Haitao Ge
email: haitao.ge@etu.unistra.fr

Juan Carlos Quezada

Vincent Le Houerou

Cyrille Chazallon

Pierre Hornych

Ferhat Hammoum

A new tire-sensor-pavement coupling chain for investigating asphalt mixture responses under rolling tire loads

Keywords: Finite Element Method, Tire contact stress, Tire-pavement interaction, Rolling tire loads, Asphalt mixture responses, Non-uniform tire load

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Asphalt mixture is a complex multi-phase composite, and its dynamic responses under rolling tire loads are crucial to understanding its serving performance. In the conventional pavement design method, elastic layer theory is widely used in calculating critical pavement responses under traffic loads [START_REF] Huang | Pavement analysis and design[END_REF][START_REF] Corté | Design of pavement structures: the french technical guide[END_REF][START_REF] Theyse | Pavement analysis and design software (pads) based on the south african mechanistic-empirical design method[END_REF]. As part of the design method, the tire contact area is considered as a circle, and the tire load is assumed to be uniform and equal to the tire inflation pressure. These assumptions have been proved practical to some extent in predicting some pavement distress such as fatigue crack and rutting.

However, with the development of traffic technology and the increasing traffic loads, more and more asphalt layer surface damage occurred with interaction with vehicle tires, which is hardly solvable by using the traditional simplified design method. There exists much research proving that the actual tire load induces quite different pavement responses, compared to the conventional uniform load [START_REF] Park | Evaluation of predicted pavement response with measured tire contact stresses[END_REF][START_REF] Siddharthan | Investigation of tire contact stress distributions on pavement response[END_REF][START_REF] Jiang | 3d fem analysis of flexible base asphalt pavement structure under non-uniform tyre contact pressure[END_REF], especially in terms of pavement surface degradation and near-surface crack development [START_REF] Al-Qadi | Dynamic analysis and in situ validation of perpetual pavement response to vehicular loading[END_REF][START_REF] Wang | Analysis of near-surface cracking under critical loading conditions using uncracked and cracked pavement models[END_REF]. This changing trend makes us shift our focus to understanding the distress mechanism of pavement surface layer under realistic tire loads.

An accurate characterization of tire-pavement contact stress distribution is a prerequisite for understanding the degradation mechanism of asphalt surface layers and predicting the distress evolution. Many researchers conclude that the tire imprint shape and tire contact stress distributions are dependent on tire loads and tire inflation pressures, and the tire contact stresses are not uniform across the contact area [START_REF] Pau | Ultrasonic measurements of contact area and pressure distribution of a pneumatic tire on a rigid surface[END_REF][START_REF] De Beer | Stress-in-motion (sim) system for capturing tri-axial tyreroad interaction in the contact patch[END_REF], Manyo et al. 2021b). Despite the fact that tire contact stress distributions on pavement surfaces are significantly affected by tire geometry, the realistic tire design blueprint is difficult to access due to commercial conflicts. Many studies have used idealized (cylinder) [START_REF] Reynaud | 3d modelling of tyre-pavement contact pressure[END_REF] or simplified tire geometries (only longitudinal grooves were kept) [START_REF] Korunović | Finite element model for steady-state rolling tire analysis[END_REF][START_REF] Wang | Simulation of tyre-pavement interaction for predicting contact stresses at static and various rolling conditions[END_REF][START_REF] Guo | Tire-pavement contact stress characteristics and critical slip ratio at multiple working conditions[END_REF]. However, since tire shapes are usually idealized or simplified, some information is lost while conducting the tire modeling and simulation, which could lead to inadequate estimating of tire contact stresses.

Reconstructing an actual tire shape could be accomplished with imaging techniques such as photogrammetry [START_REF] Manyo | 3d modeling and measuring of tire-pavement contact pressure[END_REF](Manyo et al. , 2021a) ) or laser scanning [START_REF] Ge | Multiscale analysis of tire and asphalt pavement interaction via coupling fem-dem simulation[END_REF], but the process is complicated and tedious. Moreover, a number of difficulties arise when modeling a numerical tire. Finite element modeling (FEM) of a tire based on continuum theory usually involves simplifying the tire geometry to meet meshing requirements. In addition, tire structures are complex and have multiple components (ribs, grooves, beads, sidewalls, and belt piles), making it laborious to determine the material properties of individual parts.

Moreover, contact detection between the tire and pavement surface is numerically effortful for a tire-pavement interaction system based on continuum mechanics theory. As a first step, a proper contact law should be imposed between the tire and the pavement surface. Then, for the tire-pavement contact area, a fine mesh should be used to capture precisely tire contact stresses on the pavement surface [START_REF] Wang | Impact of wide-based tires on the near-surface pavement stress states based on three-dimensional tire-pavement interaction model[END_REF], leading to a massive detection between tire and pavement bodies and finally resulting in a high computation cost.

On the other hand, a sensor measuring system provides an effective and precise solution for assessing tire contact stresses on the pavement surface. De Beer developed Stress-in-motion (SIM) system to measure the tire contact stress distribution [START_REF] De Beer | Toward using tire-road contact stresses in pavement design and analysis[END_REF][START_REF] De Beer | Stress-in-motion (sim) system for capturing tri-axial tyreroad interaction in the contact patch[END_REF][START_REF] Beer | Towards understanding tyre-pavement contact in apt research on flexible pavements[END_REF]). The SIM system was initially referred to as the Vehicle-Road Surface Pressure Transducer Array (VR-SPTA) (Beer 1996, Blab and[START_REF] Blab | Modeling measured 3d tire contact stresses in a viscoelastic fe pavement model[END_REF]. In recent years, Tekscan measuring system was also widely used to get access the tire contact stress distributions on the pavement surface. Prior research has proven that the Tekscan system is an efficient method to measure real tire contact pressures on pavement surfaces during a range of tire loading conditions [START_REF] Oubahdou | Effect of the tire-pavement contact at the surface layer when the tire is tilted in bend[END_REF], Manyo et al. 2021b). Although the aforementioned studies enrich our understanding of tire-pavement interaction mechanisms, it is still challenging to integrate realistic rolling tire loading conditions into a numerical model that can evaluate asphalt mixture dynamics quantitatively.

In the present study, we used the Tekscan system to capture realistic tire contact stress distributions on the asphalt pavement surface. Further, the asphalt mixture property was characterized by a NOnLinear ViscoElastic (VENoL) model and the model reliability was validated by conducting the complex modulus test both experimentally and numerically based on the two-point bending configuration. As static loading is inadequate to examine asphalt mixture responses under rolling tire loads, a new tire-sensor-pavement coupling chain was developed for integrating actual rolling tire loads in asphalt layer modeling. Finally, asphalt layer responses under different tire loading conditions and temperatures were analyzed and discussed.

Laboratory tests

2.1. Tire contact stress distributions on the pavement surface

Test set-up

For measuring tire contact stresses on pavement surfaces, a pressure sensor measuring system named Tekscan (https://www.tekscan.com/) was used. This system is in the form of a thin film with dimensions of length × width × thickness = 704.1 mm × 625.9 mm × 0.102 mm, on which square elementary sensors of 7.112 mm side are distributed. Creating the sensor requires the use of two polyester sheets. The first sheet was composed of evenly separated piezoresistive materials (sensors). Similarly, the same sensors were placed on the second sheet, but perpendicular to the first sheet. Tekscan sensors operate according to the principle that their resistance varies depending on the applied stress. The electronic sheet is incompressible and operates between -40 • C and 60 • C, with a moisture percentage ranging between 5 % to 90 %. Figure 1 shows the Tekscan measuring system and experimental test process.

Measuring results

In the present study, a truck tire (315/80 R 22.5) was chosen, measuring tests were conducted under different tire loading conditions including two inflation pressures (6.0 bar and 8.0 bar) and three loads (10 kN, 15 kN, and 20 kN). Figure 2 shows the tire pressure measuring results for these loading conditions. As shown in the figure, tire contact stress distributions under all tire loading conditions are nonuniform across the whole contact area. The peak values of tire contact stress concentrate on the center area of the tire imprint and they are much bigger than the tested tire inflation pressure. Besides, with the increment of tire loads, the contact area increases obviously from center-concentrated to side-flatted while the peak value of tire contact stress increases slightly for both tire inflation pressures. Additionally, the tire contact stresses significantly increase with increasing tire inflation pressures for all three tire loads. It seems that the tire contact stress distribution is more sensitive to tire inflation pressures compared with tire loads.

Asphalt mixture complex modulus test

Two point bending test configuration

The experimental campaign was conducted on trapezoidal samples, using a two point bending (2PB) configuration according to the EN 12697-26:2012 specification EN12697-26 (2012). Table 1 displays the particle size distribution (PSD) of the employed asphalt mixture. As shown in Figure 3, on each trapezoidal sample, a sinusoidal displacement z = z 0 sin(ωt) was imposed at the target frequency, with a peak displacement z 0 of 63 × 10 -6 , corresponding to a strain amplitude of 50 × 10 -6 at the top of the sample. The maximum force F 0 and the phase ange Φ were measured during the last 10 seconds of the test.

To identify the viscoelastic properties of the asphalt mixture, the real part E 1 and the imaginary part E 2 of the complex modulus E * can be calculated by Equations ( 1) and ( 2):

E 1 = γ( F 0 z 0 cos(Φ) + 10 -6 µω 2 ) (1) E 2 = γ F 0 z 0 sin(Φ) (2)
where ω is the angular frequency, γ (mm -1 ) is a shape factor depending on the dimensions of the specimen: B = 56 mm, b = 25 mm, e =25 mm and h = 250 mm, and

γ = 12h 3 e(B -b) 3 [(2 - b 2B ) b B - 3 2 -ln b B ] (3)
u = 0.135M + m (4)
where, the average total sample mass M is 0.6 kg, the mass of the mobile equipment overhead m is 0.235 kg.

Finally, the dynamic properties can be determined as:

|E * | = E 2 1 + E 2 2 (5) Φ = arctan(E 2 /E 1 ) (6)

Laboratory test results

For the measurement of the dynamic modulus |E * | and phase angle Φ, the frequency values tested were set as 1, 3, 10, 25, 30 and 40 Hz, while the selected temperature values were -10, 0, 10, 15, 20, 30 and 40 °C. The experimental results are shown in Figure 4. As expected, the dynamic modulus |E * | decreases and the phase angle Φ increases with increasing temperature and decreasing frequency, respectively. [START_REF] Bird | A nonlinear viscoelastic model for polymer solutions and melts-i[END_REF], [START_REF] Yasuda | Investigation of the analogies between viscometric and linear viscoelastic properties of polystyrene fluids[END_REF], the illustration of VENoL model parameters and equations is given in Figure 6.

