Linear viscoelastic behavior of asphalt binders and mixtures containing very high percentages of reclaimed asphalt pavement

Abstract

The primary aim of this study is to correlate the impact of aggregates, if any, on the viscoelastic behavior of rejuvenated asphalt mixtures containing very high amounts of reclaimed asphalt pavement (RAP) (> 50%). First, gradation of 100% RAP was rectified, using a modified Bailey method by adding virgin aggregates to achieve two coarse dense-graded and one fine dense-graded blends. Complex modulus test was then performed from −35 to +35 °C and 0.01–10 Hz. In addition to performance grade (PG) testing, extracted and recovered binders from different asphalt mixtures underwent shear complex modulus test within −8 °C to high temperature PG and frequencies from 0.001 to 30 Hz. Cole−Cole, Black space, complex modulus and phase angle master curves were constructed and Shift-Homothety-Shift in time-Shift (SHStS) transformation was used to compare the linear viscoelastic behavior of asphalt binders and mixtures. The influence of aggregates on the viscoelastic behavior of asphalt mixtures depends on temperature and/or frequency. The role of asphalt binders in the behavior of asphalt mixtures is more pronounced at high temperatures and the effect of the aggregate structure increases as the temperature falls. The maximum difference (60% to 70%) in the viscoelastic behavior of the binder and mixture based on SHStS transformed Cole−Cole curves is within the phase angle of 15°–20°.

Graphical abstract

Keywords

RAP / complex modulus / SHStS transformation / rejuvenation / behavior of asphalt binder and mixture

1 Introduction

The introduction of reclaimed asphalt pavement (RAP) into new asphalt pavements has economic and environmental implications. In 1973, 1990, and 2009, the oil crises forced western countries to use RAP as a rich source of bitumen. It is now used more owing to environmental concerns [1]. Although RAP had been used before, it was in 2001 that Superpave included a mix design of asphalt mixtures containing up to 25% RAP [2]. This was the first fundamental step, because mix design is the first stage of research on asphalt mixtures.

Research on high RAP content (25%–50%) has accelerated in recent decades because there has been a move to deploy increasingly more RAP in industry; there are sufficient RAP resources, and RAP is a cheaper raw material than virgin asphalt binder and aggregate. In parallel to many studies on different asphalt mixtures with low and high RAP content [3–5], the idea of using a 100% RAP mixture has attracted interest [6,7]. Several studies have been conducted on this since 2013, but there have been very few studies on the transition from 50%–100% RAP (very high RAP content mixtures).

It is evident from studies on 100% RAP mixtures that researchers have been too focused on the stiffness [6,8–15], aging potential [12,16], and mobilization [17–21] of RAP binders. Similarly, binder rejuvenation is being investigated more than aggregates to enhance the performance of asphalt mixtures [6,8–16,21]. The main reason for so much focus on the binder can be attributed to the belief that it is the viscoelastic characteristics and behavior of the binder that imparts the viscoelastic characteristics and behavior to the asphalt mixture. It is claimed that for conventional asphalt mixtures containing zero to high RAP content, the aggregate skeleton plays no role in the linear viscoelastic (LVE) behavior of asphalt mixtures [22–24]. More precisely, the LVE behavior of the asphalt mixture is the same as that of the asphalt binder and aggregates simply scale up their properties. This study investigates mixtures containing very high amounts of RAP (> 50%), and aims to verify whether the role of aggregates in the viscoelastic behavior of asphalt mixtures is insignificant. Verification was performed by establishing a correlation between the LVE behavior of the asphalt binder and the mixture.

Using different aggregate gradations skeletons improves the certainty of the aggregate impact, if any, on the viscoelastic behavior of asphalt mixtures. Hence, four asphalt mixtures with different gradations were designed. The design of aggregate blends was based on Bailey’s concepts to have a firm aggregate skeleton. In addition, minimal amounts of virgin aggregates are added to obtain coarse dense-graded (CDG) and fine dense-graded (FDG) blends to obtain asphalt mixtures with very high RAP contents. Complex modulus tests were then performed on both the asphalt mixtures and their corresponding binders that were extracted and recovered from the mixtures. The Shift-Homothety-Shift in time-Shift (SHStS) transformation was used to understand if the behavior of the asphalt binder can represent the behavior of the asphalt mixture on a smaller scale and to verify if the role of gradation is negligible.

