1 Introduction

Asphalt pavements are susceptible to rutting and fatigue cracking at upper and intermediate service temperatures, respectively [1,2,3,4]. Conventional binder grading methods such as penetration and viscosity grading may not adequately predict the performance of asphalt pavements over the entire range of service temperatures [5,6,7]. To overcome these limitations, the ‘Strategic Highway Research Program’ (SHRP) proposed the ‘Superpave Performance Grading’ (PG) methodology. In the PG system, rutting and fatigue cracking criteria are assigned so that the asphalt binders must fulfill at the corresponding pavement design temperature [5, 6, 8, 9]. PG grading of asphalt binders marked a significant shift in binder grading methodology compared to the conventional penetration and viscosity grading.

In the PG system, the upper limiting temperature (Tu) is assigned as the temperature where |G*|/sinδ ≥ 1000/2200 Pa (unaged/RTFO aged) at a frequency of 10 rad/s. Through regression analysis, literature studies have reported a correlation (R2) ranging ‘0.8–0.92’ between the PG rutting criterion (|G*|/sinδ) and rutting in asphalt mixtures [3, 10,11,12,13,14]. These studies highlight that rutting in asphalt mixture is affected by several parameters, such as properties of binders, aggregates, gradation, mix preparation methodology, etc. [15, 16]. To enhance the correlation, alternative rutting parameters are suggested in the literature. These alternate rutting parameters can be broadly categorized as; amendments to the current |G*|/sinδ criterion [17, 18], revision to the testing parameters [11, 16], utilization of zero shear/low shear viscosity [10,11,12,13,14,15, 15,16,17,18,19,20,21], etc. In the case of polymer modified asphalt binders (PMBs), parameters such as elastic recovery by multiple stress and creep and recovery (MSCR), toughness, phase angle (δ) value, etc., are adopted in addition to |G*|/sinδ [17, 18, 22,23,24,25,26,27,28,29,30]. In the MSCR test, the PMBs stress-bearing and elastic recovery characteristics are considered to evaluate the rutting performance in pavements, and the results correlate better with rutting in mixes [10, 25, 26, 28,29,30].

Asphalt pavements are susceptible to fatigue cracking at intermediate service temperature due to the increase in the stiffness of the binder [1, 2]. In the PG grading system, the intermediate limiting temperature (TI) is assigned as the temperature where the loss modulus G″ = |G*|sinδ ≤ 5000 kPa at 10 rad/s for RTFO + PAV aged binders [1,2,3]. Compared to the PG rutting criterion, the deviation in the correlation between the PG fatigue criterion (|G*|sinδ) and the fatigue cracking in asphalt mixtures is prominent [31,32,33,34,35,36,37,38,39]. To enhance the correlation, alternative methods and parameters are suggested. These alternative parameters in general can be categorized as: amendments to the SHRP fatigue criterion to energy dissipation method [40,41,42], time sweep [31, 36, 37], linear amplitude sweep [33, 35, 36, 39], R-value [38], Glover-row parameter [32, 34], etc.

Though several alternate rutting and fatigue criteria have been proposed in the literature, studies have not been carried out that critically examine the utility of the parameters, such as δ, sinδ, |G*|, |G*|/sinδ, |G*|sinδ, etc., in the PG rutting and fatigue criteria.

Thus, the key objectives of this study are

  • Through strain sweep and frequency sweep studies in oscillatory mode, and shear rate ramp studies in rotation mode, to show that the sinδ parameter in the |G*|/sinδ criterion has no benefit as the phase angle (δ) values are more than 80° at PG upper limiting temperature (Tu).

  • Rheological and asphalt mixture studies demonstrate the equivalence of viscosity and |G*|/sinδ criterion. Furthermore, illustrate that all alternate rutting criteria are also surrogate expressions of the viscosity of the unmodified binder.

