PhD Anne L Abbott
email: anne.l.abbott@gmail.com

Dr Oliseneku D Uyagu
email: ouyagu@yahoo.com

Dr Guillaume Goudot
email: guillaume.goudot@aphp.fr

Hrvoje Budincevic
email: hbudincevic@gmail.com

Prof Stavros Kakkos
email: kakkosstavros@gmail.com

S Weiner

M H Benton

B Guraziu

Y Yange

J He

Y T Chen

Asst / Prof

MD Hrvoje Budincevic

Regarding an Apparently High Stroke Rate in Patients With Medically Managed Asymptomatic Carotid Stenosis at an Academic Center in the Southeastern United States

Keywords: Carotid stenosis, carotid stenting, carotid endarterectomy, trans-carotid arterial revascularisation, medical (non-invasive) intervention, stroke prevention

Text

We respectfully disagree with Weiner et al and advise that it is premature to give up on current best non-invasive medical intervention (lifestyle coaching and medication) alone for patients with asymptomatic carotid stenosis (ACS).(1) Weiner et al reported an average annual ipsilateral 'stroke' rate of 2.9% (10 ipsilateral strokes, in 173 patients with >70% stenosis over 2 years). This is just a little more than for non-surgically managed patients in the Asymptomatic Carotid Atherosclerosis Study (2.3%/year in patients with 60-99% ACS) and significantly more than in the most recently published quality studies of non-invasively managed patients with >50-75% ACS (approximately 0.8%/year).( 2 J o u r n a l P r e -p r o o f * Lacked explanation as to whether or not only the first ipsilateral stroke or TIA was included in the analyses. Continuing to monitor patents for stroke after a TIA artificially elevates stroke rates.( 5) * Lacked explanation as to whether or not carotid endarterectomy associated strokes were included in their analysis of outcomes with non-invasive intervention alone.

Moreover, the study was not designed to assess current best medical intervention. For example, it In conclusion, the quality of medical intervention being received by the ACS patients at the academic center in the south-eastern United States is incompletely documented. However, where it is documented, the standard is poor. Rather than default to more carotid procedures, we recommend that the authors are invigorated to optimise medical intervention at their institution. After all, there is current evidence of significant patient benefit from non-invasive medical intervention. [START_REF] Abbott | Medical (nonsurgical) intervention alone is now best for prevention of stroke associated with asymptomatic severe carotid stenosis: results of a systematic review and analysis[END_REF][START_REF] Abbott | Optimizing the Definitions of Stroke, Transient Ischemic Attack, and Infarction for Research and Application in Clinical Practice[END_REF][START_REF] Abbott | Extra-Cranial Carotid Artery Stenosis: An Objective Analysis of the Available Evidence[END_REF] Further, there is no current randomised trial evidence that any carotid artery procedure provides patient benefit compared to non-invasive medical intervention alone and there is known procedural risk and cost.

  Letter to the Editor of Annals of Vascular Surgery By Anne L. Abbott, Oliseneku D. Uyagu, Guillaume Goudot, Hrvoje Budincevic and Stavros Kakkos Regarding an Apparently High Stroke Rate in Patients With Medically Managed Asymptomatic Carotid Stenosis at an Academic Center in the Southeastern United States S. Weiner, M. H. Benton, B. Guraziu, Y. Yange, J. He, Y. T. Chen, et al.

- 4 )

 4 When study results are different, almost certainly the methods are different. In contrast to the quality studies included in previous meta-analyses showing falling stroke rates in non-invasively managed ACS patients(3, 4), the single-centre study by Weiner et al: * Was retrospective * Was without a definition of stroke and transient ischaemic attack (TIA). Including patients with a deficit lasting < artificially elevates stroke rates.(4)

  was a study of clinician recommendations about medications, not of what medications were taken. Furthermore, Weiner et al gave an overly simplified definition of 'optimal -procedural medical management, including by not addressing all leading arterial disease risk factors, not considering the importance of lifestyle factors, not providing current and reproducible definitions of risk factors and medical interventions (including evidence-backed intervention targets) and not providing information about any changes in patient risk factor profiles and non-invasive interventions over the 2 years.(5)

prevention. She was part academically funded by an NHMRC grant at the time of creating this manuscript (APP1168295).

