Investigation on the low temperature properties of asphalt binder: Glass transition temperature and modulus shift factor

Construction and Building Materials 245 (2020) 118351

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Investigation on the low temperature properties of asphalt binder: Glass transition temperature and modulus shift factor Di Wang a, Augusto Cannone Falchetto a,b,⇑, Chiara Riccardi a, Michael P. Wistuba a,b a b

Braunschweig Pavement Engineering Centre-ISBS, Technische Universität Braunschweig, Beethovenstraße 51b, 38106 Braunschweig, Germany Department of Civil & Environmental Engineering, University of Alaska Fairbanks, Alaska, Fairbanks, AK 99775-5960, USA

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


The effect of glass transition

temperature, Tg, on the rheological properties of asphalt binder is studied.
Modulus shift factor bT is applied to adjust the DSR experimental data obtained below Tg.
bT can be used to mitigate the deviation caused by density changes for unmodified asphalt binders.

a r t i c l e

i n f o

Article history: Received 29 June 2019 Received in revised form 6 January 2020 Accepted 3 February 2020

Keywords: Asphalt binder Low temperature property Dynamic Shear Rheometer (DSR) Glass transition Modulus shift factor Rheological modeling

a b s t r a c t This paper investigates the effect of the glass transition temperature, Tg, and the use of modulus shift factors bT on the measured rheological properties of asphalt binders at low temperatures. First, temperaturefrequency (T-f) sweep tests are performed with the Dynamic Shear Rheometer (DSR) on asphalt binder, and, the corresponding Tg is calculated. Next, modulus shift factors bT is applied to the modulus data measured at temperatures below Tg in the Cole-Cole plot. Finally, a visual comparison of master curves and the parameter assessment of 2 Spring 2 Parabolic 1 Dashpot (2S2P1D) model are used to evaluate the effect of bT. A significant increase in dynamic shear modulus is observed when the DSR test is performed below Tg, while bT can take into account this phenomenon on the shape of the curves in the Cole-Cole plot. Hence, the combined use of the horizontal shift factor, aT, and modulus shift factor, bT, is recommended when the DSR tests are performed at temperatures lower than the corresponding asphalt binders Tg. Ó 2020 Elsevier Ltd. All rights reserved.

1. Introduction ⇑ Corresponding author at: Braunschweig Pavement Engineering Centre-ISBS, Technische Universität Braunschweig, Beethovenstraße 51b, 38106 Braunschweig, Germany. E-mail addresses: [email protected] (D. Wang), [email protected], [email protected] (A. Cannone Falchetto), [email protected] (C. Riccardi), [email protected] (M.P. Wistuba). https://doi.org/10.1016/j.conbuildmat.2020.118351 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.

Asphalt binder is one of the main constituents of asphalt mixture used for pavement applications; this material exhibits significant time-temperature dependent behavior [1,2]. While in Europe the characterization still relies on conventional penetration tests [3], in the U.S., asphalt binder is graded based on the Performance

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D. Wang et al. / Construction and Building Materials 245 (2020) 118351