  • At PG intermediate limiting temperature (TI), demonstrates that the use of fatigue criterion G″ = |G*|sinδ has no benefit as δ values were close to 45°. Thereby, highlighting the shortcoming of correlating rheological parameters measured in the linear viscoelastic region (LVE) and fatigue cracking in asphalt mixture.

  • Finally, highlight the important role of angular frequency in quantifying the properties of PMBs, and demonstrate that a better correlation can be obtained between the PMBs rheological properties and rutting in asphalt mixes at frequencies ≤ 0.1 rad/s.

2 Materials and Methods

The source, true PG upper limiting temperature (Tu), true PG intermediate temperature (TI), and conventional properties of the 18 asphalt binders are given in Table 1. To demonstrate that the findings are not limited to binder samples having a narrow range of properties, samples were selected whose source and physical properties varied significantly. All the rheological and conventional measurements were carried out according to ASTM standards within the linear viscoelastic limits (LVE) [43,44,45]. In the LVE region, the rheological properties of the unmodified and modified binders, such as modulus, viscosity, etc., are independent of the applied strain amplitude. In addition to properties presented in Table 1, flash point, mass loss after RTFO, and solubility in trichloroethylene of the binders were evaluated according to ASTM D18, D2872, and D2042, respectively. Flashpoint, mass loss, and solubility in trichloroethylene of all the asphalt binders were > 230 °C, < 1%, and > 99%, respectively.

Table 1 Source, true PG upper limiting temperature (Tu), and true PG intermediate temperature (TI) of the 18 unmodified asphalt binders
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PMB preparation: polymer modified binders (PMB) were prepared by blending different weight % of linear SBS polymer in H-62 and L-64 binders. The linear SBS polymer (Kraton’s D1101) with 30% styrene content was purchased from Rishi Chem distributors, India. The SBS polymer was first mixed with the binder at 180 °C using a Silverson high shear mixer (Model: L4RT) at 3000 rpm for 120 min. After high shear mixing, the blend was homogenized at 180 °C by mixing at 600 rpm for 120 min using a low shear mixer. To avoid phase separation of the polymer from the binder, the SBS polymer was cross-linked by adding 0.12% sulphur during low shear mixing. The preparation of the PMBs is schematically illustrated in Fig. 1. The basic properties of the PMB samples are given in Table 2.

Fig. 1
figure 1

Schematic illustration of PMB preparation

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Table 2 Properties of the 6 polymer modified asphalt binders in H-62
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Asphalt analysis: to measure the rut depth in asphalt mixes prepared using unmodified and modified binders, the analysis was carried out using the wheel tracking device (WTD) at 60 °C for 20,000 cycles. The aggregates used in the study were collected from a local quarry of Roorkee, India. The physical properties of aggregates are given in Table 3. The mid-point gradation with 19 mm nominal maximum size recommended by the ‘Ministry of Road Transport and Highways’ for bituminous concrete (BC-1) is depicted in Fig. 2.

Table 3 Properties of the aggregates
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Fig. 2
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Mid-point gradation for used aggregates

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3 Results and Discussions

3.1 PG Rutting Criterion for Unmodified Asphalt Binders

In the PG grading system, the maximum 7-day average pavement temperature is categorized in 6 °C intervals (52, 58, 64, 70, 76 °C, etc.), and asphalt binders are graded based on the |G*|/sinδ value at these temperatures. Instead of measuring the |G*|/sinδ value at 6 °C intervals, the true PG upper limiting temperature (Tu) for the 18 unaged and RTFO aged asphalt binders was determined and is given in Table 1. The true PG upper limiting temperature (Tu) is the temperature where |G*|/sinδ ≃ 1000/2200 Pa for the unaged and RTFO aged binders [45]. As shown in Fig. 3, the |G*|/sinδ value of the 18 unaged and RTFO aged binders were ≈ 1000 and 2200 Pa at their respective Tu.

