacement due to thermal contraction/expansion (Figure 62). For every test performed, the specimen was placed inside the climatic chamber the night before the test was launched, so it would adjust to the chamber base and settle, if this was the case. Before the start of the thermal test itself, in which the images are acquired, several adjustments were performed in terms of camera exposure time and lightening positioning (4.3.2 Image acquisition parameters). The yellow lightening of the chamber was not used during the tests, as it increased the temperature inside the chamber, created shades and affected the lightening coming from the LED white light sources. The windows and the door of the testing room were kept closed throughout the tests to avoid external light to enter the room.

Thermal loading cycles

The definition of the heating/cooling program of the chamber aimed at recreating daily temperature fluctuations observed in the field (temperature gradients in the order of 25-30°C in the surface of the road from midnight to midday). The curves in Figure 63 represent the temperature evolution registered in the thermocouple installed inside the chamber during two of the thermal tests (denoted as warm and cold cycles). In Phase I, the rate of increase/decrease of temperature was set to the slowest allowed by the chamber software (0.1°C per minute). During Phase I, the chamber door remained closed and a directed vertical airflow system at 2.3 m/s controlled the temperature variation. The chamber takes 5 hours to increase the temperature of 20°C

to the target temperature of 50°C (warm cycle)or to decrease to the target temperature of 10°C (cold cycle). After reaching the maximum (or minimum) temperature, the chamber is programmed to maintain this temperature for the duration of 2 hours. Phase I lasts 7 hours. Before Phase I, the specimens go through a conditioning phase, in which they remain inside the closed chamber at 20°C for the duration of 4 hours. This conditioning phase aimed to homogenize the temperature inside the specimen. The velocity of the airflow inside the chamber during the conditioning phase was also 2.3 m/s. Phase II starts when the chamber is turned off and after the door is opened.

During this phase, the images are acquired while the specimen returns to room temperature. Unfortunately, the temperature inside the testing room could not be controlled. To minimize the influence of room temperature variation on the different specimen results, the tests were launched at the same time of the day, and were all performed within the same season (summer months). Nevertheless, from the graph in Figure 63 one can observe that the curves do not reach a common temperature by the end of Phase II, as they represent tests performed in different days. In this way, it was decided to limit Phase II by a duration and not by a target final temperature equilibrium.

Phase II lasts a total of 5 hours and the velocity of the airflow is assumed to be 1.0 m/s (no vertical airflow coming from the chamber). In Figure 63, on the cold cycle curve, some temperature perturbations can be noticed in the beginning of Phase II. That is a consequence of using compressed air jets. The operator of the test used compressed air jets to eliminate the water drops that condensate at the surface of the specimen (during cold cycles only), at regular time intervals. This adaptation is expected to create additional air turbulences and thus an extra source of noise in the images acquired.

However, several other tests performed to substitute the use of compressed air jets did not succeed: image acquisition through the chamber glass window, using an antiicing spray at the surface of the specimens or placing a ventilator with its airflow directed to the specimen surface to move the air around the specimens and to minimize the accumulation of water. Finally, the novel protocol lasts a total of 11 hours. Prior and posterior to the test itself, two conditioning phases are needed to acquire the reference image and the final image at 20°C. Hence, on a regular week, solely two specimens could be tested. The thermocouple device was capable of sampling one temperature data per minute with a resolution of 0.01 °C. In Figure 64 the interface of the EyeMotion software is depicted, when the central axis of the camera is being aligned to the centre of the specimen surface using a perforated metallic target. It is by means of this software that the shooting and recording parameters are configured. The Ncorr software has the particularity of using contiguous circular group of points as subset geometry. As previously explained, a subset is a group of pixels in the image, or in a defined region of the image (ROI, for Region of Interest). In Ncorr, the correlation coefficient and the deformation parameters are calculated for the central point of the subset. The discretization of the ROI, subset size, subset spacing and strain spacing are input parameters for the DIC analysis using Ncorr. The subset spacing defines the horizontal and vertical distance between two subsets. The subset spacing (and the strain spacing) determines the number of displacement values computed in the proposed analysis. The size of the subset plays a significant role in the computational cost of the analysis. In this way, an optimal subset range is the one that results in minimal measurement errors, and it is closely related to the amount of deformation expected to be measured during the test, the granulometry of the speckle pattern and the experimental arrangement (e.g. background noise due to camera vibration).

The quality of the strain measurements of the experimental protocol proposed was assessed by means of background noise quantification, in-plane and out-of-plane displacement tests (rigid-body motion) using Ncorr. Similarly to the methodology used by SANTOS (2020) and [START_REF] Haddadi | Use of rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique[END_REF], the quantification of the measurement quality was carried out on the basis of 3 parameters: the systematic error (𝐸 𝑠𝑦𝑠 ), the root-mean-square error (𝑅𝑀𝑆𝐸), and the random error (𝜎 𝛼 ). These three parameters can be evaluated locally, for a given measurement, or globally, for all the measurements taken. For the referred measurements, all tests were performed using the same image acquisition equipment used in the thermal loading tests and the EyeMotion software. In order to eliminate possible sources of error due to temperature variations, the tests were performed using a specimen made of Teflon® ( 170

In-plane translation

The in-plane displacement experimental protocol consisted in translating the specimen laterally along the horizontal axis (x direction). The horizontal translations ranged from 0 (reference position) to +10,000 μm (10; 20; 30; 40; 50; 100; 200; 300; 400; 500; 1,000; 2,000; 3,000; 4,000; 5,000 and 10,000). The lightening and temperature inside of the testing room were kept identical during the acquisition of the images. The physical size of a pixel was 41.74 μm. The average speckle grain size was 11 pixels. The size of the images was set to 5120 x 5120 pixels 2 and the squared ROI was located in the centre of the images (1663 x 1663 pixels 2 ). The DIC analysis was carried out with different radii of subsets (ranging from 10 to 40 pixels), a subset spacing of 5 pixels and a strain spacing of 4 pixels. The local systematic error between the measured value and the displacement imposed was calculated according to the equation:

𝐸 𝑠𝑦𝑠 𝑙𝑜𝑐 = 1 𝑁 ∑ 𝑈 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 (𝑘) -𝑈 𝑖𝑚𝑝𝑜𝑠𝑒𝑑 𝑁 𝑘=1 (𝑘) Equation 26
Where 𝑈 𝑖𝑚𝑝𝑜𝑠𝑒𝑑 (𝑘) and 𝑈 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 (𝑘) are the imposed (or expected) displacement applied by the XY-table and the displacement measured by means of the DIC technique at the centre of the subset of coordinates (𝑖, 𝑗), respectively; and 𝑁 is the number of subsets of the measured field. In Figure 66, the systematic and random errors for each imposed displacement are depicted for the subset radius of 10 and 40 pixels. From the plot in Figure 66 representing the subset radius of 10 pixels, one can observe how the speckle pattern quality directly affected the selection of the subset size. In this case, the subset radius was smaller than the speckle grain size, which difficult the distinction of the intensity pattern contained in one subset from other subsets.

Figure 66. Evolution of the systematic error measured from rigid-body motion tests using the Ncorr software.

Out-of-plane translation

The out-of-plane displacement experimental protocol consisted in distancing the specimen backwards with respect to the camera position, along the longitudinal axis (z direction). The horizontal translations ranged from 0 (reference position) to -10,000 μm. The DIC parameters were kept the same as the ones used in the in-plane translation analysis. In Figure 67, the global measurement uncertainty (∆ 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙 ) with a 95% confidence interval is depicted for 𝜀 𝑥𝑥 and 𝜀 𝑦𝑦 measurements, with varying subset radii. The global measurement uncertainty was calculated according to the equations:

∆ 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙 = 2 • 𝜎 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙
Equation 27

𝜎 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙 = 1 𝑀 ∑ (√ 1 𝑁 [∑ ((𝑈 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 (𝑘) -𝑈 𝑖𝑚𝑝𝑜𝑠𝑒𝑑 (𝑘)) -𝐸 𝑠𝑦𝑠 𝑔𝑙𝑜𝑏 ) 2 𝑁 𝑘=1 ]) 𝑀 𝑙=1 𝑙 Equation 28
Where 𝑀 is the number of images analysed and 𝜎 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙 is the global random error.

Figure 67. Variation of the global measurement uncertainty as a function of the subset radius.

Noise quantification

The experimental protocol for evaluating the background noise consisted of taking stationary images at different times. The elapsed time between two consecutive images was fixed to 10 minutes and a total of 5 images were taken, plus the reference image (one hour of test). The camera as well as the specimen did not undergo any displacements during the image acquisition. In this way, the strain measured were solely linked to the presence of vibrations and air turbulence inside the testing room.

In Figure 68, the evolution of the global root-mean-square error (𝑅𝑀𝑆𝐸 𝑔𝑙𝑜𝑏𝑎𝑙 ) of the measured strain as a function of the subset radius is depicted. The 𝑅𝑀𝑆𝐸 𝑔𝑙𝑜𝑏𝑎𝑙 decreased significantly when increasing the subset radius. Nevertheless, a large subset radius causes a loss in spatial resolution and larger errors in the approximation of the deformations. Based on the results of the quality measurement tests, a subset radius of 20 pixels was found to present a good compromise between measurement accuracy and spatial resolution. Table 12, Table 13 and Table 14 show the results of the quality assessment of the measurements for the subset radius of 20 pixels. Unfortunately, the location of the XY-table could not be modified inside the laboratory facilities in order to perform this experimental protocol in the same room where the thermal loading tests took place. Hence, these results give a reference in terms of the overall equipment and software precision.

Epigraph chosen by Carla de Freitas Alves The divergences between field and model-obtained temperature curves during the first virtual hours of the simulation can be explained by the definition of an initial homogeneous temperature in the FE model (𝑇 0 = 20°C). However, within a few steps of calculation, the FE curves started fitting the temperature amplitudes and cycles observed in the field, with very good accordance in terms of magnitudes (Figure 69).

This result reassured that the thermal properties of the bituminous mixtures assumed for the calculations were representative of real field conditions. Moreover, it is concluded that, for this study, the hypotheses of heat transfers being represented by imposed temperature fluctuations at the upper surface of the pavement was satisfying. As expected, the rubbery components of the CU developed a thermal insulating effect of the area located below the assembly. More precisely, point PY1 was the most affected by this insulating condition. As we distant from the centre of the CU laterally, the less influence the unit had in the heat flow inside the structure. In point PC, which is at the same depth and also at the same layer as PY1, but closer to the borders of the charging unit, the influence of the rubbery materials was less significant. That condition was observed in the curves in Figure 71 for both pavements, with the temperature evolution of point PC remaining at an intermediary level between the evolutions of point PY1 and of the 0.10 m line-depth in the tRoads (measured from the surface).

In quantitative terms, a pseudo thermal gradient was calculated to compare the French and Brazilian pavements before and after the inclusion of the CU. This gradient was calculated by the temperature change at a given point to a reference fixed location divided by the distance between the point and the reference. In this study, the vertical gradient in points PY1 and PC was calculated in relation to the temperature in the surface, while the horizontal gradient was calculated by the variation in temperature amongst the points themselves. As an example, we can express the vertical pseudo gradient calculated in point PC by Equation 29. In Table 15, the vertical gradients for tRoads and eRoads are depicted (distance between 𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 and points PC and PY1 is 0.10 m, in depth). In Table 16, the horizontal thermal gradients for eRoad cases are depicted (distance between points PC and PY1 is 0.19 m in the transverse direction).

𝑝𝑠𝑒𝑢𝑑𝑜 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 (𝑃𝐶) = 𝑇 𝑃𝐶 -𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑦 𝑃𝐶 Equation 29Table 15. Vertical pseudo thermal gradients in points PY1 and PC. The vertical thermal gradient obtained for the Brazilian tRoad was almost two times the gradient obtained for the French tRoad. That is mainly explained by two parameters factors: the higher variation of temperature in the Brazilian pavement and the different thermal properties of the bituminous mixtures composing each pavement profile. The first factor is expressed by a higher daily variation of temperature in Brazil, coupled with a temperature not varying so much under the CU due to its insulating properties, which necessarily resulted in a higher gradient. The second factor is related to the thermal conductivity of the CBUQ mixture, which is lower than those of the BBSG and GB mixtures, meaning that heat was dissipated more slowly inside the Brazilian structure, leading to more in-depth inhomogeneity. As a reminder, the thermal gradient inside a solid is directly affected by the thermal properties of the material and its consequent ability to transfer energy.

Once the CU was included on the wearing surface of the pavements, the vertical pseudo thermal gradient increased for both structures as a consequence of the charging unit thermal insulating properties. Moreover, attention must be given to the generation of a horizontal thermal gradient due to the presence of the charging unit.

Even though this gradient appeared only directly below the unit, as observed in Figure 71, this local temperature attenuation as we moved from the corner to the central axis of the unit implies that the viscoelastic properties of the bituminous mixtures were also changing under this bulb of influence from the unit. That can lead to local changes in the strain response within the bituminous layers. The magnitudes of this horizontal gradient for the cases studied were very similar for both French and Brazilian structures (Table 16), highlighting once more that it is a major consequence of the CU thermal properties and not from the mixtures properties.

Deformed structures

From the complete thermal loading simulations (virtual 48 hours), the hour with the highest temperature on the surface in each pavement is depicted in terms of deformed structures (Figure 72 and Figure 73). The black lines represent the contour of the layers in the initial condition of the pavement, at a homogenous temperature of 20°C, and the red lines represent the contour of the structure when the maximum temperature is reached in the surface. The contours are amplified 30 times to give a better visualization of the differential volumetric changes of the eRoad components. The deformed structures give an indication that the most significant impact of the rigid inserts in the overall volumetric response of the structures happened at the surface level. The nearly-incompressibility property of the EPDM blend is clearly observed by the external spreading of the material, creating a sort of "bump" in the wearing surface, as it could not spread laterally due to technical reinforcement created by the bituminous layer. The elastomer-epoxy system, as the bonding material, was partially driven by the EPDM expansion and also kept from significant volumetric change by the bituminous mixture.

Displacement evolution

Based on the deformed structures depicted in the previous section, two points located in the upper line of the wearing surface were chosen for the investigation of displacement and strain evolutions due to thermal loadings. Points PS1 and PS2 are depicted on the French eRoad profile in Figure 74. The temperature evolution in both points is identical for each particular structure, as they belong in the 𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 line. The main objective of evaluating these points was to assess the influence of the differential thermomechanical response of the charging unit in the bituminous mixture close to the interface of the conductive system. In Figure 75 the plots of vertical and horizontal displacements in points PS1 and PS2 in French and Brazilian structures are depicted. As illustrated in Figure 75, the first important remark is related to the generation of previously non-existing horizontal displacements (𝑈 𝑥 ) after the inclusion of the CU.

Also on the horizontal displacements, one can verify that the points in the Brazilian structure endured slightly higher magnitudes of displacements than the ones in the French structure, and with a considerable lag between the imposed thermal loading and the response of the material. These higher magnitudes are possibly associated to the higher level of temperatures applied on the surface of the Brazilian pavement (Figure 76) in combination to the intrinsic viscoelastic properties of the CBUQ mixture itself. It seems that, for the CBUQ, the viscous effects were more pronounced, while the absence of phase shift on the French structure denotes a more elastic-like response of the BBSG. The horizontal displacement curves of points PS1 and PS2 in the French structure were not as smooth as expected, which can be related to the need of a finer mesh density in the area near the interface of the CU. Nevertheless, the relatively small magnitudes of this parameter allowed us to carry on with the analyses without recreating the meshes. In terms of vertical displacements (Figure 75), in the French pavement the curves mostly followed the same sinusoidal wave shape of the thermal loading curve, but without phase shift (time-dependent cyclic response of the bituminous mixture). As an example: at hour 12h the peak of temperature was reached on the French 𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 line (Figure 76(a)), and the peak of vertical displacement in point PS1 for the French tRoad was observed only at hour 16happroximately 4 hours later. For the French eRoad, the same trend was observed, only with a higher displacement magnitude than the ones obtained in the French tRoad. For the Brazilian pavement configuration, the tRoad vertical displacement curves mostly followed the same shape and trend as the thermal loading curve (Figure 76(b)), with a phase shift. However, the eRoad curves of vertical displacement did not only depict slightly higher magnitudes in point PS1, but also an out of phase response from the Brazilian tRoad curve itself. This is a good indication that the thermomechanical coupling model was effectively accounting for the rheological particularities of each bituminous mixture, represented by the GMM in terms of Prony series terms.

Similarly, as a result of the different viscoelastic characteristics of the BBSG and CBUQ, it is noticed that the peak-to-peak temperature fluctuation had a different impact in each structure. In the French tRoad and eRoad structures, that decrease in the vertical displacement almost reached the zero-value only to start increasing again as the temperature in 𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 increased. In the Brazilian eRoad, this drop was not so sharp, meaning that the CBUQ may require a longer resting period to release the thermally-induced displacement. An effect of accumulation of vertical displacement from day one to day two was also observed in point PS1 for both French and Brazilian structures.

Finally, in terms of proximity to the CU, the levels of horizontal displacements was attenuated as we moved away from the interface of the unit, in agreement with the deformed structures illustrated in the previous section. Despite the fact that the thermal loading in the Brazilian structure was higher in magnitude, the displacements calculated in PS1 and PS2 for both French and Brazilian structures remained in the same orders of magnitude (tenths of millimetres). The displacement evolutions in points PC and PY1 from the previous section are depicted in the Annexe E. As they are located 10 cm below the surface and protected from harsh daily-temperature fluctuations by the CU, the magnitudes of displacement were clearly smaller in points PC and PY1 than in points PS1 and PS2.

Strain evolution

The total strain calculated is the derivative of the total displacement. The reference adopted in this research is that positive strain values correspond to tensile strain, while negative values correspond to compressive strain. Moreover, εx is the horizontal or transverse strain (in the width of the road), while εy represents the vertical strain (in depth). In bituminous mixtures, tensile strains are major contributors to the initiation and propagation of cracks, and a parameter used for fatigue performance characterization in most design methodologies (horizontal strain at the bottom of the bituminous layer). The evolutions of strain in points PS1 and PS2 in French and Brazilian structures are depicted in Figure 77. The strain evolutions in the points PC and PY1 are depicted in the Annexe E. From Figure 77, it is observed that considerable high values of transverse compressive strain appeared in the surface after the inclusion of the charging unit:

nonzero eRoad(εx) curves, contrarily to the tRoad(εx) curves. Point PS1 was under two times more transverse compressive strain than point PS2 for both structures analyzed, French and Brazilian. That is again an indication that the influence of the thermallyinduced volumetric rearrangement in the CU cannot be neglected, as it affects the development of strain within the bituminous layer near the interface of the conductive system.

In terms of vertical strain, a simple direct comparison between tRoad and eRoad cases indicates that the presence of the CU generated additional strain in the surface of the pavement. This additional strain was attenuated as we moved away from the interface of the system transversally: εy in point PS1 is higher than εy in point PS2 (PS1 is 5 mm far from the interface, while PS2 is 30 mm distant). In order to understand the local concentration of thermal strain in the vicinities of the CU, eRoad strain fields for a given time of the thermal loading cycle are depicted in The focus is given to the impact of the CU on the thermomechanical response of the bituminous layer, and for this purpose the colour scale was mostly adapted to the levels of strain inside the wearing surface (from -2,000 𝜇𝜀 to 2,000 𝜇𝜀). The saturated red observed in the rubbery materials in the vertical strain plots points out the significant differential thermomechanical properties of the eRoad components: the rubbery materials undergo higher thermal strain magnitudes due to temperature fluctuations, while the generation of thermal strain in the bituminous mixture was much smaller (coeff. of thermal expansion of EPDM and Corkelast VA-60® were in the order of magnitude of 100 × 10 -6 m/(m⋅°C); coeff. of linear expansion of the bituminous mixture was assumed to be equal to 27 × 10 -6 m/(m⋅°C)). Moreover, the strain was dissipated as we moved away from the CU laterally and in depth in the pavement profile, even while remaining near the interface axis.

Table 17 depicts the strain magnitudes calculated in points PS1 and PS2 for the virtual hours depicted in Figure 78. The strain at the bottom of the bituminous layer is also depicted for comparative purposes. It is important to remind that the bottom of the bituminous layer in the French pavement is at -0.34 m from the surface, and at -0.12 m from the surface in the Brazilian structure. The values depicted in Table 17 for these ordinates were obtained on the symmetry axis of the 2-D geometries, at the same depth of point PY1. For the French tRoad structure, which was a robust flexible pavement with a total bituminous layer thicker than 0.30 m, the vertical and horizontal thermal strain at the bottom of the bituminous base course was significantly small when the temperature reached its maximum in the surface of the pavement (less than the average strain induced by traffic loads). Once the CU was inserted, these magnitudes decreased at the bottom of the bituminous layer in the French eRoad. These strain variations can be observed from the values depicted on the right columns of Table 17. For the Brazilian tRoad, the levels of vertical and horizontal strain were significantly higher than the ones observed in the French tRoad. The reduced total thickness of the bituminous layer (approximately one third of the French structure) and the thermomechanical properties of the mixture contributed to that divergence. When the CU was included, the thermal strains at the bottom of the Brazilian bituminous wearing surface also decreased. In the context of daily-temperature variations during a warm season, one can conclude that the inclusion of the CU can lower the strain magnitudes at the bottom of the bituminous layer, as a consequence of the thermal insulation of the area under the unit and the conservation of its viscoelastic characteristics mostly constant (throughout the width of the charging unit).

For all the configurations studied, in point PS1 the levels of strain were higher than in point PS2. As we moved away from the interface laterally, the influence of the CU was less marked, and the dissipation of the strain was directly influenced by the viscoelastic properties of the mixture composing the wearing surface. By the plots in Figure 78 and the evolution of strain in point PS1 in Figure 77, it is noted that using the levels of strain in the bottom of the bituminous layer as the single parameter to predict the fatigue life of eRoad structures can be misleading. The magnitudes of strain endured by the bituminous mixture in the surface near the interface of the CU was very high, which can generate thermal cracking distresses solely due to daily-temperature variations.

Stress evolution

The evolutions of stress in points PS1 and PS2 in French and Brazilian structures are depicted in Figure 79. The stress evolutions in points PC and PY1 are found in the Annexe E. If the temperature in the surface of the pavement at 28h is compared to the initial no-stress homogenous temperature condition of 20°C, one may expect from a simple analysis that no stresses should be generated, at least in the first centimetres of the road in depth (Figure 82). Indeed, the levels of tensile stress were small (less than 0.1 MPa), but not homogenous in the transverse direction due to the influence of CU behaviour. Another important remark concerns the need of evaluating the thermallyinduced stresses not solely associated to the magnitudes of the temperature in the road at the time of the analyses. The history of thermal loading of the road (residual strain and stress) in combination to the viscoelastic properties of the mixture play a significant role on the total amount of stress endured by the structure.