There was no specific funding for producing this manuscript. A/Prof Abbott is a neurologist. She has received several grants

Conflict of Interest:

The authors declare no conflict of interest or competing interests in relation to this manuscript.

J o u r n a l P r e -p r o o f


Jean-Claude Carret

Augusto Cannone Falchetto

Mihai O Marasteanu

Di Hervé

Michael Benedetto

Cédric Wistuba

Sauzeat

Hervé Di Benedetto

Michael P Wistuba

Cedric Sauzeat

Comparison of rheological parameters of asphalt binders obtained from bending beam rheometer and dynamic shear rheometer at low temperatures

Keywords: asphalt binder, linear viscoelasticity, dynamic shear rheometer (DSR), bending beam rheometer (BBR), creep compliance, physical hardening

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

Introduction

One of the most significant achievements in the area of paving asphalt materials characterisation was the development of the Strategic Highway Research Program (SHRP) performance grade (PG) specifications at the beginning of the 1990s. The PG tests and analyses, detailed in a number of American Association of State Highway and Transportation Officials (AASHTO) specifications (AASHTO M320, 2010;AASHTO T313, 2012;AASHTO T315, 2012), are used to specify the asphalt binders used in pavement applications and also serve as primary tools to investigate the behaviour of asphalt binders in many research studies. The success of the PG system can be attributed, on one hand, to the innovative application of fundamental concepts to asphalt binder material characterisation and, on the other hand, to the reasonable level of complexity of the test methods and analyses required as part of these specifications.

Most of the data required to determine the PG of a binder are obtained from two experimental testing procedures: frequency sweeps performed with a dynamic shear rheometer (DSR) (AASHTO T315, 2012) at high and intermediate temperatures, and bending creep tests performed with a bending beam rheometer (BBR) (AASHTO T313, 2012) at low temperatures. The parameters obtained in DSR are: |G*(ω)| that represents the absolute value of the shear complex *Corresponding author. Email: a.cannone-falchetto@tu-bs.de 1 Comparison of rheological parameters of asphalt binders obtained from bending beam rheometer and dynamic shear rheometer at low temperatures modulus, and δ(ω) that represents the corresponding phase angle. The parameters obtained from BBR are: S(t) that represents the creep stiffness (inverse of creep compliance), and m-value that represents the absolute value of the slope of the creep stiffness versus time curve on a double logarithmic scale.

Preparing BBR beams for testing requires approximately 15 g of binder per beam, while the DSR test requires only a few grams. As low-temperature tests are performed on pressure aging vessel (PAV)-aged binders or binders recovered from field cores, which are difficult to obtain in large quantities, it becomes important to explore the possibility of replacing the BBR test with the DSR test that requires much smaller quantities of materials. A number of researchers have explored this possibility [START_REF] Claudy | Characterization of asphalt cements by thermomicroscopy and differential scanning calorimetry: Correlation to classic physical properties[END_REF] and recently [START_REF] Farrar | Determining the low temperature rheological properties of asphalt binder using a dynamic shear rheometer[END_REF] proposed a new DSR geometry and inter-conversion methods to obtain creep stiffness and m-values from DSR tests at low temperature. According to the theory of viscoelasticity [START_REF] Ferry | Viscoelastic properties of polymers[END_REF], any linear viscoelastic (LVE) function can, in theory, be converted into any other viscoelastic function.

Objective

In this paper, an investigation was performed to determine if the complex modulus obtained from DSR testing can indeed be used to accurately predict the creep compliance obtained using BBR testing. As the two BBR parameters S(60s) and m(60s) are used to obtain the lower limit of the binder PG, it becomes critical to determine if DSR testing and LVE inter-conversions match the BBR results at the same temperature. The investigation was prompted by the fact that physical hardening, that significantly affects BBR results, has been well documented during SHRP research effort and received considerable attention over the years, while this effect has not been studied for DSR testing, mostly because of testing equipment limitations at low temperatures. It is also worth mentioning that DSR testing is performed in air, while BBR creep tests are performed in ethanol.