Figure 6a displays that the variations of the stiffness component ℜ E (green curves) -] is the slope/bound transition coefficient. These parameters must be calibrated for the reference curve at a reference temperature T ref .

Validation of the VENoL model

As shown in Figure 7, we built a 2PB test sample according to the experimental sample dimensions.

Then, the open-source software gmsh (https://gmsh.info/ was used to mesh the numerical sample. Finally, the open-source software LMGC90 (https: //git-xen.lmgc.univ-montp2.fr/lmgc90/lmgc90_user/-/wikis/home) is adopted to conduct the numerical simulation, in which the bottom boundary was fixed and a sinusoidal displacement z = z 0 sin(ωt) was imposed on the top surface of the sample according to the test conditions. (1955) was used to reconstruct the corresponding master curve for dynamic modulus and phase angle values of the asphlat mixture. A reference temperature T ref was firstly chosen, then the translation of all isotherm values was performed by calculating the reduced frequency as f r = a T × f , where f corresponds to each frequency value in each curve and a T is the shift factor that could be obtained by the following equation.

log a T = -C 1 (T -T ref ) C 2 + (T -T ref ) (7)
Where:

• C 1 and C 2 are two constants, and T is the test temperature.

According to the experimental results for dynamic modulus and phase angle, Table 2 gives VENoL parameters for the asphalt mixture.

ω R-T,tr = 0 ℜ E (ω R-T ) ℑ η,R-T (ω R-T ) ω R-T ⩽ ω R-T,tr ω R-T ⩾ ω R-T,tr ω R-T ⩽ ω R-T,tr ω R-T ⩾ ω R-T,tr ℜ E,low,1 ℜ E,up,2 =3.35 × 10 4 ℑ η,R-T,low,1 ℑ η,R-T,up,2 =1.1 × 10 6 λ E,R-T,1 λ E,R-T,2 =2.2 × 10 4 λ η,R-T,1 λ η,R-T,2 =8.3 × 10 1 k E,1 k E,2 =-0.163 k η,1 k η,2 =0.25 n E,1 n E,2 =2.96 n η,1 n η,2 =-0.12
Figures 8a and8a give the respective comparison of dynamic modulus and phase angle master curves (C 1 = 30, C 2 = 198.4 • C and T ref = 15 • C) for experimental, VENoL fitting, and numerical simulation results. These results agree quite well for both dynamic modulus and phase angle values.

To verifiy the results in the Cole-Cole and Black spaces which are very sensitive to the parameter variation, Figures 8c and8d plot the results of experimental tests, VENoL fitting, and numerical simulations in the Cole-Cole and Black spaces respectively. As can be seen from these two figures, the fit for numerical simulations is in good agreement with VENoL fitting and experimental tests. The comparisons from Figure 8 validate the reliability of the application of the VENoL model in characterizing viscoelastic asphalt mixture properties through the numerical simulation method.

4. Coupling chain for the tire-sensor-pavement system 4.1. Numerical asphalt layer built and coupling algorithm At first, we built an asphalt layer with dimensions along the x, y, and z-axis of 1 m, 1 m, and 0.2 m respectively. The meshing process was carried out using the gmsh software. For the loading area in the center, we used a fine mesh whose size corresponds to the Tekscan sensor dimensions, while for other parts, we used a coarse mesh to reduce the computation cost. Herein, for the loading area, the mesh element dimensions are 7.112 mm, 7.112 mm, and 10 mm in the x, y, and z directions respectively.

To study the asphalt layer responses under real tire loads. We proposed a novel tire-sensor-pavement coupling chain for applying the stress field obtained from the Tekscan measuring results to the pavement layer surface. The coupling chain is shown in Figure 10. In step 1, we conducted the measuring test of tire contact stresses by using Tekscan, the stress information was then obtained and visualized in MATLAB. In step 2, the stress information from the previous step was transferred to nodal forces for the sensor matrix. In step 3, the asphalt layer was reconstructed in FEM and the load area was refined according to the sensor dimensions. In step 4, the nodal forces were applied to the pavement surface at the corresponding nodes. In this step, a dynamic detection algorithm was used to determine the nodal force position on the FEM model. The general frame for this detection algorithm is listed in Algorithm 1. Prior to simulating tire rolling on an asphalt layer surface, asphalt mixture properties must be identified under various tire loading conditions. As previously discussed, asphalt mixtures are viscoelastic materials sensitive to temperature and load frequency. This study investigated asphalt layer response under 15 °C which is the reference value used in the French pavement design method. However, the corresponding loading frequency for the complex modulus test must still be determined from the tire loading conditions. Accordingly, we used an equation proposed by [START_REF] Cheng | Comparative analysis of strain-pulse-based loading frequencies for three types of asphalt pavements via field tests with moving truck axle loading[END_REF] to transfer vehicular loading velocity to the loading frequency during the complex modulus test, as shown below:

t in range [0, t f inal ] do ▷ t is the elapsed time while i in range [1, N um] do ▷ N um is the length of [ID] if N S coory [i] -Ed y /2 =< T coory [i] + v * t <= N S coory [i] + Ed y /2 then if N S coorx [i] -Ed x /2 =< T coorx [i] <= N S coorx [i] + Ed x /
f = 0.127V (8)
Where, f [Hz] is the frequency used in the complex modulus test and V [km/h] is the tire rolling velocity on the pavement surface.

Through validation of the full-scale accelerated pavement tests, the equation established in the original paper provides a good description of the frequency of test loading (f) and tire motion speed (V) for pavement temperatures not exceeding 31 °C. By using the equation above and the VENoL model built in the numerical simulation, we can easily identify the mixture properties of the asphalt layer model.

Dynamic simulation of asphalt layer responses under rolling tire loads

In steady-state tire rolling (angular and translational velocities are constant), tire loads are independent of time [START_REF] Wollny | Numerical modelling of tyre-pavement interaction phenomena: coupled structural investigations[END_REF]. Previous studies have indicated that the influence of the velocity is relatively small on the tire tread deformation compared with the effects of the vertical force [START_REF] Xiong | In-plane Tire Deformation Measurement Using a Multi-Laser Sensor System[END_REF], [START_REF] Besselink | An improved magic formula/swift tyre model that can handle inflation pressure changes[END_REF], and tire rolling speeds have minor effects on tire contact stresses [START_REF] Guo | Analysis of contact stresses and rolling resistance of truck-bus tyres under different working conditions[END_REF]. Herein, we assume that the tire rolling speed does not affect the tire loading state during the tire rolling.

Figure 12 shows both the external force field and the displacement distribution field during the tire rolling process on the asphalt layer in 3D rendering, in which the tire inflation pressure was 8 bar and the tire load was 20 kN. As can be seen from the figure, the external tire load derived from the sensor measuring is non-uniform on the asphalt layer surface and advances along the y-direction, the whole moving process is consistent with Figure 11, which proves the reliability of the proposed tire-sensorpavement coupling chain. Furthermore, we observed that there was a lag between the external force field and the displacement field throughout the whole tire rolling process, which originates from the viscoelastic nature of the asphalt mixture. As a result of the tire loading pass, a residual displacement field appears on the asphalt layer surface, which indicates a process of viscous material flow inside the asphalt mixture.

The deformation of the center section plane (x = 0) as shown in Figure 13 was analyzed as a way of precisely describing the displacement distribution during the rolling process. As shown below in Figure 14, we validated the efficacy of the numerical model by comparing the surface deflection from the numerical simulation to the rutting deformation from the experimental tests. The non-smooth surface deflection observed in Figure 14a is associated with a non-uniform tire contact stress and a non-smooth tire texture, contrasting with the smooth deformation shape obtained in previous simulations employing the uniform load assumption [START_REF] Ahirwar | Finite element analysis of flexible pavement with geogrids[END_REF], [START_REF] Serin | Comparative analysis of stress distributions and displacements in rigid and flexible pavements via finite element method[END_REF]. Figure 14b shows the asphalt rutting deformation induced by truck tire loads after long-term loading periods. The non-smooth tire surface texture, along with non-uniform tire contact stresses, also produce a non-smooth surface. Rutting is a result of the accumulation of residual deflection in the surface after a long period of loading. The measured rutting shape shows similarities to the surface deflection measured from the numerical simulation, which confirms the validity of the model and its performance. Establishing a relationship between the residual surface deflection and the final rutting deformation after long-term loading cycles is encouraging based on the proposed high-precision model to predict asphalt surface deterioration.

Conclusion

From tire contact stress determination and asphalt mixture property characterization through dynamic simulation of asphalt layer responses under rolling tire loads, this study introduces a tire-sensor-pavement coupling chain.

The Tekscan system was used to measure tire contact stresses on the pavement surface. The test results show that the tire contact stresses are not uniform across the whole contact patch. The contact stress value and contact area of the tire are dependent on the tire load and inflation pressures.

For characterizing the frequency-and temperature-dependant asphalt mixture The general frame of the tire-sensor-pavement coupling chain was proposed to investigate asphalt layer responses under rolling tire loads. In the tire rolling process, a lag between the external force field and the displacement field occurs due to the viscoelastic nature of the asphalt mixture. After the tire rolling, a non-smooth residual surface deflection on the asphalt layer is observed as a result of non-uniform tire loads.

By integrating the real tire contact stresses obtained from the sensor measurement into numerical asphalt layer modeling, this coupling chain could be applied to investigate tire-pavement interaction processes as well as to investigate asphalt pavement response to different tire loading and environmental conditions, providing an enriching amelioration for the asphalt pavement design.

Figure 1 .

 1 Figure 1.: Tekscan measuring system (Left), Experimental test measuring process (Right).

  Figure 3.: 2PB test configuration

  Figure 4.: Experimental results for the 2PB test

Figure 5 .

 5 Figure 5.: VENoL model Coulon et al. (2021)

  Figure 6.: VENoL model parameters and equations Coulon et al. (2021)

Figure 7 .

 7 Figure 7.: Numerical 2PB test based on FEM

  Figure 8.: Comparisons between numerical and experimental results

  2 then Apply the nodal force F no [i] to this node with id of i end if end if ▷ v is tire rolling velocity along the y direction end while end for 4.2. Asphalt layer property identification under rolling tire loads The tire rolling process is shown in Figure 11. Three critical time points (Starting time, Middle time and Ending time) describing the whole dynamic rolling process are shown in the figure.

Figure 11 .

 11 Figure 11.: Tire rolling process on the asphalt layer

  Figure 12.: Tire rolling process on the asphalt layer for V = 20 km/h

  Figure 14.: Comparisons of the numerical surface deflection and the experimental rutting measurement

Table 1 .