Summary

The simulations recreated a total of two real night-to-day temperature fluctuations (48 hours) in two traditional flexible pavements (France and Brazil). The two locations of the road profiles were characterized by mild winters and warm summers. The temperature evolution calculated using the thermomechanical FE-model in Cast3M®

was compared to field data and the differences found between the values measured were very small. This means that the proposed model and parameters well defined the heat flow inside the structure. Thanks to the calculation of the temperature evolution inside the structure for each virtual hour of the thermal loading simulations, it was possible to investigate the hour-to-hour evolution of the thermally-induced mechanical fields (displacement, strain and stress) before and after the inclusion of the conductive charging unit. The CU was included in the wearing surface of the flexible pavements, directly exposed to environmental loadings. It is important to recall that the equilibrium temperature was initially defined as 20°C, the same temperature of reference used to determine the properties of the materials; and that the amplitude of fluctuations of temperature in the surface of the pavements reached in average 25°C in 12 hours.

A few points located in the bituminous layer in the vicinities of the CU in vertical and transverse directions were investigated in terms of thermomechanical response due to thermal loading. As temperature increased in the surface, the rubbery materials composing the CU expanded at a higher rate than the bituminous mixturea direct consequence of their differential thermomechanical properties. Since the EPDM blend is nearly-incompressible and the CU was fully bonded to the bituminous layer and blocked from lateral spreading, the unit expanded upward and generated a significant amount of compressive transverse strain in the bituminous mixture near the interface of the CU. In depth, the isolating properties of the rubbery components kept the area below the CU from undergoing significant temperature fluctuations. This insulation generated a variation in the vertical pseudo thermal gradient as we moved laterally from the area below the CU to the lateral extremities of the driving lane, in the width direction of the road. The evolution of the thermomechanical fields inside the rubbery materials was depicted in the results, but were not deeply analysed in the scope of this study.

The inclusion of the CU resulted in inhomogeneous vertical and transversal thermal field evolutions inside eRoad pavements, affecting the structural response of the road locally. In all of the comparative cases, the area near the edges of the CU in the surface of the bituminous layer was the most affected in terms of strain and stress generation. The repeated volumetric variations in the CU due to temperature fluctuations generated strain in the bituminous layer that can lead to damage due to thermal fatigue. For a point located in the bituminous layer in the surface (y = 0 m) and distant only by 5 mm from the interface with the elastomer-epoxy system, the maximum transverse strain calculated reached orders of magnitude of -2,000 μm/m in the French structure (𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = 39.1°C) and of -1,000 μm/m in the Brazilian structure (𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = 46.1°C). The level of strain in the surface of the tRoads for the same thermal loading configuration was nearly zero in the transverse direction and with orders of magnitude of 1,000 μm/m in the vertical direction.

For comparison, magnitudes of transverse strain obtained at the bottom of the bituminous layers in real road sites instrumented with strain gauges ranged from: 504 to 1,600 μm/m for temperature fluctuations of 20.2°C (BAYAT; KNIGHT; SOLEYMANI, 2012); from 200 to -684 μm/m for temperatures varying from 11 to 31°C in warmer months, and -2 to -12.5°C in colder months (BISWAS; HASHEIMIAN;

BAYAT, 2016). Hence, the magnitudes of strain numerically obtained in the tRoad simulations are within the ranges of thermally induced strain experienced in field. This a good indication that the FE-model constitutes a reliable tool for a first thermomechanical analysis of flexible pavements. In the eRoad, the level of transverse strain obtained at the bottom of the bituminous layer and under the symmetry axis of the CU ranged from 93 to -115 μm/m (Brazilian eRoad) and from 6 to -47 μm/m (French eRoad). These values are smaller than the thermally-induced strain measured in real roads reported in the literature and also below admissible strain values traditionally obtained due to traffic loading. For the cases analyzed, the strain was attenuated after the inclusion of the unit in both French and Brazilian profiles at the bottom of the bituminous layer and under the CU.

In terms of thermal strain and stress generation, temperature had a double impact: it was responsible for the expansion and contraction of the eRoad components and for the viscoelastic response of the bituminous mixture. In the configurations analyzed, the differential thermomechanical properties of the rubbery materials and of pavement layers lead to the concentration of stress in the bituminous wearing surface, mainly near the interface with the CU. In the Brazilian eRoad configuration, the evolution of strain and stress was delayed from the thermal loading cycle, an indication of the thermal inertia phenomenon of the bituminous mixture composing the pavement wearing surface and its level of susceptibility to temperature. As the CU was kept equal in the two eRoad scenarios (French and Brazilian), the different evolutions of mechanical fields within the bituminous layers was a good indication that the temperature-dependent viscoelastic properties of the mixtures are well represented by the Prony series with respect to the relaxation modulus (Generalized Maxwell Model).

In addition, careful attention must be given to the proper characterization of the input thermal and mechanical properties of the bituminous mixtures for numerical analyses.

Finally, the thermos-viscoelastic model proposed constitutes a powerful tool to pre-design and to assess the behaviour of flexible eRoads. The analysis of the thermally-induced mechanical fields seems to be a suitable methodology to investigate local concentrations of strain and stress that can lead to premature failure of the structure. Traditional strain-based parameters at the bottom of the bituminous layer can present different magnitudes if they are obtained under, near or far from the CU symmetry axis. The use of FE-based models gives the possibility of assessing any component of mechanical fields at one or several depths, and to evaluate the thermal loading history of the pavement. In the structures numerically assessed, the thermallyinduced stress was not totally released after peak-to-peak cycles. Further analysis need to be performed in terms of irrecoverable deformation and loading cycle accumulations. Additionally, the current thermomechanical simulations can be used to evaluate bonding materials and adapted geometric assemblies for specific local conditions, in regards of environmental aspects.

Case II -Thermal and mechanical loadings

In this section, the mechanical loading due to the passage of a heavy vehicle was simulated using two climatic scenarios: a) an overall equivalent temperature in the pavement, and b) a temperature profile within the structure that represents the warmest hour of the day, obtained from the previous thermal loading simulations. For the French structure, the temperature profile corresponds to midday in Case I (12h);

and for the Brazilian structure it corresponds to 15h in Case I. The flowchart on Figure 83 summarizes the procedure used to simulate the cases contained in this section. For all the cases, an ideal condition of use in terms of vehicle circulation was adopted, meaning that there was no lateral misalignment between the CU and the centre of the vehicle (location of the pick-up collector). The wheel axis was far from the symmetrical centre of the road in approximately 0.9 m, in the transverse direction. The mechanical parameters evolutions were investigated in the points depicted in Figure 84, in accordance to the locations commonly used for analyses focusing on rutting and fatigue models. In Figure 84 zero. In the particular case of line L3, which was located in the transition of the laterally free bituminous layers and the blocked roadbed, the over constraint of the system resulted in the maximization of the strains calculated. Nevertheless, for the purpose of this study, the divergences were considered minimal as the main interest remains in the maximum strain value calculated under the axis of the wheels. Hence, the equivalence of loading conditions was considered valid based on the overall similarities observed in the calculated strains under the load application in lines L1, L2 and L3.

As the loading equivalence was fitted in terms of horizontal tensile strain by an equivalence of loading magnitudes per areas in the surface of the structure, the stress distributions obtained in Cast3M® within the pavement profile may have not represented the real field configuration. As an example, Figure 86

Displacement evolution

In Figure 87, the vertical displacement evolutions for the points located at the surface of the pavements are depicted. Point PS3 is located below the symmetric centre of the two wheels and point PS4 is located in the centre axis of the most external wheel in the transverse direction of the road. The abbreviation 'Teq' in the curves denominations refers to the cases where an equivalent temperature was assumed in the structure, while 'TS' refers to the temperature in the surface for the cases that considered the temperature profile from a given hour of the day. In the simulations performed using the French profile, the equivalent temperature was set to 15°C, and in the Brazilian profile simulations the equivalent temperature was set to 25°C. Even though the maximum vertical displacements were found slightly inferior in the TS curves in comparison to the Teq cases, the variation between the displacement at initial no-loading condition and at the moment corresponding to the maximum loading application remained very similar (approximately 0.5 mm for the French structure and 0.6 mm for the Brazilian structure). These absolute maximum displacements calculated in the surface of the pavements may not be representative of the real magnitudes experienced in field, due to the 2-D boundary and loading conditions simplifications assumed for the calculations. In general, the similarities of the results in French and Brazilian eRoad structures reassured that the inclusion of the CU is not expected to change significantly the levels of displacement under the wheels when the vehicles circulate relatively far from the unit, as also stated by [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF][START_REF] Chen | Towards an understanding of the structural performance of future electrified roads: a finite element simulation study[END_REF].

According to the discussions of [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF], an important parameter in the assessment of eRoads is the gap between the wearing surface and the CU in order to avoid drivability issues. In Figure 88, the differential behaviour of the eRoad components due to thermal and mechanical loadings can be observed for both From the shapes of the displacement curves depicted in Figure 88, it is concluded that evaluating the displacements solely below the wheel axis ignores an important phenomenon of differential volumetric behaviour of the CU in comparison to the pavement layers. In both cross-sections, French and Brazilian, the elastomeric materials expanded significantly due to the peak of warm temperature in the surface.

In combination with traffic-induced loadings, which generated displacements on the opposite direction than the ones resulted from the volumetric expansion, a gap was observed between the symmetrical centre of the roads and the wheel path, in the transverse direction. In the scenario evaluated, the calculated gap was of 0.29 mm in the French eRoad and of 0.63 mm in the Brazilian eRoad. These absolute values alone may not trigger pavement management maintenance procedures in conventional roads, but in the specific case of eRoads it may indicate issues in the connection between the pick-up arm and the CU by the reduction of the air gap between the vehicle and the power delivery system. Additionally to that, attention must be given also to the drastic change of behaviour endured by the elastomer-epoxy system. The more divergent the thermomechanical behaviour between the bituminous layer and the bedding of the electric rails, more importance needs to be given to the selection of suitable bonding materials in order to perform a smooth layer transition for every loading configuration possible.

Strain evolution

In Figure 89, the evolutions of strain are depicted in points PB3 and PB4 of the French structure (depth of 0.34 m from the surface), and in points PF3 and PF4 of the Brazilian structure (depth of 0.12 m from the surface). The sequence of mechanical loading pulses are also plotted on a secondary axis. As illustrated in Figure 89, the French pavement structure endured very similar levels of tensile strain at the bottom of the bituminous layer in points PB3 and PB4 for the cases simulated (tRoad, eRoad, Teq and TS). Again, an indication that for a robust structure like the French flexible pavement, no significant differences are observed in the evolution of strain in the bituminous layer under the wheel for tRoad and eRoad, in ideal conditions of use. The horizontal tensile strain displayed an increasing trend with time of loading for the longest mechanical pulse, which was a result of the timedependent response of the bituminous material to loading accounted in the model by the GMM. The maximum values were observed for the cases that considered the initial environmental condition from thermal loading simulations.

For the Brazilian pavement, the Teq curves were superposed, while the TS curves depicted different and higher magnitudes of strain. Similarly to what happened in the displacement evolution, this difference between Teq and TS curves is mainly explained by the initial non-zero strain of the TS curves due to the strain history from thermal loading cycles. Particularly for point PF3 in the Brazilian structure, a decreasing trend with time was noticed for the tensile strain in the TS cases. Table 18 summarizes the peak of horizontal tensile strain obtained in each point of analysis for both French and Brazilian structures. From the curves in Figure 89 and the values in Table 18, it is observed that the absolute strain variation between the initial no-loading condition and the moment corresponding to the maximum loading application remained within admissible levels of strain reported in the literature for flexible pavementsfrom 10 to 250 𝜇𝜀 [START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF]. Looking at fields, however, a concentration of strain near the vicinities of the CU was observed due to thermal and mechanical loadings. In Figure 90 and Figure 91, the strain distribution inside the French and the Brazilian eRoad structures is depicted for the case in which the temperature profile from thermal loading simulations was considered. When an equivalent temperature was adopted everywhere in the pavement, no differential behaviour was observed in the vicinities of the CU, as the only source of strain was the traffic loading, which is located far from the system in this case. The levels of strain resulted from one single passage of a heavy vehicle were significantly smaller than the strain resulted from temperature fluctuations, in accordance to fields measurements in flexible pavements by BAYAT, [START_REF] Bayat | Field monitoring and comparison of thermal-and load-induced strains in asphalt pavement[END_REF]. The different scale of strain range between thermal and mechanical loadings resulted in the use of a colour mapping adjusted to the levels of thermally-induced strain, with only the bituminous layers being depicted for better visualization. The main purpose is to have an overall understanding of the critical areas where the differential thermomechanical behaviour of the eRoad components may develop strain. The frames depicted in Figure 90 it is distant from the horizontal interface of the CU in 10 mm (y = -0.09 m). The evolution of strain in these points is depicted in Figure 93. Due to the impossibility of plotting the evolution of strain at every point in the same scale of magnitudes, it was chosen to set the scale to a fixed quantity of units between the maximum and minimum limits of each axis. In the left axis, in black colour, the horizontal strain is plotted and the limits vary in 80 units (𝜇𝜀); in the right axis, in red colour, the vertical strain is plotted and the limits vary in 8 units (𝜇𝜀). The strain resulted from the thermal and mechanical loadings depicted in Figure 93 corresponds to the thermal loading time at 12h in the

French pavement and at 15h in the Brazilian pavement. From the plots in Figure 93, for the French pavement structure, all the points were under compressive strain in the horizontal direction and tensile strain in the vertical direction. The maximum strain values were observed in the surface level, which were a direct consequence of the thermally-induced strains. The more we moved in depth, the more the traffic-induced strains were noticed. In the Brazilian structure, the horizontal strain did not follow the same trend for all of the points. In the surface (point P1), compressive horizontal strains were observed, with two times less the magnitudes than the ones observed in the French structure, despite enduring a higher temperature in the surface. As we moved in depth, points P2 and P3 displayed tensile horizontal strains due to thermal loadings that were comparable to the strain levels observed at the bottom of the bituminous layer under the wheel axis in flexible pavements. This is an important indication that these areas may be susceptible to fatigue simply due to daily temperature fluctuations. In point P4, compressive horizontal strains were also observed. In terms of vertical strain developed in the Brazilian structure, all of the points depicted tensile deformation, and in very similar magnitudes as the one depicted in the points on the French structure.

For illustrative purposes, the horizontal strain fields in the eRoad structures are depicted with a colour mapping scale adjusted to traffic-induced loadings in Figure 94 (-42 to 42 𝜇𝜀). In Figure 90 and Figure 91, the scales set for thermally-induced loadings (-2,000 to 2,000 𝜇𝜀) did not allow the visualization of the critical strain distribution near the corner of the CU (Figure 93). In

Stress evolution

The vertical stress evolutions in the points located on top of the subgrade of the pavements are depicted in Figure 95. In terms of stress magnitudes, the values calculated locally were not a result of the total mechanical loading, which was applied over an area in Cast3M® and divided in loading pulses. In this way, the analyses were conducted solely for comparison amongst the numerical cases and not compared to stress magnitudes measured in the field monitoring of real flexible pavements.

Point PB3 is located below the symmetric centre of the two wheels and point PB4 is located in the centre axis of the most external wheel, in the transverse direction of the road. From the frames depicted in Figure 96 and Figure 97, it is observed that the horizontal stress in the French and Brazilian eRoads followed a similar pattern. Near the interface of the CU, a zone with no stress generation was observed, in a shape of an inverted right-angled triangle (the right angle is at the top left corner). In the Brazilian eRoad, a local concentration of horizontal compressive stress was observed in the surface near the CU. In terms of vertical stress, it was observed that the traffic-induced stress was developed far from the CU under ideal conditions of use and that the concentration of stress near the surface of the CU was a result of the thermal loading cycle applied. The evolution of stress in points P1 to P4 (Figure 92) is depicted in From Figure 98, one can observe that the traffic-induced loading had a bigger impact in the evolution of stress in the French eRoad structure in comparison to the Brazilian eRoad. Points P3 and P4, which were located near the triple corner (elastomer-epoxy system, BBSG and GB) in the French pavement, displayed peaks of stress in both vertical and horizontal direction when the maximum loading pulse was applied and released. This immediate and local increase of stress can lead to the debonding of the CU from the bituminous layer near the corner of the CU, even in ideal conditions of use, when the wheel path is far from the power delivery system. One must remember that the magnitudes of stress are possibly underestimated due to the loading equivalence per area (3-D to 2-D loading equivalence), and that these simulations considered the application of only one mechanical loading cycle. Thus, if one considers a higher magnitude of loading and the repetitive aspect of traffic, it becomes essential to consider the geometry of the CU and the existing pavement profile in early design stages as to avoid the creation of critical zones for stress concentration (e.g. right-angled corners to fall in-between two different pavement layers). During the static application of each loading pulse, the relaxation of the stress in the points was observed, a good indication that the viscoelastic behaviour of the bituminous mixtures was taken into account in the model. Finally, in terms of stress evolution near the CU, an important conclusion is that the development of stress in the surface level was more a consequence of the thermal loading and the differential behaviour of the eRoad components; while in depth the influence of temperature fluctuations was less noticed and the stress generation was in the majority a consequence of the traffic loading.

Summary

The main objective of the simulations performed in this section was to evaluate the combined effect of traffic and thermal loadings in eRoads, and to compare it with the response of tRoads to the same solicitations. In this way, the mechanical loading due to the passage of a heavy vehicle was simulated using two climatic scenarios: a)

an overall equivalent temperature in the pavement (Teq), and b) a temperature profile within the structure that represented the warmest hour of the day (TS). The temperature profiles were obtained from simulations that recreated a total of two real night-to-day temperature fluctuations (48 hours). For the French structure, the temperature profile in which the mechanical loading was applied corresponded to the temperature of the pavement at midday of the first virtual day; for the Brazilian structure it corresponded to the temperature of the pavement at 15h of the first virtual day. The loading condition described two wheels with radius of 0.125m and a centre distance of 0.375m. The distance between the symmetry axis and the centre of the most external wheel was 1.075m (no wheel wander consideration) and the vehicle velocity was defined as 60 km/hthe minimum required to enable the eRoad power delivery system to be activated. ). The results obtained from the two software were mostly equal, especially in terms of maximum horizontal tensile strain developed at the bottom of the bituminous layer below the symmetric centre of the two wheels axis, at half duration of the total loading (maximum mechanical loading). For the purpose of this study, the equivalence of 3-D to 2-D wheel loading conditions was considered valid. The methodology used relied on the equivalence of total loading per area, and the moving aspect of the wheel passage was accounted by a sequence of pulse loads. In that sense, attention must be given to the fact that the levels of stress calculated using the software Cast3M® were possibly underestimated. Nevertheless, the numerical cases were compared in terms of displacement, strain and stress evolutions in predefined points in order to evaluate the impact of the inclusion of the CU in the structural response of the pavement.

In traditional M-E methodologies, the stresses and strains due to climatic variations are commonly addressed by means of an equivalent temperature consideration. In mainland France this equivalent temperature is set to 15°C, and in Brazil it is usually considered as 25°C. From the results of the coupled thermal and mechanical viscoelastic simulations, one can conclude that when an equivalent temperature was adopted everywhere in the pavement no differential behaviour was observed between the CU components and the pavement layers. In ideal conditions of use (no lateral misalignment between the CU and the centre of the vehicle), the displacement, the strain and the stress distributions inside the eRoad were found very similar to the ones observed in tRoads. In the Teq cases, strain and stress were mostly developed below the wheel application as a consequence of traffic. In reality, the variation of temperature in the surface of the pavement is responsible for the generation of additional strain and stress in the bituminous layer near the interface of the CU. Points analysed in the proximity of the CU in the surface for the TS cases were under high levels of compression due to the higher expansion rate of the elastomeric materials in comparison to the bituminous mixture. Hence, numerical analyses of eRoads using the concept of an equivalent temperature and solely ideal wheel Especially in open-air systems like the conductive ERS analyzed, the compatibility of the CU components and the viscoelastic properties of the bituminous mixtures needs to be carefully evaluated using an accurate recreation of the environmental conditions of the pavement location. The differential behaviour in terms of response to thermal loadings was more pronounced in the surface, in the bituminous layer near the interface of the CU. Moreover, the scenarios evaluated in this study considered warm thermal loadings. In regions going through cold seasons, the opposite behaviour in terms of volumetric strain could be very harmful for the structure. The generation of transverse tensile strain in the surface of the bituminous layer as temperature decreases and the CU contracts could lead to immediate and severe thermal cracking.

In terms of traffic-induced strain and stress in combination to thermal loading, differences were observed between the fields inside the French and the Brazilian eRoads. As an example, a local concentration of vertical traction stress near the vertical interface of the CU in the Brazilian pavement was observed in the TS case.

This concentration did not appear in the French structure, which displayed a local concentration of vertical compressive stress in the bituminous mixture near the rightangled corner of the CU, in depth. These divergences are possibly explained by the different location of the CU inside each structure and on how the new profile responded to the distribution of strain and stress generated by the wheel passage. In the Brazilian profile, the CU was fully located in the wearing course, which had a total thickness of 12 cm. In the French structure, the bottom of the CU rested in the interface between two bituminous layers with different viscoelastic properties, and the total thickness of the bituminous layers was 34 cm. More investigations are needed in order to propose an adapted geometry for each pavement profile, also taking into consideration the approximation of the wheel to the system (lane changing condition).

Finally, the main result of the thermomechanical numerical simulations discussed in this section is the validation of the thermo-viscoelastic model implemented in the FE software Cast3M®. The approach was found to be adequate for the configurations of From the plots in Figure 102 it is observed that, for the EPDM blend, CTE and CTC converge to a common value when the region of interest starts to cover more than 30% of the total surface area. For Corkelast VA-60®, CTE and CTC follow the same trend regardless of the size of the ROI. Hence, it was decided to assume a single thermal coefficient for each elastomeric material (hypothesis of isotropy and homogeneity), which consisted in the mean value between CTE and CTC calculated for the biggest ROI analysed (70% of the total surface area of the specimen). The measured thermal coefficient of the EPDM blend was 2.39 × 10 -4 °C-1 . The measured thermal coefficient of Corkelast VA-60® was 1.73 × 10 -4 °C-1 .

Aiming to verify the reliability of the coefficients calculated using the DIC technique, a third-party company was requested to perform thermal tests on the elastomeric materials using a LINSEIS L75 dilatometer (Figure 103). In these tests, an EPDM specimen (10 x 10 x 6 mm) and a Corkelast VA-60® specimen (10 x 10 x 8 mm) were pressurized by a mobile quartz piston. A constant force was applied over time while a furnace imposed a temperature rise ramp (-10°C to 60°C), during which the evolution of the elongation of the specimen was measured by an inductive sensor.

The measuring system had a digital resolution of 0.125nm. The heating rate was set at 2K/min for all the measurements, in order to avoid the appearance of thermal gradients in the sample. The thermal coefficients obtained were: 2.18 × 10 -4 °C-1 for the EPDM and 1.42 × 10 -4 °C-1 for Corkelast VA-60®. These values are in good accordance with the ones calculated by means of the DIC technique.

