*Article* **Analysis of Rejuvenating Fiber Asphalt Mixtures' Performance and Economic Aspects in High-Temperature Moisture Susceptibility**

**Yao Zhang 1,\* , Ye Wang 1, Aihong Kang 1, Zhengguang Wu 1, Bo Li 1, Chen Zhang <sup>1</sup> and Zhe Wu <sup>2</sup>**


**Abstract:** Non-renewable resources such as natural stone and asphalt are in short supply. Recycling technology, with its lower cost, has been used as the primary approach to asphalt pavement maintenance engineering. The inclusion of reclaimed asphalt pavement materials in producing new asphalt pavements may increase the risk of cracking. The strength and toughness of the asphalt mixture can be reduced. In this study, Hamburg wheel tracking tests (HWTT) were performed on rejuvenated asphalt mixtures with distinct maintenance processes. Different kinds of fibers have been used as additives to reinforce the rejuvenated asphalt mixtures. The HWTT rutting curve was identified as having three stages, including the post-compaction stage, the creep stage, and the stripping stage. The three-stage rutting curve model was used to determine the intersection point between the creep stage and stripping stage. The other two feature points (i.e., the post-compaction point and the stripping inflection point) were redefined with a new calculation method. Then, the rutting effect and stripping effect were separated with these feature points. The performance and economic benefits of fiber-reinforced rejuvenated asphalt mixtures were investigated through grey correlation analysis under the three maintenance processes. The feature points of the HWTT curve and the cost of the corresponding maintenance process were selected as the impact factors. Finally, the optimal scheme was developed by analyzing the influence of each factor on both performance and economic benefits.

**Keywords:** hot rejuvenated asphalt mixtures; Hamburg wheel tracking test; moisture damage; economic benefit; fiber

#### **1. Introduction**

The use of recycled materials such as reclaimed asphalt pavement (RAP) in hot mix asphalt (HMA) has increased due to the rising cost of petroleum-based products and the negative environmental impact of carbon emissions associated with asphalt binder production [1]. However, the main challenge in incorporating the RAP into the asphalt mixture is the aged binder, which makes the mixture more susceptible to cracking [2–4]. As a result, the aged binder in the RAP tends to limit the high content of recycled material in the mixture. The need to reverse the negative impact of recycled materials in the HMA has prompted researchers to identify and implement innovative and feasible approaches.

Nahar et al. detected the fusion interface between the old and new asphalt by using atomic force microscopy (AFM) [5]. It was found that the old and new asphalt were not entirely miscible. The RAP was portrayed more like a "black stone", which was directly encapsulated by the new asphalt. Therefore, it is unable to truly address the performance degradation brought on by the old asphalt. There are weak links in the recycled asphalt mixture. Zhou et al. proposed that the performance metrics of the rutting and fatigue cracking resistance of the SBS-RAP blended binders were opposed to each other [6]. New experimental methods need to be introduced to equilibrate two performances to choose the optimal RAP content. Cheng

**Citation:** Zhang, Y.; Wang, Y.; Kang, A.; Wu, Z.; Li, B.; Zhang, C.; Wu, Z. Analysis of Rejuvenating Fiber Asphalt Mixtures' Performance and Economic Aspects in High-Temperature Moisture Susceptibility. *Materials* **2022**, *15*, 7728. https://doi.org/10.3390/ma15217728

Academic Editor: Gilda Ferrotti

Received: 1 October 2022 Accepted: 29 October 2022 Published: 2 November 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

P et al. found that the freeze–thaw splitting strength ratio of hot rejuvenated asphalt mixtures (HRAM) presented a decreasing trend with the increase in RAP content [7]. The decreasing rate was slow when the RAP content was within the range of 15% to 40%, while the decreasing rate became faster beyond this range. Since the aromatic phenol and saturated hydrocarbons in the aged binder transformed into resins and asphaltenes, various rejuvenators have been developed to restore the ratio of aromatic phenol and saturated hydrocarbons in rejuvenated asphalt binder [8,9]. The rejuvenators can reverse the aging process and restore part of the binder properties [10,11]. However, the properties of the cracking resistance and moisture susceptibility of the HRAM are still poor.

The Hamburg wheel tracking test (HWTT) was introduced for the evaluation of cracking resistance and moisture susceptibility with a more accurate reflection of the properties of asphalt mixtures [12]. The test involved the real-time monitoring of the correlation between the number of load cycles and the rutting depth (RD). Test curves were divided into three main phases: (a) the post-compaction phase, (b) the creep phase, and (c) the stripping phase. The stripping inflection point (SIP) was determined by counting the number of load cycles on the HWTT curve at which a sharp increase in rut depth occurs [13]. The SIP was represented at the intersection of the fitted lines that characterize the creep phase and the stripping phase. However, different fitting point selections could lead to an inaccurate finding of SIP. This may cause a misjudgment of the cracking resistance and moisture susceptibility of asphalt mixtures. In investigations on the rutting of hot recycled asphalt mixtures in the HWTT, researchers have found that the rutting depth increased more quickly in the third stage but developed more slowly in the first two stages when increasing the RAP. The findings give an indication that the properties of the cracking resistance and moisture susceptibility of hot recycled asphalt mixtures need to be enhanced, especially at increasing recycled binder ratios and RAP contents [14].

Fiber is a kind of natural or synthetic material, which acts as a reinforcement of strength and stability in the HMA. The fiber network structure enhances the binder properties of the asphalt mixtures [15]. It can withstand a portion of the force, preventing the cracking of the asphalt mixtures [16]. The moisture susceptibility can be also improved with the addition of fibers, and different types of fibers have varied functions in asphalt mixtures [17,18]. Chen Y Z et al. found that fibers could significantly improve the residual stability and freeze–thaw splitting strength of asphalt mixtures [19]. In comparison to polyester and wood algal fibers, basalt fibers are more effective at increasing the water stability of asphalt mixtures. Zhang K et al. found that asphalt mixture containing basalt fiber achieved better results in resisting salinity and moisture environments [20]. Although adding fibers and recycling agents as well as new aggregates can perform good results in asphalt mixtures, doing so will certainly drive up the price of the HRAM. On the other side, the excessive use of RAP can reduce the cost of the HRAM, but it degrades the serviceability of asphalt mixtures.

Hence, how to select a hot rejuvenated asphalt mixture that is both affordable and high-performing among available possibilities has been the main motivation for study. This is also the actual need of the pavement maintenance industry. Meanwhile, more innovative methods are needed to gain the feature points of the HWTT curve. Moreover, the properties of the cracking resistance and moisture susceptibility of hot recycled asphalt mixtures can be improved by controlling these feature points. Therefore, the objective of this paper is to investigate the mix design of hot rejuvenated asphalt mixtures with different fiber types under three pavement maintenance processes. The analysis approach for obtaining the feature points under three stages is modified after conducting the HWTT to obtain rutting curves. Subsequently, the costs of asphalt mixtures are obtained through an economic benefit analysis. Finally, the performance and economic benefits evaluation is conducted using grey correlation analysis to provide a rational solution and guidance for asphalt pavement maintenance projects. The flowchart of this study is shown below (Figure 1).

**Figure 1.** Flowchart of the research.

#### **2. Construction Technology and Raw Materials**

Three hot regeneration maintenance techniques were employed to create hot rejuvenated asphalt mixtures to investigate the high-temperature performance and moisture susceptibility of each asphalt mixture under various pavement maintenance operations in the HWTT.

#### *2.1. Construction Technology*

There are three typical maintenance technologies in current pavement construction, including the milling resurfacing (MR) process, the hot mix plant recycling (HMPR) process, and the hot in-place recycling (HIPR) process. The RAP dosage in the asphalt mixture differs greatly for the three maintenance processes. The RAP dosage in HIPR is generally more than 70%, while it is generally less than 50% in the HMPR process. There is no RAP used in the MR process; in other words, the material is a 100% new asphalt mixture. The basic principles of the three pavement maintenance processes are shown in Figures 2–4.

**Figure 2.** Milling resurfacing process.

**Figure 4.** Hot in-place recycling process.

In the MR process, the old asphalt pavement is milled, and then 100% of the new asphalt mixture from the asphalt mixing plant is spread and compacted on the milled pavement. During the HMPR process, the RAP is transported to the asphalt mixing plant as aggregates, where it is mixed with the new asphalt mixture after adding some of the recycling agents. In the HIPR process, 10% to 30% of the new materials are transported to the construction site. The old pavement is loosened by hot raking with the HIPR equipment. Then, the recycling agent and new asphalt mixtures are stirred with the old asphalt mixtures to create rejuvenated asphalt mixtures. Finally, the rejuvenated asphalt mixtures are paved in situ and compacted to form new pavement.

