Laboratory Evaluation of Dynamic Characteristics of a New High-Modulus Asphalt Mixture

Abstract

With the rapid increase in traffic volume and heavy-duty vehicles, rutting has become one of the most serious problems threatening the service quality and life of asphalt pavement. High-modulus asphalt concrete is a promising method to overcome this problem, contributing to the sustainable development of asphalt pavement. In this study, a new composite high-modulus agent (CHMA)-modified asphalt binder and mixture were prepared, and their dynamic mechanical characteristics were investigated by the dynamic shear rheometer, dynamic modulus test, wheel tracking test, frequency sweep test at a constant height (FSCH), and repeated shear test at a constant height (RSCH) to comprehensively evaluate its high-temperature stability. Test results showed that the rheological property of the CHMA-modified asphalt binder was similar to that of low-graded asphalt binder, implying that it had a strong potential in resisting deformation. The dynamic modulus of AC-20(CHMA) was 19,568 MPa at 15 °C and 10 Hz condition, meeting the requirement for the high-modulus asphalt mixture (higher than 14,000 MPa). The dynamic stability of AC-20(CHMA) was 8094 times/mm, lower than that of AC-20(20#), but remarkably higher than that of AC-20(SBS). AC-20(20#) and AC-20(CHMA) both showed strong shear resistance according to the FSCH test results. Under the repeated shear loadings, the growth rate of the shear strain increased rapidly in the primary stage, and then slowed down gradually, finally reaching a constant growth rate. The shear slope of AC-20(CHMA) was between that of AC-20(20#) and AC-20(SBS), demonstrating that its resistance to repeated shear loadings was superior to AC-20(SBS), although slightly weaker than AC-20(20#). The findings in this study provide references for alleviating rutting problems and improving the lifespan of asphalt pavement.

1. Introduction

High-modulus asphalt concrete (HMAC) was firstly proposed by French engineers in the early 1980s for resisting permanent deformation [1]. Considering the excellent performance in alleviating the rutting problem and reducing the maximum thickness of the asphalt layer, HMAC, also known as Enrobé a Module Élevé (EME), was widely applied in both the base course and wearing course [2,3]. According to the NFP-140 standard of France [4], HMAC is generally required to have a dynamic modulus larger than 14,000 MPa at a certain testing condition (15 °C and 10 Hz). The high-modulus asphalt binder (HMAB) is an essential component for preparing the HMAC, which improves the ability of asphalt pavement to absorb stress caused by road traffic. Therefore, the development of HMAB should be an important role in the production of HMAC.

In general, HMAB is categorized into three groups, including hard-grade asphalt binder, lake/rock modified asphalt binder, and polyolefin-modified asphalt binder [5,6,7,8]. The hard-grade asphalt binder refers to those neat asphalt binders with a penetration of 10–25 (0.1 mm) at 25 °C and a softening point of 55–78 °C, which is mainly used in European countries. The second group is to use lake or rock asphalt binder as modifiers for base asphalt binder. Trinidad lake asphalt (TLA) is a common asphalt binder that is available in South America. Due to the low penetration value, TLA is not appropriate to be directly used as a binding material. Indeed, it is typically mixed with the base binder to meet specific requirements. Rock asphalt is another typical natural asphalt binder containing relatively stable physical and chemical components. Compared with the first two groups, the polyolefin-modified binder has a stronger ability in resisting thermal cracking and fatigue [9]. Considering the scarcity of the hard-grade asphalt in China and the construction convenience, the polyolefin-modified asphalt binder is the preferred selection to prepare HMAC, especially in high-temperature areas, to increase the rutting resistance of pavement.