Fig. 3
figure 3

|G*|/sinδ vs. true PG upper limiting temperature (Tu) for the 18 unaged and RTFO aged asphalt binders

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A highly insightful understanding is obtained when the ‘sinδ’ values of the 18 unaged and RTFO aged binders at Tu were analyzed. It can be observed in Fig. 4a and b that the ‘sinδ’ values of the binders were above 0.990 (≈ 1) at Tu. The sinδ values were ≈ 1 as the phase angle (δ) values of the binders were greater than 80°, as shown in Fig. 5a and b. Since sinδ ≈ 1, the SHRP defined rutting criterion (|G*|/sinδ) can be simplified to complex modulus |G*| ≥ 1000/2200 Pa (unaged/RTFO aged).

Fig. 4
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Sinδ vs. true PG upper limiting temperature (Tu) for the 18 asphalt binders a unaged b RTFO aged

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Fig. 5
figure 5

Phase angle (δ) vs. true PG upper limiting temperature (Tu) for the 18 asphalt binders a unaged b RTFO aged

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From elementary rheology [46, 47], it is known that the complex viscosity |ɳ*| = |G*|/ω. Since in PG grading the measurements are performed at ω = 10 rad/s, |ɳ*| = |G*|/10. This means that at Tu, the PG rutting criterion is equivalent to |ɳ*| = 100/220 Pa s (unaged/RTFO aged).

This is experimentally confirmed on plotting |ɳ*| vs. Tu for the unaged and RTFO aged binders, as illustrated in Fig. 6. In other words, the true PG upper limiting temperature is also the temperature where |ɳ*| of the asphalt binders is 100/220 Pa s (unaged/RTFO aged).

Fig. 6
figure 6

Complex viscosity (|ɳ*|) vs. true PG upper limiting temperature (Tu) for the 18 unaged and RTFO aged asphalt binders

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It is essential to know whether the equivalence of the PG rutting criterion and viscosity remains valid at test conditions beyond the fixed parameter of strain amplitude (10%) and angular frequency (10 rad/s). For this purpose, strain sweep and frequency sweep experiments were performed on all the 18 unaged and RTFO aged binders. The observations on the 18 binders were analogous, and only the results of H-62, L-64, M-65, and R-72 binders are presented in this section to avoid redundancy and overlapping of curves. The results of the remaining 14 binders are shown in the appendix section.

To evaluate the influence of oscillatory strain amplitude (γA) on the rheology properties of the asphalt binders at Tu, γA was varied from 1 to 50% at a constant ω = 10 rad/s. The test was performed using the cone-plate geometry of 25 mm diameter and 2° cone angle to achieve a uniform strain rate across the entire gap. It can be noticed in Fig. 7 that across the entire strain range, the complex viscosity (|ɳ*|) of the binders was close to 100 Pa s (unaged) and 220 Pa s (RTFO aged). At higher strain values, edge instability started to occur, and hence it was not possible to test the samples at higher strain amplitude values. To analyze the effect of angular frequency (ω), ω was varied from 1 to 20 rad/s at a constant γA = 10%. Similar to the results presented in Figs. 6 and 7, it can be noticed in Fig. 8 that across the entire ω range, |ɳ*| of the binders was close to 100 Pa s (unaged) and 220 Pa s (RTFO aged). Observations on the rest of the 14 binder samples were similar, and hence their results are presented in the appendix section (Figs. 16, 17). Thus, the equivalence of the |G*|/sinδ to |ɳ*| (100/220 Pa s) can be extended beyond the PG testing conditions of γA = 10% and ω = 10 rad/s.