Figure 103. Linseis DIL L75 PT Horizontal: high vacuum tight dilatometer (©2022 LINSEIS GMBH).

Bituminous mixture

The same experimental methodology used to obtain the thermal coefficients of the elastomeric materials was applied to determine CTE and CTC of the bituminous mixture (tRoad specimens). Table 19 summarizes the characteristics of the tRoad specimens tested in this part of the study. The air voids content and the density of the specimens were determined using a non-destructive method, based on the absorption of gamma rays (NF P 98-250-5 guideline). The measurements were taken by means of a vertical gamma-densitometer bench, in a ''continuous" mode: in every line intersection of a one-by-one centimetre virtual square grid. The final values represent the mean value of 468 measured points. Specimens CP01 and CP04 were subjected to cold cycles, while CP02 and CP03 went through warm cycles (CP05 and CP06 were not evaluated because they were used for the study of speckle patterning techniques). An example of the temperature evolution in the specimens and inside the climatic chamber is depicted in Figure 104 (CP01 on the left and CP03 on the right). Each specimen tested was placed inside the climatic chamber overnight and was conditioned at a temperature of 20°C for 4h prior to the acquisition of the reference image, to homogenize its temperature. The size of the images was set to 5120 x 2074 pixels 2 . Different regions of interest were also used for the DIC analysis of the bituminous mixture. The initial and final temperatures in the specimens as well as the magnification of the imaging system (in units of mm/pixel) are displayed in Table 20. All the DIC analyses were carried out with a subset radius of 20 pixels, a subset spacing of 5 pixels and a strain spacing of 4 pixels. In Figure 105, the calculated CTE and CTC for the tRoad specimens are depicted in relation to the ratio of the ROI and the total surface area of the specimen (in percentage). CHEN et al., 2015a;ISLAM;[START_REF] Islam | Measuring thermal effect in the structural response of flexible pavement based on field instrumentation[END_REF][START_REF] Teguedi | Towards the local expansion and contraction measurement of asphalt exposed to freeze-thaw cycles[END_REF][START_REF] Vu | Experimental study and modeling of the behavior of partially saturated asphalt concrete under freezing condition[END_REF]XU;[START_REF] Xu | Measurement and evaluation of asphalt concrete thermal expansion and contraction[END_REF]. In addition, some of these studies report the nonlinear behaviour of CTC and CTE in bituminous mixtures with temperature change, measured by means of field and laboratory investigations.

The BBSG used in this research is a dense graded mixture (12.5 mm maximum size of the aggregates) with 6% of air voids content. An anisotropic behaviour certainly appears due to the slab compaction method employed and the consequent random air

Thermomechanical behaviour of eRoad specimens subjected to thermal loading cycles

In this section, the DIC technique was used to measure the kinematic fields (displacement and strain) of eRoad specimens subjected to thermal loading cycles.

Six eRoad specimens were tested inside the climatic chamber according to the methodology described in Chapter 4. Each eRoad specimen tested was placed inside the climatic chamber overnight and was conditioned at a temperature of 20°C for 4h

prior to the acquisition of the reference image. The size of the images was set to 5120 x 2074 pixels 2 . Two different approaches were used to assess the behaviour of the specimens: a macroscopic qualitative analysis of the thermally-induced kinematic fields and a quantitative analysis of the horizontal displacement evolution using virtual strain gauges.

In the first approach, the analysis was performed using a ROI which covered the maximum surface area of the specimens. The deformed image taken at the end of Phase I (begin of Phase II) was compared to the reference image, which aimed at investigating the response of the specimen to a critical daily-temperature fluctuation scenario, i.e. a thermal gradient of approximately 30°C in the pavement in 12h. In the second approach, two virtual strain gauges of 3 x 3 cm were placed in the bituminous mixture, on either sides of the elastomeric components and at mid-height of the specimen. The approximation and distancing of these gauges in the horizontal direction were calculated using the images acquired during Phase II of the thermal loading cycle, when the specimens returned to room temperature after reaching the peak of the warm (or cold) loading cycles. The same pair of virtual strain gauges was placed on the tRoad specimens, in order to measure the approximation and distancing of these gauges on a conventional bituminous mixture specimen. The impact of the rigid inclusions on the thermomechanical behaviour of the bituminous mixture was evaluated by comparing the results obtained in eRoad and tRoad specimens. In Table 21, the characteristics of the eRoads specimens are displayed as well as the magnification of the imaging system (in units of mm/pixel) for each set of images studied. The reported physical dimensions (length, height and thickness) are a mean value of five measurements taken at different location of the specimens.

Macroscopic qualitative analysis

In this section, the kinematic fields calculated by means of the Ncorr software are presented. As aforementioned, the reference image was acquired after a conditioning phase which lasted 4h, and the deformed image was acquired when the specimen reached the maximum (or minimum) temperature at the end of Phase I. Examples of the temperature evolution in the components of eRoad specimens and inside the climatic chamber are depicted in Figure 106 and Figure 107. The temperatures in every component of the eRoad specimens for reference and deformed images are summarized in Table 22. The DIC analyses were carried out with a subset radius of 20 pixels, a subset spacing of 5 pixels and a strain spacing of 4 pixels. The Ncorr software provides an interface for the visualization of the calculated displacement (𝑢 𝑥𝑥 and 𝑢 𝑦𝑦 ) and strain (𝜀 𝑥𝑥 , 𝜀 𝑥𝑦 and 𝜀 𝑦𝑦 ) fields. The plots colour map can be adjusted in terms of transparency and upper and lower bounds. The eRoad specimens are multi-composite material systems, in which the components behave differently and by consequence display different deformation intensities. Initially, the upper and lower bounds of the colour map were set according to the theoretical thermal strain expected in the bituminous mixture (Equation 30).

𝜀 𝑡ℎ𝑒 = 𝛼ΔT

Equation 30

The absolute mean value of ΔT in the bituminous mixture was 27°C and the thermal coefficient 𝛼 assumed was the mean value of the CTC (1.47 × 10-5 °C-1 ) and CTE (2.59 × 10-5 °C-1 ) calculated by means of the DIC technique. The initial upper and lower bounds of the colour map were ± 548 𝜇𝜀.

As discussed throughout this study, the macroscopic deformation of a solid is also a result of the combination of several physical mechanisms. In this particular thermal loading test configuration, the thermomechanical behaviour of the eRoad specimens could not be analytically predicted and the use of the theoretical values was found to be limited and too simplistic (the strain fields were fully saturated and did not provide valid conclusions from the performed tests). With the invalidation of the initial upper and bound colour scale values, and after several combination trials, it was decided to set to the bounds equal to ten times the theoretical thermal strain expected in the bituminous mixture (10 × 548 𝜇𝜀). For simplicity, these values were rounded to ± 6000 𝜇𝜀. From the plots in Figure 108 and Figure 109 it is observed that some regions continue to depict saturated red and blue colours. However, enlarging the colour map bounds to the levels of strain in the elastomeric components would neglect the critical concentration of strain in the bituminous mixture, which is the focus of the analyses. In this way, the following discussions are performed based on the overall displacement and strain distribution in the surface of the specimens. In terms of displacement fields, the two thermal loading cycles resulted in movements of the specimens in the opposing direction. The EPDM blend, as the material with the highest thermal coefficient magnitude and responsible for the second biggest volume share of the eRoad specimen is believed to lead the overall behaviour of the assembly (in terms of volume percentage the eRoad specimens are constituted by: 47% of bituminous mixture (aggregates, binder and air voids), 35% of EPDM and 18% of Corkelast VA-60®). In warm cycles, the EPDM strong expansion in both x and y directions bended the specimen to a concave down shape. In cold cycles, its contraction bended the specimen to a concave up shape. From the displacement fields in Figure 108 and Figure 109, one can also observe that the bending phenomenon occurs asymmetrically about the y-axis (𝑢 𝑥𝑥 plot).

In terms of strain fields, the zones with a concentration of red colours indicate significant tensile strain and the zones with intense blue colours indicate significant compressive strain. In a parallel analysis to the results obtained by means of FE numerical simulations (Chapter 5), the strain distribution resulted from warm cycles corroborates to the assumption that an important impact of the rigid inclusions in the volumetric response of the structure happens at surface level. In the three specimens tested in warm cycles, the surroundings of the charging unit in the surface level displayed high levels of compressive strain in the horizontal direction (𝜀 𝑥𝑥 ). The corners of the charging unit, in depth, were also identified as critical zones for strain concentration. These significant strains were passed on to the other components, laterally in some cases and vertically in others. In the horizontal direction, for the warm cycle cases, the tensile strain from the elastomeric materials was transmitted to the bituminous mixture layer immediately below the rigid inclusions, under the trench. The level of tensile horizontal strain that reached the bituminous mixture under the CU is concerning as it may lead to damage from cracking initiation and propagation (strain magnitudes above 6000 𝜇𝜀). The behaviour of the elastomeric materials, which deformed horizontally similarly to the silhouette of tree roots, requires deeper investigations. Nevertheless, this trend appeared in all of the experimental results and it was assumed as a characteristic of the material. In terms of vertical strain due to warm cycles, the expansion of the elastomeric materials tends to create an effect of "ejection" of the unit from the specimen, which reflects on the local concentration of compressive strain near the corners of the CU under the trench. The majority of the interface perimeter of the bituminous mixture and the CU was under tensile strain (𝜀 𝑦𝑦 ).

From the specimen subjected to cold cycles (Figure 109), a first observation of the horizontal strain distribution highlights the strong concentration of tensile horizontal strain along the vertical interface of the bituminous mixture and the elastomer-epoxy system. In opposition from what was observed during warm cycles, but with an equivalent intensity and silhouette, the elastomeric materials tend to shrink when facing cold temperatures. Their strong volumetric change is not completely followed by the bituminous material due to its reduced coefficient of thermal contraction, intrinsic viscoelastic behaviour (stress relaxation), physical characteristics (weight and gravitational contribution) and test boundary conditions (resistance to the movement due to base friction). In terms of pavement design, tensile horizontal strains are generally linked to cracking and failure of the structure. The observations of the strain fields in eRoad specimens subjected to cold cycles reinforce the existence of a differential thermomechanical behaviour of the components, which can easily lead to the debonding of the assembly vertically (from top to bottom). The opening of cracks in the wearing surface of conventional flexible pavements affects the integrity of the structure as it gives place to water intrusion. In the case of an eRoad, the possible contact of electrified wiring and water present in the pavement constitutes an alarming source of hazard for the safety of users.

The temperature evolution in the components of the remaining eRoad specimens and inside the climatic chamber are depicted in Figure 110 to Figure 114. Figure 114 to Figure 117 depict the displacement and strain fields of the eRoad specimens: CP08 and CP09 specimens (warm cycle); and CP11 and CP12 specimen (cold cycle). For orders of magnitude of the displacements, Table 13 summarizes the maximum and minimum values of vertical and horizontal displacements measured in the eRoad specimens. Attention must be given to the fact that the ROI borderline was manually and individually drawn over the reference image, and that volumetric changes in the specimens may have altered the position of the contour in some of the cases. In this part of the study, two types of specimen were directly compared in terms of horizontal displacement evolution. Two pairs composed of a tRoad and an eRoad specimen were chosen taking into account the physical similarities of the specimens.

The pair "CP03 tRoad & CP07 eRoad" went through warm thermal loading cycles. The pair "CP04 tRoad & CP10 eRoad" went through cold loading cycles. Virtual squared strain gauges (3 x 3 mm) were placed in the bituminous mixture surface in the eRoad specimens, in both sides of the rigid inclusions (Figure 118). The same set of virtual strain gauges was placed in the tRoad specimens (Figure 118). The initial horizontal distance (𝐿 0 ) between the midpoints of the squared strain gauges was 400 mm. In the vertical axis, the centres of the strain gauges were aligned to the mid-height of the surface of the specimens. In ideal test conditions, the hypothesis assumed was that the strain gauges would approximate themselves during cold cycles (volumetric contraction), and move apart during warm cycles (volumetric expansion). This behaviour was expected to be more pronounced in eRoad specimens, due to the presence of the elastomeric materials (higher coefficients of thermal expansion/contraction). In order to verify the referred hypothesis, five images at specific thermal loading times were selected to be treated using the DIC technique in comparison to the reference image taken at the temperature of 20°C. In Figure 119, the temperatures registered inside the bituminous mixture for the selected deformed images are depicted. The temperatures inside the bituminous mixture in the reference images were previously depicted in Table 20 and Table 22. The DIC analysis were performed with a subset radius of 20 pixels, a subset spacing of 5 pixels and a strain spacing of 4 pixels. The thermal gradient in the specimens was characterized by the temperature variation in the bituminous mixture (temperature of the deformed image minus the temperature of the reference image). In warm cycles, this gradient was positive (CP03 and CP07) and for cold cycles it was negative (CP04 and CP10). Based on the location of the zero value in the x-y axis of Ncorr, a displacement towards the centre of the specimen during cold cycles was represented by a positive value in the left strain gauge and a negative value in the right strain gauge. In the opposing scenario (warm cycle), the left strain gauge was expected to show negative horizontal displacement values and the right strain gauge was expected to show positive horizontal displacement values. In Figure 120 a schematic of the expected directions of displacements in the strain gauges is illustrated. The measured values of horizontal displacements of the virtual strain gauges are depicted in Table 24 to Table 27. In order to have a better visualisation of the results, in Figure 121 In both cases, warm and cold cycles, the eRoad specimens had significant more variation in the horizontal right-to-left strain gauges length (2 to 3 times more than the variation measured in tRoad specimens). These findings reassure once more the importance of developing standardized tests to evaluate the compatibility in terms of thermomechanical properties of components to be used in eRoad profiles to the existing pavement material. Another important consideration is related to real pavement boundary conditions, where the bituminous mixture in the surrounding areas of the charging unit is not be free to budge as it was in this experimental test. In a real road configuration, the additional forces applied in the bituminous layer resulted from the volumetric change of the rigid inclusions would generate additional strain and stress in the layer. The intensity of volumetric change in a consequence of the thermal and mechanical properties of each individual material included and of the charging unit geometry. To this extent, the proposed test could be optimized as to constitute a first level of CU materials and geometry selection in the design methodology of eRoad pavements.

Summary

The application of the DIC technique to obtain the thermal properties of the studied materials is considered good and reliable, although some boundary conditions of the test might have had an impact on the measurements (i.e. movements of the base as a consequence of the weight of the specimens; resistance to the free volumetric expansion/contraction of the specimens due to base friction and the influence of the alternative "wood + rubber band" support system on the displacements). For the elastomeric materials, which present a more homogeneous and isotropic condition than the bituminous mixture, the calculated CTE and CTC were in accordance to the values obtained by means of a dilatometer. Also, the range of temperatures studied (-10 to 50°C), which is limited by the chamber specificities, was probably below the level of temperature required to make the transition between the elastic and the viscoelastic-viscoplastic (or hyperelastic) behaviour of the EPDM blend and Corkelast VA-60®. Nevertheless, the proposed experimental protocol combined to the DIC technique is considered suitable for the characterization of elastomeric materials of unknown composition in this specific road engineering application (first level of material sizing for eRoad prototypes).

For the bituminous mixture, a highly heterogeneous material, the calculated thermal coefficients were found within the range of values reported in the literature.

The variability in the calculated values is partially explained by the anisotropic and nonlinear behavior of CTC and CTE in bituminous mixtures, probably intensified by the randomly distributed air voids in the dense graded bituminous mixture studied.

Additionally, it is also acknowledged the impact of the test specimen boundary conditions on the measurements. The thermal loading test in its current format does not limit the asymmetric movement of the specimens laterally (horizontal direction), The CTE ad CTC were calculated taking into account the thermal gradient obtained from thermocouples installed in the heart of the specimens. The evolution of thermal fields within each specimen is dependent of the thermal properties of the material and the geometry of the specimen. For a more accurate measurement of the thermal coefficients using the proposed experimental protocol, it is suggested to use surface thermal sensors or thermal cameras in combination to the DIC technique. In this way, the region of interest for the analyses can be delimited to the areas presenting a homogenous temperature field. Also, with an accurate follow up of the temperature evolution in the specimen the conditioning phase of the test could be adjusted to each material in order to optimize the total duration of the loading cycles.

In terms of qualitative and quantitative measurements of the impact of rigid inserts on the behaviour of bituminous layers, the protocol described and tested gives a good indication of how displacements and strain evolved inside an eRoad subjected to thermal loadings. Two different macro-scale approaches were used to assess the behaviour of eRoad specimens by means of the DIC technique: a visual comparative analysis of the thermally-induced kinematic fields and a quantitative analysis of the horizontal displacement evolution using virtual strain gauges. In the first methodological approach, the specimens subjected to cold cycles bended towards its centre, while the specimens undergoing warm cycles budged upwards and laterally.

The elastomeric components of the studied conductive eRoad solution were found to lead the overall volumetric changes in the assembly, as the biggest parcel of the specimens in terms of volume. In addition, their coefficients of thermal expansion/contraction were already found significantly superior to the coefficients of the bituminous mixture by more than one experimental protocol (DIC technique and dilatometer). This differential behaviour led to concerning strain levels of more than 6000 𝜇𝜀 in the bituminous mixture, mostly concentrated in the surroundings of the charging unit, along the interface of the bituminous layer and the elastomer-epoxy system. Strain fields exhibited bands of strains in the elastomeric components in both directions, for all the specimens tested. This phenomenon could not be explained and is particularly strange if one considers the homogeneous characteristic of the EPDM blend. As quantitative studies to determine CTC and CTE were found to be suitable and accurate, the hypothesis of measurement error was discarded. However, from a mechanical point of view, the origin of this behaviour remains unclear and it will be the focus of future studies.

To a first approximation, the elongation and shrinkage of eRoad specimens due to temperature fluctuations was measured by the changes in the initial horizontal length between two virtual strain gauges placed in either sides of the charging unit, in the bituminous mixture. The strain gauges approximated themselves during cold cycles (volumetric contraction), and moved apart during warm cycles (volumetric expansion).

This change in length was two to three times more pronounced in eRoad specimens than in tRoad specimens, which is a clear evidence that the higher coefficients of thermal expansion/contraction influence the deformation of specimens. Once more, the experimental results reaffirm the conclusion obtained from the FE simulations using dimensions of the calorimeter. Two group of samples were tested for each elastomeric material. To obtain a reliable result, it was necessary to determine the temperatures of the system with precision (at least one decimal). The thermometers submerged in the beaker and in the calorimeter had a precision of two decimal digits. In Figure 122 the experimental apparatus used in the determination of the specific heat capacity of the elastomeric materials is depictedfrom left to right: the reduced samples, the calorimeter, the hotplate and the temperature sensor. The 𝐶 𝑃 values for the EPDM and

Corkelast VA-60® calculated are depicted in Table 28.

Figure 122. Experimental apparatus used to determine the specific heat capacity of the elastomeric materials.

Table 28. Specific heat capacity of the elastomeric materials (obtained using a calorimeter).

Component or material Specific heat capacity Cp (J/(kg⋅°C)) EPDM 2160

Corkelast VA-60® 1804

In an attempt to verify the reliability of the 𝐶 𝑃 values calculated, a third-party company was requested to perform measurements using a Hot Disk® 𝐶 𝑃 cell probe consisting of a gold cell of 19 mm in diameter and 5 mm height, mounted on a Hot Disk® Sensor model 5501 (6.4 mm radius) (Figure 123). The measurement consisted of first carrying out several reference measurements without sample (blank measurements). The curve produced on the sample was then subtracted from the reference measurement to deduce the value of the specific heat capacity of the elastomeric materials at a temperature level. For both materials, samples with a diameter of 18 mm and a thickness of approximately 3 mm were obtained by means of water jet cutting. The samples dried at room temperature for 24 hours before the From the plots of Figure 127, it is valid to conclude that the thermal conductivity adopted for the elastomeric materials in the simulations resulted in temperature evolutions very similar to the ones obtained experimentally. For the bituminous material, the fitting of the numerical and experimental curves was very accurate for Phase I, but less accurate for Phase II in the specimens undergoing cold cycles. In general, for the level of precision adopted in this research, the thermal conductivities obtained using the parameter estimation study proposed were assumed to be representative. The calculated thermal conductivity for each eRoad component is depicted in Table 30.

Annexe D -Dynamic Mechanical Analysis (DMA) of Corkelast VA-60®

The DMA is used to measure the viscoelastic behavior of binders and polymeric materials at different temperatures and frequencies. The DMA apparatus applies an oscillatory tension-compression force, causing a sinusoidal stress on the specimen.

The response of the material is a sinusoidal strain. The complex modulus (𝐸 * Abstract : In general, four factors need to be accurately and simply accounted for on the design of flexible pavements: traffic and loading, environmental conditions, materials properties and failure criteria [START_REF] Huang | Pavement analysis and design[END_REF]. The inclusion of charge-while-drive technologies inside road infrastructures modifies not only the common disposal of layers, but also the overall response of the structure to thermal and mechanical loadings. In order to quantify the impact of these inclusions on the performance of flexible pavements, this study proposes both numerical and experimental methodologies to measure temperature, stress and strain evolutions within electrified roads (eRoads). By means of transient 2-D FEM thermo-viscoelastic simulations, traditional and electrified road profiles were subjected to daily temperature fluctuations and to traffic.

The eRoad studied contains electrified rails embedded in the bituminous wearing course, a case of particular interest due to its direct exposure to traffic and climate. The response of the structures was analysed and compared to admissible values commonly assessed to predict distresses. In laboratory, a thermal test was proposed to evaluate eRoad specimens undergoing warm and cold cycles by means of Digital Image Correlation (DIC) technique. The strain fields measured numerically and experimentally lead to the same conclusion: the rigid inserts generate additional strain along the interface of the charging unit and the bituminous layer solely due to daily temperature fluctuations. The thermos-viscoelastic model proposed and the experimental set-up have a great potential to assess innovative pavement profiles (inductive and conductive eRoads).

LFigure 1 .Figure 4 .Figure 5 .Figure 6 .