Materials and testing

Two sets of materials were used in this study. The first set was tested as part of a previous investigation [START_REF] Marasteanu | Comparison of moduli for asphalt binders obtained from different test devices[END_REF] and the second set represents asphalt binders recently tested in Germany.

The first set consists of four of the SHRP core asphalt binders. The binders were selected based on their asphaltene content (AC) and crystallised fraction (CF), which are known to influence physical-hardening effects: AAD1 has low CF and high AC; AAF1 has high CF and high AC; AAG1 has low CF and low AC; and AAM1 has high CF and low AC. All samples were tested in the unaged condition.

DSR frequency sweep data were obtained using three types of geometries: 25, 8 mm, and torsion bar. For the torsion bar geometry, a laboratory procedure described elsewhere [START_REF] Marasteanu | Comparison of moduli for asphalt binders obtained from different test devices[END_REF] was used. To minimise potential nonlinear effects, the strain was changed with each decade change in frequency. All tests were performed in air. BBR creep tests were performed in ethanol at three consecutive specification temperatures according to the asphalt binder PG (low PG + 4°C, low PG + 10°C and low PG + 16°C) as listed in Table 1.Thethree temperatures were chosen so that the deflection values obtained were within the BBR test specification limits (from 0.08 to 4.00 mm). A summary is given in Table 1. All tests were replicated twice. The second set consists of two asphalt binders tested in the unaged condition at the Pavement Engineering Centre at the Technische Universität Braunschweig. The first asphalt binder is a plain binder having a 50/70 penetration window (EN 1426(EN , 2007)), hereafter identified as AB 50-70, while the second is a 45/80-65 polymer-modified binder with a penetration range of 45/80 (EN 1426(EN , 2007) ) and a softening temperature of 65°C (EN 1427(EN , 2007)), named AB 45-80-65.

DSR frequency sweep data were obtained according to current specifications (AASHTO T315-12, 2012;EN 14770, 2012) using two different plate sizes: 8 mm plates were used for temperatures between 0°C and 40°C (0°C, 4°C, 10°C, 16°C, 22°C, 28°C, 34°C and 40°C), while 4 mm plates were needed for lower temperatures down to -40°C ( -40°C, -36°C, -30°C, -24°C, -18°C, -12°C, -6°C, 0°C, 4°C and 10°C). For both geometries, tests were performed starting from the lowest temperature and allowing an equilibrium time of 30 min before the actual test at the specific temperature. Specimens were initially conditioned for 1.5 h at the lowest temperature corresponding to -40°C and 0°C, for the two geometries, respectively. Conditioning and testing were performed using air as the cooling medium. The range of frequencies was selected between 0.01 and 10 Hz and the lowest frequency was imposed as the initial frequency for all temperatures. Figure 1 shows the DSR device for asphalt binder together with the two testing geometries. BBR creep tests were performed according to AASHTO and EN (European Norm) specifications (AASHTO T313-12, 2012;EN 14771, 2012). Conditioning (1 h) and testing were performed using ethanol as the cooling medium. The same two testing temperatures were selected for both asphalt binders: -24°C and -18°C. These two temperatures were also used for DSR testing and, therefore, provide the possibility of a direct comparison of the experimental data obtained from oscillatory and static loading without the potential errors that may be associated with time-temperature superposition shifting. Figure 1 presents the DSR and BBR equipments used in the laboratory at Braunschweig.

Tools to analyse DSR rheological data

When performing simple or complex analyses on sets of rheological data obtained over a wide range of temperatures, it is good practice to first examine the data in a graphical form. Asphalt binders do not exhibit sudden changes in their behaviour with respect to time or temperature. Therefore, any discontinuities in the test data or any sudden change in the slope of the curves when changing test temperatures or loading time or frequency can most likely be attributed to testing error.

Plots of |G*| and of phase angle versus frequency at different temperatures are very useful for identifying errors. However, when multiple test temperatures are used, two other graphical representations can be used.

The first one is the Cole-Cole plot that is a graphical representations of the two components of the complex modulus, G ′ (horizontal axis) and G ′′ (vertical axis), when complex modulus is expressed as G* = G ′ + i G ′′ . An example is shown in Figure 2 for asphalt binder AAD1.