By comparison of the three maintenance technologies, it can be seen that the milling resurfacing process uses the highest quality raw materials to ensure excellent pavement performance. However, the cost of this process is rather high, and the old materials cannot be reclaimed, which can pollute the environment. The hot mix plant recycling process can solve part of the RAP recycling problem, and more than 70% of the raw materials are added in this process, which can also ensure the performance of asphalt pavements. The hot inplace recycling process allows for the complete use of old materials, significantly reducing material costs. It can also increase the efficiency of construction and reduce traffic. However, the incorporation of excessive RAP materials may affect the crack resistance of asphalt pavements. As seen from these pavement maintenance technologies, it is found that each of them has its characteristics. When choosing the appropriate technology for pavement maintenance, the construction process should take both the technical and financial benefits into account.

#### *2.2. Raw Materials* 2.2.1. RAP

The recycled asphalt pavement (RAP) used in the study was from the large maintenance engineering project of the Wuxi section in the Huning Expressway. The RAP gradation was stone matrix asphalt with a nominal aggregate size of 13.2 mm (SMA-13) located at the upper layer of the pavement structure. The original pavement was reclaimed using a hot milling technique to reduce the impact of the milling operation on the RAP gradation. Figures 5–7 depict the RAP reclaiming and the on-site milling construction.

**Figure 5.** Pavement heating car.

**Figure 6.** Manual milling hot pavement.

**Figure 7.** Reclaimed asphalt mixture.

#### 2.2.2. Recycling Agent

The recycling agent of RA-102 was produced by the Subbo7t Company. The physical and mechanical properties, including the viscosity, flash point, saturated fraction content, aromatic content, viscosity ratio, and quality changes before and after the rolling thin film oven test (RTFOT), were measured with corresponding test specifications. The test results are shown in Table 1.


**Table 1.** Technical index of Subtherm RA-102 Recycling agent.

#### 2.2.3. Asphalt

The performance graded 76-22 SBS-modified asphalt was used in this study. The asphalt properties were tested following the Chinese specification of the "Test Procedure for Asphalt and Asphalt Mixture for Highway Engineering" (JTG E20-2011). The test results are shown in Table 2.

#### **Table 2.** SBS-modified asphalt (PG76-22) technical index.


#### 2.2.4. Aggregate

The coarse aggregate was made of basalt with hard, clean, rough, and tough properties. The fine aggregate and mineral filler were made of limestone with properties of dry, clean, non-clumpy, and free from impurities. The technical indexes are shown in Tables 3 and 4.




**Table 4.** Technical indexes of mineral fillers.

#### 2.2.5. Fiber

Three types of fibers, including basalt fiber (BF), lignin fiber (LF), and polyester fiber (PF), were considered to create rejuvenated fiber asphalt mixtures. The basalt fiber and polyester fiber were short-cut fibers produced by Jiangsu Tianlong Basalt Continuous Fibers Co Ltd. The BF was golden brown in color, flat, and free from impurities, whereas the PF is pure white, flat, with no impurities. The lignin fiber used was the white flocculent fiber type ZZ8/1 from Riedenmei and Sons. Table 5 presents the results of the technical performance tests conducted on the three fibers, and Figure 8 displays the fiber morphology.

**Table 5.** Technical performances of fibers.


(**a**) Basalt fiber (**b**) Lignin fiber (**c**) Polyester fiber

**Figure 8.** Morphology of used fibers.

*2.3. Testing of Reclaimed Asphalt Mixture*

2.3.1. RAP Gradation and Asphalt Content

The old asphalt and old aggregates were recycled using the centrifugal separation process in accordance with T0722-1993 in the Chinese specification of JTG E20-2011. Trichloroethylene was used as the extraction solvent. The asphalt mixture mineral gradation test method (T0725-2000) was conducted to determine the asphalt content and aggregate gradation of the reclaimed asphalt mixture. The results show that the asphalt content in the RAP is 5.8%, and the gradation of the RAP is shown in Figure 9.

**Figure 9.** Gradation of RAP.

As can be seen in Figure 2, the RAP gradation is more closely aligned with the median gradation curve following the extraction and screening processes used in the layered hot milling technology. The old pavement used lignin fiber as a stabilizer, which was also extracted and shown in Figure 2. It was clear to see the quality loss and the aging phenomenon of the LF. Hence, the appropriate number of new fibers should be added to revitalize the rejuvenated SMA-13 mixture in the regeneration mix design.

#### 2.3.2. Properties of Old Asphalt

The properties of old asphalt including the penetration degree, softening point, ductility, and viscosity were tested. The test results are shown in Table 6.

**Table 6.** Old asphalt properties.


It can be seen from this table that the technical indexes of the softening point and viscosity at 135 ◦C for the old asphalt can meet the SBS-modified asphalt specification requirements, while the values of the penetration degree and ductility are lower than the requirements. The old asphalt belongs to grade II aging, and the degree of aging is light [21].

#### 2.3.3. Dosage of Recycling Agent

Since the aged asphalt might cause negative impacts on the rejuvenated asphalt mixture, the recycling agent was thought to be able to restore part of the aged asphalt properties. The performance design method was used to determine the proper dosage of the recycling agent in the total asphalt. The dosage of the recycling agent was selected at four levels, including 4%, 6%, 8%, and 10%, respectively. General performance tests of rejuvenated asphalt were conducted. The test results are shown in Table 7.


**Table 7.** Test results of rejuvenated asphalt.

Table 7 demonstrates that as the dosage of the recycling agent is increased, the penetration degree and ductility of rejuvenated asphalt increase, while the softening point declines. When the dosage of the recycling agent reaches 6%, the penetration degree and softening point of rejuvenated asphalt return to the performance level of the original SBS asphalt. Hence, the recycling agent dosage of 6% was chosen to formulate the hot rejuvenated asphalt mixtures.

#### *2.4. Mix Proportion Design of HRAM*

The HRAM was supplemented with basalt fibers (BF), lignin fibers (LF), polyester fibers (PF), and basalt–polyester compound fibers (BPCF) to evaluate the impact of various fibers on high-temperature performance and moisture susceptibility. The RAP content in the hot rejuvenated asphalt mixture for HIPR was set at 80%, while the RAP content for HMPR was set at 30%, taking into account the distinct maintenance procedures between the HIPR and the HMPR technologies.

#### Gradation Design

Marshall test was carried out for new gradation design based on the requirements of SMA-13 asphalt mixture in the Chinese specification of JTG F40-2004. The designed gradation curves under the two maintenance technologies (HIPR and HMPR) were shown in Figure 10. The gradation curve of the milling resurfacing (MR) technology was also shown in this figure as a control group, and the RAP content is 0% in this group. The optimal asphalt content of original and rejuvenated fiber asphalt mixtures is shown in Table 8, and the volumetric parameters of these mixtures are listed in Table 9.

**Figure 10.** Gradation curves with three maintenance technologies.


**Table 8.** Fiber dosage and asphalt content under three maintenance processes.

**Table 9.** Volumetric parameters of aggregate gradations.


#### **3. Experiments and Results**

#### *3.1. Hamburg Wheel Tracking Test*

According to AASHTO T 324, the Superpave gyratory compactor (SGC) was selected to create cylinder specimens with a diameter of 150 mm, a thickness of 60 mm, and a target void content of 7.0 ± 0.5%. After the SGC specimen had been cooled, a wet saw was used to cut along the equidistant line so that the specimen could be embedded in the mold. The water bath temperature of the HWTT apparatus was set at 60 ◦C, and the specimen was submerged in water for more than 20 mm. The reciprocating motion of the vehicle load on the specimen was simulated by a steel wheel with a diameter of 203.2 ± 2.0 mm and a width of 47 ± 0.5 mm under a load of 703 ± 4.5 N. The position of the steel wheel changed sinusoidally over time, traversing the specimen 52 times per minute, and reaching a top speed of 0.305 ± 0.02 m/s at the midpoint of the specimen. The linear variable differential displacement transducer (LVDT) was used to record the rut depth at 11 points along the direction of wheel crush in real time. The HWTT apparatus and specimen are shown in Figures 11 and 12. After the test was completed, the morphology of specimens such as HIPR-BF and HMPR-BF is shown in Figures 13 and 14. As can be seen from these figures, there exists a big difference in the rut depths at the end of the test with distinct maintenance technologies.