 1456 Figure 1. Overhead line electrically powered truck (a) in Germany (KANE, 2014) and (b) in Sweden (GUSTAVSSON; HACKER; HELMS, 2019). ...................................... 28 Figure 2.(a) Scheme of the in-road live rail conductive solution (adapted from EROADARLANDA, 2021) and (b) installation in Sweden by eRoadArlanda (BOFFEY, 2018). ........................................................................................................................ 29 Figure 3.(a) Scheme of the Inductive Power Transfer (adapted from CHEN, 2016) and (b) OLEV bus in South Korea (E-WAY CORRIDOR, 2018)....................................... 30 Figure 4. Typical cross section of a flexible pavement (adapted from BROWN, 2020). .................................................................................................................................. 33 Figure 5. Stress distribution in a flexible pavement due to traffic (FHWA, 1984). ...... 36 Figure 6. Environmental phenomena experienced by pavement structures (HERB et al., 2009). .................................................................................................. 38 Figure 7. Domains of behaviour for bituminous mixtures (HUANG; BENEDETTO, 2015). ........................................................................................................................ 40 Figure 8. Rheological models. ................................................................................... 41 Figure 9. Generalized Maxwell model and creep and relaxation functions (TOLA; NIKBAY, 2016).............................................................................................. 42 Figure 10.(a) Example of a railway fastening system (AGICO GROUP, 2022), (b) Embedded Rail System ERS for railway application (LOPEZ POLANCO, 2019), and (c) Corkelast® ERS pouring in tramway installations (EDILON)(SEDRA, 2016). ...... 45 Figure 11. An idealised plot of moduli and phase angle evolution as a function of temperature (CENTRE FOR INDUSTRIAL RHEOLOGY, 2022). .............................. 47 Figure 12. Maximum vertical displacement 𝑢𝑦 (m) at the wheel path (CERAVOLO et al., 2016). ........................................................................................ 49 Figure 13. Distributions of (a) von Mises stress, (b) plastic strain and (c) damage scalar inside the eRoad at wheel wander distance 𝑤 = -0.2 m (CHEN et al., 2017). ........... 51 Figure 14. Cross sectional geometry and boundary conditions of the eRoad alternative structure proposed in the work of CHABOT and DEEP (2019). ................................ 52 Figure 15. Transverse profile measured with a profilometer equipped with a laser sensor (HORNYCH et al., 2020). .............................................................................. 54 Figure 16. Scheme of the Digital Image Correlation technique (HADDADI; BELHABIB, 2008). ........................................................................................................................ 56 Figure 17.(a) Scheme of the APS for Roads [adapted from (SUUL; GUIDI, 2018)], and (b) a simplified geometry of the charging unit. ........................................................... 63 Figure 18. Cross-sectional geometries of (a) French and (b) Brazilian tRoads (not to scale). ........................................................................................................................ 64 Figure 19. Cross-sectional geometries of (a) French and (b) Brazilian eRoads (not to scale). ........................................................................................................................ 64 Figure 20.(a) Evolution of the heat flux in a solid and (b) evolution of the temperature around the wall of a solid (PILATE, 2007). ................................................................ 66 Figure 21. Stress-strain curve of a linear elastic material. ......................................... 68 Figure 22. Schematic of a 3-D continuous body subjected to a variety of surface and body forces (WIKIPEDIA, 2020). ............................................................................... 69 Figure 23. A schematic representation of the Generalized Maxwell Model, as a parallel association of 𝑛 Maxwell branches and a single spring of stiffness 𝐸0. .................... 70 Figure 24. Creep function. ......................................................................................... 71 Figure 25. Relaxation function. .................................................................................. 71

Figure 37 .

 37 Figure 26. Creep (left) and relaxation (right) functions response for a single Maxwell branch. ...................................................................................................................... Figure 27.(a) Scheme of the Embedded Rail System by edilon)(sedra (LOPEZ POLANCO, 2019) and (b) double shear specimen setup (SWARNER, 2016). .................................................................................................................................. Figure 28. Size distribution of: (a) French and (b) Brazilian wearing course granular composition. .............................................................................................................. Figure 29. Size distribution of the French base and foundation granular composition. .................................................................................................................................. Figure 30.(a) Schematic of the trapezoidal specimens in the slab and (b) complex modulus measuring machine (MATÉRIEL MLPC -3MC). ........................................ Figure 31.(a) Schematic view of test specimen with mounted axial LVDTs (BAZZAZ et al., 2018) and (b) tension-compression test apparatus used to determine the complex modulus of the Brazilian mixture (BESSA, 2017). ................................. Figure 32. Bituminous mixtures master curves from complex modulus tests. ........... Figure 33. Size distribution of the Brazilian base granular composition (ANDRADE, 2017). ........................................................................................................................ Figure 34. Thermal (left) and mechanical (right) boundary conditions of the coupledthermomechanical problem (not to scale). ................................................................. Figure 35. Temperature evolution in the French road site (year 2006). ..................... Figure 36. Temperature evolution in the Brazilian road site (years 2015 and 2016).Figure 37. Greatest diurnal-temperature variation in the French pavement. ............. Figure 38. Greatest diurnal-temperature variation in the Brazilian pavement. ........... Figure 39.(a) Dimensions and loads (in tonnes) of the vehicle of type T2S3 and (b) Brazilian legal capacity for 4-axle semi-trailer vehicles. ............................................ Figure 40.(a) French tRoad loading configuration (not to scale) and (b) maximum tensile strain in the bottom of each bituminous layer obtained with ViscoRoute©. .... Figure 41.(a) Vertical stress in the surface of the pavement and (b) scheme of the pressure loading areas obtained with ViscoRoute©. ................................................. Figure 42.(a) Mechanical loading magnitudes and duration in Cast3M®, (b) scheme of the wheel fingerprint in ViscoRoute© and (c) in Cast3M®. ........................................ Figure 43. Mesh densities analysed in the mesh convergence study. ....................... Figure 44. Influence of the mesh density on the simulations. .................................... Figure 45. Temperature evolution in point PC with varying meshes. ......................... Figure 46. Displacement, stress and strain evolution in point PC with varying meshes. .................................................................................................................................. Figure 47. Horizontal tensile strain on the bottom of the bituminous layer -𝐿𝐵(𝑦 = -0.34 𝑚) for mesh density analysis. ......................................................................... Figure 48. Schematic of the dimension factor used for mesh dimensionally studies. Figure 49. Maximum tensile strain on the bottom of the bituminous layer against the dimension factor. ....................................................................................................... Figure 50. Horizontal tensile strain on the bottom of the bituminous layer (𝐿𝐵(𝑦 = -0.34 𝑚)) for dimension analysis. ............................................................................ Figure 51. Trimming steps of the tRoad slabs to eliminate the borders (not to scale). ................................................................................................................................ Figure 52. Sawing steps of the eRoad slabs to create the trench and to eliminate the borders (not to scale). ............................................................................................. Figure 53. Preparation stages of the eRoad specimens in laboratory. .................... Figure 54. Trench excavation procedure and final texture of the eRoad slabs. .......

Figure 55 .

 55 Figure 55. EPDM original specimen and preparation of the reduced specimens to be used in the eRoad assembly. .................................................................................. Figure 56.(a) Weighting of the Corkelast VA-60® components and aspect of the elastomer-epoxy system before pouring, (b) Corkelast VA-60® shims and (c) DMA samples. .................................................................................................................. Figure 57. Steps of the eRoad assembly: (a) positioning of the EPDM and (b) woodreinforced barrier. .................................................................................................... Figure 58. Sawing steps of the tRoad slabs (not to scale) and tRoad specimen back surface with the location of the thermocouple. ........................................................ Figure 59. Sawing steps of the eRoad slabs (not to scale) and eRoad specimen back surface with the location of the thermocouples. ....................................................... Figure 60. Examples of (a) natural, (b) spray paint and (c) water transfer printing speckle patterns. ..................................................................................................... Figure 61. Aerial schematic of the experimental set-up with an eRoad specimen. ..Figure 62. Alterative system to limit out-of-plane displacements of the specimens. Figure 63. Thermal loading cycle phases. ............................................................... Figure 64. The interface of the EyeMotion software during the alignment of the camera with the specimen. ................................................................................................... Figure 65.(a) Experimental set-up and principle of the (b) in-plane and (c) out-of-plane displacement tests. .................................................................................................. Figure 66. Evolution of the systematic error measured from rigid-body motion tests using the Ncorr software.......................................................................................... Figure 67. Variation of the global measurement uncertainty as a function of the subset radius....................................................................................................................... Figure 68. Variation of the global root-mean-square error (𝑅𝑀𝑆𝐸𝑔𝑙𝑜𝑏𝑎𝑙) of the measured strain as a function of the subset radius. ................................................ Figure 69. Thermal loading verification using the French tRoad profile. .................. Figure 70. Location of points PY1 and PC in the French and Brazilian eRoad structures. ................................................................................................................................ Figure 71. Temperature evolution in the points below the CU due to thermal loading. ................................................................................................................................ Figure 72. Maximum deformed structure (French pavement, 𝑇𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = 41.0°C). . Figure 73. Maximum deformed structure (Brazilian pavement, 𝑇𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = 47.5°C). ................................................................................................................................ Figure 74. Location of points PS1 and PS2 in the French eRoad structure. ........... Figure 75. Displacement evolution in the points on the surface near the interface with the charging unit due to thermal loading. ................................................................ Figure 76. Thermal loading applied in the upper line of (a) French and (b) Brazilian pavements. .............................................................................................................. Figure 77. Strain evolution in the points on the surface near the interface with the charging unit due to thermal loading. ...................................................................... Figure 78. Strain fields for French and Brazilian eRoads due to thermal loading. ... Figure 79. Stress evolution in the points on the surface near the interface with the charging unit due to thermal loading. ...................................................................... Figure 80. Stress fields for French and Brazilian eRoads due to thermal loading. .. Figure 81. Stress fields in the Brazilian eRoad structure due to thermal loading (𝑇𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = 20.4°C). ............................................................................................... Figure 82. Temperature evolution in the Brazilian eRoad structure at hour 28h of the thermal loading cycle. ..............................................................................................

Figure 83 .

 83 Figure 83. Procedure used to simulate the thermal and mechanical loadings cases. ................................................................................................................................ 138 Figure 84. Points of analyses for the thermal and mechanical loadings simulations (not to scale). .................................................................................................................. 139 Figure 85.(a) French tRoad loading configuration (not at scale) and (b) comparison of the horizontal strain at the bottom of each bituminous layer obtained with ViscoRoute© and Cast3M®. ......................................................................................................... 140 Figure 86. Vertical compressive stress evolution in point PB3 at temperature of 20°C. ................................................................................................................................ 141 Figure 87. Displacement evolution in the points on the surface under the wheel due to thermal and mechanical loading. ............................................................................. 142 Figure 88. Vertical displacement on the surface of the structures due to thermal and mechanical loading. ................................................................................................. 143 Figure 89. Strain evolution in the points at the bottom of the bituminous layer due to thermal and mechanical loading. ............................................................................. 144 Figure 90. Strain field in the French bituminous layers due to thermal and mechanical loading (mechanical loading at 0.012 seconds; TS = 39.1°C). ................................ 146 Figure 91. Strain field in the Brazilian bituminous layer due to thermal and mechanical loading (mechanical loading at 0.012 seconds; TS = 46.1°C). ................................ 147 Figure 92. Temperature profile in the eRoad structures and location of points near the CU. .......................................................................................................................... 147 Figure 93. Strain evolution in the points in the bituminous layers near the CU due to thermal and mechanical loading. ............................................................................. 149 Figure 94. Horizontal strain fields 𝜀𝑥𝑥 (𝜇𝜀) in the eRoad bituminous layers at a given instant of mechanical loading in the two climatic scenarios. .................................... 151 Figure 95. Stress evolution in the points on top of the roadbed due to thermal and mechanical loadings. ............................................................................................... 152 Figure 96. Stress field in the French bituminous layers due to thermal and mechanical loading (mechanical loading at 0.012 seconds; TS = 39.1°C). ................................ 153 Figure 97. Stress field in the Brazilian bituminous layer due to thermal and mechanical loading (mechanical loading at 0.012 seconds; TS = 46.1°C). ................................ 153 Figure 98. Stress evolution in the points in the bituminous layers near the CU due to thermal and mechanical loadings. ........................................................................... 155 Figure 99. EPDM blend, Corkelast VA-60® and tRoad CP01 before and after speckle painting. ................................................................................................................... 161 Figure 100. Temperature evolution inside the elastomeric specimens (EPDM on the left, Corkelast VA-60® on the right). ........................................................................ 162 Figure 101. Regions of Interest (ROI) used to calculate the coefficient of thermal expansion/contraction of the elastomeric materials (EPDM on the left, Corkelast VA-60® on the right). ..................................................................................................... 163 Figure 102. CTE and CTC of the elastomeric materials calculated for different ROIs. ................................................................................................................................ 163 Figure 103. Linseis DIL L75 PT Horizontal: high vacuum tight dilatometer (©2022 LINSEIS GMBH). ..................................................................................................... 164 Figure 104. Exemplification of the temperature evolution inside tRoad specimens (CP01 on the left and CP03 on the right)................................................................. 165 Figure 105. CTE and CTC of the bituminous mixture calculated for different ROIs. 166 Figure 106. Temperature evolution inside the components of the eRoad CP07 specimen (warm cycle). ........................................................................................... 169

  to a homogenous reference temperature value defined as representative of a period/season. Moreover, most of the hypothetical eRoads studied considered a crosssection geometry of an inductive technology to compose the pavement profile in the simulations.[START_REF] Hornych | Evaluation of a solution for electric supply of vehicles by the road, at laboratory and full scale[END_REF] addressed the performance of flexible eRoad pavements in laboratory and through APT facilities. This particular investigation considered a conductive technology in which feeding rails were embedded in the pavement surface and in direct contact with traffic and environmental loadings(OLSSON, 2014a). The tests reported by[START_REF] Hornych | Evaluation of a solution for electric supply of vehicles by the road, at laboratory and full scale[END_REF] constitute the initial point of this research. The presence of a conductive open-air system is assumed to be a critical case scenario, due to its exposure to traffic and climatic conditions.Aiming to take a step forward and to propose flexible and reliable tools for the design and assessment of eRoads pavements, the present study recreates numerically and experimentally a conductive charge-while-drive technology in order to investigate its response to thermal and mechanical loadings. Real field temperature fluctuations and the viscoelastic aspect of the bituminous layers (temperaturedependent behaviour) are considered in the analyses. For the numerical methodological approach, tRoad and eRoad infrastructure scenarios representative of two different countries (Brazil and France) were simulated by means of 2-D transient structural simulations using the FE software Cast3M®. In laboratory, the experimental methodological approach proposed a protocol for the fabrication and testing of eRoad specimens subjected to warm and cold thermal loading cycles. The non-contact Digital Image Correlation technique is employed in the study of the evolution of the thermallyinduced kinematic fields (displacement and strain) inside the specimens.



  Chapter 1 (Introduction and motivation): this chapter presents the overall context of the transport sector electrification and emphasizes the main objective of the study. Chapter 2 (Literature review): this chapter provides an overview of the existing charge-while-drive technologies and the challenges linked to the design and the assessment of conventional and electrified flexible road infrastructures. The viscoelastic intrinsic behaviour of the bituminous mixtures is discussed, as well as the current state-of-the-art in structural modelling of eRoads.  Chapter 3 (Finite elements structural analysis): in this chapter the numerical methodological approach is described. The configuration of the charging unit which is based in the APS for Roads technology is detailed. The verification steps of the 2-D FEM structural computation are explained and the thermo-viscoelastic model used is presented.  Chapter 4 (Experimental campaign): in this chapter the experimental methodological approach is described. The tRoad and eRoad specimens geometries and fabrication process are detailed. A novel experimental protocol using the Digital Image Correlation technique is presented in this chapter.  Chapter 5 (Results and discussions -Part I: FE structural simulations): in this chapter the main results of the numerical simulations using the thermoviscoelastic model are discussed. The chapter contains a comparative analysis of the results of the two road scenarios (French and Brazilian) in two cases of study: structures subjected to thermal and to thermal and mechanical loadings.  Chapter 6 (Results and discussions -Part I: Experimental campaign): in this chapter the main results of the experimental campaign are discussed. The DIC technique was used to calculate the coefficients of thermal expansion (CTE) and contraction (CTC) of each individual eRoad component and to measure the kinematic fields (displacement and strain) of eRoad specimens subjected to thermal loading cycles.  Chapter 7 (Conclusion and perspectives): this chapter provides an overall conclusion of the studies performed and brings suggestions to the academic community for the continuation of this research axis.

Figure 1 .

 1 Figure 1. Overhead line electrically powered truck (a) in Germany (KANE, 2014) and (b) in Sweden (GUSTAVSSON; HACKER; HELMS, 2019). Some disadvantages of the overhead lines technology are its limitation in terms of interoperability between passenger and freight transportation, notorious visual pollution and safety issues. OLSSON (2014a) reports that the European standard for overhead lines places the contact wire at a height of 5.5 metres, thus preventing smaller vehicles from connecting to the system. At the same time, its open air transmission and distribution system requires the development of safe and intelligent technologies to overcome extreme transient fault situations, e.g. lighting strike or tree contact due to downed wiring (MÁRQUEZ-FERNÁNDEZ et al., 2019; OLSSON, 2014a). Despite those objections, overhead lines are the less invasive eRoad solution in regards to the pavement structure, being also the one with the most variety of technology suppliers on the market and with implementation/operation processes already regulated.

Figure 2 .

 2 Figure 2.(a) Scheme of the in-road live rail conductive solution (adapted from EROADARLANDA, 2021) and (b) installation in Sweden by eRoadArlanda (BOFFEY, 2018).

  Constituting the second big group of eRoad technologies, inductive solutions rely on the contactless transmission of electric power to in-motion vehicles by several wireless possibilities: Inductive Power Transfer (IPT), Capacitive Power Transfer (CPT), Permanent Magnet Coupling Transfer (PMPT), Resonant Inductive Power Transfer (RIPT), On-line Power Transfer (OLPT) and Resonant Antennae Power Transfer (RAPT)

Figure 3 .

 3 Figure 3.(a) Scheme of the Inductive Power Transfer (adapted from CHEN, 2016) and (b) OLEV bus in South Korea (E-WAY CORRIDOR, 2018) Researches on static and dynamic wireless transmission of power to vehicles dates back to the 90's, with the oldest test programme reported being performed at the University of California through the collaborative organization California Partners for Advanced Transit and Highways (PATH) (CHEN; TAYLOR; KRINGOS, 2015; PIARC,

Figure 4 .

 4 Figure 4. Typical cross section of a flexible pavement (adapted from BROWN, 2020).

Figure 5 .

 5 Figure 5. Stress distribution in a flexible pavement due to traffic (FHWA, 1984).

Figure 7 .

 7 Figure 7. Domains of behaviour for bituminous mixtures (HUANG; BENEDETTO, 2015).Bituminous mixtures can be modelled based on the interaction of the strain and stress (denoted as ε and σ, respectively) and their temporal dependencies[START_REF] Badeli | Evaluation of the Damage of an Asphalt Mix under Repeated Freeze-Thaw Cycles[END_REF]. Simple rheological models result from a combination of springs (elasticity modulus 𝐸) and dashpots (viscosity η). Maxwell and Kelvin-Voigt elements (also referred as arms or branches) are the most widespread and their combination in series or in parallel constitutes the base for the formulation of several more advanced rheological models. Some models that characterize viscoelastic materials are shown in Figure8. The Huet model is composed of a linear elastic spring of modulus 𝐸 ∞

Figure 8 .

 8 Figure 8. Rheological models.

Figure 9 .

 9 Figure 9. Generalized Maxwell model and creep and relaxation functions (TOLA; NIKBAY, 2016).

  These systems are characterized by large vertical stiffness and high levels of noise and vibration attenuation, with damage occurring either by global failure or by local rupture (e.g. tensile rupture or interface detachment) (IMBIMBO; DE LUCA, 1998; SWARNER, 2016).

Figure 10 .

 10 Figure 10.(a) Example of a railway fastening system (AGICO GROUP, 2022), (b) Embedded Rail System ERS for railway application (LOPEZ POLANCO, 2019), and (c) Corkelast® ERS pouring in tramway installations (EDILON)(SEDRA, 2016).

Figure 11 .

 11 Figure 11. An idealised plot of moduli and phase angle evolution as a function of temperature (CENTRE FOR INDUSTRIAL RHEOLOGY, 2022).

CERAVOLO

  et al. (2016) proposed a forefront computational methodology to assess the time-dependent structural performance of an eRoad containing an inductive CU.The work considered two different behaviour of the bituminous layers: elastic and viscoelastic. In the first linear elastic analyses, using an algorithm developed in MATLAB and a 3-D Finite Element (FE) model, the authors evaluated through dynamic transient calculations the impact of harmonic loadings in both tRoad and eRoad flexible pavements. In the same 3-D model, the response of the pavements to moving impulse loads was also calculated, which aimed at representing the time-history of the forces acting between the tires and the pavement surface during the passage of a heavy vehicle at 70 km/h. Additional 2-D FE simulations were also performed considering contact elements between the CU and the pavements layers under a static pressure load. The 2-D cross-section used was identical to the transversal cross-section of the 3-D model and the contact model considered both friction and separation effects.In a second analysis, the viscoelastic behaviour of the bituminous layers was accounted by means of the GMM. An important consideration in the work of[START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF] is the variation of the viscosity of the bituminous materials in respect to loading and unloading times. Here, the assumed TTSP for viscoelastic materials allowed the modification of the Prony series pairs representing the constitutive GMM law according to time and rate of solicitations (a consequence of traffic intensity and composition). The variables that were considered to define the traffic intensity were the vehicle type (standard and heavy) and the velocity. A bimodal statistical distribution was also used to calculate the combined traffic stream, the average loading, inter-arrival times and a possible overweight of electric vehicles in comparison to standard ones. Finally, the authors investigated the impact of drivability variations in the deformation of the eRoad by moving the wheels axle laterally in the transverse direction of the road. As an example of the results reported in the study, the viscoelastic vertical displacement distribution inside the structure is depicted in Figure12, as a result of an equivalent static load representative of traffic-induced dynamic cyclic loading. In this cross-section the details of the I-shaped ferrite core and of the polymer coil-box are observed, as well as the location of the CU in the pavement.

Figure 12 .

 12 Figure 12. Maximum vertical displacement 𝑢 𝑦 (m) at the wheel path (CERAVOLO et al., 2016).

CHEN

  et al. (2017) analysed the structural response of an eRoad flexible pavement under a single tire loading configuration using a viscoelastic-viscoplastic model implemented into a FE code. For the numerical simulations, a typical Swedish highway profile was considered for the tRoad structure, and the eRoad was modelled with a rectangular prefabricated massive concrete box inserted in the middle of the driving lane, at 5 cm depth from the pavement surface (inductive eRoad solution). The vehicle loading was accounted by rectangular shape loads superposed together as a creep type loading. The tRoad and eRoad were compared in terms of von Mises stress, vertical plastic strain and damage scalar by means of a parametric sweep analysis: moving the wheel laterally to the symmetrical centre of the eRoad structure from distance. The results depicted in Figure 13 represent the most critical case according to the authors, where the wheel tire is at -0.2 m from the original central location. The von Mises distribution inside the eRoad is a result of an 800kPa load lasting 0.1 seconds to simulate the passage of one heavy vehicle, at 100km/h (Figure 13(a)); while the vertical plastic strain and the damage distributions are a result from an 800kPa load lasting 5,000 seconds to simulate 1 x 10 6 passes (Figure 13(b) and Figure 13(c), respectively).

Figure 13 .