Grade (PG) [4,5]. This system makes use of two main tests methods: Dynamic Shear Rheometer (DSR) to obtain the high PG [6,7]. To determine the low PG the Bending Beam Rheometer (BBR) [8] was adopted to overcome the instrument compliance errors exhibited by DSR at relatively low temperature [6]. In the recent past, a novel method based on the DSR with a 4 mm parallel-plate geometry [9,10] was proposed by Western Research Institute (WRI) to determine the low temperature properties of asphalt binder as an alternative to BBR. Two solutions were combined to mitigate the effect of instrument compliance error. First, a smaller plate geometry can be used to reduce the compliance effect on the measured results [11,12]. Second, the instrument compliance at different frequencies is accurately measured relying on a special adhesive (‘superglue method’) [10,13], and then, two equations (see Eqs. (1) and (2)) are used to correct the compliance error [10]. The corrected DSR dynamic shear modulus and the phase angle results are then converted to the relaxation modulus [14], G(t), and the corresponding relaxation parameter, mr-value, can be further calculated and used to obtain the low PG of asphalt binder potentially avoiding the need of BBR testing. Several follow up studies [9,15–20] succeeded in implementing this testing method for measuring the low temperature properties of asphalt binder, and, to establish correlations between DSR and BBR results. Because both 4 mm DSR (oscillation) and BBR (creep) tests [21] measure the linear viscoelastic properties of asphalt binder at low temperature, the results should present strong correlations [18]. However, poor correspondence is observed, especially for the critical temperatures determined by each method, with a maximum difference of 10 °C in some cases [15]. A series of research efforts indicated that different experimental conditions between BBR and DSR, such as thermal history, which includes physical hardening (steric hardening) at very low temperatures [15–18,22–24] and cooling rate [18], and cooling media [15,17,19,20] can lead to different rheological measurements results at low temperatures. The current BBR testing procedure makes use of the Time-Temperature Superposition Principle (TTSP) principle to reduce the loading time from 2 h, as initially proposed [25], to 60 s at 10 °C above the critical temperature. However, physical hardening appears to strongly affect the poor equivalence observed when adopting this approach [17,23,26]. Physical hardening (steric hardening) is a process that asphalt binder undergoes experiencing significant time-dependent stiffening when stored at low temperatures, ultimately affecting the relaxation properties of the binder in both laboratory environment and field conditions [23]. Moreover, BBR tests are performed in ethanol, while DSR sample is conducted in air. In 2012, Cannone Falchetto et al. [27] firstly observed that the low temperature creep stiffness results obtained with the BBR are highly dependent on the cooling medium, and several following studies [19,20,28] confirmed this finding in both asphalt binder and asphalt mixture. The asphalt binders’ stiffness results measured in the air is 20% to 33% higher than the one performed in ethanol. In two recent studies from the authors [19,20], it was found that when BBR tests are performed in air, better correlation can be found between BBR and DSR results. In the recent past, it was observed that the cooling rate can also affect the BBR result [18,28]. Hence, poor correlations between DSR and BBR results may be attributed to the different experimental conditions; when the thermal histories and cooling media can be carefully controlled, much better correlations are observed [18]. Besides the controllable experimental conditions, the changing in rheological properties of asphalt binders caused by glass transition [16,22,29–31] at low temperatures may be the other dominant factor affecting the correlation. In addition, this phenomenon occurs immediately when the temperature goes below the glass

transition temperature, Tg. Glass transition can be defined as the phenomenon occurring when asphalt binders undergo the transition from the viscoelastic to the glassy state; in this circumstance, their optical, thermodynamic, and mechanical properties change significantly. The physical meaning of this phenomenon can be explained according to the free volume theory proposed by Struik [32] and Ferry [33]. This characteristic can be described at two different scales when the materials’ transition occurs from the viscoelastic to the glassy state: at the macro scale [34], asphalt binder becomes glossy in appearance and extremely brittle and stiff [30], while the density of asphalt binder increases due to the volume contraction [32,33]. At the micro level [34], the transition is associated with a significantly reduced molecular motion becoming eventually negligible for long observation time; the molecules can be assumed to be in a glassy state under these conditions [30]. The corresponding glass transition temperature, Tg, is the characteristic value chosen to represent the temperature when such a transition occurs. In previous researches on asphalt binders [16,18,22,23,29, 30,34,35], most of the studies [22,29,30,34,35] focused on the relationship between glass transition and physical hardening or on the calculation method of Tg. Only limited works [16,18,35] took into account the actual effect of glass transition on the shape of master curves and on the potentially applicable correction for the bituminous material. For this purpose, a temperature dependence parameter, modulus shift factor which can be calculated by bT = Tref q(Tref)/Tq(T) [33], was introduced to adjust the deviation caused by glass transition by using the Cole-Cole plot in the work of Laukkanen and coworkers [18]. It should be noticed that this parameter was not originally developed to mitigate the effects of the glass transition, but more generally considered the effect of densification for asphalt binders at very low temperatures [36]. In another Laukkanen’s work on a different type of asphalt binder [37], it was found that both the horizontal shift factor and bT are needed for a modified SBS binder to generate smooth master curves when the time-temperature superposition principle was used to analyze the effect of physical aging on rheological properties of asphalt binder. This parameter is conventionally known as vertical shift factor or modulus shift factor; however, since this shift factor does not only work in the vertical direction but is effect is associated with the tangent of the Cole-Cole curve, the term ‘‘modulus shift factor” is more appropriate and used in the paper [38]. Besides the work conducted on asphalt binder, Hecksher et al. [39] investigated other glass-forming liquids, such as tetraphenyl-tetramethyltrisiloxane (DC704) and 5-phenyl-4-ether, a better estimation of the shear viscosity was found after the shifting. Generally speaking, the reasons why the literature of bT is rich; however, the application of bT is always ignored for the construction of the master curve are mainly two. First, the effect of glass transition (densification) is limited to very low temperatures, not all the DSR device has the capability to test samples at such a low temperature, only limited density changing can be observed at temperatures above 0 °C for asphalt binder. Hence, when master curves are generated to evaluate the DSR results, only a moderately unsmooth shape can be observed at very high frequencies (low temperatures) caused by the glass transition [35]. Second, the adjustment of modulus shift factor, bT, on the master curve is much weaker than the horizontal shift factor aT [16]. As a whole, most of the previous studies focused on the effect of densification cause by glass transition rely on the polymeric and polyolefins materials [38,39] instead of the bituminous materials [18]. In this paper, the effect of glass transition phenomenon in combination with instrument compliance is investigated by using two unmodified asphalt binders under different aging conditions.