 1 : Particle size distribution (PSD) of asphalt mixture

	Diameter (mm) 12.5 10 8 6.3 4	2	1 0.5 0.25 0.125 0.063
	PSD (%)	100 90 64 44 36 32 22 17	13	11	7.3

Table 2 .

 2 : Modeling parameters for VENoL model Transition reduced pulsation:

(a) 10kN-6.0bar (b) 10kN-8.0bar (c) 15kN-6.0bar (d) 15kN-8.0bar (e) 20kN-6.0bar (f) 20kN-8.0bar Figure 2.: Tire contact stress distributions under different loads and inflation pressures

Herein, ω R-T,tr was set to 0.0 rad/s, only the parameters corresponding to ω R-T ⩾ ω R-T,tr were considered.

Acknowledgement(s)

The work presented in this article was supported by the French institution Agence Nationale de la Recherche (ANR, eng: National Agency for Research) (ANR-Binary project, ref. . The first author gratefully acknowledges financial support from China Scholarship Council (No. 201806560055).

Disclosure statement

The authors declare that they have no conflict of interest.


Rodrigo Shigueiro Siroma
email: rodrigo_siroma@yahoo.com

Mai Lan Nguyen

Pierre Hornych

Jean-Pascal Planche

Jeramie Adams

Joseph Rovani

Yogesh Kumbargeri

Yvong Hung

Aurélia Nicolaï

Layella Ziyani

Rodrigo Shigueiro Siroma
email: rodrigo-shigueiro.siroma@univ-eiffel.fr

Jean- Pascal Planche

Emmanuel Chailleux

Asphaltene Agglomeration Through Physical-Chemical and Rheological Testing

Keywords: Agglomeration Through Physical-Chemical and Asphalt binder, aging, rheology, binder composition, molecular weight distribution

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction and Background

Asphalt binder is a complex hydrocarbon product that corresponds to the heaviest fraction obtained from the distillation of crude oil during refining whose composition is highly dependent on the crude oil source, refining processes, and aging [START_REF] Branthaver | Binder Characterization and Evaluation[END_REF][START_REF] Hunter | The Shell Bitumen handbook[END_REF]. The broad range of molecular types that compose asphalt binders interacting together is what provides binders with unique properties. However, due to the high complexity of the binder's chemical composition, binders have traditionally been fractionated into two broad groups called maltenes (saturates, aromatics, and resins) and asphaltenes in terms of solubility [START_REF] Corbett | Composition of asphalt based on generic fractionation, using solvent deasphaltening, elution-adsorption chromatography, and densimetric characterization[END_REF].

Asphaltenes are the most polar fraction and therefore the structuring entity. In the literature, several molecular weight values can be found for asphaltenes depending on the methods and testing conditions. The significant advances in analytical chemistry, especially in mass spectrometry, enable more accurate estimations of the asphaltene molecular weight. Hence, [START_REF] Mullins | The Asphaltenes[END_REF] stated that the average molecular weight for a single asphaltene molecule obtained by Time-Resolved Fluorescence Depolarization (TRFD) is approximately 750 g/mol, varying from 500 to 1,000 g/mol.

This highly complex chemical composition induces spatial organization and arrangement of molecules impacting directly the binder overall mechanical behavior.

Among the several models presented in the literature, the colloidal model has remained the most accepted and successful in describing binder structure, although some important aspects remain to be understood. In this model, binder is regarded as a colloidal system consisting of high molecular weights asphaltene micelles dispersed in a maltenic phase (lower molecular weight oily medium). These asphaltenes micelles are peptized by aromatic resins that act as a stabilizing solvation shell in an oily medium, and thus preventing aggregation. [START_REF] Pfeiffer | Asphaltic Bitumen as Colloid System[END_REF] proposed two binder structural arrangements to explain the difference in rheological properties of two very distinguished binders called sol and gel. Sol-type binders display Newtonian behavior as they have enough aromatics and resins to completely solvate and peptize the asphaltene molecules. In contrast, if the amounts of aromatics and resins are insufficient, the asphaltene micelles can get fully interconnected, thus reducing asphaltene micelles' mobility within the binder and consequently resulting in a non-Newtonian behavior. Most binders are found to have an intermediate behavior between sol-and gel-type binders.

A better understanding of asphaltene agglomeration is therefore of utmost importance as asphaltenes play a major role in many physical and chemical properties of binders. In the early 1960s, [START_REF] Yen | Investigation of the Structure of Petroleum Asphaltenes by X-Ray Diffraction[END_REF] proposed a model of a colloidal system formed by units composed of polycondensed aromatic rings substituted by aliphatic chains and naphthenic polycyclic rings through X-Ray Diffraction (XRD). Through the advances in asphaltene science, [START_REF] Mullins | The Modified Yen Model[END_REF] proposed the Modified Yen, or Yen-Mullins, model that proposes three asphaltene hierarchical structures: asphaltene monomers, nanoaggregates with an aggregation number of around six, and clusters consisting of eight nanoaggregates.

To ensure optimum pavement serviceability and durability, an asphalt binder must meet a set of several specifications-most of them rheology-based [START_REF] Anderson | Development of SHRP Binder Specification[END_REF][START_REF] Lesueur | Impact of the Asphalt Binder Rheological Behavior on the Value of the ΔTc Parameter[END_REF]. Hence, any significant alteration in rheological behavior that may take place over service time is usually undesirable because this indicates reduced asphalt material performance and, consequently, faster deterioration of roadways. However, these changes are likely to happen due to the organic nature of asphalt binder that makes it highly prone to oxidative aging when in contact with oxygen in the air. Oxidation increases the concentration of polar functional groups and pericondensed aromatic molecular structures which favor intermolecular agglomeration [START_REF] Boysen | Automated HPLC SAR-AD Separation-Fundamental Properties of Asphalts and Modified Asphalts III Product[END_REF][START_REF] Petersen | A Review of the Fundamentals of Asphalt Oxidation: Chemical, Physicochemical, Physical Property, and Durability Relationships[END_REF]. This reduces the mobility between molecules and, consequently, causes binders to stiffen and embrittle, thus impairing the binders' ability to dissipate mechanical and thermal stresses. The accumulation of these irreversible changes triggered by binder aging over the years in service shortens the durability of pavements as they become more susceptible to cracking.

A better understanding of how the binder chemistry and microstructure change, and the consequences thereof, is of utmost importance for designing longer-lasting roads and more cost-effective maintenance strategies. For this purpose, this paper presents the findings regarding the assessment of asphaltene molecular association through innovative theoretical and experimental methods. In this case, the composition and microstructure of four laboratory-and field-aged binders were characterized via Saturates, Aromatics, Resins, and Asphaltene Determinator (SAR-AD) and Size Exclusion Chromatography (SEC), respectively. The rheological measurements were performed through Dynamic Shear Rheometer (DSR) and Metravib Dynamic Mechanical Analysis (DMA). Finally, the rheological measurements were used to estimate the apparent molecular weight distribution (AMWD) and incidence of asphaltene molecular agglomeration through the δ-method and Molecular Agglomeration Index (MAI), respectively.

Experimental Methods

Materials

Four unmodified 35/50 pen grade binder samples were rigorously characterized. Two of them were from the same supply batch of a binder grade widely used in road construction in France (binder A) conditioned at different aging levels: fresh (binder A_Fr) and laboratory-aged through Rolling Thin-Film Oven (RTFO) followed by 20 hours of Pressure Aging Vessel (PAV) (binder A_1P). The two other binders were extracted and recovered from class 3 'Grave Bitume (GB3)' mixes present in the bottommost layer of the asphalt course base (ACB) located in the trafficked zones of two thick pavement sites in France: the Test Track B of the Université Gustave Eiffel (UGE)'s Fatigue Carrousel in Nantes (western France) and RD14 departmental road near Montpellier (southern France). The UGE's Test Track B was built in 1998 and the pavement structure consists of an 8 cm asphalt wearing course, and its ACB consists of a 6 cm asphalt base layer built on two identical asphalt base layers of 15 cm each. As for RD14 road built in 2005, its structure consists of a 6 cm asphalt wearing course and a 8 cm base layer. The binders from Nantes and Montpellier are named NF3T and MB1T, respectively, and their respective base layers investigated in this study are represented in red in Figure 1.

Experimental Methods

Saturates, Aromatics, Resins, and Asphaltene Determinator (SAR-AD)

SAR-AD method is an automated separation developed by the Western Research Institute (WRI) and performed on High Performance Liquid Chromatography (HPLC) equipment that is capable of providing hundreds of separations without regenerating column packing materials [START_REF] Boysen | Automated HPLC SAR-AD Separation-Fundamental Properties of Asphalts and Modified Asphalts III Product[END_REF]. For this separation, the asphalt binder samples were initially dissolved into chlorobenzene and then filtered with a 0.45 µm syringe filter to form 20 µL of 10 wt/vol % binder solutions. With this method, the binder is separated into eight constituent fractions: saturates, aromatics 1, aromatics 2, aromatics 3, resins, CyC6-asphaltenes, toluene-asphaltenes, and CH2Cl2-asphaltenes.

Further information on each SAR-AD fraction can be found in [START_REF] Adams | Diagnostic Techniques for Various Asphalt Refining and Modification Methods[END_REF][START_REF] Adams | Innovations and developments in bitumen composition analysis[END_REF]. Peak elution is detected with an evaporative light scattering detector (ELSD), which provides an approximate weight percent of the fraction, and an optical absorbance detector at 500 nm, which determines the concentration of brown-colored pericondensed aromatic content of each fraction. For the initial stage of the separation the asphaltenes precipitate from the injected solution onto a ground polytetrafluoroethylene (PTFE) packed column charged with excess of heptane. The precipitated asphaltenes are further separated based on their solubility using solvents of increasing solvent strength (or solubility parameter): cyclohexane (CyC6), toluene, and methylene chloride: methanol (CH2Cl2) The heptane soluble maltenes are then separated by chromatography on three different sorbents to provide the saturates, aromatics 1, aromatics 2, aromatics 3 and resins fractions.

WRI developed indices based on the measurements using both ELS and 500 nm detectors. Polarity/Coking Index is the ratio of the CyC6-soluble asphaltenes to the CH2Cl2-soluble asphaltenes (both 500 nm peak areas) and quantifies the pyrolysis/thermal severity history during refining. A higher coking index is conventionally desirable and values below 1 typically indicate the presence of coke (an undesirable product from thermal or catalytic cracking for upgrading petroleum residues). Absorbance Aging Index (AAI) is the ratio of the toluene-soluble asphaltenes 500 nm peak area to the sum of aromatics 2, aromatics 3, and resins 500 nm peak areas.