As this study deals with rejuvenated asphalt mixtures with different percentages of RAP, its scope cannot be limited to the primary objective explained above. Comparison of different asphalt mixtures and binders with regard to viscoelastic behavior, as well as effectiveness of the rejuvenation are the secondary objectives of this study that accompany the primary objective.

2 Materials and methodology

As shown in Fig.1, the methodology is devised to assess how the asphalt binder imparts thermomechanical properties to asphalt mixtures that have a very high RAP content. A complex modulus test was performed on both asphalt binders and mixtures to construct characterization curves such as Cole−Cole, Black space, complex modulus, and phase angle master curves. Finally, SHStS transformation was performed on the Cole−Cole curves of the binder and mixture to determine the similarities between the two sets of curves.

2.1 Aggregates, RAP, and bitumen

The virgin aggregates used in this study were limestone that were fractionated into two stockpiles: 0–5 mm (fine) and 5–10 mm (coarse). To achieve finer gradation to rectify the RAP gradation, a finer size range (0–2.5 mm) was derived from the fine virgin aggregate. RAP contained 0–10 mm of aggregate size and was not fractionated to produce mixes because the aggregate size distributions of the blends were manipulated by proportioning the virgin aggregate stockpile. However, the RAP stockpile was fractionated to more precisely evaluate its properties. This practice is more efficient, labor-saving, and accurate because the fractionation of RAP is based on the black curve, which does not represent the real gradation, especially with respect to the fine portion. Tab.1 lists the specific gravities of the RAP and virgin aggregates. Based on laboratoire chaussée (LC) method [25], the bulk specific gravity (G_sb) and water absorption of aggregate blends were determined in the size ranges 0–2.5, 2.5–5, and > 5 mm separately, and differently. In all size ranges, the virgin aggregates had higher bulk specific gravities and less absorption. This was mainly because the RAP aggregates were a mix of different aggregate types, including granite, limestone, and siliceous aggregates, with some having more pores and cavities than the limestone.

The virgin bitumen was performance grade (PG) 58S-28, which is typical in cold regions. The specifications are presented in Tab.2.

2.2 Rejuvenator

For 100% RAP mixtures, there is consensus on the necessity of rejuvenation [6,8–16]. Zaumanis et al. [8] indicated that bio-based rejuvenators are better than petroleum-based rejuvenators. In addition, the use of bio-based materials reduces the carbon footprint. Therefore, the application of bio-based rejuvenators has become popular.

Soybean oil derivatives are the most commonly used bio-based rejuvenators in the US, mainly because of their properties and abundance, particularly in North and Latin America [11]. Asphalt binders and mixtures modified by commercial soybean derivatives have been evaluated rheologically and performance-wise in several studies [14–16]. In addition, the diffusibility of epoxidized soybean oil (ESO) into aged binder [21], its chemical and rheological resistance to aging [16], and its effectiveness were studied and verified. It has been proved that 1%–2% of soybean oil derivatives by total weight of asphalt binder (old plus new asphalt binder) in a 100% RAP mixture is capable of softening the old binder to be similar to the virgin binder [10,11,14,15]. Thus, in this study, 1% of ESO in a 100% RAP mix was converted and expressed as a percentage of the old RAP binder for application in asphalt mixes containing less than 100% RAP. All mixtures with different RAP concentrations then had the same old binder-to-rejuvenator ratio.

As a side objective, this study evaluates the efficiency of ESO inside mixtures because it is very important for asphalt mixtures with very high RAP contents. However, unlike other studies conducted that blend the rejuvenator, virgin, and RAP binders using high shear [6,8–16], rheological tests were performed on extracted and recovered binders from asphalt mixtures to obtain a binder with properties closer to those inside the mixture.

2.3 Gradation

To obtain a CDG blend of RAP, virgin coarse aggregates (5–10 mm) were added to create more space for accommodating the fine aggregates of RAP. Then, the coarse aggregate (CA), coarse part of fine aggregate (FAc), and fine part of fine aggregate (FAf) ratios were checked to satisfy the limits proposed by the Bailey method [26].

One of the challenges in using RAP is its gradation. The type of RAP gradation, whether black curve (RAP gradation), white curve (RAP aggregate gradation), or their average, which is used for calculation of the CA, FAc, and FAf ratios, impacts the gradation of the blend. In this study, the white curve and the average of the white and black curves were the two gradations deployed to build the CDG. Consequently, as shown in Tab.3, two different CDG blends were obtained by combining RAP and virgin stockpiles. However, the FDG blend was designed solely based on the average of the white and black curves because, with the available virgin stockpiles, it was impossible to have an FDG blend according to the white curve that meets the CA, FAc, and FAf ratio limits proposed by the Bailey method for FDG [26].