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D. Wang et al. / Construction and Building Materials 245 (2020) 118351

2. Objective and research approach

3. Materials and testing

In this paper, the possibility of using a modulus shift factor correction, bT, for taking into account the deviation of the asphalt binder DSR measurements at very low temperatures, due to the effect of the densification caused by the glass transition phenomena, is experimentally investigated and evaluated. First, DSR tests are performed over a wide range of temperatures (30 °C to 80 °C) on two unmodified asphalt binders under seven different aging conditions, and the original data are corrected by instrument compliance, J. Then, the glass transition temperature, Tg, is calculated based on its peak of loss modulus [40] for each binder, respectively. Next, the modulus shift factor, bT, is applied to both storage modulus and loss modulus data by using the Cole-Cole plot. Thereafter, master curves are generated and the parameters of the 2 Springs 2 Parabolic Elements 1 Dashpot (2S2P1D) [41,42] model are used to further evaluate the effect of glass transition temperature and modulus shift factor on the measured rheological properties of asphalt binder at low temperatures. The adopted research approach is summarized in Fig. 1.

3.1. Materials

RTFOT1

Virgin Binders

1×Sample

Two different unmodified 70/100 pen-graded [3] asphalt binders, provided by the RILEM (International Union of Laboratories and Experts in Construction Materials Systems and Structures) Technical Committee 252-CMB project [42], are used in this research. This set of materials is selected as it was deeply investigated and its properties thoroughly analyzed representing a solid basis for the present research effort [17,20,24,43–47]. According to the binder producers, both binders are non-waxy binders. The virgin binders are identified as B501_virgin and B504_virgin, respectively. The two materials are then artificially aged to six different aging conditions. For this purpose, the short-term aging is performed with the Rolling Thin Film Oven Test (RTFOT) [48] at three different temperatures: 123 °C, 143 °C, and the standard 163 °C. Next, the aged binders, under the three different shortterm aging conditions, are long-term aged following the standard Pressure Aging Vessel (PAV) procedure [49]. The following rules

6×Samples

RTFOT+PAV2

1×123°C

1×123°C

1×123°C

1×143°C

1×143°C

1×143°C

1×163°C

1×163°C

1×163°C

25mm diameter: +30 to +80°C, 1mm gap

Dynamic Shear Rheometer (DSR) Testing

Materials Preparation

Experimental

8mm diameter: -10 to +40°C, 2mm gap

Work 4mm diameter: -30 to +10°C, 3mm gap

Instrument Compliance: J

Glass Transition Temperature: Tg

+ Measurement and Correction

Data Analysis

Calculation

And Modulus Shift Factor: bT

Normal Shift Factor

Cole-Cole Plot

Master Curve and 2S2P1D3 Modeling

Complex Shear Modulus - G* Phase Angle - δ Characteristic Time – τ Parameters - δ, k, h and β

Evaluation of Results and Discussion RTFOT1: Rolling Thin-Film Oven Test

PAV2: Pressure Aging Vessel

3

2S2P1D : 2 Springs 2 Parabolic Elements 1 Dashpot Fig. 1. Research approach.

Modeling and Evaluation Conclusions

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D. Wang et al. / Construction and Building Materials 245 (2020) 118351