This measures the aging level of the binder as it increases with aging. Total Pericondensed Aromaticity (TPA) has also been used to estimate the aging level and is the division of the total asphaltenes ELS peak areas by the sum of the total asphaltenes 500 nm peak areas, which quantifies the amount of pericondensed aromatic structures that absorb visible light and are believed to be viscosity builders due to their high polarity [START_REF] Schabron | On-column precipitation and re-dissolution of asphaltenes in petroleum residua[END_REF]. Finally, the Colloidal Instability Index (CII), which is already commonly used as a stability index, is the ELSD peak ratio for the sum of the incompatible saturates, aromatics 1, and total asphaltenes to the sum of the asphaltene dissolving and dispersion fraction of aromatics 2, aromatics 3, and resins.

The CII value increases with aging or for asphalts that have a poorly balanced composition by having very high saturates or asphaltenes, or both.

Size Exclusion Chromatography (SEC)

SEC was conducted in an Agilent 1260 Infinity II HPLC instrument to determine the apparent molecular weight distribution (AMWD) of the binder samples. Sigma-Aldrich's tetrahydrofuran (THF ≥ 99.9, inhibitor-free) was used for the mobile phase with a flow rate of 3.5 mL/min. Each binder sample was diluted in THF at a concentration of 0.1 g/mL and filtered with a 0.45 µm syringe filter. 7.5 µL of the binder solutions were then injected into a Waters µ-styragel HR2 column (30 cm x 7.5 mm i.d.) packed with 5 µm particles at a constant temperature of 30°C. SEC detection was achieved using an ELSD and a variable wavelength optical absorbance detector set at 500 nm, 400 nm, 350 nm, 300 nm, 280 nm, and 250 nm. The calibration curve was obtained with polystyrene standard samples with MW values of 254, 1,890, and 13,000 g/mol.

Rheological Measurements

Temperature-frequency sweep testing was performed within the linear viscoelastic regime on two different instruments: Dynamic Shear Rheometer (DSR) and Metravib Dynamic Mechanical Analysis (DMA). DSR was performed on a Malvern Kinexus instrument with a 4 mm (-30°C to 30°C) and 8 mm (30°C to 60°C) diameter parallel plates, at frequencies varying from 0.0159 to 15.92 Hz (0.1 to 100 rad/s). Unlike DSR, the rheological measurements conducted in a Metravib DMA rheometer were in tension-compression mode (E*) at low temperatures, from -15 to 20°C, and annular shear mode (G*) at high temperatures, from 20 to 60°C, at 1-80 Hz (6.28 to 502.65 rad/s). The conversion between |G*| and |E*| was made considering a Poisson's ratio of 0.5. The shift factors (aT) for each experimental isotherm to build the master curves were computed through the mathematical-based method [START_REF] Chailleux | A mathematical-based master-curve construction method applied to complex modulus of bituminous materials[END_REF] that is based on the Kramer-Kronig relation between the real and imaginary components of complex functions [START_REF] Booij | Generalization of Kramers-Kronig transforms and some approximations of relations between viscoelastic quantities[END_REF] as presented in Equation 1: (1)

where aT(Ti, Tref) is the shift factor of an isotherm corresponding to Ti in relation to Tref, |E*(Tj,ω)| is the complex modulus norm at a given temperature Tj and frequency ω, and φavg is the mean value of the phase angles at Tj and Tj+1, both at frequency ω. The Williams-Landel-Ferry (WLF) [START_REF] Williams | The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids[END_REF] law's coefficients were also calculated.

The 2 Springs, 2 Parabolic elements, and 1 Dashpot (2S2P1D) rheological model [START_REF] Olard | General "2S2P1D" Model and Relation Between the Linear Viscoelastic Behaviours of Bituminous Binders and Mixes[END_REF] was used to fit the raw data, considering the static modulus (E0 or G0) equals 0 for binders, and is given by Equation 2:

𝐸 * (𝑖𝜔𝜏) = 𝐸 0 + 𝐸 ∞ -𝐸 0 1 + 𝛿(𝑖𝜔𝜏) -𝑘 + (𝑖𝜔𝜏) -ℎ + (𝑖𝜔𝛽𝜏) -1 (2)
where i is the imaginary unit, ω is the frequency in radian per second, Eꝏ is the glassy modulus, δ is the dimensionless calibration constant, k and h are the ratio Eimag./Ereal when ω tends to 0 and ꝏ, respectively, β represents the Newtonian viscosity, and τ is the characteristic time. These parameters are determined through mathematical optimization that reduces as much as possible the differences between the modeled and experimental data.

Since the rheology-based theoretical approaches employed in this study are solely based on the phase angle master curve, it is worth mentioning the approximated analytical equation (Equation 3) proposed by [START_REF] Krolkral | Quantification of asphalt binder ageing from apparent molecular weight distributions using a new approximated analytical approach of the phase angle[END_REF] to compute the phase angle derived from the 2S2P1D equation considering the [START_REF] Booij | Generalization of Kramers-Kronig transforms and some approximations of relations between viscoelastic quantities[END_REF] approximation:

𝜑(𝜔) ≈ 𝜋 2 . [ 𝑘. 𝛿(𝜔𝜏) -𝑘 + ℎ(𝜔𝜏) -ℎ + (𝛽𝜔𝜏) -1 1 + 𝛿(𝜔𝜏) -𝑘 + (𝜔𝜏) -ℎ + (𝛽𝜔𝜏) -1 ]
(3)

Theoretical Methods

In the past few years, a theoretical method based on [START_REF] Zanzotto | Molecular weight distribution of regular asphalts from dynamic material functions[END_REF]'s findings has been developed to propose an "inverse approach" to determine the AMWD of a given asphalt binder based on its linear viscoelastic behavior: the δ-method. One of the motivations behind this "inverse approach" was to circumvent some shortcomings of classical SEC such as its premise of significantly reducing associations, some of which likely resulted from processes triggered by aging, and thus preventing potential insights that could be gained into changes in the microstructure of binders with aging. In this case, the AMWD obtained via SEC may not correspond to the microstructure of the bulk, or undiluted, binder.

δ-method

The δ-method was initially inspired by the reported satisfactory sensitivity of the |G*| to the AMWD stated in previous works in polymers science [START_REF] Tuminello | Molecular weight and molecular weight distribution from dynamic measurements of polymer melts[END_REF][START_REF] Tuminello | Determining molecular weight distributions from viscosity versus shear rate flow curves[END_REF]; however, unlike polymers, the phase angle (that was referenced by the Greek letter "δ" in [START_REF] Zanzotto | Molecular weight distribution of regular asphalts from dynamic material functions[END_REF])) appears to be the most sensitive rheological parameter for estimating the AMWD of asphalt binder.

Considering that binder can be portrayed as a mixture of monodisperse molecular weight species where each molecule has a unique relaxation frequency below which this molecule is relaxed, i.e., does not contribute to the overall mechanical resistance, two scenarios can be observed: at low frequencies (or high temperatures), only apparently large molecules contribute to the overall resistance and thus generating decreased modulus and increased phase angle; and at high frequencies (or low temperatures)

where not only large molecules but also small ones contribute to the binder's mechanical resistance and thereby increasing the modulus and reducing phase angle.

Using several binders from the Strategic Highway Research Program (SHRP) library and some Alberta crude oils, [START_REF] Zanzotto | Molecular weight distribution of regular asphalts from dynamic material functions[END_REF]) establish a relation between the crossover frequency (ωc) at Tref=0°C and the molecular weight obtained from Vapor Pressure Osmometry that is expressed by Equation 4:

log(𝑀𝑊) = 2.880 -0.06768 * log (𝜔 𝑐 ) (4)
Following up [START_REF] Zanzotto | Molecular weight distribution of regular asphalts from dynamic material functions[END_REF], [START_REF] Themeli | Molecular weight distribution of asphaltic paving binders from phase-angle measurements[END_REF] stated that the Cumulative Molecular Weight Distribution (CMWD) was proportional to the phase angle master curve (δ) and was given by Equation 5:

𝐶𝑀𝑊𝐷 = 1 90°𝛿 (𝑀𝑊) (5)
The derivative of the CMWD finally resulted in the AMWD as shown in Equation 6:

𝐴𝑀𝑊𝐷 = 𝑑(𝐶𝑀𝑊𝐷) 𝑑[log (𝑀𝑊)] ≅ ∆(𝐶𝑀𝑊𝐷) ∆[log (𝑀𝑊)] (6)
Where a differential step size of 1/3,000 was suggested in [START_REF] Themeli | A new method to quantify and evaluate ageing state of asphalt from viscoelastic measurement[END_REF]. It is worth mentioning an analytical equation to determine AMWDs that takes into consideration only the rheological parameters of the 2S2P1D model proposed by [START_REF] Krolkral | Quantification of asphalt binder ageing from apparent molecular weight distributions using a new approximated analytical approach of the phase angle[END_REF].

Molecular Agglomeration Index (MAI)

Aiming to delve further into the potential of phase angle master curve relationships with multivariate statistical analyses such as Principal Component Analysis (PCA) and Hierarchical Cluster Analysis (HCA), [START_REF] Siroma | Clustering aged bitumens through multivariate statistical analyses using phase angle master curve[END_REF] it was found that with aging the most relevant change in phase angle master curve at 0°C reference temperature takes place at approximately 5.7 x 10 -6 Hz. This finding led ( Siroma et al., 2022) to revisit the δ-method so that the observed reduced frequency value corresponds to molecular sizes of approximately 1,700 g/mol. A follow-up study with a more robust data set allowed updating the most relevant reduced frequency value to 8.5 x 10 -6 Hz, which corresponds to approximately 1,500 g/mol. In the petroleum research world, it is admitted that asphaltene molecules have an average molecular weight of about 500-800 g/mol [START_REF] Mullins | The Asphaltenes[END_REF], so this threshold would correspond to the association of approximately two to three asphaltene molecules. Consequently, ( Siroma et al., 2022) proposed a new index to quantify the asphaltene agglomeration named Molecular Agglomeration Index (MAI). MAI consisted of dividing the area below the AMWD curve above 1,500 g/mol by the total area and varies from 0 to 1, where the closer to 1 the greater the incidence of agglomerated molecules, as shown in Equation 7and illustrated in Figure 2: As stated by [START_REF] Petersen | Chemical Composition of Asphalt as Related to Asphalt Durability: State of the Art[END_REF], the delicate balance, or the lack of it, between associated or agglomerated components and dispersed or solubilized components strongly impacts the performance of asphalt binders. MAI increases with aging, where a threshold value of 0.58 was proposed as a failure criterion that is in agreement with the three binder-based rheological failure criteria presented in subsection 2.4. It is worth mentioning that MAI is a shape parameter since it takes into account the entire phase angle master curve.