One advantage of this representation is that it can detect small errors in the data since both axes have normal scales. However, one big disadvantage of using the normal numerical scale is the fact that only test data at temperatures below zero are visible in this plot, while the test data above zero are basically invisible, as clearly seen from Figure 2. It should also be mentioned that the peak observed for G ′′ is associated with the glass transition temperature (Anderson & Marasteanu, 1999;[START_REF] Anderson | Dilatometric measurements of glass transition temperatures[END_REF]. One simple way to avoid this problem is using the Black diagram, which uses the two components of the complex modulus, |G*| and phase angle δ, when the complex modulus is expressed as G* =| G*|e iδ . In this representation, the vertical axis is log |G*| and the horizontal axis is the phase angle on the normal scale. While the log scale makes the identification of small errors less obvious, it allows for visible representation of the entire temperature range of testing. If the material is linear, thermo-rheologically simple, and there are no testing errors, a smooth curve is obtained. An example is shown in Figure 3 for asphalt binder AAF1. Cole-Cole and Black space representations do not require any shifting for data generated at different temperatures. While this is a big advantage, it also makes it impossible to detect errors in temperature measurement and does not provide any information on the temperature dependency of the material. For example, two asphalt binders may have similar master curves shapes but different temperature dependencies, as shown in Figure 4. Neither Cole-Cole nor Black space will detect any difference between the two binders.

A full representation of the material behaviour can be obtained through the use of master curves that are based on rheological models. These models can describe both the frequency (time) and temperature dependency of the material and some of the models can be used to obtain other viscoelastic functions, such as creep and relaxation modulus, from frequency sweep experiments. This latter approach is used in this investigation to compare DSR and BBR results at low temperature.

Rheological models

Two complementary models, developed at the Ecole Nationale des Travaux Publics de l'Etat (ENTPE) laboratory, were used in the analysis of the DSR data:

• The LVE with the continuous spectrum 2S2P1D (two springs, two parabolic elements and one dashpot) model introduced by Di Benedetto, Olard, Sauzéat, and [START_REF] Di Benedetto | Linear viscoelastic behaviour of bituminous materials: From binders to mixtures[END_REF] and Olard and Di Benedetto (2003) characterises the behaviour of bituminous materials in the linear domain (i.e. for small strain amplitudes); • The viscoplastic DBN (Di Benedetto, Neifar) model (Di Benedetto, [START_REF] Di Benedetto | Three-dimensional thermo-viscoplastic behaviour of bituminous materials: The DBN model[END_REF][START_REF] Di Benedetto | DBN law for the thermo-visco-elasto-plastic behaviour of asphalt concrete[END_REF][START_REF] Neifar | Thermo-viscoplastic law for bituminous mixtures[END_REF];O l a r d&D i Benedetto, 2005) predicts the general thermo-viscoelastoplastic behaviour of bituminous materials.

2S2P1D model

The 2S2P1D (two springs, two parabolic creep elements, one dashpot) is a generalisation of the Huet model [START_REF] Huet | Etude par une méthode d'impédance du comportement viscoélastique des matériaux hydrocarbonés[END_REF]. The Huet model has an analytical creep function (Cannone Falchetto, [START_REF] Cannone Falchetto | Analogical based approach to forward and inverse problems for asphalt materials characterization at low temperatures[END_REF][START_REF] Moon | Rheological modelling of asphalt materials properties at low temperatures: From time domain to frequency domain[END_REF] but does not simulate correctly asphalt materials behaviour on the whole frequency and temperature range, especially at high temperature and/or low frequency. The 2S2P1D model is based on a simple combination of physical elements (springs, parabolic creep element, and dashpot) as shown on its analogical representation in Figure 5. This model can also simulate the threedimensional behaviour of bituminous mixtures, binders, or mastics (Di Benedetto, [START_REF] Di Benedetto | Three-dimensional linear behaviour of bituminous materials: Experiments and modeling[END_REF][START_REF] Di Benedetto | Linear viscoelastic behaviour of bituminous materials: From binders to mixtures[END_REF]. Calibration of the 2S2P1D model is obtained from an optimisation using experimental data. At a given temperature, complex modulus of the 2S2P1D model is given by Equation ( 1)