Fig. 7
figure 7

Complex viscosity (|ɳ*|) vs. strain amplitude (γA) at true PG upper limiting temperature (Tu) for the four unaged and RTFO aged asphalt binders

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Fig. 8
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Complex viscosity (|ɳ*|) vs. angular frequency (ω) at true PG upper limiting temperature (Tu) for the four unaged and RTFO aged asphalt binders

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Generally, for viscous liquids with high δ values, complex viscosity (|η*|) will be similar to shear viscosity (ɳ) measured in rotational shear [48]. Therefore, for unmodified asphalt binders at Tu, similar viscosity values (100/220 Pa s) should be observed when determined in rotational shear. Moreover, one of the most common ways of determining the viscosity of liquids is through rotational shear. For this purpose, strain rate ramp experiments in the rotational shear mode were carried out at Tu using cone-plate geometry from 0.1 to 10/s. It can be seen in Fig. 9 that across the applied shear rate of 0.1–10/s, viscosity (ɳ) of the four binders is close to 100/220 Pa s (unaged/RTFO aged). At shear rates > 10/s in the cone-plate geometry, edge instability began to occur, due to which experiments were not carried out at higher shear rates. Thus, for unmodified asphalt binders at true PG upper limiting temperature and shear rate = 1–10/s, PG rutting criterion |G*|/sinδ equates to shear viscosity ɳ. For Newtonian liquids, the viscosity will remain constant as a function of the applied shear rate, strain amplitude, and frequency. While for non-Newtonian liquids, the viscosity will either decrease (shear thinning) or increase (shear-thickening) as a function of the applied shear rate, strain amplitude, and frequency. It can be observed in Figs. 6, 7, 8 and 9 that the unmodified asphalt binders exhibited a behavior close to that of Newtonian liquids.

Fig. 9
figure 9

Shear viscosity (ɳ) vs. shear rate at true PG upper limiting temperatures (Tu) for the four unaged and RTFO aged asphalt binders in rotational mode

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3.1.1 Correlation of |G*|/sinδ and |ɳ*| with Rut Depth

Asphalt mix analysis was carried out to measure the rut depth of the asphalt mixes prepared using the 18 binders. The rutting analysis was carried out using a wheel tracking device (WTD) at 60 °C. The correlating factor (R2) between rut depth at 20,000 cycles vs. |G*|/sinδ and |ɳ*| of the unmodified binders are shown in Fig. 10a and b. It can be noticed from Fig. 10a and b that the R2 value for |G*|/sinδ and |ɳ*| is similar, supporting the observation made in Figs. 6, 7, 8 and 9. Similar to unaged binders, the |G*|/sinδ and |ɳ*| of RTFO aged binders also had similar R2 values against rut depth, as shown in Fig. 11a and b. Thus, due to the equivalence of |ɳ*| and |G*|/sinδ, the two parameters resulted in a similar correlation with rutting in asphalt pavements. Shenoy et al. suggested an alternate parameter ‘|G*|/(1 − (1/tanδsinδ))’ to predict the performance of asphalt binders at upper service temperature [18]. This is one way to measure the susceptibility to resist rutting in the pavements by measuring the non-recovered compliance of the binder [49]. The equation is valid in between δ = 52° and 90° to encompass most binder data in the high specification temperature regime. Since the δ values of the unmodified asphalt binders are more than 80°, even Shenoy’s parameter can be equated to binder viscosity. Sybilski suggested the ZSV concept to characterize the rutting behavior of binders [50]. Since at upper service temperature and low shear rate, the viscosity is independent of the applied shear rate [19]. Therefore, PG rutting criterion, Shenoy’s parameter, low shear viscosity, zero shear viscosity, and viscosity by vacuum capillary viscometer all are based on the same principle of correlating viscosity of the binder to rutting in asphalt pavements [16, 20, 21, 51].