Fig.2 shows the particle size distribution of all blend types. It can be seen that FDG has coarser gradation than CDG. This is because different stockpiles were used to correct 100% gradation, whereas if the same stockpiles had been used, CDG would have the coarser gradations.

2.4 Mix design and sample preparation

It has been proven that heating RAP using a forced-draft oven, and microwaves, results in similar mixture characteristic [27]. Therefore, to save time, microwaves were used to heat the RAP and reach the desired temperatures of 100 and 110 °C for 100% RAP and the other mixture types, respectively. Using a rejuvenator made it possible to decrease the mixing temperature to the aforementioned values with no negative impact on the coating and negligible clustering formation (Fig.3).

Tab.4 shows the optimum binder content (OBC) of the mixtures with different very high RAP contents, along with other important mix design properties. As recommended by Imaninasab et al. [28], except for 100% RAP, the target air voids for asphalt mixtures containing very high amounts of RAP must be 3% to have sufficient coating. For 100% RAP, 4% target air voids were recommended [28]. It can be seen that a very high RAP content significantly reduces the amount of virgin binder, which not only benefits the environment, but also decreases the cost of asphalt mixture production.

Loose specimens with 57%, 65%, 73%, and 100% RAP content were prepared with OBCs and compacted at 7% ± 0.5% air void content with a height of 150 mm to obtain 75 mm cores with 5% ± 0.5% air voids, as recommended by Clyne et al. [29].

2.5 Complex modulus of mixtures

Tension/compression complex modulus tests were performed at temperatures of −35, −25, −15, −5, 5, 15, 25, and 35 °C and frequencies of 0.01, 0.03, 0.1, 0.3, 1, 3, and 10 Hz with a strain amplitude of 50 µm/m [30]. The complex modulus and phase angle were then both measured for all combinations of temperature and frequency. The useful curves that such testing provides are Cole−Cole, Black space, phase angle, and complex modulus master curves [31]. Cole−Cole plots the real vs. imaginary complex modulus of asphalt mixtures that can be well modeled by two springs, two parabolic elements, and one dashpot (2S2P1D). As shown in Fig.4, this model contains two parallel springs for elastic behavior, one dashpot for viscous behavior, and two parabolic elements (k and h) for creep behavior that subsequently address the impact of temperature on behavior. The 2S2P1D is a continuous model and cannot be used for finite element analysis; however, it is the best model for calibrating discrete models, such as Maxwell or Kelvin-Voigt, for further finite element analysis [30]. Equation (1) yields the formulation of 2S2P1D, which is plotted in Fig.5 (Cole−Cole curve).

(1)E^{\text{*}}\left(\omega \right)= E_{00}+ \frac{E_0-E_{00}}{1+\delta {\left(\mathrm{j}\omega \tau \right)}^{-k}+{\left(\mathrm{j}\omega \tau \right)}^{-h}+{\left(\mathrm{j}\omega \beta \tau \right)}^{-1}},

where j² = −1; E^{\text{*}} is the complex modulus modeled by 2S2P1D; ω is the angular speed (ω = 2πf and f is the frequency); τ is the characteristic time depending on temperature; E₀ is the glassy modulus when ω→ + ∞; E₀₀ is the static modulus when ω→0; k and h are constants and, as depicted in Fig.4, multiplied by π/2, they yield the initial and terminal slopes of the Cole−Cole curve, respectively (0 < k < h < 1); δ is a dimensionless constant; and β is a constant relating to the Newtonian viscosity of the dashpot (η = (E₀− E₀₀)βτ).

While the Cole−Cole curve is useful for low temperatures (high frequencies) representation, the Black curve (phase angle against complex modulus curve) is suitable for high temperature (low frequencies) [31].