E * 2S2P1D (ω) = E 00 + E 0 -E 00 1 + δ(jωτ ) -k + (jωτ ) -h + (jωβ τ ) -1 , ( 1
)
where j is the complex number defined by j 2 =-1; ω is the angular frequency, ω = 2π f , where f is the frequency; k, h constants such as 0 < k < h < 1; δ constant; E 00 is the static modulus when ω tends towards 0, for asphalt it is equal to 0; E 0 is the glassy modulus when ω tends towards+∞; η the Newtonian viscosity of the dashpot, η = (E 0 -E 00 ) βτ and τ the characteristic time, whose value varies only with temperature. The time-temperature superposition principle is verified in linear and non-linear domains [START_REF] Nguyen | Time-temperature superposition principle for bituminous mixtures[END_REF]Nguyen, Sauzéat, Di Benedetto, & Tapsoba, 2013;Nguyen, Di Benedetto, Sauzéat, & Tapsoba, 2013) using:

τ(T) = a T (T)τ 0 , (2)
where a T is the shift factor at the temperature T given by: the WLF (Williams-Landel-Ferry) [START_REF] Ferry | Viscoelastic properties of polymers[END_REF]

equation (Equation (3)) log(a T ) =- C 1 (T -T r ) C 2 + T -T r . (3)
C 1 and C 2 represent the two WLF constants and T r the reference temperature. At a given temperature, six constants (E 0 , δ, k , h, β, τ 0 ) are required to model the LVE properties of asphalts on the whole range of frequencies. When temperature effects are considered, eight constants are needed, including the two WLF constants (C 1 , C 2 ).

DBN model

Research performed at ENTPE led to the development of the DBN model which is an attempt to describe with one formulation the different types of behaviour observed for bituminous mixtures. This model is also able to simulate the behaviour for any bituminous materials such as binders, mastics, and mixes. Only the main aspects of the DBN model are presented in this paper. More details can be found elsewhere (Di Benedetto, [START_REF] Di Benedetto | Three-dimensional thermo-viscoplastic behaviour of bituminous materials: The DBN model[END_REF][START_REF] Di Benedetto | DBN law for the thermo-visco-elasto-plastic behaviour of asphalt concrete[END_REF][START_REF] Neifar | Thermo-viscoplastic law for bituminous mixtures[END_REF][START_REF] Olard | The DBN model: A thermo-visco-elasto-plastic approach for pavement behavior modeling. Application to direct tension test and thermal stress restrained specimen test[END_REF].

The 1D representation of the DBN model is composed of one spring (modulus E 0 ) and n elementary bodies (each of them composed by an elastoplastic (i.e. non viscous) body (EP) in parallel with a dashpot (linear V body) as shown in Figure 6. The number of elementary bodies (n) can be chosen arbitrarily as the calibration procedure always needs the same number of constants (the constants from the 2S2P1D model and plastic functions not introduced in this paper). If n is high, simulation becomes closer to the experimental data. In the LVE domain (i.e. for small strain amplitude domain) EP bodies become springs of rigidity E i , and the DBN model becomes a Generalised Kelvin Voigt (GKV) model (Figure 6). In that case, calibration of the n elementary bodies is made from parameters of the 2S2P1D model (also developed at LGCB-ENTPE and presented in the previous section). 2S2P1D is a continuous spectrum model with a limited number of constants (nine in the mono-dimensional case). When increasing number n of elementary bodies, the difference between the optimised DBN model and 2S2P1D model decreases on the whole temperature-frequency range. Theoretically, this difference becomes nil for n equal to infinity. In this paper, the number of considered elementary bodies is n = 90, and E 00 = E n = 0 since only asphalt binders were considered. Figure 7 shows that n = 90 gives quite a good approximation of 2S2P1D on the whole temperature-frequency range. Due to lack of space, readers are invited to read given references on LGCB-ENTPE work, for more details on the general procedure.