 13 Figure 13. Distributions of (a) von Mises stress, (b) plastic strain and (c) damage scalar inside the eRoad at wheel wander distance 𝑤 = -0.2 m ([START_REF] Chen | Towards an understanding of the structural performance of future electrified roads: a finite element simulation study[END_REF].According to[START_REF] Chen | Towards an understanding of the structural performance of future electrified roads: a finite element simulation study[END_REF], for all of the parameters used for comparison, in an ideal condition of loading (i.e. wheel located relatively far from the unit and no wheel wander), the predicted distribution of traffic-induced stress, strain and damage in tRoad and eRoad are found to be very similar. Once the wheel approaches the CU, however, a concentration of stress around the surfaces and corners of the CU is observed. Significant vertical plastic strain and damage concentration are also observed around the upper corner of the CU, in the bituminous layer. Based on these results, the authors propose optimisations in terms of material (varying stiffness), of geometry (round shaped corners with varying radius) and of embedding depths of the CU in order to minimize damage susceptibility in the vicinities of the box. Despite giving a great contribution to the understanding of the mechanical response of eRoads to traffic loading, the magnitudes of distresses calculated in this study picture a much stronger loading configuration than the one experienced in real roads. Carefully analysing the 2-D boundary conditions of the model, one can conclude that the lateral wader of the wheel towards the symmetrical centre of the road is actually reducing the wheel axis, thus intensifying the levels of stress, strain and damage calculated.Additionally, even though an advanced thermodynamics-based finite strain viscoelastic-viscoplastic model with damage coupled is used to characterize the bituminous layers, all of the cases simulated were carried out at a constant and homogenous temperature of 20°C.Considering the same cross-section geometry and properties of the CU adopted by[START_REF] Chen | Towards an understanding of the structural performance of future electrified roads: a finite element simulation study[END_REF],[START_REF] Chabot | 2D multilayer solution for an electrified road with a built-in charging box[END_REF] numerically assessed the structural behaviour of eRoad profiles with the focus in the bonding conditions between the CU

Figure 14 .

 14 Figure 14. Cross sectional geometry and boundary conditions of the eRoad alternative structure proposed in the work of CHABOT and DEEP (2019).

Figure 15 .

 15 Figure 15. Transverse profile measured with a profilometer equipped with a laser sensor (HORNYCH et al., 2020). The real scale investigations reported by HORNYCH et al. (2020) compared the rut depth and deflection levels of the eRoad to traditional acceptance levels used to monitor traditional French roads. In all of the cases, the eRoad response to traffic loadings remained under admissible levels of settlement, which were developed mainly during the first 100,000 load cycles and due to the densification of the bituminous layer.

Figure 16 .

 16 Figure 16. Scheme of the Digital Image Correlation technique (HADDADI; BELHABIB, 2008).

3 FINITE

 3 ELEMENT STRUCTURAL ANALYSISBituminous layers play a significant role on the design and performance of flexible pavements. For an eRoad configuration, this role becomes even more relevant, with the inclusion of the CU possibly generating additional stress in the wearing surface of the pavement. The origin of these stresses could simply be the result of the differential response of each material to thermal and mechanical loadings. Hence, the design of the unit alone has a major influence on the performance of the eRoad, in regard to the components intrinsic properties and to its geometric disposal. Additionally, an eRoad flexible pavement can no longer be considered as purely layered, due to the presence of discontinuous interfaces in the joints of the CU. The development of electrified transportation modes may lead to a rearrangement on road engineering concepts. The use of new mechanistic-based methodologies is an alternative, since the simplicity of empirical and M-E models tend to ignore some variables inherent to the thermomechanical behaviour of the structure under typical conditions of use. To assess the overall performance of eRoads, one possible evolution of methodologies uses constitutive models to describe each road component in Finite Elements Method (FEM) based software.Only a few studies have investigated the structural behaviour of eRoads, as discussed in the last chapter.[START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF][START_REF] Chen | Structural performance of electrified roads: A computational analysis[END_REF] evaluated the response of an inductive eRoad technology to traffic-induced mechanical loading, whileCHABOT and[START_REF] Chabot | 2D multilayer solution for an electrified road with a built-in charging box[END_REF][START_REF] Chen | Towards an understanding of the structural performance of future electrified roads: a finite element simulation study[END_REF] studied the effects of wheel lateral wander on the discontinuities between the CU and the pavement. In flexible pavements, however, the levels of stress, strain and damage are also dependent on temperature, due to the viscoelastic intrinsic behaviour of bituminous mixtures. Cyclic processes of cooling and heating are also responsible for the volumetric rearrangement of those materials (thermal expansion and contraction), which, in combination with repeated traffic-induced loading, may lead to a premature failure of the structure. Several factors impact the non-uniform temperature distribution in bituminous layers. They generally include geometric, thermal, physical and chemical properties, as well as process parameters (i.e. solar radiation, air temperature and moisture content). In summary, the consideration of climate in the design of flexible pavements remains a challenge. FEM models are reliable approaches on the characterization of heterogeneous, complex and discontinuous media behaviour. In this chapter, a mathematical model relating the viscoelastic properties and the time-temperature profile of flexible pavements is proposed. This study considers as reference two conventional flexible pavement structures (one Brazilian and one French), from which instrumented sections provided hourly temperature variation for certain periods of a year. The hypothetical eRoad structures are created by including a conductive CU in the wearing surface of the reference structures. The configuration of the CU is based on the APS for Roads technology, developed and commercialized by the French multinational Alstom. The performance of the eRoads in comparison to the tRoads for each country configuration is numerically assessed through a 2-D FEM structural computation using the software Cast3M®, a powerful numerical programme for solving nonlinear calculations based on differential equations. The characterization of the components and materials constituting the tRoad and eRoad structures is also described. Most of the thermomechanical properties of the materials were determined through standardized laboratory testing. The bituminous mixtures are assumed to behave as rheologically simple viscoelastic materials, defined in Cast3M® by a Generalized Maxwell Model. The thermosuceptibility of the mixtures are considered in the simulation by varying the Prony series terms according to the Williams-Landel-Ferry equation for each temperature. The rail, elastomeric materials

  Figure 17.(a) Scheme of the APS for Roads [adapted from (SUUL; GUIDI, 2018)], and (b) a simplified geometry of the charging unit.For simplicity, the assembly modelled in 2-D contained only two rails, each rail being disposed substantially equidistant and parallel to a longitudinal axis (Figure17(b)). These rails were laid on an Ethylene-propene-diene terpolymer (EPDM), which was bounded to the pavement wearing surface by an elastomer-epoxy system (Corkelast VA-60®, by edilon)(sedra).

3. 1 . 2

 12 Figure 18. Cross-sectional geometries of (a) French and (b) Brazilian tRoads (not to scale).

Figure 19 .

 19 Figure 19. Cross-sectional geometries of (a) French and (b) Brazilian eRoads (not to scale).

  ⋅ (4.84 + 3.36𝜈 𝑤𝑖𝑛𝑑 ) ⋅ 294.16 (273.16 + 𝑇 𝑎𝑖𝑟 ) Equation 9

  Figure 20 illustrates the conduction and convection phenomena.

  Figure 20.(a) Evolution of the heat flux in a solid and (b) evolution of the temperature around the wall of a solid (PILATE, 2007). In Cast3M®, the evolution of temperature in a solid from an initial steady-state condition to a new final thermal equilibrium was calculated using the derivation of Fourier's partial differential equation. To this end, consider that the cube of Figure 20(a) has a volume 𝑑𝑉 = 𝑑𝑥 𝑑𝑦 𝑑𝑧 and is part of a three-dimensional body. The overall net heat fluxes 𝑞 𝑛 ̇ and 𝑞ṅ +𝑑𝑛 (𝑛 = 𝑥, 𝑦, 𝑧) through the six corresponding surfaces of the cube under the influence of a temperature gradient 𝑇(𝑥) inside the body is given: 𝑄 ̇𝑛𝑒𝑡 = 𝜕𝑞̇𝑥 𝜕𝑥 𝑑𝑉 + 𝜕𝑞̇𝑦 𝜕𝑦 𝑑𝑉 + 𝜕𝑞̇𝑧 𝜕𝑧 𝑑𝑉 = div(𝜆∇𝑇)𝑑𝑉

  volume (shrinkage), denoted as thermal contraction. The variations in terms of length, thickness and width of materials according to heat fluctuations are expressed by a thermal coefficient in three basic types: linear, superficial and volumetric thermal expansion/contraction. The thermal coefficient 𝛼 is defined as the rate of change in the original unit (length, area or volume) per degree of change in temperature, at a constant pressure. The change in length of a solid due to a variation in temperature is calculated by the formula:

  loading and deformations. No material can go through unlimited stretching nor compression without some permanent deformation, change of state or failure. For constitutive models, the definition of Cauchy for linear elastic materials is more precise: in an elastic material the state of tension is a function only of the deformation state, or vice versa, meaning that the trajectories of loading, unloading or reloading are all coincident (Figure 21).

Figure 21 .

 21 Figure 21. Stress-strain curve of a linear elastic material.

Figure 22 .

 22 Figure 22. Schematic of a 3-D continuous body subjected to a variety of surface and body forces (WIKIPEDIA, 2020).𝜎 𝑖𝑗 = 𝐾𝜀 𝑘𝑘 𝛿 𝑖𝑗 + 2𝐺(𝜀 𝑖𝑗 -𝜀 𝑘𝑘 3 𝛿 𝑖𝑗 )

  (a)). The elastic element behaviour is defined by the time-independent linear relationship between stress and strain, with 𝐸 representing the stiffness of the element (Figure 23(c)). The viscous element behaviour is defined by the linear relationship between stress and strain rate, with 𝜂 representing the viscosity coefficient of the element (Figure 23(d)). Each Maxwell branch is composed by a linear Hookean spring and a Newtonian dashpot, connected in series (Figure 23(b)).

Figure 23

 23 Figure 23. A schematic representation of the Generalized Maxwell Model, as a parallel association of 𝑛 Maxwell branches and a single spring of stiffness 𝐸 0 .

Figure 24 .

 24 Figure 24. Creep function.

Figure 25 .

 25 Figure 25. Relaxation function. For a Maxwell branch, in both tests, the time-independent immediate response of the material is attributed to the spring, while the time-dependent non-instantaneous response is attributed to the piston movement through the viscous fluid in the dashpot. Equation 20 and Equation 21 describe creep and relaxation functions for a single Maxwell branch, respectively. An important feature of this model is the definition of the characteristic relaxation time 𝜏, which is the ratio of the viscosity of the dashpot over the stiffness of the spring, here represented by its elastic modulus (𝜏 = 𝜂 𝐸 ) (Figure 26).

  𝐻 denotes the Heaviside step function [𝐻 𝑡 0 (𝑡) = 0, if 𝑡 < 𝑡 0 ; 𝐻 𝑡 0 (𝑡) = 1, if 𝑡 ≥ 𝑡 0 ].

Figure 26 .

 26 Figure 26. Creep (left) and relaxation (right) functions response for a single Maxwell branch.

  elastomeric resin commercialized under the name of Corkelast VA-60®, by edilon)(sedra. Corkelast VA-60® is a two-component material that react chemically when mixed. As detailed in the product packaging, "Component 1" contains diethyltoluenediamine, while "Component 2" contains aromatic polyisocyanate prepolymer and 4-methyl-m-phenylene diisocyanate. The correct manipulation of the product and its overall mechanical properties were provided by edilon)(sedra in the Product Data Sheet (Annexe A). Corkelast VA-60® is widely used for joint and crack sealing in road infrastructures, and to attenuate vibration damping in light rail train systems[START_REF] Lopez | Comportement d'un enrobé bitumineux sollicité par des rails posés sur des appuis continus[END_REF][START_REF] Swarner | Material Evaluation of an Elastomer, Epoxy and Lightweight Concrete Rail Attachment System for Direct Fixation Light Rail Applications[END_REF].As previously discussed, the nonlinear behaviour of elastomeric materials is dependent on factors such as specimen geometry, temperature, loading type and extension rate. Additives like filler of cork (present in Component 1) and the chemical cross-linking method used in the production of Corkelast VA-60® have an impact on the behaviour of this multi-component elastomer. However, a complete chemical and physical characterization of this material was beyond the scope of this research.Instead, a set of tests were performed by a third-party service provider to determine specific material parameters for the FE-based model. All of the tests were performed at room temperature (23 ± 2°C), namely: simple tension test, biaxial extension test, planar tension test, simple shear test and volumetric compression tests at different shape factors[START_REF] Bakker | Material parameters for FE purposes. MG technical solutions[END_REF].Full-scale tests with Corkelast VA-60® were conducted in TU München[START_REF] Bakker | Material parameters for FE purposes. MG technical solutions[END_REF] and in the University of Washington[START_REF] Swarner | Material Evaluation of an Elastomer, Epoxy and Lightweight Concrete Rail Attachment System for Direct Fixation Light Rail Applications[END_REF]. For the first study, a set of static tests were performed in samples of an Embedded Rail System commercialized by edilon)(sedra (Figure27(a)). The samples measured 600 mm in length and were tested in vertical stiffness, inclined stiffness and longitudinal stiffness.

For

  the second study by[START_REF] Swarner | Material Evaluation of an Elastomer, Epoxy and Lightweight Concrete Rail Attachment System for Direct Fixation Light Rail Applications[END_REF], Corkelast VA-60® was tested as part of a light rail system, to attach plinths to a concrete bridge deck. Different-sized samples were tested in tension (pull-off test adapted from ASTM C1583), compression and shear loading (similar procedure to ASTM D4014) (Figure27(b)). Both studies had as main objective to compare the results obtained through single-material standard laboratory characterization with results obtained from samples that were more representative of the in situ configuration (loading conditions and geometric aspects).

Figure 27 .

 27 Figure 27.(a) Scheme of the Embedded Rail System by edilon)(sedra (LOPEZ POLANCO, 2019) and (b) double shear specimen setup (SWARNER, 2016). In this research, the mechanical parameters obtained in full-scale tests by SWARNER (2016) were considered as accurate to characterize Corkelast VA-60® in the FE-model. The density of Corkelast VA-60® was determined in laboratory from hydrostatic weighing. The procedure used to obtain the thermal properties of EPDM blend and Corkelast VA-60® is described in Annexe B. It is assumed for both

Figure 28 .

 28 Figure 28. Size distribution of: (a) French and (b) Brazilian wearing course granular composition. For the French pavement, base and foundation layers were composed by a GB 0/14 Classe 3 (Grave Bitume, in French). The GB mixture was composed by a neat 35/50 penetration grade bitumen and limestone aggregates, meeting with the required criteria for base course in the NF EN 13108-1 Standard. The granular composition of the mixture is depicted in Figure 29. The properties of all bituminous mixtures are presented in Table4.

Figure 29 .

 29 Figure 29. Size distribution of the French base and foundation granular composition.

Figure 30 .

 30 Figure 30.(a) Schematic of the trapezoidal specimens in the slab and (b) complex modulus measuring machine (MATÉRIEL MLPC -3MC).For the Brazilian mixture (CBUQ), the complex modulus tests were carried out in the research of BESSA (2017). The tests consisted in applying a tension-compression sinusoidal loading in cylindrical specimens, at five different temperatures(-10, 4, 20, 40, 54°C) and frequencies (0.1, 0.5, 1, 5 and 10 Hz). The axial strain was measured by extensometers located in the middle section of the specimens (Figure31), where a homogeneous stress-strain state is found as a result of the tension-compression cycles applied.

Figure 31 .

 31 Figure 31.(a) Schematic view of test specimen with mounted axial LVDTs (BAZZAZ et al., 2018) and (b) tension-compression test apparatus used to determine the complex modulus of the Brazilian mixture (BESSA, 2017).

Figure 32 .

 32 Figure 32. Bituminous mixtures master curves from complex modulus tests.

  (8) Chosen average value based on the experimental investigations of[START_REF] Olard | Properties of bituminous mixtures at low temperatures and relations with binder characteristics[END_REF] = 30 to 15 * 10 -6 m/(m⋅°C), measured between 5 to -30°C;TEGUEDI et al. (2017) = 30.8 to 33.2 * 10 -6 m/(m⋅°C), measured between -10 to 20°C; and VU et al. (2018) = 25 * 10 -6 m/(m⋅°C), measured at -20°C.3.3.3 Unbound granular layersIn the Brazilian structure, the base layer was composed of crushed granitic stone (Brita Graduada Simples -BGS). The material characterization in laboratory and the construction of the reference experimental site were described in the work of ANDRADE (2017). The continuous granular distribution of the BGS attends the requirements for unbound granular base and subbase of the São Paulo State Department of Highways (EP-DE-P00-008). The moisture content of 5.2% was determined in situ. The granular composition of the mixture is depicted in Figure 33, with the continuous red curve representing the gradation of the mixture and the two black dashed lines representing the allowed limits set by the São Paulo State Department of Highways (DER-SP), in Brazil.

Figure 33 .

 33 Figure 33. Size distribution of the Brazilian base granular composition (ANDRADE, 2017). Both Brazilian and French structures rested on subgrade treated with hydraulic binder. KTARI et al. (2019) described the French roadbed as type PF3, from which it was possible to obtain the design parameters for calculation in the French guidelines (LCPC-SETRA, 1998). Due to the lack of more detailed information on the composition of these layers, the thermomechanical properties characterizing the roadbed in the FEmodel were based in values reported in literature for the numerical assessment of French and Brazilian flexible pavements (Table9):

Figure 34 .

 34 Figure 34. Thermal (left) and mechanical (right) boundary conditions of the coupledthermomechanical problem (not to scale).

3. 5 . 1

 51 Simulation of environmental loading (thermal loading)For this first simulation, the initial homogeneous steady-state temperature of both French and Brazilian pavements was defined as a constant 𝑇 0 equal to 20°C (temperature at which the model parameters of the bituminous mixtures were determined). This temperature corresponds to the mean value between the constant equivalent temperatures in France mainland (15°C) and in Brazil (25°C)[START_REF] Ktari | Consideration of Seasonal Temperature Changes in the French Pavement Design Method[END_REF][START_REF] Santos | Modélisation intrinsèque de la fissuration par fatigue des enrobés bitumineux à partir de mesures de champs: Application à la correspondance entre différents types d'essais de fatigue[END_REF] SOARES;[START_REF] Santos | Influência da temperatura e da velocidade de trafego na previsão de área trincada de pavimentos as-fálticos[END_REF]. It also recreates the same weather condition in which the efficiency of the conductive pick-up energy transfer was tested, at the real scale test track in Sweden (OLSSON, 2014a). The French pavement of reference is located near Bordeaux, in the Aquitaine region, which is characterized by very warm summers. Figure35depicts the temperature variation measured at different depths in an instrumented section of the French highway for the year 2006[START_REF] Ktari | Consideration of Seasonal Temperature Changes in the French Pavement Design Method[END_REF]. The Brazilian highway is located in the city of Extrema, in the state of Minas Gerais (southeastern region of Brazil), which is characterized by warm and humid summers. Figure36depicts the temperature variation in the Brazilian experimental road section extracted from a Weight-in-Motion (WIM) system temperature probe, for a period of 7 monthsover the years of2015 and 2016[START_REF] Bosso | Uso da tecnologia Weigh-in-Motion para a caracterização do tráfego rodoviário e do excesso de carga em veí-culos comerciais[END_REF]. Both regions are characterized by very mild winters.

Figure 35 .

 35 Figure 35. Temperature evolution in the French road site (year 2006).

Figure 36 .

 36 Figure 36. Temperature evolution in the Brazilian road site (years 2015 and 2016).

  depicts the greatest diurnal-temperature variation in the Brazilian pavement registered with the WIM thermal sensor (maximum |∆𝑇 12ℎ | of 29.19°C). In both figures, the 𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 curve describes the temperature evolution imposed on the upper line of the modelled structures for the transient thermal analysis. Particularly for the Brazilian pavement, the WIM sensor was installed at a depth of 1.5 cm measured from the surface of the pavement and covered with a polyurethane resin. In the absence of more details, it was decided to consider the temperatures registered by the sensor as the temperatures observed in the surface level of the Brazilian pavement.

Figure 37 .

 37 Figure 37. Greatest diurnal-temperature variation in the French pavement.

Figure 38 .

 38 Figure 38. Greatest diurnal-temperature variation in the Brazilian pavement.

3. 5 . 2

 52 Simulation of traffic loading (mechanical loading)Usually, in the classical pavement design of a given road, a 3-D elastic computation associated to a 3-D load is performed in order to define strain and stress evolutions inside the given structure. In most pavement structure software, a 3-D elliptical-shaped dual wheels loading can be defined for that purpose. For this study, this loading needed to be converted to a 2-D surface equivalent loading area for the simulations in Cast3M®. This simplification was possible by modelling the vertical contact stress on the upper surface of the 2-D structure in Cast3M® which generated a maximum horizontal tensile strain at the bottom of the bituminous equivalent to the one obtained with the software ViscoRoute©, using the same pavement structure in both simulations.According to the French pavement design methodology, heavy goods vehicles multiple passages are expressed by a converted equivalent number of passages of a reference single axle with dual wheels (NF P 98-086). The 5-axle vehicle of type T2S3 described in the field measurement campaign of DUONG (2017) (Figure39(a)) was very similar to a conventional semi-trailer reported in the Brazilian Traffic Code and allowed to circulate by the 2264/81 Resolution of the National Department of Transport Infrastructure (Figure 39(b)). Hence, the characteristics of the T2S3 vehicle were assumed as the reference for simulating the heavy goods vehicle loading for both French and Brazilian highways.

Figure 39 .

 39 Figure 39.(a) Dimensions and loads (in tonnes) of the vehicle of type T2S3 and (b) Brazilian legal capacity for 4-axle semi-trailer vehicles. 3.5.2.1 Traffic simulation using ViscoRoute©

Figure 40 .

 40 Figure 40.(a) French tRoad loading configuration (not to scale) and (b) maximum tensile strain in the bottom of each bituminous layer obtained with ViscoRoute©.The loading condition studied was defined by dual wheels with 0.662 MPa unit pressure (32.5 KN per wheel). The wheels "fingerprint" were described in the software by two ellipses with a radius of 0.125m and a centre distance of 0.375m. The distance

  Figure 41.(a) Vertical stress in the surface of the pavement and (b) scheme of the pressure loading areas obtained with ViscoRoute©. In order to replicate the stress condition in the French pavement modelled in Cast3M® with good approximation, only ViscoRoute© z-coordinates associated to compressive stress magnitudes were considered (𝑧 1 to 𝑧 6 ). As initially defined in the loading characteristics in ViscoRoute©, the ellipse-shaped wheel fingerprint had a diameter of 0.25 m (Figure 42(b)) and a velocity of 16.667 m/s. The 2-D plain strain configuration of the problem in Cast3M® limited ℎ 𝑤 to a unit-value and 𝐴 𝑤 to rectangular-shaped areas (Figure 42(c)). By keeping the same length 𝑙 𝑤 of each zcoordinate of ViscoRoute© in Cast3M®, together with the mean vertical stress associated to it, the equivalent force magnitude to be applied in the upper surface of the Cast3M® geometry was obtained, in Newton. The duration of each loading application in 𝑙 𝑤 was a direct implication of the chosen velocity of the moving wheel.