**Figure 11.** SGC specimen.

**Figure 12.** HWTT apparatus.

**Figure 13.** Specimen of HIPR-BF.

**Figure 14.** Specimen of HMPR-BF.

#### *3.2. Test Results*

The rut depth of eight rejuvenated asphalt mixtures and four new asphalt mixtures was recorded during the HWTT test, and the total rut depth of each mixture is shown in Figure 15. It can be seen from this figure that the HMPR asphalt mixture (i.e., 30% RAP) has the lowest rut depth when compared to the other two types of combinations, while the HIPR asphalt mixture (i.e., 80% RAP) has the maximum rut depth at the end of the test. The hydrothermal coupling performance of HWTT tends to improve and then decline with the increase in RAP materials. This is primarily caused by the modification to the aged asphalt content in the RAP materials, which increases the early-stage rutting resistance of rejuvenated asphalt mixtures. However, the ability of rejuvenated asphalt mixtures to resist moisture damage is insufficient to support cyclic heavy loads when the RAP content goes above a certain point. Based on three maintenance techniques, the BF combinations show better rutting resistance than the other three types of rejuvenated fiber asphalt mixtures.

**Figure 15.** Total rutting depth at the end of HWTT.

Since the HWTT can simultaneously characterize the rutting resistance and water stability of the asphalt mixture, many researchers have tried to find the feature points of the HWTT curve to study its performance at different periods. There are three main stages for the specimen under wheel load, including the post-compaction stage (PCS), the creep stage (CS), and the stripping stage (SS) [22], as shown in Figure 15. The specimen in the PCS is subjected to a high compression force given by the HWTT wheels, and the air voids are post-compacted. Hence, the rut depth in the PCS changes at a faster rate and for a shorter period as the number of wheels increases. At the CS, the rut depth increases steadily, and materials in the specimen tend to have shear flow and continue to produce rutting damage under the wheel load. At the SS, the asphalt mixture is subjected to the double effects of wheel load as well as high-temperature moisture damage; part of the asphalt loses its adhesive bonds, the asphalt mixture begins to peel off, and the rutting and stripping of the specimen are accelerated.

Currently, the total rut depth (TRD) and stripping inflection point (SIP) are widely recognized as HWTT performance indicators. The SIP is the inflection point from CS to SS, which is commonly recognized as the intersection of the two straight lines fitted by CS points and SS points, as seen in Figure 16. In a sense, the value of SIP is greatly affected by the slope of two fitting lines. However, the slope of two fitting lines in the CS and SS seems not to be unified. Hence, a new methodology or mathematical model is needed to be developed to give a higher accuracy of SIP determination.

The HWTT curve is made up of two parts, the first of which has a negative curvature and is followed by the other, which has a positive curvature, according to the findings of earlier studies on rutting prediction models conducted by our research group [14] and Fan Y et al. [22]. This curve can be completely represented by Equation (1).

$$RD = \rho \ast \left[ \ln \left( \frac{N\_{ult}}{N - N\_0} \right) \right]^{-\frac{1}{\mathcal{F}}} \tag{1}$$

where *N* = the number of load cycles; *RD* = the rut depth at a certain number of load cycles (mm); *N*<sup>0</sup> = the number of load cycles where rut depth occurs; *ρ*, *Nult*, and *β* = model coefficients.

**Figure 16.** Schematic diagram of a conventional HWTT curve.

Using the above formula to fit the HWTT data under the three maintenance technologies, the fitting curves are shown in Figures 17–20, and the relevant fitting parameters are shown in Table 10. From this figure, it can be seen that all four fiber asphalt mixtures have been wheeled 20,000 times. The HIPR asphalt mixtures show good resistance to high-temperature rutting in the post-compaction and creep stages, but they present poor water stability in the stripping stage.

**Figure 17.** HWTT curve of BF asphalt mixture.

**Figure 18.** HWTT curve of LF asphalt mixture.

**Figure 19.** HWTT Curve of PF Asphalt Mixture.

**Figure 20.** HWTT curve of BPCF asphalt mixture.



There are three feature points in the HWTT rutting curve, which can be used to separate the post-compaction stage, the creep stage, and the stripping stage. Finding the feature points in the curve fitting model can better characterize the HWTT results. The first derivative of Equation (1) is taken to obtain the slope of the HWTT curve, as given in Equation (2).

$$RD' = \frac{\rho}{N \ast \beta} \left( \ln \frac{N\_{\text{ult}}}{N} \right)^{-\frac{1}{\beta} - 1} \tag{2}$$

When the curvature of the HWTT curve turns from negative to positive, the second inflection point can be determined. The second derivative of Equation (1) is given as,

$$RD'' = -\frac{\rho}{\beta \ast N^2} \left[ \left( \ln \frac{N\_{\rm ult}}{N} \right)^{-\frac{1}{\beta} - 1} + \left( -\frac{1}{\beta} - 1 \right) \left( \ln \frac{N\_{\rm ult}}{N} \right)^{-\frac{1}{\beta} - 2} \right] \tag{3}$$

When the second derivative is set to zero, two solutions exist in Equation (3).

$$\mathbf{x}\_1 = \mathbf{N}\_{ult\prime} \quad \mathbf{x}\_2 = \frac{\mathbf{N}\_{ult}}{e^{1 + \frac{1}{\beta}}}$$

Since *Nult* is much larger than 20,000 loads, the unique solution of *x*<sup>2</sup> is taken. This solution is the intersection (i.e., *NSN*) from the positive curvature to the negative curvature, as shown in Figure 21. The value of *NSN* for each asphalt mixture is shown in Figure 22. In front of the point of *NSN*, the adhesion between the aggregate and asphalt in the specimen is good, and the specimen is in the post-compaction stage with a positive curvature. After the point of *NSN*, the rutting curve enters the negative curvature phase. The asphalt adhesion performance decreases when the asphalt mixture starts to produce rapid damage, and the rut depth of the specimen is accelerated by the moisture effect.

The intersection point (i.e., *NSN*) manifests itself earlier as the RAP content increases, indicating that the RAP is more moisture-sensitive than new asphalt mixtures. The RAP in the mixture has the potential to accelerate moisture damage, causing the mixture to reach the stripping stage earlier.

To distinguish the damage to the asphalt mixture under the effects of high temperature and water immersion, the HWTT curve before the point of *NSN* is fitted by Equation (4), and the schematic diagram is shown in Figure 18. The curve fitting parameters were obtained, as shown in Table 11.

$$RD = A \times NP^B \tag{4}$$

**Figure 21.** Intersection from positive curvature to negative curvature.

**Figure 22.** *NSN* of each fiber asphalt mixture.


The fitting curves can be extended to the end of the test to obtain the high-temperature rutting effects in the HWTT. The rut depth at 20,000 loads calculated by Equation (4) was obtained, as shown in Figure 23. The stripping effects can be obtained by using the total rut depth minus the high-temperature rutting effects, which are expressed in Figure 18. The results of the rut depth related to the stripping effects at 20,000 loads are shown in Figure 24. Figure 23 shows that the high-temperature rutting performance decreases with the increase in the RAP content in terms of single-doped fiber asphalt mixtures, and the LF asphalt mixture in the HIPR process performed the best. Figure 24 shows that the stripping resistance displays a contrary tendency compared with high-temperature rutting resistance. The asphalt mixture with basalt-polyester compound fibers in the MR process has the best performance.

**Figure 23.** High-temperature rutting effects of fiber asphalt mixtures.

**Figure 24.** Stripping effects of fiber asphalt mixtures.

From the above study, it is found that the inflection point of *NSN* can be obtained by setting the second derivative to zero in the three-stage curve fitting model. However, the other two critical points separate the three stages of the development of the HWTT curve, which cannot be determined directly from this model. Hence, the concept of a stationary point in the HWTT curve is introduced to mathematically redefine the post-compaction critical point and the stripping critical point. Take the BF asphalt mixture in the MR process as an example, connect the *NSN* with the curve starting point to find the first line segment: *<sup>y</sup>*<sup>1</sup> <sup>=</sup> 5.44 <sup>×</sup> <sup>10</sup>−4*x*, (<sup>0</sup> <sup>≤</sup> *<sup>x</sup>* <sup>≤</sup> 7238.3). Then, connect the *NSN* with the point at end of the test to obtain the second line segment: *<sup>y</sup>*<sup>2</sup> <sup>=</sup> 3.09 <sup>×</sup> <sup>10</sup>−4*x*+1.71, (7238.3 <sup>≤</sup> *<sup>x</sup>* <sup>≤</sup> <sup>20000</sup>). Form the vertical line between the HWTT curve and the two line segments to obtain the maximum value of Δ*h*<sup>1</sup> and Δ*h*2. The loading cycle at the maximum value of Δ*h*<sup>1</sup> is defined as the first stationary point (i.e., PCP) between the post-compaction stage and the creep stage. Likewise, the loading cycle at the maximum value of Δ*h*<sup>2</sup> is defined as the second stationary point (i.e., SIP) between the creep stage and the stripping stage. A schematic diagram of the stationary point is shown in Figure 25. The corresponding line segments and three feature points (i.e., first stationary point, inflection point, and second stationary point) are obtained in this method for all HWTT curves of asphalt mixtures, as shown in Table 12.