Fig. 10
figure 10

Correlation between a rut depth and |G*|/sinδ, b rut depth and complex viscosity (|ɳ*|) for the 18 unmodified binders

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Fig. 11
figure 11

Correlating factor (R2) between a rut depth and |G*|/sinδ, b rut depth and complex viscosity (|ɳ*|) for the 18 RTFO aged unmodified binders

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3.2 PG Fatigue Cracking Criterion for Unmodified Asphalt Binders

In SHRP studies, a good correlation was demonstrated between fatigue cracking in asphalt mixture and loss modulus (G″) of asphalt binders. Hence, loss modulus G″ = |G*|sinδ indicating the energy dissipation capacity of the binder, was chosen as the fatigue cracking criterion. The specification requirement was set as the temperature where the loss modulus G″ = |G*|sinδ ≤ 5000 kPa for ‘RTFO + PAV’ aged binder at ω = 10 rad/s and γA = 1%. The true PG intermediate temperature (TI) of the 18 ‘RTFO + PAV’ aged binders is listed in Table 1.

An essential understanding of the rheological behavior of ‘RTFO + PAV’ aged asphalt binders was obtained when the δ values at the true PG intermediate limiting temperature (TI) were analyzed. It can be seen in Fig. 12 that at TI and linear viscoelastic (LVE) condition of ω = 10 rad/s, γA = 1%, the δ values of ‘RTFO + PAV’ aged binders were between 40° and 50° [52]. In this δ range, the value of sinδ will be close to cosδ, which means that elastic modulus (G′) and loss modulus (G″) values will be similar to each other, as shown in Fig. 13. In other words, the energy dissipation capacity of the ‘RTFO + PAV’ aged binders will be the same as its energy-storing tendency. Hence, in SHRP studies, a good correlation was found among several of the rheological properties of asphalt binders (|G*|, G′, and G″) and fatigue behavior of asphalt mixture [1, 2, 5, 6]. Thus, for ‘RTFO + PAV’ aged binders, using the loss modulus (G″) as the fatigue criterion will offer limited benefit. Since phase angle values of RTFO + PAV aged binders are close to 45°, the fatigue criterion of |G*|sinδ can also be represented as |G*|≤ 7000 kPa. Along similar lines, ‘R-value’ analysis utilizes the |G*| values obtained from the master curves of the ‘RTFO + PAV’ aged binders to determine the fatigue performance [38].

Fig. 12
figure 12

Phase angle (δ) vs. true PG intermediate limiting temperature (TI) for the 18 ‘RTFO + PAV’ aged asphalt binders

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Fig. 13
figure 13

Loss modulus (G″) and elastic modulus (G′) vs. true PG intermediate limiting temperature (TI) for the 18 ‘RTFO + PAV’ aged asphalt binders

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Moreover, the drawback in using δ of asphalt binders to predict the fatigue behavior in asphalt mixes is illustrated in Fig. 14. Figure 14 presents the |G*| and δ values of unaged and ‘RTFO + PAV’ aged R-72 binder. It can be seen in Fig. 14 that the |G*| of the binder increases significantly due to ‘RTFO + PAV’ aging. It is well documented that the brittleness of asphalt binders also increases after ‘RTFO + PAV’ aging, due to which failure by fatigue cracking increases considerably. On the contrary, it can be noticed in Fig. 14 that the δ value of the binder decreases after ‘RTFO + PAV’ aging implying that elasticity in the binder sample increases. Thus, if an analysis is made considering the δ value, it will lead to the incorrect conclusion that fatigue cracking reduces after aging [32, 53]. In studies such as linear amplitude sweep (LAS) and glover-row analysis, efforts are made to predict the fatigue performance of asphalt binders through |G*| and δ values [32,33,34,35,36, 38, 39]. But the results in Fig. 14 demonstrate that fatigue cracking and δ show opposing trends after aging in asphalt binders. Also, the ‘RTFO + PAV’ aged binders will be highly susceptible to detachment at the surface of measuring geometry during LAS testing due to the high stiffness [54].