Figure 42

 42 Figure 42(a) depicts an example of how the force in Cast3M® for each z-coordinate

Figure 42 .

 42 Figure 42.(a) Mechanical loading magnitudes and duration in Cast3M®, (b) scheme of the wheel fingerprint in ViscoRoute© and (c) in Cast3M®.

Figure 42 (

 42 Figure 42(a), at constant temperature 𝑇 = 20°C in the whole structure; and ii) a transient thermal calculation with the temperature imposed in the surface described by the 𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 curve depicted in Figure 37, an initial constant 𝑇 0 = 21.8°C and no trafficinduced loading. The types of elements used in the FE mesh are listed in Table10:

Figure 43 .

 43 Figure 43. Mesh densities analysed in the mesh convergence study. Also in Figure 43, in the mesh entitled Case E, the location of point PC (Point in the Corner) is depicted. Point PC is located in the bituminous base layer of the French eRoad structure, in the same axis of the vertical interface between the charging unit

Figure 44 .

 44 Figure 44. Influence of the mesh density on the simulations. The evolution of temperature resulted from the transient thermal calculation in point PC is depicted in Figure 45. It is observed by the overlapping curves that, for thermal loading simulations, there was no impact in varying the mesh density near the critical position of point PC.

Figure 45 .

 45 Figure 45. Temperature evolution in point PC with varying meshes.

Figure 46 .

 46 Figure 46. Displacement, stress and strain evolution in point PC with varying meshes.

Figure 47 .

 47 Figure 47. Horizontal tensile strain on the bottom of the bituminous layer -𝐿𝐵 (𝑦= -0.34 𝑚) for mesh density analysis.

a 2 -

 2 D geometrical model of 5 x 5 metres. This dimension was used for all the roadscale FE simulations performed in this research (Brazilian and French tRoads and eRoads). In this section, it is defined how big the model needed to be to ensure that the results of the analysis in the vicinities of the charging unit were not affected by the boundary conditions of the model. Once again, the scenario of the traffic simulation of a passing wheel at 𝑇 = 20°C (Figure42(a)) was used. This time, French tRoad and eRoad configurations were analysed. The criterion adopted for comparison was the variation in the maximum horizontal tensile strain at the bottom of the bituminous layer in relation to an increase of a dimension factor (𝑥/𝑐). Due to symmetry, the schematic of Figure48represents half of the French eRoad profile with: x and y referring to the total width and depth of the structure, respectively; 𝐶 representing the width of the charging unit; and line 𝐿𝐵 y = -0.34m indicating the bottom of the bituminous layer.

Figure 48 .

 48 Figure 48. Schematic of the dimension factor used for mesh dimensionally studies.

Figure 49 .

 49 Figure 49. The final dimension of 5 x 5 metres was made considering the relative error below 5% in the two structures simulated.

Figure 49 .

 49 Figure 49. Maximum tensile strain on the bottom of the bituminous layer against the dimension factor. The maximum horizontal tensile strain in line 𝐿𝐵 y = -0.34m for the different dimension factors is depicted in Figure 50. From visual comparison to the maximum tensile strain obtained with ViscoRoute© simulation (Figure 40), it is concluded that using a 2-D geometrical model of 5 x 5 metres for mechanical simulations is valid. Finally, for all thermal and mechanical simulations of both Brazilian and French structures (tRoad and hypothetical eRoads), a 5 x 5 metres 2-D model was used, with mesh density of Case E.

Figure 50 .

 50 Figure 50. Horizontal tensile strain on the bottom of the bituminous layer (𝐿𝐵 (𝑦= -0.34 𝑚) ) for dimension analysis.

  of the study, two types of specimens were manufactured and subjected to thermal loading tests: six tRoads and six eRoads. For the tRoad specimens, bituminous mixture slabs were simply sawn into rectangular beams. For the eRoad specimens, a trench was created in the centre of the slabs in order to accommodate the EPDM bedding and a bonding layer of Corkelast VA-60®; and sawn into rectangular beams after the assembly. The eRoad specimen geometry and fabrication process aimed at representing the APS for Roads conductive system and the most common field practises in terms of road renovation. The characteristics of the elastomeric components are not discussed beyond what is publicly available.A novel experimental protocol is also described in this chapter. The goal of the test proposed is to characterize the response of eRoad specimens to daily temperature fluctuations by means of Digital Image Correlation technique. Hence, all of the specimens tested first received a speckle pattern treatment on their flat front surfaces.They were then subjected to thermal loading cycles inside a climatic chamber. As the specimens faced temperature fluctuations, temperatures inside the chamber and inside each specimen component were registered using thermocouples. At specific times, images were captured using the full-featured software EyeMotion in combination with a camera Mikrotron EoSens® 25CXP+. These images were further processed using the Ncorr v1.2 software in the MATLAB environment. Some of the laboratory adaptations used in the experimental protocol described are based in the works of SANTOS (2020),[START_REF] Teguedi | Towards the local expansion and contraction measurement of asphalt exposed to freeze-thaw cycles[END_REF] WANG and[START_REF] Wang | A high resolution DIC technique for measuring small thermal expansion of film specimens[END_REF].

Figure 51 .

 51 Figure 51. Trimming steps of the tRoad slabs to eliminate the borders (not to scale).

Figure 52 .

 52 Figure 52. Sawing steps of the eRoad slabs to create the trench and to eliminate the borders (not to scale).

  , the different preparation stages of the eRoad specimens are depicted. From Figure 53, respectively: compaction of the slab, elimination of the borders, trench excavation and bottom of the trench surface preparation. In Figure 54 the subdivision of the trench into smaller subsections and the final texture of the trench bottom are depicted. The target depth of the shallow grooves created in the bottom of the trench was 5 mm. The specimens were left to dry for a minimum period of one week and cleaned with jets of compressed air before the final assembly. The remaining slab was used to identify bituminous mixture properties, including Prony series coefficients and timetemperature shift factors. (Section 3.3.2.1.2 Complex modulus tests).

Figure 53 .

 53 Figure 53. Preparation stages of the eRoad specimens in laboratory.

Figure 54 .

 54 Figure 54. Trench excavation procedure and final texture of the eRoad slabs.4.1.2 Charging unit

Figure 55 .

 55 Figure 55. EPDM original specimen and preparation of the reduced specimens to be used in the eRoad assembly.

  (a)). Prior to the assembly of the eRoad specimens, a batch of small Corkelast VA-60® beams was moulded in order to produce shims for the support of the EPDM specimen in the eRoad assembly (Figure 56(b)). The use of shims facilitated the flow of Corkelast VA-60® through the interface of the bituminous mixture and the EPDM bedding without affecting the target alignment. Corkelast VA-60® specimens were also fabricated for viscoelastic characterization by means of the Dynamic Mechanical Analysis (DMA) (Figure 56(c)) -Annexe D. No primers nor epoxy adhesive were used to treat the moulds, the contact surfaces of the bituminous mixture and of the EPDM specimen. The Corkelast VA-60® specimens were cured for at least 72 h before mold-release and testing.

Figure 56 .

 56 Figure 56.(a) Weighting of the Corkelast VA-60® components and aspect of the elastomerepoxy system before pouring, (b) Corkelast VA-60® shims and (c) DMA samples. 4.1.3 General specimen asse-mbly

Figure 57 .

 57 Figure 57. Steps of the eRoad assembly: (a) positioning of the EPDM and (b) woodreinforced barrier. Finally, the fours slabs were ready for the last sawing stage (two for tRoad and two for eRoad specimens). The target dimensions of each tRoad specimen were 540 mm in length (x direction) by 90 mm in height (y direction) by 100 mm in thickness (z direction). Upper and bottom surfaces of each specimen were trimmed to obtain flat surfaces and a symmetric geometry (Figure 58). The air voids content and the density of the specimens were measured by means of gamma rays, according to the EN 12697-7:2022 Standard. Each tRoad specimen received a speckle pattern treatment on the flat front surface (Section 4.2 Speckle pattern) and, on the back surface, a hole was drilled for the installation of a thermocouple (Ø = 4 mm). A tRoad specimen is depicted in Figure 58.

Figure 58 .

 58 Figure 58. Sawing steps of the tRoad slabs (not to scale) and tRoad specimen back surface with the location of the thermocouple.For the eRoad specimens, the last sawing stage started by eliminating the borders which contained the shims and some remaining pieces from the wood forms,

Figure 59 .

 59 Figure 59. Sawing steps of the eRoad slabs (not to scale) and eRoad specimen back surface with the location of the thermocouples.

Figure 60 .

 60 Figure 60. Examples of (a) natural, (b) spray paint and (c) water transfer printing speckle patterns.

Figure 61 .

 61 Figure 61. Aerial schematic of the experimental set-up with an eRoad specimen.

Figure 62 .

 62 Figure 62. Alterative system to limit out-of-plane displacements of the specimens.

Figure 63 .

 63 Figure 63. Thermal loading cycle phases.

4. 3 . 2

 32 Image acquisition parameters (EyeMotion software)The 2-D DIC method used in this research involved the use of a single camera mounted on a tripod to measure displacements in plane. The acquisition equipment consisted of a 25CXP+ high-speed CMOS camera with a 25 Megapixel sensor (resolution of 5120 x 5120 pixels 2 ) and lens with a 50mm focal length. The actual pixel size of the camera is 4.5 x 4.5 μm 2 and, at full resolution, the frame rate can go up to 81 fps at 8-bit and to 69 fps at 10-bit grayscale encoding. The image acquisition was set to an 8-bit grayscale encoding. As the main objective of this study was to investigate the overall thermally-induced strain fields within eRoad specimens, the measurement zone comprised the whole visible surface of the specimen containing the three different eRoad components. As aforementioned, an attempt was made to block external sources of light to enter the testing room. Nevertheless, a full isolation of the room was not achieved and the exposure time parameter needed to be redefined for each test individually, depending on the luminosity of the day. In the same way, the positioning of the LED light sources was adjusted when necessary. It is important to highlight that, once the image acquisition parameters were set for a specimen, they remained the same for all the images acquired during the complete thermal test cycle of that specimen (reference image, conditioning phase, Phase I, Phase II and final conditioning phase to return to a steady-state temperature of 20°C).

Figure 64 .

 64 Figure 64. The interface of the EyeMotion software during the alignment of the camera with the specimen. As illustrated in Figure 64, the size of the images was set to 5120 x 2054 pixels 2 . The number of frames was equal to 50 frames per image and the exposure time varied from 1650 to 2300 μs, depending on the luminosity inside the testing room. The EyeMotion software is equipped with an Image Statistics tool, in which the histograms of the full image or of parts of it can be plotted in real time. During the pre-test adjustments, the histograms of the area containing the bituminous mixture were analysed in order to avoid saturations and to obtain a uniform distribution of pixel intensity values. The recordings started and stopped manually by the operator of the test. The images were exported as Portable Network Graphics files (PNG extension) and further processed using the MATLAB open-source software Ncorr. The tests were relatively long, so there was not enough space on the storage disk for a high-frequency image acquisition. Hence, for each thermal loading cycle, the number and frequency of images saved were defined as follows: i) for the reference image and the final image at 20°Can image was captured every 5 seconds for the duration of one minute (total of 12 images); ii) for the images acquired during Phase II of the thermal loading cyclethree images were captured every 2 minutes for the duration of five hours (total of 450 images). The time-based synchronization of the images with the temperature data were performed manually after the conclusion of the tests.

  x 170 x 15 mm)high thermal stability and low thermal conductivity. An XY-table (also known as cross slides) was used to precisely translate the specimen along the horizontal and vertical axis (Figure65(a)). The temperature of the quality measurement testing room was set at 20°C ± 1°C.

Figure 65 .

 65 Figure 65.(a) Experimental set-up and principle of the (b) in-plane and (c) out-of-plane displacement tests.

Figure 68 .

 68 Figure 68. Variation of the global root-mean-square error (𝑅𝑀𝑆𝐸 𝑔𝑙𝑜𝑏𝑎𝑙 ) of the measured strain as a function of the subset radius.

"

  Valeu a pena? Tudo vale a penaSe a alma não é pequena.Quem quer passar além do BojadorTem que passar além da dor." analysis aimed at verifying the evolution of the temperature fields in the French tRoad section as a result of a transient calculation. The research site provided data from thermocouples installed at different depths of the French highway[START_REF] Ktari | Consideration of Seasonal Temperature Changes in the French Pavement Design Method[END_REF], to which the temperature evolutions in points PY1, PY2 and PY3 on the model were compared to (Figure69). The simulation recreated 48 hours of thermal loading measured in the field.

Figure 69 .

 69 Figure 69. Thermal loading verification using the French tRoad profile.

5. 1 . 2

 12 Temperature evolutionTwo additional points were investigated in order to compare the impact of the rigid inserts on the temperature evolution inside the structure. Point PY1 is located 2 cm below the CU and in the symmetry axis of the 2-D geometry; while point PC is located in the same height of point PY1, but in the axis of the interface between the elastomer-epoxy system and the wearing surface (Figure70). For the French eRoad, both PY1 and PC are located in the bituminous base layer (GB). For the Brazilian eRoad, both points remain in the bituminous wearing surface (CBUQ). The evolution of temperature in points PY1 and PC are depicted in Figure 71. On the right side of each plot in Figure 71, the temperature profiles correspond to the virtual hour following the first peak of warm temperature in the surface. For the French pavement, it displays the temperature profile at hour 13h; for the Brazilian pavement, it displays the profile at hour 15h.

Figure 70 .

 70 Figure 70. Location of points PY1 and PC in the French and Brazilian eRoad structures. (a) French structure

Figure 72 .

 72 Figure 72. Maximum deformed structure (French pavement, 𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = 41.0°C).

Figure 73 .

 73 Figure 73. Maximum deformed structure (Brazilian pavement, 𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 = 47.5°C).

Figure 74 .

 74 Figure 74. Location of points PS1 and PS2 in the French eRoad structure.

Figure 75 .

 75 Figure 75. Displacement evolution in the points on the surface near the interface with the charging unit due to thermal loading.

Figure 76 .

 76 Figure 76. Thermal loading applied in the upper line of (a) French and (b) Brazilian pavements.

Figure 77 .

 77 Figure 77. Strain evolution in the points on the surface near the interface with the charging unit due to thermal loading.

Figure 78 .

 78 Figure 78. Strain fields for French and Brazilian eRoads due to thermal loading. As illustrated in Figure 78, a local concentration of transverse compressive strain appears in the surface of the bituminous mixture as a result of temperature fluctuations, in the proximity of the CU. The strain fields inside the rubbery materials are depicted in Figure 78, but they are not deeply analysed in the scope of this study.

Figure 79 .Figure 80 .

 7980 Figure 79. Stress evolution in the points on the surface near the interface with the charging unit due to thermal loading. In both structures, French and Brazilian, the generation of transverse stress in the vicinity of the CU was higher in point PS1. Particularly for the French configuration, the stress amplitude and the stress cycle was in accordance with the thermal loading cycle applied in the surface of the pavement (Figure 76(a)). For the Brazilian structure, a delayed response in terms of stress is observed, similarly to what was observed for the displacement and strain evolutions. The association of the stress amplitude with the thermal loading amplitude can give an indication of the ability of the bituminous

Figure 82 .

 82 Figure 82. Temperature evolution in the Brazilian eRoad structure at hour 28h of the thermal loading cycle.

Figure 83 .

 83 Figure 83. Procedure used to simulate the thermal and mechanical loadings cases.

  (a), the French eRoad cross-section is depicted, in which the end of the bituminous layer corresponded to the beginning of the granular roadbed, in depth. For the Brazilian eRoad, a granular base layer is located between the bituminous layer and the roadbed, which explains the additional points of investigation(Figure 84(b)).

Figure 84 .

 84 Figure 84. Points of analyses for the thermal and mechanical loadings simulations (not to scale). 5.2.1 Equivalence of 3-D to 2-D loading conditions

Figure 85

 85 Figure 85.(a) French tRoad loading configuration (not at scale) and (b) comparison of the horizontal strain at the bottom of each bituminous layer obtained with ViscoRoute© and Cast3M®. In the plot of Figure 85(b), the curves obtained with the software ViscoRoute© for every depth refer to values calculated in the middle axis of the wheel, in the driving direction of the road (strain at coordinate 𝑧 6 ). For Cast3M®, the curves refer to the strain obtained at half duration of the total loading. It is important to recall that the time duration of a single load cycle in Cast3M® was estimated by dividing the size of the footprint area in the driving direction and the vehicle velocity. Hence, the total loading time was 0.0149 seconds, and the half duration of loading happened at 0.00745 seconds. Despite accounting for the viscoelastic properties of the bituminous mixtures through different rheological models (Huet-Sayegh in ViscoRoute© and Generalized Maxwell Model in Cast3M®), the two software give strain levels at the bottom of each bituminous layers with very good approximation. Some slight divergences in the results were observed in the symmetry axis of the 2-D structure and when approaching the outer right side of the geometry in Cast3M®, in line L3. That is explained by the set of boundary conditions adopted in the 2-D model, in which the roadbed was constrained in stretching direction (𝑢 𝑥 = 0) in the right extremity of the mesh and a symmetry plane boundary condition fixed the fluxes/normal components across the symmetry axis to

  illustrates the evolution in time of the vertical stress in point PB3 calculated in ViscoRoute© and in Cast3M®. One can observe that the simplification of the time-history of the force acting on the pavement from 3-D to 2-D using the methodology proposed generated a stronger and much faster solicitation of this point in the 2-D structure (rapid pulse load).Yet, for the main comparative purpose of tRoad and eRoad behaviour due to coupled environmental and traffic-induced loadings, the displacement, strain and stress fields calculated in the pavements were considered satisfactory and are discussed in the following sections of results.

Figure 86 .

 86 Figure 86. Vertical compressive stress evolution in point PB3 at temperature of 20°C.

Figure 87 .

 87 Figure 87. Displacement evolution in the points on the surface under the wheel due to thermal and mechanical loading. The first remark in terms of displacement evolution concerns the superposition of the tRoad and eRoad curves for each climatic consideration. The curves of the French structures simulated at an equivalent temperature of 15°C started with zero values of displacement, reached maximum levels of magnitude of -0.5 mm in both points PS3 and PS4, and returned to zero once the mechanical loading was ceased. The same behaviour was observed for the Brazilian structure, with only slightly higher maximum magnitudes of vertical displacement obtained (-0.6 mm). The superposition of the tRoad and eRoad curves for the combined thermal and mechanical simulations considering a temperature profile are also observed in Figure 87. One can notice that, when the temperature profiles from thermal loading simulations were taken into account (TS curves), the displacement curves depicted positive displacement values in the initial time before the mechanical loading was applied. This indicates that the peak of warm temperature in the surface of the structures has caused an expansion of the pavement layers in the vertical direction, which is in accordance to the deformed structures depicted in Figure 72 and Figure 73. That means that the effect of temperature was satisfactorily accounted in this second level of simulations.

French

  Figure 88. Vertical displacement on the surface of the structures due to thermal and mechanical loading.

Figure 89 .

 89 Figure 89. Strain evolution in the points at the bottom of the bituminous layer due to thermal and mechanical loading.

  Figure 90. Strain field in the French bituminous layers due to thermal and mechanical loading (mechanical loading at 0.012 seconds; TS = 39.1°C).

  Figure 91. Strain field in the Brazilian bituminous layer due to thermal and mechanical loading (mechanical loading at 0.012 seconds; TS = 46.1°C).

  Figure 92. Temperature profile in the eRoad structures and location of points near the CU. In Figure 92, four points located in the vicinities of the CU in the bituminous layers are depicted. Points P1 to P3 distant 5 mm from the interface of the CU and the bituminous layer, in the transverse direction. In depth: point P1 is located in the surface of the structure (𝑦 = 0 𝑚), point P2 is at the same depth of the EPDM corner (y = -0.06 m) and point P3 is at the same depth of the Corkelast VA-60® corner (y = -0.08 m). For the French and Brazilian structures, points P1 to P3 are located in the wearing surface. Particularly for point P4, which is located below the CU, in the French structure it is located in the bituminous base layer (GB3) and in the Brazilian structure it belongs in the bituminous wearing surface (CBUQ). Point P4 is in the axis

Figure 93 .

 93 Figure 93. Strain evolution in the points in the bituminous layers near the CU due to thermal and mechanical loading.

  Figure 94, figures (a) and (b) in the first row correspond to the loading time at 0.012 seconds in the Teq climatic case. The temperature in which the properties of the materials were determined was 20°C, which explains why for the French eRoad the CU elastomeric components were under compressive strain, while for the Brazilian eRoad tensile strain was observed (French Teq = 15°C < 20°C < Brazilian Teq = 25°C). In the bottom row of Figure 94, figures (c) and (d) correspond to the loading time at 0.012 seconds past 12h of thermal loading in the French pavement and past 15h in the Brazilian pavement. Attention must be given to the critical strain distribution near the CU corner of the French eRoad, in which three different materials intersect: Corkelast VA-60®, BBSG and GB3 (Figure 94(c)).In Figure94(d), the transition of compressive strain in point P1 to tensile strain in points P2 and P3, and back to compressive strain in P4 is observed in the Brazilian structure, in accordance to the curves in Figure93.

  Figure 94. Horizontal strain fields 𝜀 𝑥𝑥 (𝜇𝜀) in the eRoad bituminous layers at a given instant of mechanical loading in the two climatic scenarios.

Figure 95 .

 95 Figure 95. Stress evolution in the points on top of the roadbed due to thermal and mechanical loadings.From the plots in Figure95, it is observed that the maximum compressive stress on top of the subgrade was obtained below the symmetric centre of the two wheels axis (points PB3) in all the cases. The tRoad and eRoad curves were superposed for all of the climatic scenarios. In all of the cases, the curves started with zero values of stress, reached maximum levels of compressive stress when the maximum mechanical loading pulse was applied, and returned to zero once the loading was ceased. This indicates that far from the CU and from significant temperature fluctuations (mainly in the surface), the magnitudes of stress on top of the subgrade under the wheel application in tRoads and eRoads are very similar. These findings are in accordance with the results of numerical analyses performed by[START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF] and by[START_REF] Chen | Towards an understanding of the structural performance of future electrified roads: a finite element simulation study[END_REF], who also stated that even simplified elastic simulations of eRoads give similar results when evaluated far from the CU in ideal conditions of use (no wheel wander). Nevertheless, in terms of stress fields within the structure, a local concentration of stress was observed near the interface of the CU and the bituminous layers, following the opposite trend of the strain distribution discussed previously. In Figure96and Figure97the stress fields corresponding to the loading time at 0.012 seconds past 12h of thermal loading in the French pavement and past 15h in the Brazilian pavement are depicted. The

Figure 98 .

 98 Figure98. In the right axis, in red colour, the vertical stress is plotted and the limits vary from 0.4 to -0.4 MPa in steps of 0.1 units (MPa). In the left axis, in black, the horizontal stress is plotted and the limits vary from 0.8 to -0.8 MPa in steps of 0.2 units (MPa). The stress resulting from the thermal and mechanical loading depicted in Figure98corresponds to the thermal loading time at 12h in the French pavement and at 15h in the Brazilian pavement.