**Figure 25.** Schematic diagram of PCP and SIP redefinition.



As can be seen from Table 12, the HIPR asphalt mixtures pass in the creep stage at around 500 to 600 cycles of the wheel rolling with a low value of rut depth. The MR asphalt mixtures and HMPR asphalt mixtures entered the creep stage at around 800 to 950 cycles of wheel millings. The results show that the PCP of the HIPR asphalt mixture is earlier than that of the MR asphalt mixture and the HMPR asphalt mixture. However, the SIP seems to have a reverse trend in these mixtures. Compared with the new definition of SIP and the conventional calculation of SIP, it is found that this new method can provide more scientific theoretical support for the HWTT results for different asphalt mixtures. The PCP and SIP calculation methods can provide a theoretical basis for decision-making in maintenance projects.

#### **4. Comprehensive Analysis of Cost and Performance**

#### *4.1. Economic Cost Analysis*

The economic benefit is one of the key factors which should be also considered. The costs incurred under different maintenance methods are different, and the cost is an unavoidable problem in the practical application of the project. By constructing an economic model to analyze the costs under the three maintenance methods, it is possible to guide the concrete implementation of maintenance works.

The cost of the asphalt pavement maintenance process can be divided into four parts, namely, the milling cost, mixing cost, paving and rolling cost, and transportation cost [23].

To intuitively reflect the economic effects, the unit of price is standardized in this paper as Yuan (CNY) per ton and the expression of economic cost is shown in Equation (5).

$$O = \sum\_{i=1}^{n} M\_i + \sum\_{i=1}^{m} C\_i + \sum\_{i=1}^{l} P\_i + \sum\_{i=1}^{\mathcal{S}} T\_i \tag{5}$$

where *M* is the milling cost, *C* is the asphalt mixture and mixing cost, *P* is the paving and rolling cost, *T* is the transportation cost.

The asphalt mix and mixing costs are modeled as Equation (6).

$$\mathcal{C} = \left(\mathbb{C}\_{as}\mathbb{P}\_{as} + \mathbb{C}\_{ag}\mathbb{P}\_{ag} + \mathbb{C}\_{fi}\mathbb{P}\_{fi}\right) \times \left(1 - \mathbb{R}\_p\right) + \mathbb{R}\_p \times \mathbb{C}\_{ra} + \mathbb{C}\_{mi} \tag{6}$$

where *Cas* is the cost per ton of asphalt, *Cag* is the cost per ton of aggregates, *Cf i* is the cost per ton of fiber, *Cra* is the cost per ton of regeneration agent, *Cmi* is the mixing cost per ton if asphalt mixture; *Pas* is the asphalt ratio, *Pag* is the aggregate content, *Pf i* is the fiber dosage, and *Rp* is the RAP content. The calculation models for milling, paving and rolling, and transportation are simply cumulative and will not be repeated here.

In the MR maintenance process, the RAP content is zero percent, and there is a regeneration agent cost. The transportation cost only includes one-way transportation of the new asphalt mixture, so the cost function is given in Equations (7) and (8).

$$O\_{r\varepsilon} = M + \sum\_{i=1}^{3} \mathcal{C}\_i + P + T \tag{7}$$

$$\mathbf{C}\_{r\varepsilon} = \mathbf{C}\_{as}\mathbf{P}\_{as} + \mathbf{C}\_{ag}\mathbf{P}\_{ag} + \mathbf{C}\_{fi}\mathbf{P}\_{fi} + \mathbf{C}\_{mi} \tag{8}$$

In the HMPR maintenance process, the RAP content is 30%. The transportation cost includes the round-trip cost of transporting the old asphalt mixture to the mixing plant and the recycled asphalt mixture back to the construction site. The cost calculation model is Equations (9) and (10).

$$O\_{pl} = M + \sum\_{i=1}^{4} C\_i + P + \sum\_{i=1}^{2} T\_i \tag{9}$$

$$\mathbf{C}\_{pl} = \left(\mathbf{C}\_{as}\mathbf{P}\_{as} + \mathbf{C}\_{ag}\mathbf{P}\_{ag} + \mathbf{C}\_{f\dot{i}}\mathbf{P}\_{f\dot{i}}\right) \times 70\% + \Re{\%} \times \mathbf{C}\_{ra} + \mathbf{C}\_{mi} \tag{10}$$

In the HIPR maintenance process, the RAP content is 80%. Since the HIPR equipment is used, the fuel consumption and vehicle rental cost of the HIPR equipment are used to replace the separate costs of milling and paving, and the model is shown in Equations (11) and (12).

$$O\_{ip} = \sum\_{i=1}^{4} \mathbf{C}\_i + \sum\_{i=1}^{3} T\_i \tag{11}$$

$$\mathcal{C}\_{ip} = \left(\mathcal{C}\_{as}P\_{as} + \mathcal{C}\_{ag}P\_{ag} + \mathcal{C}\_{f\bar{i}}P\_{f\bar{i}}\right) \times 20\% + 80\% \times \mathcal{C}\_{ra} + \mathcal{C}\_{mi} \tag{12}$$

Through the on-site investigation of the actual project, it is assumed that the asphalt mixing plant is 30 km away from the construction site. The cost list under the three maintenance processes and the cost details of each maintenance stage are obtained, as shown in Tables 13 and 14. The final costs for the three maintenance processes are shown in Figure 26.


**Table 13.** Price list of each maintenance process.

**Table 14.** Cost details of each maintenance process.


**Figure 26.** Maintenance cost of each maintenance process.

As can be seen from Figure 26, with the incorporation of RAP, the costs of the three maintenance processes are listed in descending order: MR > HMPR > HIPR. The cost of a new asphalt mixture in the HIPR process is only 29% of that in the MR process. The HIPR process is a little expensive in terms of equipment leasing and fuel consumption compared with the MR process. In general, the HIPR process cost only accounts for 55% of the MR process cost. The HMPR process is similar to the MR process, but due to the saving materials in the new asphalt mixture, the cost of the HMPR process is 80% of the MR process. As for fiber types, the BF is more expensive than the LF and PF when making fiber asphalt mixtures. However, the asphalt absorption for the LF is much larger than that of the BF and PF, hence the asphalt content for the LF asphalt mixture is relatively high. The cost of asphalt is greater than the cost of aggregate, making the cost of the LF asphalt mixture slightly higher than that of the PF asphalt mixture.

#### *4.2. Comprehensive Benefit Analysis Based on the Grey Relational Method*

The above study investigated the resistance to HWTT test performance and the respective economic benefit of asphalt mixture with different types of fibers incorporated in asphalt pavements under three maintenance processes. The MR process is found to be more resistant to HWTT rutting with a higher cost, and the HIPR process is found to be less resistant to moisture damage in the stripping stage but at a significant price advantage. Considering the need for test performance and economic cost in practical engineering, this study extracts the main factors affecting performance and cost through grey correlation analysis. Then, the optimal maintenance process and fiber type are selected with the highest comprehensive benefit.