The complex modulus master curve is probably the most important curve used to interpret complex modulus test results. This provides the complex modulus (E^{\text{*}}) of the asphalt mixtures over a wide range of frequencies at any temperature. This curve can be obtained if two conditions are satisfied: (a) the material is thermo-rheologically simple, and (b) it shows LVE behavior under loading [31]. The unique Cole−Cole and black curve for a material, regardless of frequency and temperature, indicate that the two conditions are met. As a result, there is equivalency between pairs of temperatures and frequencies, that is, E^{\text{*}} of a specific temperature (T) at different frequencies is equal to E^{\text{*}}s of a different arbitrary temperature (reference temperature (T_ref)) at the frequencies (reduced frequencies (freq.)) obtained by multiplying the frequencies of T with a constant (shift factor (a_T)). This concept, namely the Time−Temperature Superposition Principle (TTSP), can be expressed as Eq. (2):

(2)E^{\text{*}}\left(f,T\right)=E^{\text{*}}\left(f\cdot a_{\mathrm{T}}\left(T\right),T_{\mathrm{r}\mathrm{e}\mathrm{f}}\right).

The shift factor itself depends on the temperature (T), and each selected reference temperature yields a unique shift factor vs. T curve. This unique curve can be found using the William−Landel−Ferry (WLF) equation (Eq. (3)) [33]:

(3)\mathrm{l}\mathrm{o}\mathrm{g}\left(a_{\mathrm{T}}\right)=\frac{{-C}_1(T-T_{\mathrm{r}\mathrm{e}\mathrm{f}})}{C_2+T-T_{\mathrm{r}\mathrm{e}\mathrm{f}}},

where C₁ and C₂ are constants that vary with respect to T_ref. In this study, T_ref was set as 15 °C_.

With the same shift factors as those obtained for E^{\text{*}}, the master curve of the phase angle can also be drawn to see how the response is delayed with frequency variation. The phase angle reveals the viscous properties of a material at different frequencies.

The goodness of fit of the 2S2P1D model in fitting the data points obtained from the complex modulus testing, was verified using statistical analysis. First, S_e (standard error of estimation) and S_y (standard error of deviation) are calculated using Eqs. (4) and (5), and then R² (the coefficient of correlation) is determined using Eq. (6) [34].

(4)S_{\mathrm{e}}= \sqrt{\frac{\sum {(X-x)}^2}{n-k}},

(5)S_{\mathrm{y}}= \sqrt{\frac{\sum {(X-\overline{X})}^2}{n-1}},

(6)R^2= 1-\frac{n-k}{n-1}\times {\left(\frac{S_{\mathrm{e}}}{S_{\mathrm{y}}}\right)}^2,

where X is the data point (measured complex modulus), x is the predicted value (computed complex modulus using 2S2P1D), \overline{X} is the mean value of the measured complex modulus, n is the sample size, and k is the number of variables.

2.6 Performance grade testing and shear complex modulus master curve

In addition to the compacted specimens, loose asphalt mixtures containing 57%, 65%, 73%, and 100% RAP were prepared at their OBCs using a procedure similar to that described in the previous section. After mixing with the virgin binder, they were maintained at their compacting temperature for at least 2 h and no more than 4 h to induce short-term aging. Subsequently, the asphalt binders of these mixtures were extracted and recovered according to ASTM D8159-19 [35] and ASTM D5404/D5404M [36], respectively, for rheological testing.

First, PG testing was performed to determine the high- and low-temperature (HT and LT) PG [37]. Because the extracted binders had already been short-term aged, they were taken as RTFO-aged binders. Hence, RTFO aging was not performed, and only the criteria of G^{\text{*}}/sinδ < 2.2 kPa was used to determine the HT PG. Additionally, multiple stress creep recovery (MSCR) based on AASHTO T 350 [38] was performed to determine the traffic designation of asphalt binders, such as standard (S), heavy (H), very heavy (V), and extremely heavy (E).

A complex shear modulus test was performed on intact asphalt binders (non-pressure vessel aging (PAV)-aged) within a temperature range of −8 °C to the HT PG temperature in increments of 6 °C at 0.1–1 Hz frequency in increments of 0.1 Hz, and at 1–10 Hz in increments of 1 Hz. From −8 to 34 °C, an 8 mm diameter and 2 mm gap geometry was used, whereas a 25 mm diameter and 1 mm gap was used for 40 °C upward.