Methodology used in this paper

For each tested asphalt binder, data from DSR experiments are fitted using the 2S2P1D model. As the DSR device gives complex shear modulus (G*), the experimental data are multiplied by 3 to obtain complex modulus (E*) (E* = 3G*). To apply coefficient "3", an isotropic behaviour and Poisson's ratio of 0.5 are assumed. This last hypothesis, made to simplify the analysis, could be improved if three-dimensional expression of 2S2P1D is considered (Di Benedetto, [START_REF] Di Benedetto | Three-dimensional linear behaviour of bituminous materials: Experiments and modeling[END_REF][START_REF] Tiouajni | Approximation of linear viscoelastic model in the 3 dimensional case with mechanical analogues of finite size -Application to bituminous materials[END_REF]. The 2S2P1D model fitting was presented in several papers from the ENTPE team, for different types of bituminous materials [START_REF] Baaj | Thermomechanical characterisation of asphalt mixtures modified with high content of asphalt shingle modifier (ASM ® ) and reclaimed asphalt pavement (RAP)[END_REF][START_REF] Delaporte | Linear viscoelastic properties of bituminous materials including new products made with ultrafine particles[END_REF][START_REF] Di Benedetto | Stiffness of bituminous mixtures using ultrasonic wave propagation[END_REF][START_REF] Mangiafico | Influence of RAP content on complex modulus of asphalt binder blends and corresponding mixes: Experimental results and modeling[END_REF][START_REF] Mangiafico | New method to obtain viscoelastic properties of bitumen blends from pure and reclaimed asphalt pavement binder constituents[END_REF][START_REF] Mounier | Determination of bituminous mixtures linear properties using ultrasonic wave propagation[END_REF]Pouget, Sauzéat, Di Benedetto, & Olard, 2010a, 2010ab, 2012;[START_REF] Tapsoba | Behavior of asphalt mixtures containing RAP and asphalt shingles[END_REF]. The number of analysed cycles should be correctly chosen to avoid biased effects, such as heating and thixotropy as shown elsewhere [START_REF] Di Benedetto | Nonlinearity, heating, fatigue and thixotropy during cyclic loading of asphalt mixtures[END_REF][START_REF] Nguyen | Determination of thermal properties of asphalt mixtures as another output from cyclic tension-compression test[END_REF].

The list of 2S2P1D constants for the two sets of tested asphalt binders presented in this paper is given in Table 2.

Then, the GKV model (asymptotic expression of DBN model) having 90 elements is optimised from the calibrated 2S2P1D model for each material. The optimisation process is explained in [START_REF] Tiouajni | Approximation of linear viscoelastic model in the 3 dimensional case with mechanical analogues of finite size -Application to bituminous materials[END_REF]. The process is quite simple as it is made by an excel sheet developed at ENTPE Laboratory. The GKV model simulation with 90 elements gives a quite similar result than the 2S2P1D model as seen in Figure 7 where an example of 2S2P1D fitting is presented for asphalt binder AAD1.

From values η i and E i of the GKV model it is quite easy to write the creep function (F simul DSR(t) ) for simple tension and compression loading (compliance). This creep function is given in Equation ( 4)

F simul DSR(t) = 1 E 0 + n-1 i=1 1 E i (1 -e -t/τ i ) + 1 η n . ( 4
)
The inverse of F simul DSR(t) gives the creep stiffness function S simul DSR(t) (Equation ( 5)), which is compared with BBR creep stiffness data, S(t), in the next sections, for the different asphalts

S simul DSR(t) = 1 F simul DSR(t)
.

(5)

Comparison of DSR and BBR data

The procedure described above was used to convert DSR frequency sweep data to BBR creep stiffness (inverse of creep compliance). To eliminate any errors associated with the applicability of the time-temperature superposition principle, the comparisons were performed at the same test temperatures. Since Poisson's ratio is not commonly determined for asphalt binders, a constant value of 0.5 was assumed for all conversions from shear to tension to simplify the analysis, as explained in the previous section. Typical plots of the data obtained for the two sets of asphalt binders are shown in Figures 8 and9.