The grey correlation analysis is considered as a systematic approach to analyzing finite and irregular data. It can create a grey series that gives a holistic view and comparison to determine the optimal solution. In this study, 12 kinds of asphalt mixtures with different maintenance processes and fiber types are selected as the scheme. The feature points in the HWTT curve and the cost for the corresponding maintenance process are used as the impact factors, and the optimal scheme is obtained by analyzing the influence of each factor on the comprehensive benefit. Asphalt mixtures of different types can be used to construct scheme A, where *A* = {*A*1, *A*1, ..., *Am*}, *m* = 12. For each type of asphalt mixture, the total rut depth (TRD), *NSN*, rut depth for high-temperature rutting effect, rut depth for stripping effect, rut depth and loading cycle at PCP, rut depth and loading cycle at SIP, and the cost of maintenance process are taken as scheme B, where *B* = {*B*1, *B*1, ..., *Bn*}, *n* = 9. Constructing matrix *X* from A and B, in which *X* = *xij <sup>m</sup>*×*n*, and *xij* is the *<sup>j</sup>*th test indicator for the *i*th scheme. The column preference matrix *X* is given as,

$$X = \begin{pmatrix} 8.033\ 7238.3\ 5001\ 2.884\ 810\ 1.95\ 1450\ 59.67\ 12.5\\ 8.284\ 6730.8\ 4.546\ 3.801\ 780\ 1.40\ 14325\ 6.11\ 667.6\\ 7.785\ 6961.8\ 4.101\ 3.899\ 790\ 1.43\ 14410\ 5.95\ 663.0\\ 6.034\ 8919\ 3.909\ 1.851\ 950\ 1.63\ 18120\ 5.35\ 687.8\\ 5.490\ 7446.2\ 3.623\ 2.125\ 810\ 1.16\ 14615\ 4.41\ 568.7\\ 8.104\ 7811.9\ 4.804\ 3.370\ 820\ 1.81\ 14780\ 6.41\ 537.9\\ 7.093\ 7219\ 1.3\ 852\ 3.424\ 800\ 1.39\ 14515\ 5.50\ 534.1\\ 5.490\ 7446.3\ 3.688\ 2.062\ 810\ 1.16\ 14610\ 4.41\ 551.4\\ 8.861\ 4827\ 4.3\ 084\ 6.140\ 550\ 1.00\ 13960\ 5.64\ 386.5\\ 10.92\ 402\ 2.653\ 8.372\ 570\ 0.63\ 13260\ 6.17\ 372.6\\ 15.11\ 3316.7\ 3.981\ 13.41\ 505\ 0.63\ 12930\ 8.56\ 373.4\\ 16.15\ 6643.3\ 10.82\ 6.96\ 60\ 4.34\ 14530\ 13.43\ 78.3\$$

In order to facilitate calculation and comparison, the indicators need to be dimensionless. For the larger and better indicators, the dimensionless formula is: *yij* <sup>=</sup> *max*(*xj*)−*xij max*(*xj*)−*min*(*xj*) . For smaller and better indicators, the dimensionless formula is: *yij* <sup>=</sup> *xij*−*min*(*xj*) *max*(*xj*)−*min*(*xj*) , of which, *j* = 1, 2, ... , *n*. Where *yij* is the value of the *j*th index of the *i*th scheme, *max xj* and *min xj* represent the maximum and minimum values in indicator *j*, respectively. After dimensionless processing, the matrix *Y* can be obtained.

$$Y = \begin{pmatrix} 0.76\ 0.70\ 0.70\ 0.91\ 0.69\ 0.64\ 0.30\ 0.83\ 0.00\\ 0.74\ 0.61\ 0.76\ 0.82\ 0.62\ 0.79\ 0.27\ 0.81\ 0.13\\ 0.78\ 0.65\ 0.81\ 0.82\ 0.64\ 0.78\ 0.29\ 0.83\ 0.15\\ 0.95\ 1.00\ 0.84\ 1.00\ 1.00\ 0.73\ 1.00\ 0.90\ 0.07\\ 1.00\ 0.74\ 0.87\ 0.98\ 0.69\ 0.86\ 0.32\ 1.00\ 0.42\\ 0.75\ 0.80\ 0.73\ 0.87\ 0.71\ 0.68\ 0.36\ 0.78\ 0.51\\ 0.85\ 0.70\ 0.84\ 0.86\ 0.66\ 0.80\ 0.31\ 0.88\ 0.52\\ 1.00\ 0.74\ 0.86\ 0.98\ 0.69\ 0.86\ 0.32\ 1.00\ 0.47\\ 0.68\ 0.27\ 0.94\ 0.63\ 0.10\ 0.90\ 0.20\ 0.86\ 0.96\\ 0.49\ 0.13\ 1.00\ 0.44\ 0.15\ 1.00\ 0.06\ 0.80\ 1.00\\ 0.10\ 0.00\ 0.95\ 0.00\ 0.00\ 1.00\ 0.00\ 0.54\ 1.00\\ 0.00\ 0.59\ 0.00\ 0.56\ 0.21\ 0.00\ 0.31\ 0.00\ 9.8\$$

The *Hj* is defined as the entropy of the *j*th indicator, which can be expressed as *Hj* <sup>=</sup> <sup>−</sup>∑*<sup>m</sup> <sup>i</sup>*=<sup>1</sup> *fijln*(*fij*) *lnm* , *<sup>j</sup>* <sup>=</sup> 1, 2, ... , *<sup>n</sup>*, in which, *fij* <sup>=</sup> *yij* ∑*<sup>m</sup> <sup>i</sup>*=<sup>1</sup> *yij* . In order to make sense of *ln fij* in the entropy formula, it is assumed that *fij* = 0, *ln fij* = 0. Thus, the *Hj* can be obtained. *Hj* = [0.93 0.93 0.96 0.95 0.91 0.96 0.90 0.96 0.88].

The entropy weight *Wj* can be expressed as *Wj* <sup>=</sup> <sup>1</sup>−*Hj* ∑*n <sup>j</sup>*=1(1−*Hj*) , and the entropy weight matrix *Wj* is given as,

$$\mathcal{W}\_{\hat{\jmath}} = \text{diag}\{0.11, 0.11, 0.06, 0.07, 0.15, 0.06, 0.17, 0.06, 0.20\}$$

Transforming matrix *Y* to attribute matrix *R*, which can be expressed as *R* = *Y* × *Wj*.


Then, the ideal point of the matrix (*P*) can be selected and expressed as *P* = [*p*1, *p*2, ..., *pn*]. In which, *pj* = *max rij* ! !*<sup>i</sup>* <sup>=</sup> 1, 2, . . . , *<sup>m</sup>*; *<sup>j</sup>* <sup>=</sup> 1, 2, . . . , *<sup>n</sup>* " .

*P* = [0.107 0.112 0.061 0.074 0.149 0.063 0.170 0.064 0.200]

The distance to the ideal point for each scenario (*L*) can be calculated, where *L* = [*l*1, *l*2, ..., *lm*], of which, *li* = *n* ∑ *j*=1 *rij* − *pj* 2 , *i* = 1, 2, . . . , *m*. *L* = ⎡ ⎣ 0.059 0.052 0.049 0.035 0.030 0.025 0.027 0.027 0.045 0.056 0.079 0.054 ⎤ ⎦

Therefore, the ordering of the 12 scenarios is: *L*<sup>6</sup> < *L*<sup>7</sup> = *L*<sup>8</sup> < *L*<sup>5</sup> < *L*<sup>4</sup> < *L*<sup>9</sup> < *L*<sup>3</sup> < *L*<sup>2</sup> < *L*<sup>12</sup> < *L*<sup>10</sup> < *L*<sup>1</sup> < *L*11. According to the grey relational analysis data, it can be seen that the HMPR process has the highest comprehensive benefit among the three maintenance processes. The HMPR asphalt mixture with LF has the best performance, followed by that of the PF and BPCF. The MR fiber asphalt mixture has a similar trend. In the HIPR maintenance process, BF is the first choice. Combined with the HWTT test data, it can be seen that the HIPR maintenance process has poor stripping resistance, while the performance can be significantly improved with the addition of BF in the HIPR mixture. Therefore, the BF can be used as the preferred reinforcement and toughening material for asphalt mixtures with a high RAP dosage.

#### **5. Conclusions**

This study proposes an innovative method to analyze the performance and economic aspects of rejuvenating fiber asphalt mixtures in high-temperature moisture susceptibility. Under different maintenance processes, Hamburg wheel tracking tests are conducted to investigate the rutting and stripping effects of rejuvenated fiber asphalt mixtures. Major conclusions can be drawn as follows:

(1) The best performance in terms of resistance to hydrothermal coupling effects is achieved at the HMPR maintenance process, with the asphalt mixtures incorporating the BF and BPCF. Both of these two mixtures have a TRD of about 5.49 mm. The high-temperature rutting performance of asphalt mixtures improves with the increase in RAP content. The HIPR asphalt mixture with the LF has the best high-temperature rutting performance, with a rutting depth of 2.55 mm at a 20,000 cycle. The moisture damage resistance is negatively correlated with the high-temperature rutting performance. The asphalt mixture with the MR process is the best, and the rutting depth under the stripping effect is 1.85 mm.