Prior to running the shear complex tests, a linearity test was performed for each geometry to ensure that the specimens remained within the LVE domain. Shear strain amplitude sweeps at −2 °C and 10 Hz (except 100% that was 4 °C and 1 Hz) were conducted for the 8 mm spindle while 40 °C and 10 Hz (except 100% that was 46 °C and 10 Hz) was conducted for the 25 mm spindle. To determine the linearity limit, the applied shear strain was increased, and the complex modulus was measured. With an increase in shear strain, the complex modulus decreases. The shear strain increase continues to a 5% reduction in the shear complex modulus. The shear strain corresponding to 95% of the initial shear complex modulus was set as the LVE strain limit and used to determine the shear complex modulus [39]. It is well known that, as the temperature increases and the frequency decreases, the shear complex modulus decreases. A decrease in the complex modulus results in an increase in the LVE strain limit [39,40]. Therefore, for each geometry, the lowest possible temperature and highest possible frequency were used to determine the LVE strain limit for use throughout the temperature and frequency sweep.

To construct the shear modulus master curves, the same equation (WLF) was used to determine the shift factor for the asphalt binder, and the mixture behaved similarly. The reference temperature (T_ref) was set to 16 °C to be closest to the T_ref of the mixture master curve (15 °C). Using Eq. (7), the complex modulus of the asphalt binders can then be derived, which can subsequently be used for fitting in the 2S2P1D model.

(7)E^{\text{*}}=2G^{\text{*}}\left(1+{\nu }^{\text{*}}\right),

where G^{\text{*}} is the shear complex modulus and {\nu }^{\text{*}} is the complex Poisson’s ratio.

2.7 Shift-Homothety-Shift in time-Shift transformation

The SHStS transformation involves one shift along the horizontal axis, followed by a homothetic transformation, and then one shift of the characteristic time and another shift along the horizontal axis. In a study by Mangiafico et al. [24], the SHStS transformation was successfully used to transform the Cole−Cole of the asphalt binder into the Cole−Cole of the asphalt mixture by assuming {\nu }^{\text{*}} = 0.5, which results in the E^{\text{*}} binder being equal to 3G^{\text{*}}. Although successful, setting {\nu }^{\text{*}} = 0.5 is not a precise assumption because {\nu }^{\text{*}} is a complex number (Eq. (8)). The master curve of {\nu }^{\text{*}} has the same shift factor as that of E^{\text{*}} for asphalt mixtures [30] and it is believed that the same is true for asphalt binders. Combining Eqs. (8) and (7) yields Eq. (9):

(8){\upsilon }^{\text{*}} =\left|{\upsilon }^{\text{*}}\right|{\mathrm{e}}^{\mathrm{j}{\phi }_{\text{υ}}},

(9)E^{\text{*}}=2(\left|G^{\text{*}}\right|{\mathrm{e}}^{\mathrm{j}{\phi }_{\mathrm{G}}}+\left|G^{\text{*}}\right|\left|{\upsilon }^{\text{*}}\right|{\mathrm{e}}^{\mathrm{j}\left({\phi }_{\mathrm{G}}+{\phi }_{\text{υ}}\right)}),

where {\phi }_{\mathrm{G}} and {\phi }_{\text{υ}} are the complex shear modulus and Poisson’s ratio of the phase angle, respectively.

The transformation of E_{\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{r}}^{\text{*}}=3G^{\text{*}} for the E^{\text{*}} of mixtures reveals that the lag of the lateral response ({\phi }_{\nu }) must be negligible for the asphalt materials they studied. So, Eq. (8) could have been rewritten as Eq. (10) in the research they carried out.

(10)E^{\text{*}}=2\left(\left|G^{\text{*}}\right|{\mathrm{e}}^{\mathrm{j}{\phi }_{\mathrm{G}}}+\left|G^{\text{*}}\right|\left|{\upsilon }^{\text{*}}\right|{\mathrm{e}}^{\mathrm{j}{\phi }_{\mathrm{G}}}\right)=2 \left|G^{\text{*}}\right|{\mathrm{e}}^{\mathrm{j}{\phi }_{\mathrm{G}}}\left(1+\left|{\upsilon }^{\text{*}}\right|\right).

As a result, it does not matter whether E^{\text{*}} or G^{\text{*}} of asphalt binder are used for SHStS transformation; the Cole−Cole of both complex modulus can establish a relationship with the Cole−Cole of the asphalt mixture, so G^{\text{*}} was used in this study to assess whether it works.