𝑀𝐴𝐼 = 𝐴𝑟𝑒𝑎𝑎𝑏𝑜𝑣𝑒1,500𝑔/𝑚𝑜𝑙(𝐴 1,500 ) 𝑇𝑜𝑡𝑎𝑙𝑎𝑟𝑒(𝑇𝐴) (7)

Rheology-based failure criteria

Rheology has proven to be a powerful tool to assess binder durability as it is the backbone of some current performance-related binder specifications. Furthermore, some thresholds based on the linear viscoelastic behavior of binders found in cracked zones of roadways have been proposed over the years to indicate a possible critical point for maintenance, i.e., the state from which asphalt materials are more susceptible to degradation.

Glover-Rowe (G-R) parameter

The intermediate temperature G-R criterion [START_REF] Rowe | Prepared discussion for the AAPT paper by Anderson et al.: Evaluation of the relationship between asphalt binder properties and non-load related cracking[END_REF] has widely been used to evaluate the non-load cracking performance of asphalt materials. The G-R combines the effect of stiffness (complex modulus |G*|) and viscoelasticity (phase angle φ) and is expressed as follows:

𝐺 -𝑅 = |𝐺 * |(cos 𝜑) 2 (sin 𝜑) (8)
where |G*| and φ are calculated at 15°C and 0.005 rad/s. [START_REF] Rowe | Prepared discussion for the AAPT paper by Anderson et al.: Evaluation of the relationship between asphalt binder properties and non-load related cracking[END_REF] proposed that the damage onset and significant cracking susceptibility due to non-load-related cracking were likely to arise when G-R was higher than 180 kPa and 600 kPa, respectively.

Limiting temperatures corresponding to the 27° and 45° phase angles

Among the rheological parameters employed in several surveys conducted in the 1990s on several French roads after 7 years of service (Groupe National Bitume, 1999), the temperatures corresponding to the phase angles of 27° and 45° at 7.8 Hz of the extracted and recovered binders presented one of the best correlations with the cracking incidence on the surface of the studied sections. Further discussion on both criteria can be found in ( Siroma et al., 2022). Both temperatures increase with aging and limiting values of T(φ=27°) = 12°C and T(φ=45°) = 35°C, both at 7.8 Hz, were settled for unmodified 35/50 pen grade binders.

Results

Chemical and microstructure changes

The percent of each SAR-AD fraction and some indices are summarized in Table 1. The RTFO+PAV aging condition on fresh control A_Fr results in a reduction of aromatics (mainly in aromatics 2 and 3) and an increase in asphaltenes (more marked in the toluene-soluble asphaltenes). The saturates and resins contents remained practically unchanged. Depending on the binder and aging level, it can be seen positive or negative net production of resins as it is a transition fraction from aromatics to asphaltenes.

According to the coking index, the binders do not appear to have undergone thermal or catalytic cracking and the presence of coke is unlikely, even though a slight reduction in the coking index value can be observed for A_1P. As for the aging indices, the AAI, TPA, and CII increase when A_Fr is subjected to accelerated laboratory aging conditions. According to these SAR-AD aging indices, the four binders can roughly be ranked, from least to most aged, as following: A_Fr, NB3T, MB1T, and A_1P.

Depending on the aging indice, binder MB1T does not follow the aforementioned rank since it displays the highest TPA value and its AAI is the second lowest one. SEC with ELSD and optical absorbance detector at 500 nm, 400 nm, 350 nm, 300 nm, 280 nm, and 250 nm. The shift of the AMWD curve towards higher molecular weights with increasing wavelength shows that the longer the wavelength, the heavier the molecules captured during the measurements at the expense of smaller ones. Since the higher the detection wavelength the more pericondensed the molecules, this multiwavelength detection allows to also link the molecular weight to the chemical structure. Therefore, three AMWD curves encompassing the most diverse molecules that make up binder will be used to compare the four studied binders as shown in Figure 4: ELSD (left), and optical absorbance detector at 500 nm (middle) and 350 nm (right).

Figure 3. All the SEC AMWD of control binder A_Fr

According to WRI's previous works, ELSD is sensitive to detecting all different binder fractions. ELSD curves for all the binders are quite similar: a unimodal-shaped curve centered at approximately 1,100 g/mol with a slight divergence in high molecular masses where the AMWD of control binder A_Fr is lower than those of the three other binder samples. On the other hand, measurements with the optical detector at 500 nm are more sensitive to the highly conjugated aromatic molecules such as asphaltenes with a minor contribution from resins. Resembling a negative-skewed distribution curve with a shoulder at approximately 10,000 g/mol, the peak of the 500 nm AMWD curves increases with aging and this trend is in line with the SAR-AD results. 350 nm AMWD is more adequate to detect the aromatics content in aromatics 2, aromatics 3, resins, and asphaltenes. In this case, the AMWD curves display two peaks that increase with aging.

NB3T and MB1T are in between A_Fr and A_1P, which is in line with the overall trend observed with the SAR-AD results. Note these high values are typical of apparent molecular weight (MW) and confirm the high degree of molecular association that can occur particularly after aging. This also shows that the SEC solvent does not destroy all molecular associations. The high MW shoulders show that associations grow upon aging both for asphaltenes and more polar/aromatic maltenes.

Figure 4. SEC AMWD with ELSD (left) and optical absorbance detector at 350 nm (middle) and 500 nm (right).

Rheological testing results

Although different rheometers with significantly different settings and solicitation modes (shear vs. traction/compression) have been used in this work, the experimental raw data obtained with 4-mm-and 8-mm-DSR and the respective 2S2P1D parameters (Table 2) and fitted curves correspond satisfactorily with those obtained with Metravib DMA for all the binder samples. Figure 5 shows a good match between the phase angle master curves and the δ-method AMWDs of all the four binders obtained from both measurements. Figure 6 illustrates the phase angle master curves of the four binders and their corresponding AMWD derived from the δ-method. The more aged the binder, the lower its phase angle master curve, indicating an increasingly elastic and less viscous material.

The phase angle mater curves of A_1P and MB1T overlap reasonably well with each other at high frequencies and/or low temperatures; however, at low frequencies and/or high temperatures, i.e., conditions under which asphalt binder would display a more viscous-like behavior, it can be seen that the phase angle values of binder A_1P are lower than those corresponding to MB1T. The δ-method AMWDs are also portrayed in Figure 6. Control binder A_Fr presents a unimodal distribution-shaped AMWD with one shoulder on each side, where the left is higher, and centered at around 1,000 g/mol.

With aging, the AMWD is shifted towards higher molecular weights and a new peak at approximately 2,000 g/mol emerges. This is believed to represent a new molecular population that is widely seen in SEC corresponding to asphaltene molecular agglomeration [START_REF] Adams | Diagnostic Techniques for Various Asphalt Refining and Modification Methods[END_REF][START_REF] Krolkral | Quantification of asphalt binder ageing from apparent molecular weight distributions using a new approximated analytical approach of the phase angle[END_REF][START_REF] Themeli | Molecular weight distribution of asphaltic paving binders from phase-angle measurements[END_REF][START_REF] Themeli | A new method to quantify and evaluate ageing state of asphalt from viscoelastic measurement[END_REF]. Figure 8 compares the AMWDs obtained through the δ-method (left) and SEC with the 350 nm detector (right). The same trend can be observed in both cases where the AMWDs shift toward higher molecular weights. It is worth noting that the changes in the δ-method AMWD curves with aging appear to emphasize the increase in the incidence of asphaltene molecular agglomeration through the new peak that emerges at around 2,000 g/mol. Despite their differences in shape and AMWD range, the AMWDs obtained by both methods are centralized at around 1,000 g/mol and present the same trend with AMWD obtained via SEC. When applying the concept of MAI to the AMWD curves obtained via SEC, a good relationship can be observed between the ELSD curves and MAI as presented in Figure 9 (left). Figure 9 (right) reveals that MAI is directly and indirectly proportional to the SAR-AD total saturates and total asphaltenes contents, respectively.

Conclusions

Based on the primary findings of this research work, the following conclusions can be drawn:

 The experimental and theoretical methods employed may provide valuable insights into binder aging since they have proved to be effective in assessing binder chemistry and microstructure.

 SAR-AD showed that binder polarity and pericondensed aromaticity increase with aging, principally from the oxidation of aromatics 2 and 3 containing 2+ aromatic rings, which tend to decrease.

 SEC data from the 350 nm optical absorbance detector presents the overall AMWD curve, where a marked increase in the incidence of large molecular sizes is observed for less pericondensed aromatic molecules, essentially maltenes, with aging. On the other hand, 500 nm focuses on highly pericondensed asphaltenes, which also evolve under aging. This also shows the power of SEC when using proper detectors and conditions.

 As for the relatively new theoretical methods, both δ-method and MAI, which are determined solely from rheology, satisfactorily corresponded with the SAR-AD and SEC results. This reinforces the soundness of both theoretical techniques to be used as a part of routine pavement evaluation testing to track cracking susceptibility of both laboratory-and field-aged binders.

 The satisfactory relationship observed between the experimental and theoretical methods opens encouraging perspectives towards a better understanding of how the changes in binder chemistry and microstructure affect binder performance.

Figure 1 .

 1 Figure 1. Pavement structures of the field sections in Nantes and Montpellier and the base layer (in red) from which the field-aged binders were extracted and recovered.

  𝑙𝑜𝑔 (𝑎 𝑇(𝑇 𝑖 ,𝑇 𝑟𝑒𝑓 ) ) = ∑ 𝑙𝑜𝑔 (|𝐸 * (𝑇 𝑗 , 𝜔|) -𝑙𝑜𝑔 (|𝐸 * (𝑇 𝑗+1 , 𝜔|) 𝜑 𝑎𝑣𝑔 [(𝑇 𝑗 , 𝑇 𝑗+1 ), 𝜔] 𝑗=𝑟𝑒𝑓 𝑗=1

Figure 2 .

 2 Figure 2. Molecular Agglomeration Index (MAI)

Figure 5 .

 5 Figure 5. (a), (c), (e), and (g) represent the phase angle master curves obtained with Metravib DMA and DSR rheometers of binders A_Fr, A_1P, NB3T, and MB1T, respectively, and (b), (d), (f), and (h) are their corresponding δ-method AMWDs.

Figure 6 .

 6 Figure 6. Phase angle master curves (left) and δ-method AMWDs (right) obtained from the measurements performed with DSR.