are used to designate the binders: ‘‘Binder type_Aging condition_Temperature of short-term aging”. For example, B501_R_123, ‘‘B501” indicates the type of the virgin binder, ‘‘R” represents the RTFOT aging (‘‘R&P” for RTFOT + PAV), while ‘‘123” (143 and 163) represents the aging temperature used for the RTFOT aging. The conventional penetration [50] and ring & ball softening point [51] tests are performed to characterize the asphalt binders according to the European grading system [42]. The Performance Grade (PG) [5] of the two unmodified asphalt binders is also obtained through DSR [6,7] and BBR [8] tests and also reported in Table 1. 3.2. Testing DSR [6,7] tests are performed on the entire set of asphalt binders listed in Table 1 by using an available DSR device. The testing temperature ranges from 30 °C to +80 °C with an interval of 10 °C over a frequency window from 0.05 to 10 Hz (0.05, 0.1, 0.5, 1, 1.59, 2, 3, 4, 5, 6, 7, 8, 9 and 10 Hz). The classical parallel-plate configuration with three different plate geometries (25 mm, 8 mm, and 4 mm) was used. At high temperatures, +30 °C to + 80 °C, the 25 mm diameter with a gap of 1 mm is selected, while at intermediate temperatures, between 10 °C and +40 °C, the diameter of 8 mm with a gap of 2 mm is used. It should be noticed that the definition of intermediate temperatures is only from +10 °C to +40 °C, the reason why more temperatures are performed is to obtain more overlapping temperatures between the different geometries. At very low temperatures, a new experimental procedure proposed at the Braunschweig Pavement Engineering Centre (ISBS) at the Technische Universität Braunschweig [52] with a 4 mm diameter and 3 mm gap is selected. This experimental procedure has been successfully validated in the authors’ previous study, more detailed information about the sample preparation process is available in that paper [20,24,52]. At least two replicates for each type of binder listed in Table 1 and for each plate are tested. Such a range of temperatures was chosen in order to generate the master curves and to facilitate the fitting of the 2S2P1D model [41,42]. In order to remain in the Linear Viscoelastic (LVE) range, an amplitude sweep test is performed prior to testing to identify the optimal strain or stress levels to be used in the temperature frequency sweep (T-f-sweep) tests with different temperatures and the different geometries. For high temperatures, strain-controlled mode is selected, while for low and intermediate temperatures, stress-controlled mode is chosen; more details on the experimental devices and procedure together with instrument compliance correction can be found in previous studies [10,13,19,20,52]. 4. Data preparation and analysis 4.1. Glass transition temperature Tg Conventionally, the glass transition temperature, Tg, can be defined as the temperature where the loss modulus, G00 , attains

its peak [40]. Hence, a temperature sweep test with a constant frequency is usually performed to measure the material’s rheological properties, especially for the loss modulus over a wide temperature range. Alternatively, and more conveniently, Tg can be derived, based on the same approach (maximum value of G00 ), from temperature-frequency sweep tests and assuming the validity of the Time-Temperature Superposition Principle (TTSP) used for generating master curves of norm of the complex shear modulus, G*, and phase angle, d [29,53]. Then, the corresponding master curve of loss modulus, G00 , can be used to determine the value of Tg. In accordance with the Christensen-Anderson-Marasteanu (CAM) model [54,55] and TTSP [29,53], the master curves of dynamic shear modulus, |G*|, and phase angle, d, can be generated at a selected reference temperature T0. The formulation of CAM model can be expressed as:

G  ðf ; TÞ ¼ h

d¼

G1 k

1 þ ðf c =aT f Þ

ð1Þ

ime =k

90me

ð2Þ

k

1 þ ðf c =f Þ

where, f is the frequency (Hz); fc is a location parameter where loss modulus equals to storage modulus; aT is horizontal shift factor at a given temperature T; G1 is the glassy shear modulus when frequency tends to infinite, and k and me are dimensionless shape parameter. The horizontal shift factor in time-temperature superposition, aT, can be derived according to the Williams–Landel–Ferry (WLF) [56] formulation:

logaT ðTÞ ¼ 

c1 ðT  T 0 Þ c2 þ ðT  T 0 Þ

ð3Þ

where, T0 is the reference temperature, 20 °C is selected in this paper; c1 is a constant and c2 is the temperature constant. After the master curves of dynamic shear modulus, |G*|, and phase angle, d, are generated, the corresponding master curve of loss modulus, G00 , can be derived by the following relationships:

G ¼ G0 þ iG00 ;

G00 ¼ jG jsind; and G0 ¼ jG jcosd

ð4Þ

0

where, G is the storage modulus, and tan d is the loss factor. Since the master curve of the G00 is generated in the reduced frequency domain rather than in the temperature domain, Tg has to be back-calculated using Eq. (6) and the following expression (Eq. (9)) for the shift factor can be derived [34]:

aT ðT g Þ ¼

f red ðT g Þ f0

ð5Þ

where, fred is the reduced frequency, and f0 is a reference frequency defined as 1.59 Hz is selected in this paper. The calculation process is graphically illustrated in Fig. 2, it appears that the fitted master curve is not very good. Especially two sub-curves (temperatures) at very high frequencies/low temperatures, they are higher than the entire master curve. Actually, these two curves are affected by the densification caused by glass

Table 1 Conventional test results and PG grade for asphalt binders in different aging conditions. Binder B501

Soft Point (°C)

25 °C Penetration (0.1 mm)

Binder B504

Soft Point (°C)

25 °C Penetration (0.1 mm)

B501_virgin B501_R_123 B501_R_143 B501_R_163 B501_R&P_123 B501_R&P_143 B501_R&P_163 PG 70–22

46.2 47.4 48.9 50.7 56.5 57.4 57.0

77.0 73.7 56.7 55.3 33.7 30.3 31.7

B504_Virgin B504_R_123 B504_R_143 B504_R_163 B504_R&P_123 B504_R&P_143 B504_R&P_163 PG 64–22

47.3 45.8 48.2 50.0 56.2 57.4 58.6

83.7 82.7 65.7 57.3 49.3 44.7 38.7

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D. Wang et al. / Construction and Building Materials 245 (2020) 118351

the corrected measured data are plotted in a Cole-Cole plot, then bT is applied by using the following formulation [18].