3 Results and analysis

3.1 Performance grade

As shown in Tab.5, the HT and LT PG of asphalt binders extracted from 57%, 65%, and 73% RAP mixtures is one level (6 °C) lower than that of the 100% RAP mixture; that is, 57%, 65%, and 73% of RAP can shift the PG of 100% RAP one level down. The rejuvenator and/or a small amount of virgin binder (12.6%) in the 100% RAP mixture resulted in a one-level shift down of the HT PG of the RAP binder (88 to 82 °C). The PG span of all the rejuvenated binders remains as high as 98 °C, which is reasonably high and comparable to that of the modified binders. This proves the high value of the RAP binder rather than the waste. In addition, unlike the others, 57% RAP cannot satisfy the criteria of a standard binder at its HT PG (76 °C), when it comes to PG + designation. However, at 70 °C (one level lower than the original HT PG), it meets the requirement for a high-traffic binder, that is, H.

As shown in Fig.6, the effective HTs (HT_e) and LTs (LT_e) linearly decrease as the virgin binder content increases. This is consistent with the general concept of the blending chart in the NCHRP-452 report developed for determining the RAP percentage corresponding to a desired PG [2]. However, it was found that the linear correlation can be well established by using the virgin to total binder ratio rather than the percentage of RAP.

ΔT_c, on the other hand, is the difference between the stiffness- and m-value-based effective LT (LT_e) and is an indicator of the aging potential [11]. Most aged asphalt binders have a stiffness-based LT_e smaller than the m-value-based LT_e [11]. Therefore, LT is generally controlled by m-value and ΔT_c is generally negative. It can be inferred that a higher value of ΔT_c indicates a higher ability to relax stress and less aging potential. Tab.5 shows that 65% RAP results in the lowest aging potential, whereas 57%, 73%, and 100% RAP have almost the same sensitivity to aging. Compared to virgin binders, these ΔT_c values are quite promising and show the high potential of rejuvenated binders against aging.

3.2 Linearity and complex modulus of asphalt binders

Before conducting the shear complex modulus tests, linearity tests were performed on 25 mm diameter and 1 mm gap geometry (HT geometry), and with 8 mm diameter and 2 mm gap geometry (low- and intermediate-temperature geometry) to determine the LVE limits of the asphalt binders. As shown in Fig.7, for each geometry, the LVE limits of the different binder types were approximately the same. For low- and intermediate-temperature geometries, a shear strain of 1% guarantees the LVE domain, whereas it is approximately 3% for HT geometry. In addition, as shown in Fig.8, for both geometries, the phase angles of the different binders are fairly close (less than 6° difference).

Fig.9 and Fig.10 show the Cole−Cole and Black space curves, respectively, based on the 2S2P1D model, whose calibration is given in Tab.6. Tab.7 evaluates the closeness of fit of the model for the data obtained from the shear complex modulus testing. Because R² is greater than 0.9 and S_e/S_y is greater than 0.35, the 2S2P1D model is confirmed as an excellent fit for the data [34]. They indicate that 100% RAP clearly possesses stiffer characteristics at low temperatures (dashed circle in Fig.9) and high temperatures (dashed circle in Fig.10) compared to the others. The asphalt binders extracted and recovered from 57%, 65%, and 73% RAP have approximately the same stiffness characteristics as can be seen through Cole−Cole, Black space, shear complex modulus (Fig.11), and phase angle master curves (Fig.12).

3.3 Complex modulus of mixtures

Tab.8 shows the calibrated parameters of 2S2P1D for the asphalt mixtures under investigation. Tab.9 indicates that the modeling has been done perfectly and the model is an excellent fit for the data. All asphalt mixtures have approximately the same E₀, k, h, and δ but different E₀₀. The difference in E₀₀ mainly makes the Cole−Cole plot illustrated in Fig.13 different from mixture to mixture. Considering the right side of the post-peak, which represents low and intermediate temperatures, 57%, 65%, and 73% RAP are stiffer than 100% RAP mixture even though 100% RAP contains stiffer asphalt binder. This signifies the importance of the aggregate skeleton in imparting characteristics to asphalt mixtures. While 57% and 65% RAP have almost the same Cole−Cole curve, 73% RAP shows a slightly stiffer curve. This can be attributed to higher RAP binder compared to 57% and 65% RAP rather than a significant difference in aggregate structure. Also, black space curves confirm the same pattern for high temperatures, that is 57%, 65%, and 73% RAP are stiffer than 100% RAP (Fig.14). Therefore, as shown in Fig.15 and can be inferred from the Cole−Cole and Black curves, the complex modulus master curves of 57%, 65%, and 73% indicate stiffer asphalt mixtures compared to 100% RAP. Similarly, 73% RAP’s complex modulus master curve stands above the 57% and 65% RAP curves. Phase angle master curves, as depicted in Fig.16, are consistent with former curves corresponding to Cole−Cole, Black space, and complex modulus master curves. These results contradict those obtained from binder testing. There, asphalt binder extracted and recovered from 100% RAP stands stiffer than the others, both at high and low temperatures. Although extracted and recovered binders may not represent the exact binders inside the asphalt mixtures, the stiffness comparison is valid since all binders underwent the same extraction and recovery procedure. Hence, a conclusion can be drawn that, from whole RAP to partial RAP (57%, 65%, and 73%), the contributive impact of aggregate structure on asphalt mixture’s stiffness takes over the reverse impact of binder stiffness on asphalt mixture’s stiffness and causes stiffer asphalt mixtures for partial than whole RAP mixtures.