Figure 7 .

 7 Figure 7. Rheology-based failure criteria and their corresponding thresholds: (a) G-R parameter, (b) MAI, (c) T(δ=27° at 7.8 Hz), and T(δ=45° at 7.8 Hz).

Figure 8 .

 8 Figure 8. AMWDs with the δ-method AMWD (left) and optical absorbance detector at 350 nm (right).

Figure 9 .

 9 Figure 9. SEC MAI with ELSD and optical absorbance detector at 350 nm and 500 nm versus δ-method MAI (left) and SAR-AD total aromatics, resins, and total asphaltenes contents versus MAI (right).

Table 1 .

 1 SAR-AD results.

		A_Fr	A-1P	NB3T	MB1T
	Detector	ELS	500 nm	ELS	500 nm	ELS	500 nm	ELS	500 nm
	Saturate	11.70	-	12.07	-	9.86	-	11.13	-
	Aromatics 1	6.07	-	6.27	-	5.66	-	5.19	-
	Aromatics 2	20.58	0.2	18.88	0.16	18.75	0.18	15.55	0.18
	Aromatics 3	36.44	17.36	31.53	13.18	34.94	15.61	32.94	14.28
	Total Arom.	63.09	-	56.68	-	59.35	-	53.68	-
	Resins	11.44	20.24	11.67	15.52	13.64	19.00	16.67	20.77
	CyC6 asph.	2.81	13.48	3.57	13.01	3.54	13.89	4.10	14.67
	Toluene asph.	10.73	46.59	15.69	55.96	13.40	49.55	14.13	48.14
	CH2Cl2 asph.	0.23	2.13	0.32	2.17	0.22	1.78	0.27	1.97
	Total Asph.	13.77	-	19.58	-	17.15	-	18.51	-
	Coking Index	-	6.34	-	5.99	-	7.78	-	7.45
	AAI	-	1.23	-	1.94	-	1.42	-	1.37
	TPA	22.14	-	27.53	-	26.30	-	28.57	-
	CII	0.46	-	0.61	-	0.49	-	0.53	-
	Figure 3 presents all the AMWD curves of control binder A_Fr obtained via

Table 2 .

 2 2S2P1D and WLF parameters at Tref = 0°C obtained for all the binders characterized with Metravib DMA and DSR rheometers (Eꝏ in MPa).

	Binder Device		2S2P1D rheological model		WLF model
			Eꝏ	δ	k	h	β	τ	C1	C2
	A_Fr	DMA	2183 5.94 0.30 0.71 32.4 0.094 20.46 127.7
		DSR	2299 5.74 0.26 0.65 111.6 0.033 26.56 167.3
	A_1P	DMA	2426 6.01 0.24 0.60 684.0 0.363 25.23 152.8
		DSR	2015 5.96 0.25 0.58 880.6 0.509 30.03 195.9
	NB3T	DMA	2313 5.13 0.24 0.60 274.6 0.412 26.25 158.4
		DSR	2406 5.70 0.25 0.63 203.7 0.537 31.19 199.9
	MB1T DMA	2255 5.68 0.24 0.60 273.1 1.434 26.73 161.5
		DSR	2280 5.67 0.24 0.62 308.5 1.444 34.83 228.7

Table 3 .

 3 Coefficient of variations of the G-R parameter, T(δ=27°C at 7.8 Hz), T(δ=27°C at 7.8 Hz), and MAI of all the studied binders.

		A_Fr	A_1P	NB3T	MB1T
	G-R	38.4%	36.9%	1.9%	8.4%
	T(δ=27° at 7.8 Hz)	6.5%	9.8%	2.4%	0.1%
	T(δ=45° at 7.8 Hz)	3.4%	10.4%	0.8%	0.3%
	MAI	10.0%	3.4%	0.8%	1.3%

Acknowledgments

The authors gratefully acknowledge the French National Research Agency (ANR) funding this study under the MOVEDVDC project (ANR-17-CE22-0014). Also, the authors would like to thank Nadège Buisson (UGE), Christopher Seago (WRI), and Alex Literati (WRI) for providing the experimental data for the analyses presented in this paper.


Chong Wang
email: chong.wang@insa-strasbourg.fr

Cyrille Chazallon

Peng Jing

Pierre Hornych

Effect of self-cementing properties on the mechanical behaviour of recycled concrete aggregates in unbound pavement layers

Effect of self-cementing properties on the mechanical behaviour of recycled concrete aggregates in unbound pavement layers ABSTRACT: Recycled concrete aggregates (RCA) are increasingly being used in pavement base and subbase layers to replace the natural unbound granular materials (UGM), while the influence of their self-cementing properties on the mechanical behaviour has not been thoroughly studied. In this paper, the self-cementing properties, permanent deformation and resilient deformation behaviour of two RCA, NRCA and ORCA, showing significantly different self-cementing properties, after curing for different times (1, 180, 360 and 720 days), were investigated by pH value measurements, calorimeter tests and repeated load triaxial tests (RLTT). The results show that the self-cementing properties can significantly improve the mechanical behaviour of RCA, which is comparable to that of lightly treated materials. The permanent deformations of NRCA, showing strong self-cementing properties, decreases to a very low value quickly after curing for 180 days, and then stabilizes. While the resilient modulus of NRCA increases continuously with curing time, up to the studied curing time (720 days), 4.3 times larger than that curing for 1 day. It was also found that the traffic loads can damage the bonds between particles formed due to the self-cementing properties. On the contrary, for ORCA, showing negligible self-cementing properties, curing has no influence on the mechanical behaviour.

Introduction

In Europe, over 800 million tonnes of construction and demolition wastes (CDW) are produced each year (Eurostat, 2018), with concrete wastes representing up to 75% of total CDW by weight [START_REF] Nwakaire | Utilisation of recycled concrete aggregates for sustainable highway pavement applications; a review[END_REF]. To achieve a sustainable development of pavement construction, recycling and reuse of concrete wastes into pavement base and subbase layers has become a topic of global concerns in recent years [START_REF] Lu | Resilient and permanent deformation behaviors of construction and demolition wastes in unbound pavement base and subbase applications[END_REF][START_REF] Poltue | Strength development of recycled concrete aggregate stabilized with fly ashrice husk ash based geopolymer as pavement base material[END_REF][START_REF] Saberian | Permanent deformation behaviour of pavement base and subbase containing recycle concrete aggregate, coarse and fine crumb rubber[END_REF][START_REF] Yaghoubi | Impact of compaction method on mechanical characteristics of unbound granular recycled materials[END_REF].

During the hydration process of cement, part of the cement particles are surrounded by the hydration products, preventing further hydration of inside cement particles [START_REF] Lin | Hydration kinetics modeling of Portland cement considering the effects of curing temperature and applied pressure[END_REF][START_REF] Mills | Factors influencing cessation of hydration in water cured cement pastes[END_REF]. As a result, those unhydrated cement particles may never be hydrated. However, the crushing process, to produce recycled concrete aggregates (RCA), can release those unhydrated cement particles [START_REF] Amin | Residual Cementing Property in Recycled Fines and Coarse Aggregates: Occurrence and Quantification[END_REF], which will hydrate slowly with moisture after the pavement construction and form bonds between particles. Consequently, the unbound RCA base and subbase layers gradually evolves into bound layers, and a continuous increase of strength and stiffness of unbound pavement base and subbase layers can be observed even up to 10 years after construction [START_REF] Korkiala-Tanttu | Long-term behavior of crushed concrete in road structure[END_REF][START_REF] Lancieri | C&D waste for road construction: long time performance of roads constructed using recycled aggregate for unbound pavement layers[END_REF][START_REF] Wang | Re-cementation of Recycled Concrete Aggregate in Pavement Base or Sub-base[END_REF], known as self-cementing properties of RCA.

Permanent and resilient deformation properties determined by repeated load triaxial tests (RLTT) are the most important parameters for pavement design, to estimate the resistance to rutting and cracking under traffic loading. A lot of research has been conducted during the past years to study the permanent and resilient deformation behaviour of RCA in unbound pavement base and subbase layers. [START_REF] Gabr | Properties of Recycled Concrete Aggregate for Unbound Pavement Construction[END_REF] observed a significant decrease of permanent deformation of RCA with a decrease of water content, and concluded that the studied RCA have better performance than the studied quartzitic aggregates. [START_REF] Arulrajah | Resilient Moduli Response of Recycled Construction and Demolition Materials in Pavement Subbase Applications[END_REF] performed RLTT on RCA, crushed brick (CB) and waste rock (WR) with varying water contents. They found that RCA have better performance over CB and WR, with the smallest permanent deformations and highest resilient moduli for different water contents. [START_REF] Lu | Resilient and permanent deformation behaviors of construction and demolition wastes in unbound pavement base and subbase applications[END_REF] showed that permanent deformations of RCA and recycled clay masonry (RCM) blends increase with increasing RCM content. C. [START_REF] Wang | Permanent and resilient deformation behaviour of recycled concrete aggregates from different sources, in pavement base and subbase[END_REF] found that RCA with low strength and containing a high amount of rounded particles can lead to high permanent and resilient deformations. Although these research results have demonstrated the feasibility of using RCA in pavement base and subbase layers, to the , the influence of self-cementing properties on the permanent and resilient deformation behaviour has been rarely studied.

Some laboratory test programs were undertaken to study the self-cementing properties and their effect on the mechanical behaviour of RCA. [START_REF] Arm | Self-cementing properties of crushed demolished concrete in unbound layers: results from triaxial tests and field tests[END_REF] studied the growth in stiffness of RCA by conducting both laboratory tests and field measurements. It was found that resilient moduli show a clear increase with curing time, especially in the first months. [START_REF] Poon | The cause and influence of self-cementing properties of fine recycled concrete aggregates on the properties of unbound sub-base[END_REF] reported that self-cementing properties are most likely governed by the fine fraction of RCA (< 0.15 mm and 0.3-0.6 mm), as the increase of compressive strength was only observed with these two fine fractions. [START_REF] Jitsangiam | Recycled Concrete Aggregates in Roadways: Laboratory Examination of Self-Cementing Characteristics[END_REF] also observed an increase of resilient modulus with curing time and found that adding other non-active materials can reduce the effect of selfcementing properties. [START_REF] Amin | Residual Cementing Property in Recycled Fines and Coarse Aggregates: Occurrence and Quantification[END_REF] confirmed the presence of residual unhydrated cement in RCA by measuring the heat of hydration, with large heat release when RCA were mixed with water. Paige-Green (2010) observed a relationship between self-cementing properties and initial pH values of RCA, and concluded that RCA show self-cementing properties if the pH value is above 9.5, and particularly above 11.