(

G0 shifted ¼ bT  G0 original G00 shifted ¼ bT  G00 original

ð6Þ

where, G0shifted and G00shifted are shifted storage and loss modulus, while

Fig. 2. Calculation of Tg for asphalt binder B501_R_123.

transition. Hence, the G00 peak was determined by the fitted master curve instead of the experimental data. The resulting glass temperature Tg and the corresponding log reduced frequency are summarized in Table 2. It can be seen that the glass transition temperatures are between 11 °C and 17 °C for the entire type of asphalt binders under different aging conditions. Since the DSR testing is performed between 30 °C and +80 °C with a 10 °C temperature step and the effect of glass transition occurs overall below Tg [22,29,30], it may be expected that only the experimental data tested at 20 °C and 30 °C are substantially affected.

4.2. Modulus shift factor bT The main consideration of using the modulus shift factor is due to the generation master curves to further calculate different rheological parameters. Commonly, only the horizontal shift factor, aT, is applied to generate master curves based on TTSP [1,9,10,56]; the modulus shift factor, bT, in literature is commonly assumed to be equal to 1 or ignored [40,57]. This is mainly due to the relatively small magnitudes of deviation compared with the effect of horizontal shift factors within the superposition process [40,58–60]. However, during the fitting procedure of master curve, bT becomes important for moduli and data set obtained at low temperature (compliance segments - both in the time and frequency domains) which cover asymptotic regions; for example, when the material is under the glassy or equilibrium state at very low temperatures [61]. In both asymptotic ranges, small ‘vertical/modulus’ shifting may introduce tremendous differences in horizontal shifting; not only is the combined error given by the deviation in the time scale and compliance effects but also the error is cumulative. Disregarding the modulus shifting adjustment may lead to a large deviation [59]. Hence, when the DSR tests are performed below Tg, both shift factors aT and bT are needed to construct the master curve [40]. As previously mentioned, bT is conventionally named vertical or modulus shift factor [16,18,34]; it is called modulus shift factor in this study as discussed in the introduction [18,38]. In this paper,

G0original and G00original are the original storage and loss modulus. Fig. 3 graphically presents how to use bT, as a shift factor, to adjust the storage and loss modulus data in a Cole-Cole plot for asphalt binder B501_R_143, as an example. The blue circle markers represent the original experimental data after the instrument compliance correction, while the green markers show the data measured at T = 20 °C after shifting. The red circles refer to the experimental measurement obtained at T = 30 °C. As shown in Fig. 3, the data points obtained at a temperature below Tg follow a smooth continuous curve in the Cole-Cole plot after the modulus shifting. When bT is used, the raw data are not just vertically shifted; hence, this factor cannot be simply defined as a vertical shift factor. Consider the shifting mode, the definition of modulus shift factor is more appropriate for bT (see the direction of arrows in Fig. 3). The physical meaning of the modulus shift factor, bT, for asphalt binder is still a matter of debate as it involves concepts associated with the molecular structure of the material [40]. Asphalt binder is a complex composite consisting of molecules having size spanning over a wide scale range [29]. For this reason, previous studies on polymers may help to understand the physical significance of bT [59,60]. In the work on polymeric materials from Tschoegl et al. [62], the effect of temperature-induced density change was considered; both densification or thermal expansion cause deviation from a continuous variation in density which needs to be adjusted to the normal level [62]. Stadler et al. [38] focused on thermal expansion of polyolefins materials, they suggested using bT when a wide testing temperature range was applied for measurement purpose, otherwise, the shifting is not necessary. In another work investigating polycarbonate [60], the researchers concluded that the measurements should be adjusted to take into account the effects of densification. Recently, Kriz et al. [57] investigated the glass transition effect on the asphalt binder. Results showed that when asphalt binder is in the glassy state, it may contain a certain amount of crystalline phase; in most cases, the molecular motion decrease, and the ordered crystalline phase possesses higher density. Based on this series of past research efforts, it appears that the need for modulus shifting is strictly related to the densification of the material. This seems to be further supported by a different study [18] in which the density of asphalt binder under different temperatures was experimentally measured, and the corresponding bT was calculated. It was found that bT is around 1 when the temperatures are above Tg; however, these values are in the range of 0.85–0.97 when the measurement temperatures are below Tg. Hence, bT is only needed when the DSR tests are performed below Tg. Table 3 summarizes the modulus shift factor for each binder in this study at the testing temperature of 20 °C and 30 °C.