3.4 Shift-Homothety-Shift in time-Shift transformation

To understand if the aggregate gradation has an impact on the behavior of asphalt mixtures, the SHStS transformation was conducted. The SHStS transformation provides curves with their basic shapes. As a result, it is a useful tool for assessing the similarity of material behavior regardless of the scale of their properties. The SHStS transformed Cole−Cole curves of the asphalt binder and asphalt mixture can be compared and, if approximately the same, the asphalt binder imparts viscoelastic properties to the asphalt mixture.

Fig.17 indicates that they are not the same within a wide domain, ending with the temperature and frequency corresponding to the lowest and highest, respectively. At the same real E^{\text{*}}, the normalized Cole−Cole diagrams of binders have a greater loss modulus (imaginary E^{\text{*}}) than the normalized Cole−Cole diagrams of the asphalt mixtures. Hence, within this temperature and/or frequency domain, aggregates lessen the viscous properties of binders that can be imparted to asphalt mixtures. On the other hand, asphalt binders and mixtures behave similarly at higher temperatures and lower frequencies, as the SHStS-transformed Cole−Cole diagrams are almost the same within a domain starting from the origin and ending somewhere before the peak.

Fig.18 shows the complex modulus vs. the phase angle of the asphalt mixtures. There are two curves for each mixture type: one is based on real results and the other is the prediction or estimation based on asphalt binder results. The two curves converge at phase angles between 25° and 35°. These correspond to higher temperatures and lower frequencies, respectively. Within the domain corresponding to low temperatures and/or high frequencies, the prediction based on the asphalt binder overestimated the complex modulus.

Thus, at high temperatures, the asphalt binder becomes more representative of the complex modulus and phase angle of the asphalt mixtures, where the asphalt binder deforms more because of less cohesion. In other words, as the temperature increases, the asphalt binder becomes more predictive of the complex modulus of the asphalt mixture (|E^{\text{*}}|) and phase angle. Between the phase angle of 15°–20°, which corresponds to the intermediate temperature of 5 °C with a frequency range of 0.01–0.3 Hz to 15 °C with a frequency range of 1–10 Hz, the viscoelastic behavioral dependency of the asphalt binder and mixture based upon |E^{\text{*}}| is minimized because, as depicted in Fig.19, the percentage difference between the normalized |E^{\text{*}}| of the asphalt binder and mixture is at a maximum. Fig.20 shows that the maximum percentage difference can reach as high as 60%–70%. This means that in asphalt mixtures with very high RAP content, the impact of the aggregate on the reduction of the complex modulus of the asphalt binder is between 60% and 70%. In addition, for 57%, 73%, and 100% RAP mixtures, the aggregates decreased both the real and imaginary parts of the complex modulus of the asphalt binder by approximately 60%–70%. It was approximately 75%–80% for a 65% RAP mixture. However, from Fig.20, the difference between the percentage reduction of the real and imaginary parts of the complex modulus of the asphalt binder < 5%; that is, aggregates reduce both the real and imaginary parts of the complex modulus of the asphalt binder almost equally. Thus, it can be inferred that the impact of the aggregate on the phase angle of asphalt mixtures with a very high RAP content is negligible, and their effect is on the magnitude of E^{\text{*}}.