Thus, this study aims to explore the influence of self-cementing properties on the permanent and resilient deformation behaviour of RCA. Firstly, the self-cementing properties of two RCA, NRCA and ORCA, showing significantly different self-cementing properties, were evaluated by pH value measurements and calorimeter tests. Then, the influence of self-cementing properties on the permanent and resilient deformation behaviour was investigated by conducting a series of RLTT on NRCA and ORCA, after curing for different periods (1, 180, 360 and 720 days), which gives a complementary point of view on the long-term performance of RCA in unbound pavement base and subbase layers.

Materials and methods

Materials and physical properties

The two RCA materials used in this study (NRCA and ORCA) during the long-term storage, reducing the self-cementing properties of ORCA [START_REF] Kim | Evaluation of Recementation Reactivity of Recycled Concrete Aggregate Fines[END_REF].

After the crushing process, the two RCA were reconstituted to a same 0/20 mm grading curve, close to mean values between the upper and lower limits used for pavement base and subbase layer, (NF EN 13285, 2018), except for the fine contents which are slight lower than the minimum specified value, to represent standard unbound granular materials, as shown in Figure 1. The main physical properties of the two RCA are summarized in Table 1. Each result is the average value of two or three measurements. The water absorptions of NRCA and ORCA, varying between 4.3% and 10.86% for different fractions, are higher than those of natural aggregates, typically lower than 3%, and increase with the decrease of particle size, which can be attributed to the attached mortar [START_REF] Belin | Cement paste content and water absorption of recycled concrete coarse aggregates[END_REF] Table 1. Physical properties of RCA materials.

2.2 Self-cementing properties pH value and heat of hydration are parameters widely used by researchers [START_REF] Amin | Residual Cementing Property in Recycled Fines and Coarse Aggregates: Occurrence and Quantification[END_REF][START_REF] Kim | Evaluation of Recementation Reactivity of Recycled Concrete Aggregate Fines[END_REF][START_REF] Paige-Green | Preliminary evaluation of the reuse of cementitious materials[END_REF][START_REF] Poon | The cause and influence of self-cementing properties of fine recycled concrete aggregates on the properties of unbound sub-base[END_REF] to evaluate self-cementing properties of RCA. Only 0-2 mm fine aggregates, previously dried in the oven at 60 , were used to evaluate self-cementing properties of RCA, as self-cementing properties are mainly influenced by fine particles [START_REF] Poon | The cause and influence of self-cementing properties of fine recycled concrete aggregates on the properties of unbound sub-base[END_REF]. For pH value measurements, 30 g of RCA fine aggregates (0-2 mm) and 75 g of distilled water were mixed and stirred for 2 minutes (BS 1377(BS -3, 2018)).

Then, the pH value of the suspension, stored for 24 h, was measured by a pH meter.

The heat of hydration was measured by the semi-adiabatic method (NF EN 196-9, 2010). To reach an equilibrium temperature, the mixing water, RCA fine aggregates and the calorimeter device were stored in the test room at a temperature of 20 5 for at least 24 hours prior to the test. Then, the previously weighted 360 g of RCA and 180 g of water were mixed quickly and placed in the calorimeter device to measure the heat of hydration of RCA for 24 hours. Another calorimeter, containing the same mass of water (180 g), was considered as the reference calorimeter.

Specimen preparation, RLTT apparatus and test program

For RLTT, all the samples were prepared using a standard procedure (NF EN 13286-7, 2004).

Firstly, the aggregates were mixed with water, to the targeted water content, and then sealed in plastic bags for 24h for moisture homogenization. After that, each sample, with a diameter of 150 mm and a height of 285 mm, was compacted in a split mould to the targeted dry density, by a vibrating hammer, in 7 layers. To improve the comparison of the permanent and resilient deformation behaviour of the two RCA, tests were performed at the same targeted water content (OMC-1%) and targeted dry density (optimum dry density at the targeted water content), selected from the Modified Proctor curves (Figure 2), as summarized in Table 2. Finally, the specimens were demolded, wrapped in plastic bags and stored indoors for 1, 180, 360 and 720 days at a temperature of 18±5 , to study the effect of self-cementing properties on the permanent and resilient deformation behaviour of RCA.

Table 2. Targeted water content and dry density.

After curing for specific periods (1, 180, 360 and 720 days), the specimen weight was first measured to check that no water evaporated during the curing stage. The mass loss of each specimen after curing was less than 0.04% (30 g). Subsequently, the specimens were installed in the triaxial cell. The repeated load triaxial tests (RLTT) were performed using a large-scale triaxial apparatus (Wykeham Farrance), for 150 mm diameter specimens, with a servo pneumatic loading system, as shown in Figure 3. The axial strain and radial strain were measured using three Hall-Effect transducers, attached to supports anchored inside the sample.

After RLTT, the tested sample was cut into 3 layers, and the water content of each layer was measured. Duplicate samples were tested for each curing time.

The RLTT tests were performed This procedure consists of a conditioning phase (permanent deformation test) followed by a phase of study of the resilient behaviour, which is not presented in this article During the conditioning phase, the specimen was subjected to a constant confining pressure (70 kPa) and a cyclic axial stress (340 kPa), at a frequency of 1 Hz. 20000 loading cycles were applied, and the permanent and resilient deformation behaviour with the number of load cycles were studied.

Figure 3. Triaxial apparatus and instrumented specimen.

Results and discussion

Self-cementing properties

The pH values of the two RCA are given in Table 1. The results show that the pH value of NRCA (13.07) is much higher than that of ORCA (10.53). Several researchers have also evaluated self-cementing properties of RCA using pH values, ranging from 8.5 to 12.6 (Paige-Green, 2010; [START_REF] Poon | The cause and influence of self-cementing properties of fine recycled concrete aggregates on the properties of unbound sub-base[END_REF]. They have shown that RCA with high pH values (above 11) exhibit self-cementing properties, while those with low pH values (less than 11) show no selfcementing properties. According to these results, NRCA exhibits self-cementing properties while ORCA exhibits negligible self-cementing properties after long-term storage.

Figure 4 shows the rate of heat generation and the total released heat of NRCA and ORCA, due to the hydration of unhydrated cement. It appears that the hydration of unhydrated cement takes place immediately after mixing the RCA with water, even for ORCA, with a maximum rate of heat generation at the beginning of the test, which then decreases quickly in the next few hours. For NRCA, the initial rate of heat generation is 2.3 mW/g and this value gradually decreases to a stable value after 24 hours. By contrast, ORCA has a much lower rate of heat generation (0.48 mW/g) and lower duration of the heat release (1 hour). As a result, after 24 hours, the average released heat of NRCA is 14.7 J, in good agreement with the value (lower than 15 J) reported by [START_REF] Oksri-Nelfia | Reuse of recycled crushed concrete fines as mineral addition in cementitious materials[END_REF]. The released heat of ORCA is much lower

(1.97 J), indicating that the self-cementing properties of NRCA are significant while those of ORCA are negligible, which is in good agreement with the measured pH values. These results also indicate that long-term storage can decrease self-cementing properties of RCA, as observed also by [START_REF] Kim | Evaluation of Recementation Reactivity of Recycled Concrete Aggregate Fines[END_REF].

It is pointed out that for the typical Portland cement, the curves of rate of heat generation present two main peaks [START_REF] Hewlett | Lea's chemistry of cement and concrete[END_REF]. The first peak, observed a few minutes after mixing, which is visible for both RCA in Figure 4, is due to the initial rapid hydration of tricalcium aluminate phases (C3A) and alite (C3S). Then, after a few hours, and up to several days, the hydration of C3S and the formation of calcium silicate hydrate (C-S-H) phase lead to the second, main exothermic peak (around 10 hours) [START_REF] Hewlett | Lea's chemistry of cement and concrete[END_REF][START_REF] Kim | Evaluation of Recementation Reactivity of Recycled Concrete Aggregate Fines[END_REF], and the strength and stiffness of cement paste develop in this phase. This second peak, in which the strength and stiffness develop, is not visible on the curves of NRCA and ORCA (Figure 4).

However, the longer duration of the heat releasee of NRCA (until 24 hours) suggests that a small amount of calcium silicate hydrate (C-S-H) phase is formed. ORCA specimens were cured only for 360 days. Table 3 summarizes the average values of 1 p and permanent strain rate at the end of each test, as well as their standard errors. For both RCA, permanent deformations 1 p increases rapidly at the beginning of the cyclic loading, owing to particle rearrangement, and then stabilize, according to the criterion of the European standard (NF EN 13286-7, 2004), as the values of 1 p / N are less than 10 -7 per cycle at the end of the tests.

To illustrate the effect of self-cementing properties on permanent deformations, Figure 6 presents the final permanent deformations 1 p obtained after 20000 load cycles in function of the curing times. For NRCA, crushed recently, showing strong self-cementing properties, permanent deformations 1 p decrease largely after 180 days of curing, and then tend to stabilize.

Abu-Farsakh et al. ( 2015) observed that permanent deformations 1 p of soils decreases largely when they are treated with a small percentage of cement (0.5%), compared with untreated soils.

Then, the effect of cement content on 1 p decreases with increasing cement content, showing that the further hydration of cement has a limited effect on the reducing 1 p . This is in good agreement with the evolution of 1 p of NRCA, which tend to stabilize even after curing for longer time. For ORCA, showing negligible self-cementing properties, 1 p does not vary with curing time, but is sensitive to water content variations, as for other unbound granular materials [START_REF] Jing | Permanent deformation behaviour of a granular material used in low-traffic pavements[END_REF][START_REF] Soliman | Permanent deformation behavior of unbound granular base materials with varying moisture and fines content[END_REF], as can be seen in Figure 5 (b). It can be noted that ORCA still presents a good performance, with values of 1 p 20000 cycles are lower than .

These values of 1 p are lower than those of most traditional unbound granular materials, which generally present 1 p values between 50×10 4 and 200×10 4 et al., 2021; Jing et al., 2018).