Table 2 Glass transition temperature Tg and corresponding Log reduced frequency. Binder B501

logfred (Hz)

Tg (°C)

Binder B504

logfred (Hz)

Tg (°C)

B501_virgin B501_R_123 B501_R_143 B501_R_163 B501_R&P_123 B501_R&P_143 B501_R&P_163

5.35 5.00 5.10 5.10 5.40 5.40 5.40

13.33 11.60 12.52 12.43 13.14 13.92 13.65

B504_virgin B504_R_123 B504_R_143 B504_R_163 B504_R&P_123 B504_R&P_143 B504_R&P_163

5.40 5.60 5.75 5.65 5.70 5.80 5.75

14.37 15.37 16.17 16.00 15.80 15.33 14.37

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D. Wang et al. / Construction and Building Materials 245 (2020) 118351

Fig. 3. Cole-Cole plot for asphalt binder B501_R_143 before and after modulus shifting.

It can be seen that the modulus shift factor bT is between 0.90 and 0.94 for 20 °C, and between 0.82 and 0.86 for 30 °C. No correlation could be found between Tg and bT. The comparison between the original and the corrected data for two different binders are presented in Fig. 4. As shown in Fig. 4, the blue curve presents the original modulus data without any correction, the red one provides the data corrected only by the instrument compliance while the green curve shows the data corrected by instrument compliance and adjusted through modulus shifting. It is interesting to observe that the green curve remains in the same area of the plot compared to the original curve at 30 °C. The adjusted modulus data are further used to back-calculate the dynamic shear modulus and phase angle to generate the master curve in the next section. 5. Modeling 5.1. Master curves In this study, the CAM model [54,55] is used in combination with the TTSP [29,53] to generate the master curve at a reference

temperature of 20 °C. The master curves of dynamic modulus, | G*|, and phase angle, d, of asphalt binders B501 and B504 are reported in Figs. 5 and 6, respectively and the effect of modulus shift factor is visually compared. In each figure, the dynamic shear modulus master curve before and after the modulus shifting is first presented, followed by the corresponding phase angle master curves. As shown in Figs. 5 and 6, all the binders have a similar rheological trend. The virgin binders show the lowest dynamic modulus and the highest phase angle. Meanwhile, the short-term aged binders exhibit intermediate values, and the long-term aged binders present the highest dynamic modulus and the lowest phase angle. It is true that only a slight difference for dynamic shear modulus can be visually observed in the master curves before and after the modulus shifting. This is also due to a narrowing of the curves in the top right portion of the plot. A closer observation, in the bigger ellipse, indicates a lower dynamic shear modulus after shifting. These findings are confirmed by previous studies [10,18,35,40]. For the case of phase angle, no differences can be found before and after the shifting, since the modulus shift factor affects both storage and loss modulus at the same time with the same level. Master curves are conventionally plotted in the log–log coordinate and therefore only provide a general overview partially hiding from a visual point of view the differences in the low temperature region, suggesting that the effect of glass transition might be considered as potentially negligible [35,40,58,60]. In order to further evaluate this effect, the CAM model parameters are compared; Tables 4 and 5 provide all the parameters for asphalt binders B501 and B504 before (light grey) and after (dark grey) the modulus shifting for the entire set of aging conditions. The master curves’ parameters provide a clear understanding of the effect of the glass transition temperatures and the modulus shift factor. G1 decrease while fc increases dramatically after shifting, with respect to the location parameter fc (also known as crossover frequency), higher fc corresponds to softer asphalt binder after the modulus shift is applied. Parameter k and me show a moderate increasing and decreasing trend, respectively. G1 is the maximum asymptotic modulus in shear that represents response at very high frequencies or low temperatures for asphalt binder. According to Laukkanen study [63], this value should be between 1000 and

Table 3 Modulus shift factor bT for each asphalt binders at 20 °C and 30 °C. 20 °C

30 °C

Binder B504

20 °C

30 °C

B501_virgin B501_R_123 B501_R_143 B501_R_163 B501_R&P_123 B501_R&P_143 B501_R&P_163

0.93 0.93 0.94 0.91 0.92 0.92 0.92

0.85 0.85 0.86 0.84 0.85 0.85 0.85

B504_virgin B504_R_123 B504_R_143 B504_R_163 B504_R&P_123 B504_R&P_143 B504_R&P_163