Figure 98 .

 98 Figure 98. Stress evolution in the points in the bituminous layers near the CU due to thermal and mechanical loadings.

  Initially, in order to convert a 3-D load used to describe traffic in classical pavement design methodologies into a 2-D configuration, a 3-D elliptical-shaped dual wheels loading was applied in the French tRoad profile using the software ViscoRoute©. A vertical contact stress was applied on the upper surface of the same French tRoad profile in 2-D using the software Cast3M®. The solicitation in Cast3M® was fitted to the solicitation in ViscoRoute© considering the horizontal strain developed at the bottom of each bituminous layer as the fitting parameter. A homogeneous and constant temperature of 20°C was considered for the analysis (temperature of reference used to determine the properties of the materials) and the viscoelastic properties of the bituminous mixtures were accounted in the two software by means of rheological models

  circulation paths are not recommended. These findings are in accordance with the results of[START_REF] Ceravolo | A computational methodology for assessing the time-dependent structural performance of electric road infrastructures[END_REF][START_REF] Chen | Towards an understanding of the structural performance of future electrified roads: a finite element simulation study[END_REF], who also state that observations of local concentration of strain and stress in the vicinities of the CU are important for the correct design and assessment of eRoads, in addition to the locations of analysis below the wheel. In this research, the observations of points far from the CU and at the bottom of the bituminous layer in simplified Teq analyses were found to give similar and even better structural behaviour in eRoads, especially for robust pavements like the French flexible pavement studied.Temperature-induced distresses happened at a different frequency than the traffic-induced distresses (BAYAT; KNIGHT; SOLEYMANI, 2012; BISWAS; HASHEIMIAN;[START_REF] Biswas | Investigation on seasonal variation of thermal-induced strain in flexible pavements based on field and laboratory measurements[END_REF] ISLAM;[START_REF] Islam | Measuring thermal effect in the structural response of flexible pavement based on field instrumentation[END_REF][START_REF] Ongel | Analysis of 30 years of pavement temperatures using the enhanced integrated climate model[END_REF] HARVEY, 2004).In this way, for the particular case of the eRoads studied, it is suggested to evaluate three important factors when designing eRoads: a) thermal loading history of the location of the pavement, b) the compatibility of the CU components and the bituminous mixture in terms of thermomechanical response, and c) the adaptation of the geometry of the CU in relation to the existing pavement profile. Hourly, daily, seasonal and yearly temperature fluctuations are important to estimate the repetitive effect of volumetric variation of the elastomeric materials that constitute the CU and to compare it with the thermomechanical behaviour of the existing wearing surface.

  loading endured by flexible pavements, and the viscoelastic properties of the bituminous mixtures were well taken into account by the Prony series terms. The procedure developed in Cast3M® opened a wide sort of possibilities of parametric studies to size components of the CU and practical inclusion techniques in existing pavements. These initial analyses served to indicate that the interface between the CU and the pavement layer constitutes a critical zone in terms of thermomechanical response, which needs to be better investigated in laboratory.Epigraph chosen by Silvia de Freitas Alves "Para frente, custe o que custa!" Colégio Militar de Fortaleza -CMF (Casa de Eudoro Corrêa)In this section, the DIC technique was used to calculate the coefficients of thermal expansion (CTE) and contraction (CTC) of each individual eRoad component. For this purpose, single material specimens were tested in both warm and cold cycles. For the EPDM blend and Corkelast VA-60®, one specimen was tested in both warm and cold thermal loading cycles. The EPDM specimen dimensions were: 270 mm in length (x direction) by 60 mm in height (y direction) by 140 mm in thickness (z direction). The Corkelast VA-60® dimensions were: 350 mm in length (x direction) by 100 mm in height (y direction) by 100 mm in thickness (z direction). For the bituminous mixture, virgin tRoad specimens were subjected to one single thermal loading cycle each, in order to avoid the development of plastic deformation in the material. In Figure99, some specimens before and after the speckle pattern treatment are depicted.

Figure 99 .

 99 Figure 99. EPDM blend, Corkelast VA-60® and tRoad CP01 before and after speckle painting. 6.1.1 Elastomeric materials

Figure 100 .

 100 Figure 100. Temperature evolution inside the elastomeric specimens (EPDM on the left, Corkelast VA-60® on the right). The displacement fields calculated from the images by means of the DIC technique allowed the measurement of the global thermal expansion/contraction of the materials. The mean 𝜀 𝑥𝑥 and 𝜀 𝑦𝑦 were calculated from the displacements of the subsets (group of pixels) in the x and y direction, respectively. The coefficient of thermal expansion/contraction of the specimens was measured by calculating the isotropic deformation (𝜀 0 = (𝜀 𝑥𝑥 𝑚𝑒𝑎𝑛 + 𝜀 𝑦𝑦 𝑚𝑒𝑎𝑛 )/2) on a predefined region of interest divided by the temperature variation in the specimen (∆𝑇 = 𝑇 𝑓𝑖𝑛𝑎𝑙 -𝑇 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ). The size of the images was set to 5120 x 2074 pixels 2 . The total front surface of the specimens of the EPDM was 2470.5 x 391.3 pixels 2 and of Corkelast VA-60® was 3166.3 x 747.1 pixels 2 The physical size of a pixel was 0.11096 mm for the EPDM and 0.11133 mm for Corkelast VA-60®. The different regions of interest in comparison to the total surface of the elastomeric specimens are illustrated in Figure 101.

Figure 101 .

 101 Figure 101. Regions of Interest (ROI) used to calculate the coefficient of thermal expansion/contraction of the elastomeric materials (EPDM on the left, Corkelast VA-60® on the right). The centre of the squared and rectangular ROIs were aligned to the centre of the specimen surface, and by consequence to the centre of the image. All the DIC analyses were carried out with a subset radius of 20 pixels, a subset spacing of 5 pixels and a strain spacing of 4 pixels. In Figure 102, the calculated CTE and CTC for the EPDM and Corkelast VA-60® specimens are depicted in relation to the ratio of the ROI and the total surface area of the specimen (in percentage). The coefficients of the EPDM were calculated for a thermal gradient of 24.58°C (CTE) and -26.09°C (CTC).The coefficients of Corkelast VA-60® were calculated for a thermal gradient of 22.16°C(CTE) and -23.84°C (CTC).

Figure 102 .

 102 Figure 102. CTE and CTC of the elastomeric materials calculated for different ROIs.

Figure 104 .

 104 Figure 104. Exemplification of the temperature evolution inside tRoad specimens (CP01 on the left and CP03 on the right).

Figure 105 .

 105 Figure 105. CTE and CTC of the bituminous mixture calculated for different ROIs.From the plots in Figure105, it is observed that the bituminous mixture coefficients display significantly smaller magnitudes than the ones of the elastomeric materials. For CTC measurements, the thermal coefficient of the two specimens tested converge to a common value once the region of interest starts to cover more than 20% of the total surface area. For CTE measurements, the thermal coefficient values continue to change with the increase of the ROI. It is important to remind that CTC and CTE were obtained from the mean 𝜀 𝑥𝑥 and 𝜀 𝑦𝑦 calculated within each ROI delimited area. The variability in the calculated values (more pronounced in CTE) in relation to the size of the area analysed can be partially explained by the heterogeneity and anisotropic characteristics of bituminous materials. Several studies have reported the influence of the bituminous mixture microstructure on its the thermal properties: different-sized and orientation of aggregates, mineralogy of the aggregates, distribution of air voids, thermo-sensitivity of the binder (grade of the bitumen), binder and moisture content, among others(CHEN et al., 2015a; ISLAM;[START_REF] Islam | Measuring thermal effect in the structural response of flexible pavement based on field instrumentation[END_REF]

  voids distribution in both longitudinal and transversal directions (DUBOIS; DE LA ROCHE;[START_REF] Dubois | Influence of the compaction process on the air void homogeneity of asphalt mixtures samples[END_REF]. Hence, the definition of a representative region of interest for the DIC analysis becomes a challenge, especially for large sized specimens (surface of the images treated covering almost the totality of the slabs in longitudinal and vertical direction) and the range of temperatures studied (-10 to 50°C)using the bituminous mixture as reference, as elastomeric materials generally withstand temperatures above 200°C. For simplicity, the CTE/CTC was represented as the slope of a linear relationship between temperature and strain in a ROI that covers 50% of the total surface area of the specimens. The measured CTC of the bituminous mixture was 1.47 × 10 -5 °C-1 (mean value of CP01 and CP04). The measured CTE of the bituminous mixture was 2.59 × 10 -5 °C-1 (mean value of CP02 and CP03). These values are within the range of values reported in literaturefrom 1.45 × 10 -5 °C-1 to 3.48 × 10 -5 °C-1 (ISLAM;[START_REF] Islam | Determining thermal properties of asphalt concrete using field data and laboratory testing[END_REF] LUCA;[START_REF] Luca | New measurement of thermal properties of Superpave asphalt concrete[END_REF][START_REF] Teguedi | Towards the local expansion and contraction measurement of asphalt exposed to freeze-thaw cycles[END_REF] XU;[START_REF] Xu | Measurement and evaluation of asphalt concrete thermal expansion and contraction[END_REF].

Figure 106 .

 106 Figure 106. Temperature evolution inside the components of the eRoad CP07 specimen (warm cycle).

Figure 107 .

 107 Figure 107. Temperature evolution inside the components of the eRoad CP10 specimen (cold cycle).

  Figure 108 and Figure 109 depict the displacement and strain fields of two eRoad specimens: CP07 specimen (warm cycle) and CP10 specimen (cold cycle). The zero values of displacement in both x and y axis are located on the upper right corner of the images.

Figure 108 .

 108 Figure 108. Thermomechanical kinematic fields of the eRoad CP07 specimen (warm cycle).

Figure 109 .

 109 Figure 109. Thermomechanical kinematic fields of the eRoad CP10 specimen (cold cycle).

Figure 110 .

 110 Figure 110. Temperature evolution inside the components of the eRoad CP08 specimen (warm cycle).

Figure 111 .

 111 Figure 111. Temperature evolution inside the components of the eRoad CP09 specimen (warm cycle).

Figure 112 .

 112 Figure 112. Temperature evolution inside the components of the eRoad CP11 specimen (cold cycle).

Figure 113 .

 113 Figure 113. Temperature evolution inside the components of the eRoad CP12 specimen (cold cycle).

Figure 114 .

 114 Figure 114. Thermomechanical kinematic fields of the eRoad CP08 specimen (warm cycle).

Figure 115 .

 115 Figure 115. Thermomechanical kinematic fields of the eRoad CP09 specimen (warm cycle).

Figure 116 .

 116 Figure 116. Thermomechanical kinematic fields of the eRoad CP11 specimen (cold cycle).

Figure 117 .

 117 Figure 117. Thermomechanical kinematic fields of the eRoad CP12 specimen (cold cycle).

Figure 118 .

 118 Figure 118. Virtual strain gauges position in the specimens (eRoad on the left, tRoad on the right).

Figure 119 .

 119 Figure 119. Deformed images selected for the quantitative analysis using virtual strain gauges.

Figure 120 .

 120 Figure 120. Schematic of the strain gauge displacements due to temperature variation.

  the evolution of the changes in the right-to-left gauges length (∆𝐿 = 𝐿 𝑓 -𝐿 0 ) is depicted for the two pairs of specimens analysed. The length change which is plotted in the vertical axis of the graphs is defined as of the sum of the calculated 𝑢 𝑥𝑥 for right and left strain gauges (absolute values). From the values of displacement depicted in Table26, it is observed that the right strain gauge of CP04 did not follow the expected trend of displacements (positive values instead of negative values) in Images 2 to 5. The same behaviour is noticed for the right strain gauge of CP10 in Image 5 (Table27). This behaviour is possibly explained by the motion of the specimen in the experimental set-up due to the use of compressed air jets during cold cycles, which might have impacted on the positioning of the specimen throughout the acquisition of the images. For those particular cases, the length change was calculated as the result of the difference between measured 𝑢 𝑥𝑥 for right and left strain gauges (absolute values).

Figure 121 .

 121 Figure 121. Change in the horizontal length of the specimens due to thermal expansion/contraction. A rigorous comparison between tRoad and eRoad configurations is not possible due to the different characteristics of the specimens, the uncertainties linked to the experimental test set-up and the fact that they were not faced with the exact same temperature variations throughout the sequence of images treated by means of the DIC technique. Nevertheless, the curves plotted in Figure 121 indicate that the rigid inclusions were responsible for a source of additional horizontal displacements resulted from the differential thermal expansion/contraction of the eRoad components.

  which makes it difficult to differentiate through 2-D DIC analysis the parcel of the displacements linked to the volumetric change of the specimen (due to temperature fluctuations) from the displacements linked to the motion of the specimen. An improvement to the thermal loading test would be to couple the DIC technique to other measuring techniques in order to distinguish the sources of displacement in the specimens (e.g. to place strain gauges on the back surface of the specimen). Another source of uncertainties is related to the movement of the base as a consequence of the weight of the specimens and of the temperature change. These instabilities of the base combined to the long duration of the test may have induced the bending of the specimens due to settlement.

a

  coupled thermomechanical transient viscoelastic model: it is crucial to take into account thermal loadings in the design of electrified flexible pavements. Finally, as more general conclusion, it is valid to infer that the experimental set-up developed in this study has a great potential to be used to assess innovative pavement profiles (inductive and conductive systems). An optimization in terms of test boundary conditions and a validation of the measurements by means of other conventional strain measurements techniques constitutes the next step towards the improvement of the protocol.Epigraph chosen by Julianne Melo, Marcela Gondim, Marina Castilho and Mateus César "Scientists say that human beings are made of atoms, but a little bird told me that we are also made of stories." "Os cientistas dizem que somos feitos de átomos, mas um passarinho me disse que também somos feitos de histórias."Eduardo Galeano7. CONCLUSIONS AND PERSPECTIVESThe present dissertation studied the thermomechanical behaviour of flexible eRoad pavements using two approaches: by means of 2-D FEM structural simulations and by means of thermal loading tests combined to the DIC technique. A thermoviscoelastic model was proposed for the numerical assessment of traditional and electrified road profiles, which was considered a suitable methodology to investigate local concentrations of strain and stress induced by thermal and mechanical loadings.An experimental protocol was proposed as a first step towards the development of testing procedures adapted to multi-components road profiles. It is valid to conclude that the DIC technique constitutes a reliable tool for the characterization of materials applied in the road engineering domain and on the assessment of eRoad specimens.The importance of this work relies on the consideration of a critical source of deformation in the investigation of flexible pavement structures behaviour: the impact of daily temperature fluctuations on the cyclic volumetric rearrangement of the eRoad components (thermal expansion and contraction) and on the changes in the mechanical properties of the bituminous mixture (linear viscoelasticity). In laboratory, an experimental device was set up for the continuous measurement of kinematic fields by means of the DIC technique as the specimens were subjected to warm and cold thermal cycles. The use of the DIC technique was found particularly powerful for a level of investigation in which the main goal is to recognize critical zones of strain concentration (in macro-scale). In addition, due to the secretive aspect of the technologies developed by industry for Electric Road Systems, the thermal loading test combined to the DIC analysis was considered suitable to initially size charging unit materials and to evaluate their compatibility to the existing infrastructure, without the need for a full characterization of patented components and before further expensive prototype testing.Finally, the formulated hypothesis that the rigid inserts would generate additional strain and stress concentrations in the bituminous layer due to the differential response of each material is confirmed. Nevertheless, for the numerical and experimental studies contained in this dissertation, assumptions were made in order to simplify the measurements (e.g. 2-D symmetry boundary conditions, homogeneous and isotropic behaviour of the bituminous mixtures, linear stress-strain relationships for elastomeric materials, non-temperature dependency of thermal properties, among others). Hence, as main suggestions for the continuation of this work and to the accurate quantification of the impact of rigid inserts in flexible pavements, it is listed:  To perform parametric studies using the thermo-viscoelastic model using different pavement profiles as reference and varied loading scenarios (different traffic and environmental conditions);  To implement contact elements to simulate the interaction between the charging unit and the pavement layers;  To model different charging unit geometries in order to validate the applicability of the FEM model in the pre-design phase of ERS in general, and not only the conductive system studied in this dissertation;  To include in the thermal loading the source of heat coming from the charging unit when this is activated and transferring energy to vehicles;  To improve the boundary conditions of the thermal loading test proposed in order to consider the confining aspect of real pavement layers;  To evaluate the behaviour of widely known isotropic and homogeneous materials in the thermal loading test to quantify the uncertainties of the DIC technique for this specific application;  To make use of conventional strain measurement devices in combination to the DIC technique in thermal loading tests to locally calibrate the imaging measurement system; and,  To perform repeatability tests using the thermal loading experimental protocol.These aforementioned research topics constitute a continuation of the work developed throughout this dissertation, focusing on a macro-scale analysis of the differential thermomechanical behaviour of eRoad components. Moreover, several micro-scale aspects of each individual material were found to be equally important for the successful comprehension of eRoad responses to thermal and mechanical loadings: the hyperelastic behaviour and the shape factor of elastomeric components, the nonlinear viscoelasticity and self-heating phenomenon of bituminous mixtures due to cyclic loading applications, and the impact of the aging of each material in the behaviour of the assembly. Finally, it is highlighted the necessity of defining failure criteria adapted to multi-components road profiles and of the development of rehabilitation and maintenance procedures which contemplate both tRoads and eRoads.

Figure 127 .

 127 Figure 127. Fitting of the temperature evolution obtained in FE simulations with the temperature evolution acquired during the thermal tests.

  ) and the phase angle (𝛿) of Corkelast VA-60® and of a conventional binder are plotted in Figure 129 and Figure 130. The tests were performed for a frequency sweep of 1 to 80 Hz, and temperatures ranging from -20 to 60°C. The bitumen 35/50 composes the French bituminous mixture studied (BBSG).

Figure 129 .

 129 Figure 129. Complex modulus master curves of Corkelast VA-60® and of 35/50 bitumen.

Figure 130 .

 130 Figure 130. Phase angle master curves of Corkelast VA-60® and of 35/50 bitumen. The moduli measured by the DMA is the complex tension-compression modulus 𝐸 * , composed by the real part and the imaginary part. The real part represents the ability of the material to store energy and the imaginary part represents the ability of the material to dissipate energy.

Figure 133 .

 133 Figure 133. Stress evolution in the points PC and PY1.

Table 1 .

 1 Summary of main eRoad feasibility studies and test track demonstrations.

Table 2 .

 2 Thermomechanical properties of the rail. ....................................................

Table 3 .

 3 Thermomechanical properties of the elastomeric materials. .......................

Table 4 .

 4 Bituminous mixtures properties. ..................................................................

Table 5 .

 5 Parameters of the Huet-Sayegh model (𝑻𝑹 = 20°C). ..................................

Table 6 .

 6 Bituminous mixtures Prony series terms (wearing surfaces). ......................

Table 7 .

 7 Bituminous mixtures Prony series terms (base and foundation). .................Table 8. Thermomechanical properties of the bituminous materials. ........................ Table 9. Thermomechanical properties of the unbound granular layers. ................... Table 10. FE mesh element types. ............................................................................ Table 11. Summary of results for mesh dimensionally study..................................... Table12. In-plane translation error estimation for a subset radius of 20 pixels. ...... Table13. Out-of-plane translation error estimation for a subset radius of 20 pixels.

................................................................................................................................

Table 14. Background noise estimation for a subset radius of 20 pixels. ................ Table 15. Vertical pseudo thermal gradients in points PY1 and PC. ....................... Table 16. Horizontal pseudo thermal gradients in points PY1 and PC. ................... Table 17. Strain magnitudes in the points on the surface near the interface with the charging unit at a given calculation time. ................................................................. Table 18. Maximum tensile strain 𝜀𝑥𝑥 (𝜇𝜀) in the points at the bottom of the bituminous layer. ....................................................................................................................... Table 19. Characteristics of the tRoad specimens. ................................................. Table 20. DIC analyses parameters and temperatures of tRoad specimens........... Table 21. DIC parameters and physical characteristics of the eRoad specimens. .. Table 22. Initial and final temperatures inside the eRoad specimen components. .. Table 23. Maximum and minimum displacements of eRoad specimens. ................ Table 24. Strain gauges horizontal displacements (𝑢𝑥𝑥 in mm) in CP03 tRoad. ..... Table 25. Strain gauges horizontal displacements (𝑢𝑥𝑥 in mm) in CP07 eRoad. .... Table 26. Strain gauges horizontal displacements (𝑢𝑥𝑥 in mm) in CP04 tRoad. ..... Table 27. Strain gauges horizontal displacements (𝑢𝑥𝑥 in mm) in CP10 eRoad. .... Table 28. Specific heat capacity of the elastomeric materials (obtained using a calorimeter). ............................................................................................................ Table 29. Specific heat capacity of the elastomeric materials (obtained using a Hot Disk® 𝐶𝑃 cell probe). ........................................................................................ Table 30. Thermal conductivity of the eRoad components. .....................................

TABLE OF CONTENTS

 OF 1 INTRODUCTION AND MOTIVATION ................................................................. 1.1 Introduction ...................................................................................................... 1.2 Objective.......................................................................................................... 1.3 Dissertation outline .......................................................................................... 2 LITERATURE REVIEW ......................................................................................

Table 1 .

 1 Afar from exploring all of the research projects in development, Table1lists the publicly mentioned projects up to this date and with accessible general information. For more detailed information, it is suggested:

	 the 'Review of existing power transfer solution' (EMRE et al., 2014) for a
	complete review on technical aspects of wireless technologies;

 the report of the World Road Association (PIARC, 2018) for a chronological catalogue of ERS developments since 1998;  the doctoral thesis of CHEN (2016) and the project reports of OLSSON (2014a, 2014b), HIGHWAYS ENGLAND (2015), E-WAY CORRIDOR (2018) and SUUL and GUIDI (2018) for feasibility studies of ERS solutions; and,  the works of LEDESMA (2015) and BALIEU; CHEN and KRINGOS (2019) for life cycle analysis discussions.

Table 1 .