To evaluate the performance of NRCA, p values of NRCA after curing (for 180, 360 and 720 days) were compared with those of lightly cementitious treated materials, soils or granular materials treated with low content of cement (around 3%) [START_REF] Ardah | Evaluating the performance of very weak subgrade soils treated/stabilized with cementitious materials for sustainable pavements[END_REF][START_REF] Senanayake | Evaluation of rutting resistance and geotechnical properties of cement stabilized recycled glass, brick and concrete triple blends[END_REF]. It was found that after curing (for 180, 360 and 720 days), NRCA presents very low 1 p , than 10×10 -4 (see Table 3), similar to those of other lightly treated cementitious materials reported by [START_REF] Ardah | Evaluating the performance of very weak subgrade soils treated/stabilized with cementitious materials for sustainable pavements[END_REF] and [START_REF] Senanayake | Evaluation of rutting resistance and geotechnical properties of cement stabilized recycled glass, brick and concrete triple blends[END_REF]. In comparison, traditional unbound granular materials, tested in similar conditions, generally present 1 p values higher than 20000 cycles [START_REF] Alnedawi | Investigation of non-standard unbound granular materials under cyclic loads: experimental and regression analyses[END_REF][START_REF] Jing | Hydro-Mechanical Behaviour of an Unbound Granular Base Course Material Used in Low Traffic Pavements[END_REF].

This shows that self-cementing properties can improve very significantly the resistance to permanent deformations of RCA. 406.9

±1.1 408.9

±7.5

Modelling of permanent deformation behaviour

To predict the evolution of permanent deformations of RCA, improved by self-cementing properties, the widely used model, proposed by [START_REF] Hornych | Étude des déformations permanentes sous chargements répétés de trois graves non traitées[END_REF] for unbound granular materials, was adopted to simulate the evolution of permanent axial deformations with the number of load cycles N: 0

(1 ( ) )

p B N A N (1)
where 1 p is the permanent strain (in 10 -4 m/m) after N cycles, N0 is the number of cycles before the first measurement (N0=100 in this parameter A represents the final permanent axial deformation and parameter B (B<0) controls the evolution of permanent deformation with increasing N.

According to the test results presented in Figure 6, a power relationship can be obtained between the final permanent axial deformation A and the curing time t. This relationship can be expressed as follows:

0 b t A a t (2)
where a and b are parameters (b < 0), t is the curing time in days, and t0=1 day is the minimum curing time.

The evolution of permanent deformations with N was controlled by another parameter B, becoming flatter when B increases (absolute value). A exponential function is adopted to describe the relationship between parameter B and curing time t:

0 0 t t d B c e B ( 3
)
where c, d and B0 are constant parameters.

Substituting ( 2) and ( 3) into ( 1), the proposed model, accounting for the effect of curing time t, can be obtained: The average permanent deformations after different curing times, presented in Table 3, were used to determine the parameters of the proposed model, summarized in Table 4. Figure 7 presents a comparison between experimental results and predictions obtained with the model.

Resilient modulus

During the permanent deformation tests, resilient modulus, defined as a ratio of applied axial deviator stress q (q=340 kPa in this study) and recoverable axial strain 1, can be calculated for each load cycle. Figure 8 plots the evolution of the resilient modulus Mr of NRCA and ORCA with the number of load cycles, for different curing times. is much higher than that of natural unbound granular materials, showing the excellent longterm performance. By contrast, for ORCA, the resilient modulus Mr remains constant, which is consistent with the evolution of permanent deformations.

Figure 8 also shows that for both NRCA and ORCA, the resilient modulus gradually increases during the first load cycles, and then gradually reaches a constant value, except for the NRCA specimens curing for 360 and 720 days. This behaviour is due to the particle rearrangement and consolidation during the permanent deformation test, also observed for unbound granular materials [START_REF] Jing | Unsaturated mechanical behaviour of a granular material[END_REF][START_REF] Yang | Correlation Between Resilient Modulus and Plastic Deformation for Cohesive Subgrade Soil Under Repeated Loading[END_REF].

Interestingly, for NRCA specimens after curing for 360 and 720 days, resilient modulus decreases during the first load cycles, especially for NRCA curing for 720 days. This can be explained by the fact that for lightly treated materials, some weak bonds probably break under traffic loading, thus decreasing the resilient modulus. These results are consistent with observations made by other researchers on cement treated materials [START_REF] Rios | On the shearing behaviour of an artificially cemented soil[END_REF][START_REF] Vranna | Undrained Monotonic and Cyclic Response of Weakly Cemented Sand[END_REF]Chong Wang et al., 2023).

Figure 9 shows the evolution of the final resilient moduli of NRCA and ORCA with curing time. For NRCA, unlike permanent deformation, which stabilized after 180 days of curing, resilient modulus continues to increase up to 720 days of curing, which can be described by an exponential function. However, this observation is valid only for the studied material (NRCA), and until 720 days of curing. It is clear that with increasing curing time, the hydration of unhydrated cement will stop and resilient modulus will reach a constant value. This could be confirmed by tests with longer curing time.

Discussion

The results presented above allow to understand the influence of self-cementing properties on the behaviour of RCA. The permanent deformations of NRCA decrease with curing, but tend to stabilize after curing for 180 days (Figure 6), while the resilient modulus continues to increase much longer with curing time, at least up to 720 days (Figure 9). Similar observations were made by [START_REF] Barbieri | Design and sustainability analyses of road base layers stabilized with traditional and nontraditional additives[END_REF], who studied the effect of curing on the permanent deformations and resilient modulus of cement treated materials. They reported that the permanent deformations of cement treated materials become constant, while the resilient modulus continues to increase after curing for 180 days.

For unbound granular materials, deformations are governed by the densification, distortion and attrition of particles [START_REF] Lekarp | State of the art. I: Resilient response of unbound aggregates[END_REF]. However, once the bonds between particles are formed, due to the hydration of unhydrated cement, and provide sufficient resistance to the stresses induced by traffic loads, the densification, distortion and attrition of particles are reduced, and the permanent deformations decrease immediately. Then, once a sufficient level of bonding has been attained, the further hydration of unhydrated cement has a limited effect on the permanent deformations, since the previously formed bonds can already resist to the stresses due to traffic loads. As a result, the permanent deformations of NRCA stop decreasing after about 180 days of curing.

On the contrary, the further hydration of unhydrated cement increases the number of bonds, increasing the number of particle contacts and their contact area. Thus, the resilient modulus of NRCA continues to increase with curing time, until all the unhydrated cement is consumed, unlike the permanent deformation.

Conclusions

In this study, the effect of self-cementing properties of RCA on their mechanical behaviour was investigated. Two different RCA, NRCA and ORCA, both sourced from demolished buildings, with different dates of manufacture, were selected. The self-cementing properties and mechanical behaviour of two RCA, after curing for different times (1, 180, 360 and 720 days), were investigated by pH value measurements, calorimeter tests and repeated load triaxial tests.

Based on the test results, the following conclusions can be made:

The results of pH value measurements and calorimeter tests showed that the self-cementing properties of NRCA, which was freshly crushed, are very strong, indicated by a high pH value and total released heat. On the contrary, ORCA, crushed in 2012 and submitted to long term storage, presented only negligible self-cementing properties.

Repeated load triaxial tests indicated that the permanent deformations of NRCA decrease rapidly during the first months of curing, and then reach a constant low value after curing about 180 days, which is similar to values obtained on lightly cement treated soils or granular materials. For ORCA, the permanent deformations do not change with curing time, but are influenced by water content, like unbound granular materials, due to the negligible selfcementing properties.

The RLTT tests also indicated that the resilient modulus of NRCA increases continuously with curing time, up to the studied curing time (720 days). However, it was also found that cyclic loading can reduce the effect of self-cementing, by partially damaging the bonds formed between particles, as it was observed that for NRCA specimens curing for 360 and 720 days, the resilient modulus decreases slightly under cyclic loading. In contrast, curing time had no influence on the resilient modulus of ORCA.

Finally, the study shows that RCA with good self-cementing properties (like NRCA) represent excellent materials for use as unbound pavement layers, because their properties increase significantly with time, and can reach, in the long term, much higher values than those of natural unbound granular materials, with levels of permanent deformation in RLTT tests as low as 10×10 -4 m/m, and moduli of the order of 1600 MPa, 3 to 4 times higher than those of natural unbound granular materials. However, this evolution, evolved from unbound RCA layers, governed by rutting failure in the short term, to partially bound RCA layers, governed by fatigue and cracking in the long term, could lead to other deterioration mechanisms. RLTT tests have shown that traffic loads can damage some weak bonds formed by unhydrated cement, and this long-term behaviour, under cyclic loading, should be further investigated.

Figure 2

 2 Figure 2 shows the Modified Proctor curves of NRCA and ORCA. The optimum moisture

Figure 1 .

 1 Figure 1. Particle size distributions of NRCA and ORCA.

Figure 2 .

 2 Figure 2. Modified Proctor curves of NRCA and ORCA.

Figure 4 .

 4 Figure 4. Hydration heat of NRCA and ORCA.

Figure 5 .

 5 Figure 5. Evolution of permanent axial deformation 1 p with the number of load cycles for

Figure 6 .

 6 Figure 6. Final permanent axial deformations of NRCA and ORCA after 20000 load cycles, at

  time has no influence on 1 p of ORCA due to the negligible self-cementing properties, only the results of NRCA were used to model the permanent deformation behaviour.

Figure 7 .

 7 Figure 7. Average test results and model predictions of 1 p for NRCA, after different curing

Figure 8 .

 8 Figure 8. Evolution of resilient moduli of NRCA and ORCA with the number of load cycles,

Figure 9 .

 9 Figure 9. Evolution of final resilient moduli of NRCA and ORCA with curing time.

Table 3 .

 3 RLTT results on NRCA and ORCA, after different curing times.

	Results		NRCA			ORCA
		1 day	180 days	360 days 720 days	1 day	28 days 360 days
	p	28.9±5.3 7.1±0.03	7.2±3.7	6.7±1.0 26.7±3.3 38.5±5.8 34.3±6.8
	(10 -4 m/m)
		1.07±0.7 0.09±0.01 0.1±0.01 0.06±0.03 0.68±0.2 0.6±0.14 0.21±0.12
	(10 -7 m/m)
	Mr (MPa)	370.9	606.7	857.6	1598.7	395.3
		±7.6	±12.3	±10.4	±41.8	±8.4

  Table 3 also summarizes the average final values of resilient modulus Mr, after 20000 load cycles. For NRCA, a clear increase of Mr with curing time can be observed due to the self-cementing properties. After curing for 180, 360 and 720 days, the average final resilient modulus Mr of NRCA is 606, 858 and 1600 MPa, increasing by factors of 1.6, 2.3 and 4.3, respectively, compared with the resilient modulus curing for 1 day (370 MPa). The resilient modulus of NRCA curing for 720 days (1600 MPa)

Acknowledgments

The authors are grateful to colleagues Benjamin Latour from INSA de Strasbourg, and Sandrine Braymand from University of Strasbourg for the measurement of released heat. This work is supported by the China Scholarship Council.

Recycled concrete aggregate

Self-cementing properties

Permanent deformation

Resilient modulus

Repeated load triaxial test