0.91 0.92 0.93 0.91 0.92 0.92 0.90

0.82 0.82 0.84 0.82 0.84 0.83 0.82

1.8E+08 1.6E+08 1.4E+08 1.2E+08 1.0E+08 8.0E+07 6.0E+07 4.0E+07 2.0E+07 0.0E+00 0.0E+0

(a)

original Cole-Cole plot Cole-Cole plot after corrected by compliance Cole-Cole plot after modulus shifting

G'' [Pa]

G'' [Pa]

Binder B501

2.0E+8

4.0E+8

6.0E+8

G' [Pa]

8.0E+8

1.0E+9

1.2E+9

1.8E+08 1.6E+08 1.4E+08 1.2E+08 1.0E+08 8.0E+07 6.0E+07 4.0E+07 2.0E+07 0.0E+00 0.0E+0

(b)

original Cole-Cole plot Cole-Cole plot after corrected by compliance Cole-Cole plot after modulus shifting 2.0E+8

4.0E+8

6.0E+8

8.0E+8

G' [Pa]

Fig. 4. Cole-Cole plot comparison between original and two corrections: a) B501_R_143; b) B504_R&P_123.

1.0E+9

1.2E+9

D. Wang et al. / Construction and Building Materials 245 (2020) 118351

7

Fig. 5. Master curves for asphalt binders B501: a) original dynamic shear modulus; b) dynamic shear modulus after modulus shifting; c) original phase angle; d) phase angle after modulus shifting.

1350 MPa for unmodified asphalt binders, it can be higher only due to aging or modification. In Tables 4 and 5, the value of 1150 and 1300 MPa for both B501_virgin and B504_virgin can be accepted. It should be noticed that the fitted parameters can only reflect the measured properties of asphalt binder, the materials’ real properties will not be affected with or without the shifting.

5.2. 2S2P1D model More sophisticated models can be adopted to explain the rheological response of the material [42]. In order to better evaluate the rheological properties of asphalt binders, the 2S2P1D model [41,42,64] (Fig. 7), was adopted in this study.

Fig. 6. Master curves for asphalt binders B504: a) original dynamic shear modulus; b) dynamic shear modulus after modulus shifting; c) original phase angle; d) phase angle after modulus shifting.

8

D. Wang et al. / Construction and Building Materials 245 (2020) 118351 Table 4 Parameters of CAM model for master curves of asphalt binders B501 before and after modulus shifting.

Table 5 Parameters of CAM model for master curves of asphalt binders B504 before and after modulus shifting.

The 2S2P1D model expression for complex modulus at reference temperature T0 is given by the following formula:

G ðixsÞ ¼ G0 þ

G1  G0 1 þ dðixsÞ

k

þ ðixsÞ

h

þ ðixbsÞ

1

G ∞- G 0 k, δ h η

Fig. 7. 2S2P1D Model [35,36].

G0

ð7Þ

where, i is the complex number defined by i2 = -1; x is angular frequency such that x = 2p  f ; k and h are exponents such as 0 < k < h < 1; d and b are constants; G0 is shear modulus: when x ? 0, G0 = 0 for asphalt binders and G0 > 0 for asphalt mixture; G1 is glassy shear modulus when x?1; g is Newtonian viscosity such that g= (G1-G0)  bs; s is the characteristic time (function of temperature), at a given temperature T, s(T) = aT  s0 where aT is the shift factor at temperature T based on the WLF formulation (Eq. (3)). This parameter is associated with the relaxation time of the material. Since this study is restricted to asphalt binders, the experimental static modulus is close to zero and can be assumed as negligible. In addition, the initial kernel parameters G1 can be derived from the original CAM model [54,55]. Figs. 8 and 9 present a comparison between the black diagram and Cole-Cole plot for asphalt binder B501_R_143 and B504_R&P_123, respectively. In each figure, the black diagram before and after modulus shifting is first reported, followed by the corresponding Cole-Cole plots. As shown in both Figs. 8 and 9, the 2S2P1D models can fit very closely the experimental DSR results after the modulus shifting, while poor fitting was obtained on the original data for the ColeCole plot. Similar to the master curves, only a moderate improvement can be visually observed in the top left portion of the black diagram where the low temperature data are located. The experimental measurements obtained at 20 °C and 30 °C consistently deviate from the 2S2P1D fitting curve in the Cole-Cole plane before shifting, as the experimental results at these two temperatures appear to lie on two distinct curves with respect to the other