(2) The HWTT curve fitting model considers the positive and negative curvature of the curve in two separate phases. The starting and ending points of the HWTT curves are connected with the intersection point to obtain two line segments. The unique solution of the PCP and SIP points is obtained by finding the maximum vertical distances between the HWTT curve and two line segments. This method can give a generalized approach to determining the value of stripping inflection points mathematically. The results show that the three feature points of the PCP, N\_SN, and SIP are the earliest for the HIPR maintenance process, while these points for asphalt mixtures with the BF and BPCF under the MR maintenance process are the latest, at 950,892,018,120 loading cycles, respectively.

(3) The economic model of three maintenance processes was established. The results found that the cost of the MR maintenance process is the most expensive, while the asphalt mixtures incorporated with the BF increase the cost of maintenance to 712.5 ¥/t. The HIPR maintenance process is more expensive in terms of fuel consumption and equipment leasing, but the cost of raw materials such as aggregates and asphalt is significantly lower. The cost of the HIPR maintenance process is only 55% of the cost of the MR maintenance process.

(4) The performance and economic benefits of 12 rejuvenated asphalt mixtures were investigated by grey correlation analysis. Nine indicators including TRD, N\_SN, the RD of high-temperature rutting effect, the RD of stripping effects, RD and N at PCP, RD and N at SIP, and maintenance cost are used as the impact indicators. The results indicate that the HMPR maintenance process is the most efficient within the three maintenance processes, and the HMPR maintenance process with LF is the best choice. In the HIPR maintenance process, the incorporation of BF improves the HWTT performance of the asphalt mixture.

Recycling and recovering are the main trends in the future development of the pavement maintenance industry. In this study, the HWTT curve analysis method was improved on the background of three maintenance technologies. The proposed approach can be used to identify three feature points to better control rutting resistance and moisture susceptibility. A comprehensive benefits analysis combining performance and economic benefits can be investigated. However, a full life cycle analysis is still lacking and should be focused on in future research.

**Author Contributions:** Conceptualization, Y.Z. and A.K.; methodology, Y.Z. and Y.W.; formal analysis, Y.Z. and Z.W. (Zhengguang Wu); validation, B.L. and C.Z.; resources, Z.W. (Zhengguang Wu), Z.W. (Zhe Wu) and A.K.; data curation, C.Z. and Y.W.; writing—original draft preparation, Y.Z. and Y.W.; writing—review and editing, Y.Z. and B.L.; project administration, Y.Z. and B.L.; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 52108422, and the High-level Talent Introduction Project of Yangzhou University, grant number 137012062.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

For reading convenience, a list of abbreviations is given below.


#### **References**


**Yiming Li 1,2,\* and Simon A. M. Hesp <sup>2</sup>**

<sup>2</sup> Department of Chemistry, Queen's University, Kingston, ON K7L 3N6, Canada; simon@chem.queensu.ca

**\*** Correspondence: liyiming@nefu.edu.cn

**Abstract:** Testing small amounts of extracted and recovered asphalt binder as used in construction allows for the acceptance of materials in accordance with traffic and climate requirements. This approach facilitates the sustainable use of resources and thus prepares the paving industry for the true circular economy. Oscillatory, creep, and failure tests in a rheometer are compared for the performance grading of 32 asphalt binders extracted and recovered from real-world contract samples. Films 8 mm in diameter and 0.5 mm thick were tested from 35 to −5 ◦C in dynamic shear, followed by shear creep at 0 and 5 ◦C, and finally in tertiary tensile creep at 15 ◦C. The enhanced protocol uses a very small amount of material in contrast to current methods, yet it provides comparable results. Phase angle measurements appear to be optimal for performance grading, but further field study is required to determine if additional binder properties such as stiffness and/or failure strain would be required for the control of cracking.

**Keywords:** asphalt performance grading; thermal cracking; fatigue; phase angle; creep rate; failure strain

#### **1. Introduction**

Optimal pavement design involves balancing material properties and structure to provide a long-life cycle with only minimal distress. It is generally accepted that rutting and moisture damage are largely controlled through the selection of appropriate aggregate types and gradation, with the addition of polymer, fiber, and/or antistrip additives when needed [1]. On the other hand, load-induced fatigue and cold temperature transverse cracking are kept in check by the selection of an appropriate pavement thickness, asphalt binder quality, and durability [1–6].

It is essential that the most accurate acceptance specification tests are conducted on carefully extracted and recovered binder, as it best reflects what is actually placed in the contract [7–10]. The presence of reclaimed asphalt pavement (RAP) in the mix, as well as associated overheating of the virgin asphalt binder during production, are factors that can have a detrimental impact on long-term performance of the pavement. Hence, these and other issues need to be accounted for in an effective quality assurance testing program.

Several Ontario municipalities have recently switched to testing of the extracted and recovered asphalt binder according to the extended bending beam rheometer (EBBR) and double-edge-notched tension (DENT) tests with promising results [7–10]. To illustrate, Figure 1a provides representative 2020 photographs for pavement on three blocks of Princess Street and King Street in downtown Kingston, Ontario, constructed before the switch. The asphalt surface was reconstructed on fresh granular base ten years ago as part of a program that replaced all downtown sewer infrastructure. The properties of the asphalt storage tank sample were used for acceptance, but—according to the current Ontario municipal asphalt specification—up to 15% RAP was allowed in the binder course and none in the surface. It is obvious that this pavement is failing through thermal cracking well before its expected design life.

**Citation:** Li, Y.; Hesp, S.A.M. Enhanced Acceptance Specification of Asphalt Binder to Drive Sustainability in the Paving Industry. *Materials* **2021**, *14*, 6828. https://doi.org/10.3390/ ma14226828

Academic Editor: Milena Pavlíková

Received: 22 October 2021 Accepted: 10 November 2021 Published: 12 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

(**b**)

**Figure 1.** (**a**) Representative photographs of pavement reconstructed in 2010 on three blocks of Princess Street and King Street in downtown Kingston, Ontario, (**b**) Representative photographs of pavement reconstructed in 2011–2012 on seven adjacent blocks of Princess Street.

Figure 1b provides representative photographs for the remainder of the contract completed over the next two years on an adjacent seven blocks of Princess Street. Here, the City of Kingston had switched to acceptance of the asphalt based on properties of the extracted and recovered binder and RAP was banned from both the surface and binder courses. It is obvious that there is a stark contrast in performance after only eight to ten years of service. Hence, if the acceptance is based on extracted and recovered binder properties, then the use of RAP would be allowed as long as minimum performance is obtained in the materials as placed in the contract.

The acceptance of the asphalt for the City of Kingston has been based on extracted and recovered binder properties since 2010 and this has so far provided pavements that are meeting their design expectations [7]. While providing improved specification grading, the EBBR and DENT tests used for contract acceptance have their drawbacks. Both tests require a rather large quantity of extracted and recovered binder and take a considerable amount of time to complete. Hence, current research is focused on the development of simplified methods that use less material, take less time to complete, and with equal or better precision and accuracy [7,11–13]. Improved specification tests lower risk, which benefits both users and producers of asphalt for the betterment of the entire industry. The objective of the current research project is to develop a more practical approach for acceptance testing of extracted and recovered asphalt binder. In order to learn more about all issues involved, the research assessed a wide range of performance properties for 32 binders from commercial contracts. Future efforts will involve a detailed performance assessment of the involved pavement locations.

#### **2. Background**

It was Dow [14] of the Washington, D.C., engineering department, who in the early 1900s developed both a ductility test and an improved penetrometer for the grading of asphalt binder. With a keen eye, he had noticed that those binders that elongate when pulled by hand would perform better than those that ruptured early [15]. Both ductility and penetration tests went on to become the most widely used specification methods for straight asphalt binder and remain used with great success in many parts of the world today. In general, binder that flows well suffers little from cracking at ambient and cold temperatures. Dow [14] also commented on the fact that some binders when freshly poured perform much better compared to those that had been left to equilibrate for a time on the bench.

It was not until the publication from Hubbard and Pritchard [16] in 1916 that a quantitative assessment was made of this gradual aging phenomenon. Penetration testing showed that the consistency of binders can increase (i.e., penetration decreases) for periods of weeks and months, and that this was independent of oxidative hardening as reheating the sample could largely restore the original properties.

A series of publications by Traxler and coworkers [17–19] in the 1930s were the first to provide a comprehensive assessment of what is best described as a thermoreversible aging effect. Using tensile and shear creep experiments, major changes in rheological properties were revealed after days and weeks of isothermal storage. These authors noted that binders physically age at different rates depending on their source and production technology. They found that air oxidized binders were particularly sensitive to the effects of thermal conditioning. Filler had little effect on the degree of aging. Reheating could erase the changes. The impact of thermal equilibration was large compared to the effects of volatilization and oxidation. Finally, they described the change in consistency as a sol-to-gel transition.