4 Discussion

In this study, ESO was applied in proportion to the RAP percentage of the mixtures so that all mixtures contained the same ESO to RAP binder ratio. However, the viscoelastic characteristics of asphalt binders extracted and recovered from different mixtures are not the same. On the other hand, the PG and PG + of the binder extracted and recovered from 57%, 65%, and 73% RAP were the same, even though the amount of virgin binder in them changed. Thus, there is a high probability that the ESO partially softened the old RAP binder. This can be due to one or more of the following: (a) evaporation or modification of the ESO during the extraction and recovery process, (b) inefficiency of the ESO or the method of application, and (c) insufficient amount. This is subject to further study beyond the scope of this research.

Furthermore, previous studies have shown that the aggregate skeleton does not impart viscoelastic properties to asphalt mixtures; rather, it simply scales up the viscoelastic properties of asphalt binder [22–24]. This study finds that for asphalt mixtures with very high RAP contents (> 50%), this claim is a matter of temperature and/or frequency. At high temperatures that correspond to rutting performance, the binder imparts viscoelastic properties, and the aggregate skeleton simply scales up the viscoelastic properties. This does not mean that the aggregate skeleton does not contribute to the rutting resistance of asphalt mixtures; it does contribute, but by scaling up, not by shaping the viscoelastic behavior. However, at intermediate and low temperatures, the role of the aggregate skeleton in shaping viscoelastic behavior signifies that the asphalt mixture acts more like a composite material. In contrast, its impact on the thermal and fatigue resistance as a low and intermediate phenomenon is negligible [41]. This negligible impact occurs because cracking is an act of tension, and the aggregate structure engages in compressive loading rather than tensile loading.

5 Conclusions

In this study, PG, linearity, and complex modulus tests were performed on asphalt binders. Linearity and complex modulus were also determined for asphalt mixtures containing very high RAP content (> 50%), whose gradation was modified through the Bailey method concepts. The main purpose was to correlate the LVE behavior of asphalt mixtures with that of their corresponding binders to determine whether aggregates affect the viscoelastic properties of asphalt mixtures. In addition, as a side objective, the rejuvenation efficiency was investigated through PG testing and characterization of the asphalt binders extracted and recovered from the asphalt mixtures. From the obtained results, the following conclusions can be drawn.

1) The asphalt binder cannot predict the behavior of the asphalt mixture at all temperatures because it is not the only element that depends on it. At high and partially intermediate temperatures, the viscoelastic characteristics of asphalt binders and mixtures are aligned, whereas at low and partially intermediate temperatures, asphalt mixtures tend to behave like a composite material with both their elements effectively contributing to the behavioral characteristics.

2) Viscoelastic behavior corresponds to the non-destructive domain of a material, whereas rutting or cracking performance is related to its destructive domain. The influence of the aggregate structure on imparting viscoelastic behavior to the asphalt mixture (non-destructive domain) has nothing to do with the influence of the aggregate structure on rutting or cracking resistance (destructive domain). Rather, the impact of aggregates on rutting or cracking resistance depends on the effective type of loading (compressive or tensile) that corresponds to the resistance.

3) The asphalt binder extracted and recovered from the 100% RAP mixture is stiffer than the others, but the viscoelastic characterization of the asphalt mixtures proves that it is less stiff than the others. This indicates that the effect of the aggregate structure on the viscoelastic characteristics of the asphalt mixtures is significant.

4) The effect of aggregates on the LVE properties of asphalt mixtures is limited by the magnitude of E^{\text{*}}, and its influence on the phase angle is negligible.

5) The rejuvenator and/or virgin binder used in this study, namely ESO, softened the old asphalt binder of RAP.

6) Coupling rejuvenation with a firm aggregate structure leads to marginalization of the RAP percentage effect. The 57%, 65%, and 73% RAP mixtures behaved similarly, even though they contained different amounts of RAP. This is an achievement for increasing the RAP content without compromising viscoelastic characteristics. However, further investigation is required in this respect.

The viscoelastic characteristics of asphalt mixtures were measured based on both tensile and compressive action, while the rutting and cracking resistance were investigated based on compressive and tensile action, respectively. Consequently, rutting and cracking resistance cannot be evaluated via viscoelastic characterization. In future work, it is recommended that compressive loading be applied at high temperatures and/or low frequencies, tensile loading at low temperatures and/or high frequencies, and tensile/compressive loading at intermediate temperatures and frequencies.

In addition, the findings of this study limit the materials used. A round-robin testing campaign with different RAP and virgin aggregate sources is suggested for further verification.

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