D. Wang et al. / Construction and Building Materials 245 (2020) 118351

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Fig. 8. Experimental data and 2S2P1D fitting for asphalt binders B501_R_143: a) original black diagram; b) black diagram after instrument compliance revision; c) black diagram after modulus shifting; d) original Cole- Cole plot; e) Cole-Cole plot after instrument compliance revision; f) Cole-Cole plot after modulus shifting.

temperatures. This not only leads to a much higher G1 but also results in unreliable fitting. After visual inspection of the plots, the 2S2P1D model parameters were compared. Tables 6 and 7 provide all the model parameters for asphalt binders B501 and B504 before (light grey) and after (dark grey) modulus shifting for the entire set of aging conditions. The parameters of the 2S2P1D model provide a clear understanding of the effect of the glass transition and the modulus shift factor. G1 and parameter d decrease dramatically after shifting; parameter k shows a slight increase trend, meanwhile, there is almost no difference between the characteristic time, s, and the two constant, h and b, before and after shifting. It must be remarked that parameter d controls the slope at the low temperatures/high frequencies for master curve and the height of the peak point of the Cole–Cole plot while parameter h controls the slope at lower values of G00 in the Cole-Cole plot [42,65,66]. Therefore, it may be hypothesized that higher G1, d and lower k correspond to stiffer and more brittle, measured property instead of the real property, asphalt binders without modulus shifting.

6. Summary and conclusions In the present work, Dynamic Shear Rheometer (DSR) tests were performed to study the effect of densification caused by the glass transition and the modulus shift factor bT on the rheological properties of unmodified asphalt binders at low temperatures. First, the original experimental data were corrected by the compliance and then the glass transition temperature Tg was calculated. Next, the modulus shift factor bT was applied to the experimental data measured below Tg and visualized in the Cole-Cole plot. Finally, the master curve and 2S2P1D model were used to evaluate the effect of glass transition and modulus shift factor on the asphalt binders’ rheological properties. Based on the experimental analysis and modeling, the following conclusions can be drawn:
The correction of instrument compliance at low temperatures can result in higher loss and storage modulus; this ultimately magnifies the effect associated with the measurements obtained at a temperature below the glass transition.

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D. Wang et al. / Construction and Building Materials 245 (2020) 118351

Fig. 9. Experimental data and 2S2P1D fitting for asphalt binders B504_R&P_123: a) original black diagram; b) black diagram after instrument compliance revision; c) black diagram after modulus shifting; d) original Cole- Cole plot; e) Cole-Cole plot after instrument compliance revision; f) Cole-Cole plot after modulus shifting.

Table 6 Parameters of 2S2P1D model for asphalt binders B501 before and after modulus shifting.

D. Wang et al. / Construction and Building Materials 245 (2020) 118351

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Table 7 Parameters of 2S2P1D model for asphalt binders B504 before and after modulus shifting.


The modulus shift factor bT can be used to mitigate the deviation of the densification caused by the glass transition phenomenon for asphalt binder at temperatures below the glass transition temperature Tg.
The parameters of the 2S2P1D model indicate that the glass transition has a significant effect on the low temperature properties of unmodified asphalt binders, confirming the need of bT to avoid unrealistic material properties such as extremely high dynamic shear modulus. The overall results of the present research effort support that DSR measurements are strongly affected by the glass transition phenomenon at low temperatures. However, modulus shift factor bT can be used to reduce and mitigate this deviation in the experimental data at low temperature. Based on the results of this present study, the application of modulus shift factor will be adopted for research purposes at the German institution of origin of the authors (TU Braunschweig - ISBS) when DSR testing is performed lower than the asphalt binder’s glass transition temperature Tg. The results obtained in this study, although promising, need to find additional experimental support by extending the present research effort to the investigation of more types of asphalt binders. Declaration of Competing Interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The RILEM Technical Committee on Chemo-Mechanical Characterization of Bituminous Materials (CMB) 252 is gratefully acknowledged. The authors would also like to thank the China Scholarship Council, National Natural Science Foundation of China (51508064, 51408083) for the financial support to the graduate studies of the first author. Augusto Cannone Falchetto would like to acknowledge the support of the Japan Society for Promotion of Science – JSPS international research in Japan program. References [1] M. Marateanu, D. Anderson, Time-temperature dependency of asphalt binders–An improved model (with discussion), J. Assoc. Asphalt Paving Technol. 65 (1996) 408–448. [2] B.S. Underwood, Y.R. Kim, Experimental investigation into the multiscale behaviour of asphalt concrete, Int. J. Pavement Eng. 12 (4) (2011) 357–370. [3] EN 12591, Bitumen and bituminous binders. Specifications for paving grade bitumens. European Committee for Standardization, 2015

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