Visual inspection of all the plots prepared for the four core asphalt binders at three different test temperatures showed that in all cases the measured BBR creep stiffness was larger than the creep stiffness calculated from DSR data. The largest differences were observed for asphalt binders AAD1 and AAF1. The smallest differences were observed for asphalt binder AAG1. Reducing Poisson's ratio values did not improve the match. A Poisson ratio of 0.3 results in a multiplication factor of 2.6 instead of 3, a drop of only 13% that cannot explain differences more than double observed for some of the binders. A less clear trend is observed for the two German asphalt binders. For binder AB 45-80-65, the DSR and BBR almost match while for binder AB 50-70 the opposite of what was observed for the core binders is noticed. It can also be observed that using vertical shifting does not provide a good matching between the BBR experimental results and the creep stiffness curves obtained from the conversion of the DSR data. A horizontal shift on the time scale appears to be a better alternative, similar to the trend observed in the BBR physical-hardening data; in a previous paper (Anderson & Marasteanu, 1999) it was shown that the effect of physical hardening on BBR stiffness could be approximated with a shift to a higher test temperature, which translates to a shift on the time axis. This approach was also used with the binders used in this study and it was found out that horizontal shifting of the BBR creep compliance results in an almost perfect match of the converted DSR data. The shifting factors for asphalt binder AAD1 were 2.3, 2.9 and 4.1 for temperature -18°C, -24°C and -30°C, respectively. In the case of asphalt binder AAM1 the following shifting factors were used: 1.3, 2.9 and 6.0 corresponding to temperatures -12°C, -18°C and -24°C. Examples are shown in Figures 10 and11. The logarithmic scale was used to show all three temperatures.

It is therefore plausible to explain the difference between the BBR data and the converted DSR data as the result of a difference in physical-hardening effects on the two samples. A limited experiment was performed on the four SHRP core asphalt binders to investigate this issue.

Physical-hardening effects

Physical hardening of asphalt binders tested at low temperatures has been well documented during SHRP [START_REF] Anderson | Binder characterization and evaluation (SHRP A-369[END_REF][START_REF] Bahia | Low-temperature isothermal physical hardening of asphalt cements[END_REF]. However, these conclusions were based entirely on BBR data. No studies have been reported on physical-hardening effects for the DSR at low temperatures. For this reason, the asphalts used in this study were tested after varying conditioning times to identify the effects of physical ageing for both DSR and BBR conditions. Due to the difficulties associated with longer conditioning times for DSR, conditioning time was limited to a maximum of 2 h. For BBR, individual samples were tested at each test temperature after 1, 2, 24, and 48 h conditioning times.

No significant differences in complex modulus (absolute value) or phase angle were observed in DSR torsion bar tests for the various conditioning times for any of the four asphalt binders; the differences observed were less than the testing errors associated with the test results obtained.

As expected, physical hardening did play a significant role in the BBR tests. The magnitude of the effect was loading time dependent and asphalt binder dependent. The change in stiffness and m-value increases with the increase in loading time. Asphalt AAG1, characterised by low asphaltene and wax content, showed an increase in stiffness after 48 h of isothermal cooling to be between 0% and almost 10% (Figure 12). For AAD1, with high AC and low wax content, the increase in stiffness after 48 h ranged from 35% to 60%, while for AAM1 that has high wax content, ranged from 60% to 110% (Figure 13).

Cooling medium effects

Other factors may be responsible for the differences observed when comparing DSR and BBR data. One possible factor is the cooling medium: the DSR uses refrigerated air, while the BBR uses ethanol to condition the sample. This difference may result in different cooling rates in the DSR and BBR samples. In addition, ethanol has been shown to interact with the asphalt binder and significantly affect strength properties of the binders (Cannone Falchetto, [START_REF] Cannone Falchetto | Investigation of asphalt mixture strength at low temperatures with the bending beam rheometer[END_REF][START_REF] Marasteanu | Development of a simple test to determine the low temperature strength of asphalt mixtures and binders[END_REF].

A simple study, performed as part of a different investigation, brings support to this hypothesis. Four asphalt binders were tested using BBR at one single testing temperature corresponding to 10°C above the lower limit of the performance (PG) of the binders. The tests were performed in three cooling media: ethanol (E), potassium acetate (PA) typically used in binder direct tension testing, and air. For two of the binders, two conditioning times were also used: 1 and 20 h. Table 3 presents materials details and experimental design. 4(a) and 4(b) presents the results of the statistical analysis (ANOVA) for creep stiffness and m-value at t = 60s: S(60) and m(60).