Fig. 14
figure 14

Complex modulus (|G*|) and phase angle for unaged and ‘RTFO + PAV’ aged R-72 binder at 27 °C

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3.3 Rutting Criterion for Polymer Modified Binders

Polymer modified binders (PMBs) enhances the rutting, fatigue cracking, and thermal cracking performance of asphalt pavements [55, 56]. Pavements constructed using PMBs have a longer service life and lower maintenance requirements [57, 58]. Styrene–butadiene–styrene (SBS) is one of the most frequently used polymers for binder modification. Other polymers such as styrene–butadiene rubber (SBR), reactive terpolymer, ethylene-vinyl-acetate (EVA), ethylene-glycidyl-acrylate (EGA), etc. are also used for binder modification, but to a lesser extent [59,60,61,62]. In PMBs, it is widely documented that the rutting criterion (|G*|/sinδ) is inadequate to predict the rutting performance of asphalt mixtures [12]. Hence, state highway organizations have opted to incorporate additional tests such as multiple stress and creep and recovery (MSCR), minimum δ value, toughness, tenacity, etc. [17, 18, 24, 26]. After evaluating unmodified asphalt binders, rheological measurements were carried out on SBS modified binders to determine the reason for the poor correlation between the PG criterion |G*|/sinδ and rutting in asphalt mixtures. H-62 and L-64 binders were modified by adding different weight percent of linear SBS polymer. A brief analysis of PMBs rheological behavior is presented in this paper, while a detailed study will be reported subsequently.

The main factor influencing the correlation between the rheological properties of the PMBs to the rutting performance can be acknowledged in Fig. 15a–c. |G*|, δ, and |G*|/sinδ vs. ω of the six PMB samples at 60 °C are presented in Fig. 15a–c. Unlike unmodified binders, it can be seen in Fig. 15a–c that |G*|, δ, and |G*|/sinδ of the PMB samples varies significantly as a function of ω. Most importantly, the difference among the PMBs is noticeable mainly at lower frequencies, which indicates that the effect of SBS polymer in the binder is better quantified at lower frequencies [16, 63]. At ω < 1 rad/s, the |G*| of the SBS modified binders began to plateau when the SBS content was ≥ 4 wt%, the concentration above which morphological observations have shown the formation of an interconnected polymer-rich network in the binder [58, 61]. Unlike unmodified binders, the complex viscosity of SBS modified binders varies strongly with applied frequency even in the LVE region because of the plateau of the |G*| vs. ω curve. This can be further understood from the δ values of the PMBs, as shown in Fig. 15b. It can be noticed in Fig. 15b that up to 3 wt% SBS content, δ values are weakly dependent on the applied ω. However, above 3 wt%, δ varied significantly as a function of ω. Above 3 wt%, the decrease in δ value shows that the response from the SBS polymer is mainly reflected at lower frequencies. Lower ω implies deformation happening over a longer time scale which resonates with the sluggish dynamics of the long SBS polymer in the binder. At higher frequencies, the binder molecules and smaller segments of SBS polymer (Rouse, Kuhn, etc.) dominate the rheological response [64].

Fig. 15
figure 15

a Complex modulus (|G*|), b phase angle (δ), and c |G*|/sinδ vs. ω at 60 °C for the PMBs in H-62 binder

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Several researchers have analyzed the viscoelastic behavior of PMBs through |G*| and δ values, temperature sweep measurements, isochronal plots, Palierne model, etc. [65,66,67,68,69]. Airey et al. have examined the rheological properties of SBS-MBs through master curves [70]. Xia et al. have investigated the evolution in morphology and alteration in the viscoelastic properties of PMBs as a function of SBS content [64]. The study is based on quantifying the area shrinking kinetics through morphological observation, effects on rheological parameters, and Han plot due to the addition of SBS polymer. Along similar lines, Rossi et al. have measured the influence of SBS polymer on binder phase transition via temperature sweep analysis [71]. However, very few studies have directly signified the role of angular frequency in quantifying the properties of SBS modified binders, and its relevance in the correlation with rut depth.