Traxler and his contemporaries actively discussed the sol and gel nature of asphalt binder, as reflected by publications of Nellensteyn [20–22], Sakhanov [23], Sachanen [24], Mack [25,26], Saal [27], Pfeiffer and Van Doormaal [28], and many others. Asphalt binder is a material that is composed of a spectrum of organic molecules with molar weights that range from a few hundred to a few thousand grams per mole [29]. The individual molecules can be classified as either aliphatic (paraffins and naphthenes) or combined aliphatic and aromatic (naphthene aromatics, resins, and asphaltenes). The aliphatic fraction is defined by its molar weight and degree of branching, with those binders largely composed of linear alkanes (paraffins) providing lesser performance compared to those containing mostly branched and cyclic (napthenic) alkanes [29]. The more aromatic fractions are called asphaltenes that are typically of a higher molar weight and contain fused ring systems that could be associated with small amounts of metals such as nickel, vanadium, and iron [29].

There is a significant amount of ambiguity in the literature as the asphaltenes fraction, defined by its insolubility in n-heptane, can also be contaminated with paraffin of high enough molar weight that makes it co-precipitate [30]. The general consensus is that the asphaltenes fraction together with the paraffin slowly precipitates out into a soltype, sol/gel-type, or gel-type structure that, depending on temperature, viscosity, and composition, takes from days to weeks or months to equilibrate [16–19,31–40].

Blokker and Van Hoorn [33] coined the term "physical hardening" and stated that it involves the rather rapid crystallization of waxes and the slower precipitation of asphaltenes. Binders with high contents of both linear paraffins (wax) and asphaltenes are most susceptible to cracking distress as, due to their gelled state at ambient and low temperatures, they are unable to relax thermal and traffic-induced stresses [38,40,41] and suffer from weak spots at the somewhat sharp interface between the crystalline and amorphous phases [42–44].

Current specifications in most of Canada and the United States are based on the work done under the U.S. Strategic Highway Research Program (SHRP) [45]. The product of SHRP was the Superpave™ specification, which grades asphalt binders at high, intermediate, and low temperatures to control rutting, fatigue, and thermal cracking distress [45].

At high temperatures, Superpave sets a lower limit on the complex modulus divided by the sine of the phase angle, G\*/sinδ, which for straight run binders is close to the complex viscosity [46]. It is generally accepted that the high temperature Superpave grade is reasonably effective at controlling rutting distress, although it should be recognized that aggregate structure and pavement thickness are two factors that can often be more important than binder properties.

At intermediate temperatures, an upper limit of 5 MPa is set on the loss modulus, G\*sinδ, for a residue aged for 20 h in a pressure aging vessel (PAV) at a temperature of 100 ◦C and pressure of 2.08 MPa [45]. It has been found that the intermediate temperature Superpave grade is unable to correlate well with fatigue performance largely because it confounds the beneficial effects of viscous energy dissipation and the formation of damage [47–50]. It also favors the use of binders with low phase angle and low stiffness, which are known to suffer more from oxidative age hardening, phase separation, and exudative aging [51].

At low temperatures, the Superpave specification sets limits on the creep stiffness, measured in the BBR in three-point bending at 60 s of loading, S(60 s), and creep rate (i.e., the slope of the logarithmic creep stiffness master curve) also measured after 60 s of loading, m(60). The maximum S(60 s) of 300 MPa came from a decision to increase it from 200 MPa, as otherwise, too many asphalt binders sold at the time of SHRP would not have met the specification [45]. The original 200 MPa limit was based on a single field validation study many years earlier by Readshaw [52] in British Columbia. The m-value limit of 0.300 was a late addition to the specification that was based on the average for the relaxation rate at the limiting stiffness temperature for the eight core asphalt binders used in SHRP. The m(60 s) value was intended to prevent the use of heavily air-blown binders that were known to suffer from reduced creep, reduced stress relaxation, and exudative aging.

In general, asphalt binders are highly susceptible to changes in temperature and, due to their high viscosity at and below room temperature, are often graded in a state of non-equilibrium. This problem is one that has confounded pavement design since the work of Dow [14,15], Hubbard and Pritchard [16], Traxler [17–19], and others [53–62], and was similarly of concern to SHRP researchers developing the BBR [35,36]. Hence, the SHRP program spent a considerable amount of time and resources investigating physical hardening phenomena (thermoreversible aging). An early draft of the Superpave specification contained an option to test binders after one and 24 h of conditioning at the test temperature, but for reasons that are not well documented that provision never found wide acceptance [45].

Shortly after the complete implementation of the Superpave binder specification in Ontario, the Ministry of Transportation of Ontario (MTO) initiated research projects to

investigate resultant widespread premature cracking around eastern and northeastern parts of the province [3–6]. These investigations eventually resulted in an improved asphalt cement specification by incorporating both the DENT and EBBR tests [63,64].

The DENT test provides an approximate critical crack tip opening displacement (CTOD), which is a value for the strain tolerance of binders in their ductile state and is highly correlated with fatigue cracking performance [50]. The CTOD is best described as a somewhat improved measurement of ductility. It is measured under more severe constraint in deeply notched specimens and at lower temperatures compared to a regular ductility test. However, it should be noted that there is a high correlation between CTOD and conventional ductility [12,65]. The DENT test provides essential and plastic works of failure in addition to the CTOD and the relevance of those to pavement performance remains to be better understood.

The EBBR was developed to be as similar as possible to the regular BBR test. It conditions samples for 1, 24, and 72 h at Td + 10 and Td + 20, where Td is the design temperature of the pavement according to climatic requirements [2–5]. The 72 h grade loss from the one-hour result at Td + 10 (roughly equal to the AASHTO M320 grade) is calculated and serves as a measure of durability. Grade losses found for tank and recovered binders range approximately from 0 to 15 ◦C, depending on the quality and durability of the binder [5–7].

While both the DENT and EBBR have proven to provide much enhanced performance grading, there is a need to find simpler test methods that can be completed in less time with less material to replace these protocols for future specifications. To that end, a butt joint test (BJT) for the ductile performance grading of asphalt binders was recently proposed [13]. Introducing the BJT as an alternative method for the DENT was able to significantly reduce material requirement and testing time. Compared with the DENT test, the BJT only takes 30 min and at the same time provides precise, sensitive, and accurate ductile strain tolerances. However, the BJT test has a problem with stiff binders that can generate tensile loads that exceed the capacity of the rheometer [13]. Hence, in this research a tertiary tensile creep test is investigated, which provides a measure of strain tolerance within the load capacity of the rheometer used. In addition, dynamic and creep shear tests are conducted at ambient and just below ambient temperatures in order to provide a comparison with results obtained in the EBBR protocol at much lower temperatures.

In spite of the numerous investigations that have come to similar conclusions to those found in the seminal publications by Traxler and coworkers [17–19] on thermoreversible aging, the problems created by this gradual change in properties in specification grading remain to be effectively sorted out today. This paper focusses on the measurement of phase angle as it has been shown in previous studies to be highly correlated to EBBR limiting grades and field cracking performance [66–71]. Testing of the extracted and recovered asphalt binder allows for the proper acceptance of materials as placed in the contract, thus facilitating the proper and responsible design for a true circular economy.

#### **3. Experimental**

#### *3.1. Materials*

A total of 32 asphalt binders were used in this study from hot mix asphalt (HMA) provided by five different user agencies. Samples were shipped directly by the user agency to Queen's University by overnight courier and processed within a maximum of 1–2 months.

#### *3.2. Methods*

Binders were extracted using dichloromethylene (DCM) solvent [8,9]. All solutions were twice fed through a high-speed centrifuge (Ploog Engineering, Crown Point, IN, USA) to remove the fines. Recovery of the asphalt binder was done under a dry nitrogen gas atmosphere at moderate to high vacuum in a rotary evaporator (BUCHI Corporation, New Castle, DE, USA). Once no further DCM was visibly being distilled, the temperature

of the oil bath was raised to 160 ◦C and the flask was subjected to vacuum below 50 mbar for an additional one hour. Asphalt binders were aged in a pressure aging vessel (PAV, Prentex, Dallas, TX, USA) according to standard procedures embodied in AASHTO R 28–09 [72] before testing at intermediate and low temperatures.