 1 Summary of main eRoad feasibility studies and test track demonstrations.

	Project	Location	Solution	Demonstration start
	eHighway (Siemens)	Germany	Overhead lines
	eWayBW	Germany	Overhead lines	NA
	ELISA	Germany	Overhead lines	NA
	FESH	Germany	Overhead lines	NA
	eHighway (Siemens/Scania)	Sweden	Overhead lines
	eHighway (Siemens/SCAQMD/Volvo)	USA	Overhead lines
	APS for Roads (Alstom/CEREMA)	France	Rails on the road
	Elways	Sweden	Rails on the road
	eRoadArlanda (Elways)	Sweden	Rails on the road
	Slide-in Electric Road Systems (Alstom/Volvo)	Sweden	Rails on the road	NA
	ElonRoad	Sweden	Rails on the road
	EVolutionRoad (ElonRoad)	Sweden	Rails on the road
	HPDC (Honda)	Japan	Rails on the side of the road	NA
	Slide-in Electric Road Project (Bombardier Primove)	Germany/Sweden	Static induction
	UNPLUGGED project (ENIDE)	Germany/Spain	Static and dynamic induction	NA
	VICTORIA project (CIRCE)	Spain	Static and dynamic induction	NA
	Flanders' DRIVE	Belgium	Dynamic induction
	FABRIC project (Vedecom/ Qualcomm)	France	Dynamic induction
	INCIT-EV (Renault, Vedecom,	Netherlands/France	Static and dynamic
	Collas, Eurovia and others)	Italy/Estonia/Spain	induction
	Slide-in Electric Road Project (Bombardier Primove)	Germany	Dynamic induction	NA
	Integrated Infrastructure Solutions (INTIS and partners)	Germany/Sweden	Dynamic induction	NA
	ElectRoad	Germany/Israel/Italy Dynamic induction
	IPV (Seat Group)	Italy	Dynamic induction
	FABRIC project (Polito CWD)	Italy	Dynamic induction
	Japanese Railway Technical Research Institute (RTRI)	Japan	Dynamic induction	NA
	University of Tokyo	Japan	Dynamic induction	NA
	Oak Ridge National Laboratory (ORNL)	USA	Dynamic induction	Laboratory demonstrator
	Utah State University (WAVE)	USA	Dynamic induction
	OLEV / KAIST	South Korea	Dynamic induction

Table 2 .

 2 Thermomechanical properties of the rail.

	Component or material	Young's modulus E (Pa)	Poisson's ratio ν ( -)	Density ρ (kg/m 3 )	Coeff. of linear thermal expansion α (m/(m⋅°C))	Thermal conductivity λ (W/(m⋅°C))	Specific heat capacity Cp (J/(kg⋅°C))
	Rail	2.1 * 10 11 (1,

Table 4 .

 4 Bituminous mixtures properties.

	Parameter	BBSG 0/10	CBUQ	GB 0/14
	Aggregate type	Diorite	Granite	Limestone
	Bitumen content (%)	4.9	4.4	4.4
	Maximum specific gravity, Gmm (g/cm 3 )	2.640	2.533	2.509
	Bulk specific gravity, Gmb (g/cm 3 )	2.493	2.451	2.353
	Voids content, Vv (%)	5.6	4.0	6.5

Table 5 .

 5 Parameters of the Huet-Sayegh model (𝑻 𝑹 = 20°C).

		𝑬0 (MPa)	𝑬∞ (MPa)	𝜹	𝒌	𝒉	𝑨𝟎	𝑨𝟏	𝑨𝟐
	BBSG	1.14E+7	3.27E+10 2.003 0.215 0.677 3.543 -0.387 0.001748
	CBUQ	5.29E+7	3.05E+10 3.206 0.259 0.478 8.295 -0.447 0.001470
	GB	6.37E+6	2.97E+10 1.721 0.189 0.603 3.277 -0.396 0.002093

Table 6 .

 6 Bituminous mixtures Prony series terms (wearing surfaces).

		BBSG 0/10			CBUQ
	𝑬 𝟎 (MPa)	30.5779	𝑻 𝑹 (°C)	20	𝑬 𝟎 (MPa)	48.2194	𝑻 𝑹 (°C)	20
	𝑬 𝟏 (MPa)	1958.4126	𝝉 𝟏 (s)	5.1844e-8	𝑬 𝟏 (MPa)	809.6209	𝝉 𝟏 (s)	1.7751e-9
	𝑬 𝟐 (MPa)	3337.1412	𝝉 𝟐 (s)	1.0316e-6	𝑬 𝟐 (MPa)	2696.1457	𝝉 𝟐 (s)	1.7146e-7
	𝑬 𝟑 (MPa)	4474.1898	𝝉 𝟑 (s)	2.0526e-5	𝑬 𝟑 (MPa)	5351.8395	𝝉 𝟑 (s)	1.6562e-5
	𝑬 𝟒 (MPa)	6490.7672	𝝉 𝟒 (s)	4.0842e-4	𝑬 𝟒 (MPa)	11035.9966	𝝉 𝟒 (s)	1.5997e-3
	𝑬 𝟓 (MPa)	6972.4287	𝝉 𝟓 (s)	8.1266e-3	𝑬 𝟓 (MPa)	7862.5644	𝝉 𝟓 (s)	1.5452e-1
	𝑬 𝟔 (MPa)	5758.4631	𝝉 𝟔 (s)	1.6170e-1	𝑬 𝟔 (MPa)	3681.3805	𝝉 𝟔 (s)	14.926
	𝑬 𝟕 (MPa)	1600.6369	𝝉 𝟕 (s)	3.2175	𝑬 𝟕 (MPa)	549.2087	𝝉 𝟕 (s)	1.4417e-3
	𝑬 𝟖 (MPa)	204.2352	𝝉 𝟖 (s)	64.0202	𝑬 𝟖 (MPa)	124.2241	𝝉 𝟖 (s)	1.3925e-5
	𝑪𝟏	32.519	𝑪𝟐	229.6672	𝑪𝟏	27.7908	𝑪𝟐	157.1958

Table 7 .

 7 Bituminous mixtures Prony series terms (base and foundation).

		GB 0/14
	𝑬 𝟎 (MPa)	50.3744	𝑻 𝑹 (°C)	20
	𝑬 𝟏 (MPa)	1862.5913	𝝉 𝟏 (s)	3.8075e-8
	𝑬 𝟐 (MPa)	2897.0658	𝝉 𝟐 (s)	7.5589e-7
	𝑬 𝟑 (MPa)	3869.7859	𝝉 𝟑 (s)	1.5006e-5
	𝑬 𝟒 (MPa)	5238.7908	𝝉 𝟒 (s)	2.9792e-4
	𝑬 𝟓 (MPa)	6019.3108	𝝉 𝟓 (s)	5.9145e-3
	𝑬 𝟔 (MPa)	5260.4220	𝝉 𝟔 (s)	1.1742e-1
	𝑬 𝟕 (MPa)	1890.9248	𝝉 𝟕 (s)	2.3311
	𝑬 𝟖 (MPa)	348.7441	𝝉 𝟖 (s)	46.2777
	𝑪𝟏	23.3512	𝑪𝟐	169.5735

Table 8 .

 8 Thermomechanical properties of the bituminous materials.

	Component or material	Young's modulus E (Pa)	Poisson's ratio ν ( -)	Density ρ (kg/m 3 )	Thermal conductivity λ (W/(m⋅°C))	Specific heat capacity Cp (J/(kg⋅°C))

Table 9 .

 9 Thermomechanical properties of the unbound granular layers.

	Component or material	Young's modulus E (MPa)	Poisson's ratio ν ( -)	Density ρ (kg/m 3 )	Thermal conductivity λ (W/(m⋅°C))	Specific heat capacity Cp (J/(kg⋅°C))	Coeff. of linear thermal expansion α (m/(m⋅°C))
	PF3

Table 10 .

 10 FE mesh element types.

	Index	Geometric element	Number of nodes	Interpolation type
	TRI6	triangular	6	quadratic
	QUA8	quadrangular	8	quadratic

Table 11 .

 11 Summary of results for mesh dimensionally study.

			French tRoad	French eRoad
	Dimension	Factor (x/c)	𝜺 𝒙𝒙 𝒎𝒂𝒙	(με)	Error (%)	𝜺 𝒙𝒙 𝒎𝒂𝒙	(με)	Error (%)
	2m x 2m	10.53	20.38	47.76	20.30	41.99
	3m x 3m	15.79	30.11	14.13	28.83	13.82
	4m x 4m	21.05	34.36	7.29	32.81	7.26
	5m x 5m	26.32	36.87	3.70	35.19	3.62
	6m x 6m	31.58	38.23	1.85	36.46	1.74
	7m x 7m	36.84	38.94	-	37.10	-

Table 12 .

 12 In-plane translation error estimation for a subset radius of 20 pixels.

		𝐸 𝑠𝑦𝑠 𝑔𝑙𝑜𝑏𝑎𝑙 𝑅𝑀𝑆𝐸 𝑔𝑙𝑜𝑏𝑎𝑙 𝜎 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙	∆ 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙
	𝑢 𝑥 (𝜇𝑚)	28.68	33.38	5.86	11.72
	𝑢 𝑦 (𝜇𝑚)	-1.43	4.09	1.06	2.12
	𝜀 𝑥𝑥	-3.74E-05	5.85E-04	5.83E-04	1.17E-03
	𝜀 𝑥𝑦	1.37E-04	3.90E-04	3.51E-04	7.01E-04
	𝜀 𝑦𝑦	-2.50E-05	4.01E-04	3.99E-04	7.99E-04

Table 13 .

 13 Out-of-plane translation error estimation for a subset radius of 20 pixels.

		𝐸 𝑠𝑦𝑠 𝑔𝑙𝑜𝑏𝑎𝑙 𝑅𝑀𝑆𝐸 𝑔𝑙𝑜𝑏𝑎𝑙 𝜎 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙	∆ 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙
	𝑢 𝑥 (𝜇𝑚)	-5.40	71.76	63.73	127.45
	𝑢 𝑦 (𝜇𝑚)	-91.66	112.05	63.63	127.25
	𝜀 𝑥𝑥	-3.13E-03	3.30E-03	7.93E-04	1.59E-03
	𝜀 𝑥𝑦	4.03E-06	5.35E-04	5.35E-04	1.07E-03
	𝜀 𝑦𝑦	-3.15E-03	3.31E-03	7.80E-04	1.56E-03

Table 14 .

 14 Background noise estimation for a subset radius of 20 pixels.

		𝐸 𝑠𝑦𝑠 𝑔𝑙𝑜𝑏𝑎𝑙 𝑅𝑀𝑆𝐸 𝑔𝑙𝑜𝑏𝑎𝑙 𝜎 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙	∆ 𝛼 𝑔𝑙𝑜𝑏𝑎𝑙
	𝑢 𝑥 (𝜇𝑚)	-11.67	11.84	2.05	4.11
	𝑢 𝑦 (𝜇𝑚)	-8.53	8.80	2.17	4.35
	𝜀 𝑥𝑥	1.01E-04	3.44E-04	3.28E-04	6.57E-04
	𝜀 𝑥𝑦	1.04E-05	2.25E-04	2.25E-04	4.50E-04
	𝜀 𝑦𝑦	1.02E-04	3.28E-04	3.11E-04	6.23E-04

Pavement structure French structure (13h) Brazilian structure (15h)

	𝑇 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 (°C)	38.80	46.10
	FEM tRoad PC = PY1 (°C)	30.03	32.65
	Pseudo gradient tRoad (°C / cm)	-0.88	-1.35
	FEM eRoad Point PC (°C)	27.21	29.74
	Pseudo gradient Point PC (°C / cm)	-1.16	-1.64
	FEM eRoad Point PY1 (°C)	23.98	26.74
	Pseudo gradient Point PY1 (°C / cm)	-1.48	-1.94

Table 16 .

 16 Horizontal pseudo thermal gradients in points PY1 and PC.

	Pavement	French	Brazilian
	structure	structure (13h)	structure (15h)
	FEM eRoad Point PC (°C)	27.21	29.74
	FEM eRoad Point PY1 (°C)	23.98	26.74
	Pseudo gradient (°C / cm)	0.17	0.16

Table 17 .

 17 Strain magnitudes in the points on the surface near the interface with the charging unit at a given calculation time.

	French structure	Point PS1 tRoad eRoad	Point PS2 tRoad eRoad	x = 0 ; y = -0.34 m tRoad eRoad
	𝜀 𝑥𝑥 (𝜇𝜀)	1.5	-2005.3	1.5	-808.0	0.4	-12.5
	𝜀 𝑦𝑦 (𝜇𝜀)	1065.4	1994.9	1065.4	1490.1	15.0	4.2
	Brazilian structure	Point PS1 tRoad eRoad	Point PS2 tRoad eRoad	x = 0 ; y = -0.12 m tRoad eRoad
	𝜀 𝑥𝑥 (𝜇𝜀)	10.2	-1079.4	10.3	1.4	10.3	-106.7
	𝜀 𝑦𝑦 (𝜇𝜀)	1452.5	1905.0	1452.5	1447.6	615.7	377.8

Table 18 .

 18 Maximum tensile strain 𝜀 𝑥𝑥 (𝜇𝜀) in the points at the bottom of the bituminous layer.

	French structure	Point PB3 tRoad eRoad	Point PB4 tRoad eRoad
	Teq = 15°C	32.2	30.3	30.3	28.7
	TS = 39.1°C	37.1	36.9	35.5	35.9
	Brazilian structure	Point PF3 tRoad eRoad	Point PF4 tRoad eRoad
	Teq = 25°C	30.5	30.7	40.7	40.6
	TS = 46.1°C	40.0	47.9	51.3	56.2

Table 19 .

 19 Characteristics of the tRoad specimens.

	Specimen Dimensions (cm)*	Weight (kg)	Air voids (%) Mean Standard value deviation	Density (g/cm3) Mean Standard value deviation
	CP01	54.00 x 9.23 x 9.83	12.22	6.23	2.21	2.48	0.06
	CP02	54.00 x 9.13 x 9.80	11.90	6.61	2.78	2.47	0.07
	CP03	54.00 x 9.00 x 8.20	9.98	6.18	2.09	2.48	0.06
	CP04	54.00 x 8.97 x 7.93	9.46	6.33	2.02	2.47	0.05
	CP05	54.00 x 9.20 x 7.50	9.34	6.40	2.12	2.47	0.04
	CP06	54.00 x 9.62 x 8.00	9.36	6.60	2.05	2.47	0.06
	* Length (x direction) by height (y direction) by thickness (z direction)

Table 20 .

 20 DIC analyses parameters and temperatures of tRoad specimens.

	Specimen Cycle	Factor (mm/pixel)	Temperature (°C) Reference Deformed Thermal image image gradient
	CP01	Cold	0.10803	20.73	-7.09	-27.82
	CP02	Warm	0.10779	20.76	47.69	26.93
	CP03	Warm	0.10776	20.85	48.08	27.23
	CP04	Cold	0.10773	20.54	-7.73	-28.27

Table 21 .

 21 DIC parameters and physical characteristics of the eRoad specimens.

	Specimen	Dimensions (cm)*	Weight (kg) Cycle	Factor (mm/pixel)
	CP07	53.00 x 10.83 x 10.00	9.90	Warm	0.10873
	CP08	53.40 x 10.70 x 10.00	9.44	Warm	0.10847
	CP09	53.50 x 11.10 x 10.50	10.40	Warm	0.10715
	CP10	53.80 x 10.50 x 10.00	9.50	Cold	0.10890
	CP11	53.70 x 10.26 x 10.25	9.64	Cold	0.10907
	CP12	53.00 x 10.60 x 10.30	9.26	Cold	0.10864
	* Length (x direction) by height (y direction) by thickness (z direction)

Table 22 .

 22 Initial and final temperatures inside the eRoad specimen components.

	Specimen

Temperature in the BBSG (°C) Temperature in Corkelast VA-60® (°C) Temperature in the EPDM (°C)

		Reference	Deformed	Reference	Deformed	Reference	Deformed
		image	image	image	image	image	image
	CP07	20.58	47.55	20.62	46.94	20.71	46.29
	CP08	20.60	47.76	20.67	47.29	20.83	46.33
	CP09	20.58	47.43	20.70	46.48	20.84	45.74
	CP10	20.51	-7.53	20.56	-7.12	20.69	-6.24
	CP11	20.43	-7.43	20.47	-7.00	20.61	-6.12
	CP12	20.40	-7.60	20.44	-7.07	20.55	-6.46

Table 23 .

 23 Maximum and minimum displacements of eRoad specimens.

		Max.	Min.	Max.	Min.
	CP07	1.829 -0.755	0.535	-0.664
	CP08	1.822 -1.309	0.477	-0.584
	CP09	1.496 -0.854	0.849	-0.616
	CP10	2.196 -1.474	0.851	-1.769
	CP11	2.078 -0.889	0.897	-1.634
	CP12	1.549 -1.137	1.290	-1.776
	6.2.2 Quantitative analysis using virtual strain gauges

Specimen

𝒖 𝒙𝒙 (mm) 𝒖 𝒚𝒚 (mm)

Table 24 .

 24 Strain gauges horizontal displacements (𝑢 𝑥𝑥 in mm) in CP03 tRoad.

	Specimen

CP03 Thermal gradient (°C) Strain gauge left Strain gauge right Mean value

				Standard	Mean	Standard
				deviation	value	deviation
	Image 1	27.23	-0.043	0.038	0.485	0.070
	Image 2	19.73	-0.133	0.060	0.321	0.080
	Image 3	14.96	-0.090	0.062	0.238	0.039
	Image 4	12.30	-0.074	0.056	0.214	0.016
	Image 5	9.98	-0.088	0.062	0.183	0.052

Table 25 .

 25 Strain gauges horizontal displacements (𝑢 𝑥𝑥 in mm) in CP07 eRoad.

	Specimen CP07	Thermal gradient (°C)	Strain gauge left Mean Standard value deviation	Strain gauge right Mean Standard value deviation
	Image 1	26.97	-0.430	0.009	1.517	0.012
	Image 2	19.78	-0.346	0.062	1.285	0.015
	Image 3	14.21	-0.229	0.009	1.083	0.012
	Image 4	10.94	-0.211	0.006	0.906	0.052
	Image 5	7.83	-0.163	0.042	0.735	0.076

Table 26 .

 26 Strain gauges horizontal displacements (𝑢 𝑥𝑥 in mm) in CP04 tRoad.

	Specimen CP04	Thermal gradient (°C)	Strain gauge left Mean Standard value deviation	Strain gauge right Mean Standard value deviation
	Image 1	-28.27	0.265	0.027	-0.011	0.005
	Image 2	-20.68	0.236	0.004	0.027	0.007
	Image 3	-9.90	0.211	0.001	0.037	0.008
	Image 4	-5.45	0.205	0.002	0.178	0.009
	Image 5	-0.14	0.150	0.036	0.210	0.003

Table 27 .

 27 Strain gauges horizontal displacements (𝑢 𝑥𝑥 in mm) in CP10 eRoad.

	Specimen CP10	Thermal gradient (°C)	Strain gauge left Mean Standard value deviation	Strain gauge right Mean Standard value deviation
	Image 1	-28.04	0.912	0.133	-0.640	0.103
	Image 2	-20.19	0.918	0.120	-0.346	0.090
	Image 3	-10.39	0.658	0.053	-0.178	0.050
	Image 4	-5.89	0.467	0.041	-0.002	0.006
	Image 5	0.16	0.211	0.004	0.233	0.005

Table 30 .

 30 Thermal conductivity of the eRoad components.

	Component or material	Thermal conductivity λ (W/(m⋅°C))
	EPDM	0.5
	Corkelast VA-60®	0.32
	BBSG	2

Annexe A -Product Data Sheet of Corkelast VA-60®.

Annexe B -Thermal properties of eRoad components.

 Determination of the specific heat capacity of the elastomeric materials.

The specific heat capacity (𝐶 𝑃 ) is defined by the amount of heat required to cause a change in temperature by 1°C of a material's unit of mass. An examination of the open literature revels the existence of a wide range of 𝐶 𝑃 values for elastomeric materials depending on their composition. In this study, the biggest challenge was to deal with materials from which the compositions were unknown, and for that reason it was necessary to use alternative laboratory apparatus to obtain accurate thermal parameters of the eRoad components. The specific heat capacities of the EPDM and Corkelast VA-60® were calculated with the use of a calorimeter. Simply put, the 𝐶 𝑃 values were initially measured by immersing heated samples of each material in water, inside the calorimeter. After temperature stabilization, the specific heat of the samples was calculated on the basis of the temperature difference between the beginning and the end of the experiment (Equation 31). The calorimeter participates in the heat exchange of the system, so, prior to any manipulation, its specific heat capacity was determined (𝐶 𝑐𝑎𝑙𝑜 ). During the experiment, all the solutions used had a density of 1 g.cm -3 and behaved thermally like water (𝐶 𝑤𝑎𝑡𝑒𝑟 = 4.18 J⋅°C -1 ⋅g -1 ).

𝑚 𝑒𝑙𝑎𝑠𝑡𝑜𝑚𝑒𝑟 𝐶 𝑒𝑙𝑎𝑠𝑡𝑜𝑚𝑒𝑟 (𝑇 𝐹 -𝑇 2 ) + 𝐶 𝑐𝑎𝑙𝑜 (𝑇 𝐹 -𝑇 1 ) + 𝑚 𝑤𝑎𝑡𝑒𝑟 𝐶 𝑤𝑎𝑡𝑒𝑟 (𝑇 𝐹 -𝑇 1 ) = 0

Equation 31

Where 𝑚 is the mass, in g; 𝐶 is the specific heat capacity, in J⋅°C -1 ⋅g -1 ; 𝑇 1 is the temperature of the water inside the calorimeter before adding the sample; 𝑇 2 is the stabilized temperature of the water inside the beaker containing the sample being heated; and 𝑇 𝐹 is the final temperature of the water inside the calorimeter after the inclusion of the sample, in °C. Moreover, the solutions used take a certain time to come into equilibrium with the calorimeter, so it is necessary to follow the evolution of the temperature until it stabilizes: the temperature of the solution in the equation is the temperature registered after stabilization.

Considering that the elastomeric materials are insulating, the amount of time required to heat the samples was estimated to one hour, at the end of which the temperature 𝑇 2 of the water was registered (the closest possible to an equilibrium temperature of 100°C). Instead of using one single sample of 100g of mass per material, it was decided to use groups of smaller samples that would sum up to the same total mass of 100g. The size and weight of the samples was defined by the measurement and the tests were carried out at room temperature. The 𝐶 𝑃 values for the EPDM and Corkelast VA-60® provided are depicted in Table 29. A simple comparison indicates the good accordance between the two types of measurements. Finally, it was decided to use the values obtained using the calorimeter as input properties for the numerical simulations performed in this research.

 Determination of the thermal conductivity of the eRoad components.

In order to calculate the thermal conductivity of the eRoad components, a thermal test was performed using single materials specimens inside a climatic chamber. The specimens were tested in both warm and cold cycles, while thermocouples registered the temperature evolution in the heart of the specimens and inside the climatic chamber. For the EPDM blend and Corkelast VA-60®, one specimen was tested in both warm and cold thermal loading cycles. For the bituminous mixture, four virgin tRoad specimens were subjected to one single thermal loading cycle each. The specimens' geometries were modelled in 3-D using the software Gmsh and imported to the software Cast3M® for transient thermal simulations. The dimensions of the specimens and the location of the thermocouples are depicted in Figure 124 to Figure 126. Particularly for tRoad specimens, the simulations considered the specimens to be symmetric with respect to y-axis.

Annexe E -Complementary results of FE structural simulations

The displacement, strain and stress evolutions for points PC and PY1 due to thermal loadings are depicted in Figure 131 to Figure 133.