These results follow the same trend observed in the previous section: the measured BBR creep stiffness (in ethanol) was less than the creep stiffness calculated from DSR data (in air). It also indicates that the changes are binder specific, which makes this problem more complex.

Conclusions

Based on the materials, laboratory equipment, testing protocols, and analyses used in this study, it was found that significant differences are observed between the creep stiffness obtained with DSR and BBR devices. The most probable factor responsible for these differences is the different cooling media used in the two instruments that may result in different cooling rates as part of the preparation and conditioning of the samples (DSR -air, BBR -ethanol fluid) and, therefore, in different physical-hardening effects. The observations and findings from this study do not render the viscoelastic properties measured in the DSR and BBR invalid. They demonstrate, however, that there are other factors associated with their measurement that makes a direct comparison, based strictly on LVE concepts, inaccurate. Therefore, replacing the current BBR specification with a similar specification based on DSR experimental data cannot be successful until these issues are addressed.

Disclosure statement

No potential conflict of interest was reported by the authors.

DSR•

  Figure 1. (a) DSR testing device, (b) BBR testing device.

Figure 2 .

 2 Figure 2. Cole-Cole plot for asphalt binder AAD1.

Figure 3 .

 3 Figure 3. Black space plot for asphalt binder AAF1.

Figure 4 .

 4 Figure 4. Temperature dependency of two asphalt binders having similar master curves shapes.

Figure 5 .

 5 Figure 5. Analogical representation of the 2S2P1D model: general case (left), for asphalt (right).

Figure 6 .

 6 Figure 6. Analogical 1D representation of the DBN model, which corresponds to the GKV model in the LVE domain (small strain amplitude).

Figure 7 .

 7 Figure 7. Experimental results of the complex modulus test on binder AAD1 with 2S2P1D and the GKV model (90 elements): simulation plotted for the complex Young's modulus E*. Above: Cole-Cole diagram; below: mastercurve at -18°C diagram.

Figure 8 .Figure 9 .

 89 Figure 8. Comparison of DSR and BBR data for two of the core asphalt binders at -18°C.

Figure 10 .Figure 11 .

 1011 Figure 10. Creep stiffness for AAD1, shifted BBR and converted DSR data.

Figure 12 .Figure 13 .

 1213 Figure 12. Change in creep stiffness for AAG1 due to physical hardening.

  Figure 14. BBR creep stiffness curves for Citgo PG58-28.

Figure 15 .

 15 Figure 15. BBR creep stiffness curves for MIF PG58-34.

Table 1 .

 1 Summary of testing protocol.

Table 2 .

 2 2S2P1D constants for tested asphalt (E* modulus from DSR data).

	Parameters	E 0 (MPa)	δ	khβτ -18°C (s)	C 1	C 2
	AAD1	3200	2.7	0.28	0.62	220	0.15	26.87	135.22
	AAF1	3100	2.6	0.25	0.52	170	6	25.06	107.62
	AAM1	2300	3.8	0.27	0.58	200	12	24.57	99.96
	AAG1	2900	2.1	0.26	0.52	30	140	18.02	56.52
	AB 50-70	1850	2.2	0.20	0.53	120	35	5.4E7	3.2E8
	AB 45-60-80	1400	6	0.23	0.57	450	15	1.5E6	9.8E6

Table 3 .

 3 Asphalt binder details and experimental design.

Table 4 .

 4 ANOVA F tests results of asphalt binder for (a) S(60) and (b) m(60).Figures 14 and 15 show the average (Av) creep stiffness curves for Citgo and MIF asphalt binders, and Table

	Source -S(60s)	Fp -Value
	(a)
	Binder type	489.6	1E -08
	Cooling medium	114.7	1E -08
	Conditioning time	92.9	1E -08
	Ageing	338.8	1E -08
	Cooling medium.ageing	4.8	.011
	Source -m(60s)	Fp -value
	(b)
	Binder type	123.9	1E -08
	Cooling medium	242.7	1E -08
	Conditioning time	136.8	1E -08
	Ageing	836.7	1E -08
	Conditioning time.cooling medium	3.8	.029