Small amounts of PAV residues were mounted in the dynamic shear rheometer (DHR-1 or DHR-2, TA Instruments, New Castle, DE, USA) at 64 ◦C and rapidly brought to 34 ◦C for testing at a film thickness of 2 mm. Samples were equilibrated for 10 min at each test temperature prior to testing at 12 ◦C intervals from 34 ◦C to −2 ◦C to determine the intermediate temperature complex modulus, G\*, and phase angle, δ. Test frequency and strain level were kept constant at 10 rad/s and 0.1%, respectively.

The PAV residues were tested according to the DENT protocol described in AASHTO method TP 113-15 [73]. In brief, samples were poured in silicone molds with aluminum end inserts to facilitate shear transfer of the load from the test frame to the specimen. Notch depths varied to provide ligaments of 5, 10, and 15 mm in 10 mm thick specimens. The total works of failure were divided by the ligament area and plotted versus ligament length. The extrapolated intercept provided the essential work of failure, which was subsequently divided by the net section stress in the smallest ligament to determine the CTOD.

The PAV residues were tested in the EBBR protocol as described in AASTHO method TP 122-16 [74]. In brief, six samples each were conditioned at Td +10 and Td + 20 (where Td is the design temperature of the pavement), for 1, 24, and 72 h. After each conditioning time, the samples were tested at Td + 10 and Td + 16 to determine pass and fail properties. From the individual stiffness and m-value measurements, actual grade temperatures were calculated by interpolation or extrapolation. The limiting low temperature grade (LLTG) was determined as the warmest of all limiting grade temperatures and the grade loss (GL) was determined as the difference between the 1 h limiting grade at Td + 10 and the LLTG [74].

All PAV residues were also tested in the dynamic hybrid rheometer as 8 mm diameter by 0.5 mm thin films according to the three-in-one protocol. First, samples were mounted at 64 ◦C and after equilibration for 10 min at 35 ◦C, tested at 10 ◦C intervals from 35 ◦C to −5 ◦C, at frequencies of 0.1, 0.316, 1, 3.16, and 10 rad/s at a strain level of 0.1%. From these results, the temperature at which the phase angle at 10 rad/s reached 30◦ was calculated as a low temperature performance grade. Second, the same samples were subsequently equilibrated at 0 ◦C and tested for 240 s in creep shear at 1000 Pa followed by recovery for 760 s. Next, the creep test was repeated at 5 ◦C. From the two creep tests in shear, the temperature at which the creep rate, m, reached 0.5, was calculated according to the following equations [75]:

$$\log \text{S}'(\mathbf{t}) = \mathbf{A} + \mathbf{B}[\log(\mathbf{t})] + \mathbf{C}[\log(\mathbf{t})]^2 \tag{1}$$

$$|\mathbf{m}| = \mathbf{B} + 2\mathbf{C}[\log(\mathbf{t})] \tag{2}$$

where S (t) is the time-dependent shear creep stiffness, m is the creep rate in shear, t is the time in seconds, A, B, and C are regression coefficients.

Finally, the same samples as measured in the first two steps of the three-in-one protocol were subsequently equilibrated at 15 ◦C and subjected to a tensile creep load of 8 N to failure in order to determine strain tolerance in the ductile state. Figure 2 provides a representative tertiary creep test result with an illustration of how the failure point was determined at the sudden loss of the creep load control.

The results from the three-in-one protocol to determine phase angle, creep rate and ductile failure strain were compared with findings from the standard DSR, DENT and EBBR tests. The advantage of the three-in-one protocol is obvious as it uses less than a gram of material versus approximately 150 g for the combined DENT/EBBR testing, it is automated and might therefore be more repeatable, and produces similar insights as the DENT/EBBR.

**Figure 2.** Tertiary creep test results on a 0.5 mm film to measure the failure point (FP).

#### **4. Results and Discussion**

#### *4.1. Oscillatory Shear Testing*

The limiting phase angle temperatures determined as part of the intermediate temperature Superpave grading and the three-in-one protocol are given in Figure 3a. It is obvious that there is a strong correlation and that the reproducibility is high (short of three outliers in squares). Tests were done by the same person several months apart. The results for the two film thicknesses are 2.63 ◦C apart, which is due to the thinner film being more constrained and thus less able to flow.

**Figure 3.** (**a**) Reproducibility of limiting phase angle temperature determinations using 2 and 0.5 mm thin films in the DSR; (**b**) Correlation between limiting phase angle temperature T(δ = 30◦) (2 mm) and BBR (red symbols) and EBBR (blue symbols) limiting grades.

The correlation between the limiting phase angle temperature and the BBR and EBRR grades are in Figure 3b. These comparisons show that there are strong similarities, but that the T(δ = 30◦) and EBBR have a higher sensitivity (wider range) compared to the regular BBR. The slope for the EBBR straight line fit is about 46% higher than what it is for the regular BBR (0.83 versus 0.57), which reflects the significantly improved sensitivity for the T(δ = 30◦) and EBBR. The EBRR LLTG and T(δ = 30◦) are most closely correlated, suggesting that cracking control may be achieved with similar efficiency when utilizing a T(δ = 30◦) acceptance criterion. The difference for this limited set of data is in agreement with data from previous studies on other binders [8,11,76,77]. However, a switch from the somewhat lengthy EBBR protocol to the more practical T(δ = 30◦) would mean that the information provided by the grade loss is lost. It has also been recognized that for more severely aged material, the limiting phase angle temperatures also start to suffer from the effects of thermoreversible aging [78,79].

#### *4.2. Creep Testing*

Representative creep test results for one of the binders are in Figure 4. Use of Equation (1) provides a high correlation with the raw displacement data. The correlation between T(m = 0.5) and BBR and EBBR is provided in Figure 5. As can be seen, the creep data fit Equation (1) with a high degree of accuracy. The correlation between the limiting creep rate temperature, T(m = 0.5), and the BBR and EBBR limiting temperatures is also reasonably good. As for the phase angle data in Figure 3, the range for the T(m = 0.5) at 19.6 ◦C is significantly wider than what it is for the BBR at 10.7 ◦C, somewhat wider than what it is for the EBBR at 16.5 ◦C, but not quite as wide as the span for the T(δ = 30◦) at 20.9 ◦C. A wider range with equal or better precision is beneficial in a grading protocol as it allows for the better differentiation between samples.

**Figure 4.** (**a**) Raw and (**b**) processed shear creep test results at 1000 Pa and two temperatures.

#### *4.3. Tertiary Creep Testing*

The final comparison is between the failure point in tertiary creep and the DENT CTOD as given in Figure 6a. The graph shows that there is a very high correlation and that both measurements provide nearly the same ranking. Figure 6b shows the repeatability for the tertiary creep test, which is also reasonable, although not as good as for the phase angles in Figure 3a.

**Figure 5.** Correlation between T(m = 0.5) and limiting BBR and EBBR temperatures.

**Figure 6.** (**a**) Correlation between failure point (FP) and DENT CTOD; (**b**) Repeatability of the tertiary creep test (failure point FP2 is a repeat of FP1 as determined by one of the authors (Y.L.), at a time several months after the determination of FP1).

#### **5. Summary and Conclusions**

Given the results and discussion presented, the following summary and conclusions are provided:


temperature (10.7 ◦C). Hence, the limiting phase angle temperature is significantly more responsive to changes in binder properties than both the BBR and EBBR.


Given the pervasiveness and seriousness of premature and excessive pavement cracking in cold climates, it is up to the user agencies to make the best use of the information provided.

**Author Contributions:** Conceptualization, Y.L. and S.A.M.H.; data collection and data processing, Y.L.; writing of draft manuscript, Y.L.; supervision, writing and editing of final manuscript, S.A.M.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research was made possible through funding in part by Imperial Oil of Canada (URA 2018–2021) and the Ontario Ministry of Transportation (HIIFP 2018–2021). Yiming Li was generously supported by the Chinese Scholarship Council to spend one year at Queen's University in Kingston, Canada, as part of his doctoral program at Northeast Forestry University in Harbin, China.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The raw/processed data required to reproduce these findings cannot be shared.

**Acknowledgments:** Yiming Li wishes to thank the China Scholarship Council (CSC) for financial support, which was provided to support his study at Queen's University. Additional appreciation goes out to the Ministry of Transportation of Ontario, Imperial Oil of Canada, and the five municipal and state user agencies for their continuing support of this research program.

**Conflicts of Interest:** Hesp, S.A.M. receives professional consulting fees from municipal, state and federal transportation agencies.

**Disclaimer:** None of the sponsors necessarily concurs with, endorses, or has adopted the findings, conclusions, or recommendations either inferred or expressly stated in the subject data developed.

#### **References**