The important role of ω in predicting the rutting performance of PMBs is demonstrated in Table 4, where the correlation between rut depth at 20,000 cycles and rheological properties of the PMBs at different frequencies are given. The rut depth of the asphalt mixes prepared using the six PMB samples was measured at 60 °C. It can be observed that the R2 value between ‘|G*|/sin’ and rut depth approaches 1 (0.969) at lower frequencies. Another vital observation that can be made is that other rheological parameters also exhibited a good correlation with rut depth at lower frequencies. Similar results were obtained in the case of PMBs prepared using L-64 binder. Several studies have reported that the MSCR measurements provide a better correlation with the rut depth in asphalt mixes [12, 14, 72,73,74]. Sajjad et al. have also used the MSCR test method to compare the performance properties of SBS and green composite modified binders [72]. Hence, MSCR measurements were carried out on the six PMBs samples prepared in H-62 binder, and regression analysis was performed. The correlation (R2 value) of elastic recovery (ER) and non-recoverable creep compliance (Jnr) with rut depth were 0.954 and 0.971, respectively. It can be seen in Table 4 that R2 values between the rheological properties at 0.1 rad/s and rut depth were close to the MSCR value. Therefore, it can be concluded from Fig. 15a–c and Table 4 that for better grading and performance evaluation of PMBs, analysis at lower frequencies is highly beneficial.

Table 4 Correlating factor (R2) between the rut depth and rheological properties of PMBs in H-62 and L-64 binders
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4 Conclusions

In this study, the rheological parameters in the PG rutting and fatigue cracking criteria were evaluated. Based on the obtained results, the following conclusions can be drawn.

  • The phase angle (δ) values of the unmodified asphalt binders were > 80° at true PG upper limiting temperature (Tu), due to which the PG rutting criterion ‘|G*|/sinδ’ and viscosity of the binder becomes equivalent. Furthermore, the viscosity of the binders at Tu was independent of the applied strain amplitude (1–50%) and frequency (1–20 rad/s) in oscillatory deformation, and strain rate (1–10/s) in rotational shear. Thus, both ‘|G*|/sinδ’ and viscosity of the binder had identical correlation with the rut depth in asphalt mixes.

    At upper service temperatures, all the different rutting parameters, such as |G*|/sinδ, Shenoy’s parameter, low shear viscosity, zero shear viscosity, etc., are equivalent to viscosity. Thus, all the rutting parameters will have a similar correlation with rutting in asphalt mixes. At upper service temperatures, the viscosity of the binder is the dominant parameter, and therefore we recommend using viscosity to predict rutting in asphalt mixes.

  • The PG fatigue cracking criterion is based on the energy dissipating capacity (loss modulus G″ = |G*|sinδ ≤ 5000 kPa) of rolling thin film oven (RTFO) and pressure aging vessel (PAV) aged binders. But, at PG intermediate temperature (TI), the phase angle (δ) values of ‘RTFO + PAV’ aged binders was close to 45° due to which the loss modulus G″ and elastic modulus G′ values were similar. Since G″ ≈ G′ ≈ 1.4 G*, the three parameters will have a similar correlation with the fatigue performance of asphalt mixes.

    Additionally, the stiffness and brittleness of asphalt binders increase significantly after ‘RTFO + PAV’ aging. On the contrary, the δ value decreases, falsely indicating an increase in elasticity in the asphalt binders. The conflicting observations arise due to the measurements carried out in the LVE region. In the LVE region, even highly brittle solid materials exhibit low δ values. Thus, similar to G″, fatigue analysis based on δ may result in incorrect analysis.

  • The rheological properties of PMBs at upper service temperatures strongly depend on the frequency (ω), and the rheological signature of the polymer molecules manifests predominantly at lower ω. At ω ≤ 0.1 rad/s, the correlation between rheological parameters of PMBs and rut depth is close to that obtained from the MSCR test. Hence, for PMBs analysis at ω ≤ 0.1 rad/s is recommended.