Asphalt pavements in China have been designed for a 20-year service period. However, with the rapid development of traffic volume, in particular truck traffic, rutting has become one of the most serious problems threatening the service quality and lifespan of pavement [10]. When subjected to both heavy traffic loadings and high-temperature conditions, traditional asphalt pavements usually suffer severe deterioration in the early stage of the service period. Dense-graded asphalt concrete (DGAC) is commonly used as pavement material in most areas of China. Meanwhile, as the traffic volume increases dramatically, DGAC needs frequent maintenance to ensure pavement performance. Furthermore, many newly constructed asphalt pavements suffer rutting problems with the opening to traffic, which needs high maintenance costs. One solution to increase the life of pavement is to use material with a high modulus in its asphalt base layer. The effectiveness of this layer as a part of pavement is closely dependent on how well its material is designed. Due to the excellent anti-rutting performance, HMAC is regarded as a promising method to overcome the current problem [11,12,13]. However, considering the limitation of petroleum resources and production methods, the French HMAC design methodology cannot be directly used in China. Therefore, taking full advantage of the French design methodology based on the Chinese pavement design methodology is necessary to alleviate the rutting distress.

For assessing the rutting behavior of HMAC, various test methods have been adopted by researchers [14]. According to the Superpave standard, $G^{*}/sin\delta$ was used to evaluate the rutting potential of asphalt binder, which could be obtained by performing tests on the dynamic shear rheometer (DSR) [15,16]. Higher rutting resistance can be achieved when increasing the complex shear modulus or increasing its relative storage modulus [17]. In recent years, the multiple stress creep and recovery (MSCR) test has been recognized as a better method for evaluating the rheological property of modified asphalt binders, where the nonrecoverable creep compliance (J_nr) and the recovery percent (R) are two main parameters [18,19]. For the asphalt mixtures, the wheel-tracking test is the most common method to simulate the effect of tire loading on the pavement. Moreover, the Hamburg wheel tracking test [20,21,22,23] and asphalt pavement analyzer [24] are also proposed to quantitatively assess the rutting performance of asphalt mixtures. Compared with the static permanent deformation test, researchers have demonstrated that the dynamic modulus test correlated well with the actual pavement rutting behavior [25,26,27]. The dynamic modulus is the key index of the HMAC design methodology, and it is obtained by monitoring the response of φ 100 mm × 150 mm cylindrical specimens to dynamic compressive–shear loadings [28]. Nowadays, the published investigations on the dynamic modulus are mainly concentrated on test configurations, conditions [29], and the establishment of the dynamic modulus master curve [30,31]. It should be noticed that the shear failure, namely the lateral movement, is a primary cause of permanent deformation. However, the existing rutting tests are not able to represent the shear properties of asphalt mixtures [32,33]. Thus, conducting the shear tests is necessary to replenish the routine rutting test of asphalt mixture in the laboratory. The uniaxial penetration test (UPT) is usually applied to evaluate the shear performance of asphalt mixture at high-temperature conditions [34,35]. The Superpave shear tester (SST) is also broadly accepted by many countries. By applying different loading modes, the tests include the repeated shear test at a constant height (RSCH) and frequency sweep test at a constant height (FSCH) [36,37,38].

In this paper, a new high-modulus asphalt mixture was prepared, and a variety of tests were conducted to evaluate its dynamic characteristics that were rarely reported in previous researches. The high-temperature stability of HMAC was evaluated by conducting the rheological property test, dynamic modulus test, wheel tracking test, and shear resistance test. The hard-grade asphalt concrete representing the France high-modulus asphalt concrete and SBS-modified asphalt mixture widely applied in road engineering were also prepared and tested as the control group. The research results may provide some useful suggestions for asphalt mixture design to improve the rutting resistance and reduce the unnecessary cost of production, construction, and maintenance. In addition, this paper lays the experimental foundation for promoting and optimizing the new high-modulus asphalt mixture to ensure the high-temperature stability of asphalt pavement.

2. Materials and Specimen Preparation

2.1. Materials

2.1.1. Asphalt Binder

Base asphalt binder (70#, 20#) and SBS-modified asphalt binder were used in this study. The main technical indicators of asphalt binders were tested according to JTG E20-2011 (Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering) in China, as listed in

Table 1. Technical indicators of base and SBS-modified asphalt binders.

Indicators	Unit	70#		20#		SBS
		Test Value	Standard Value	Test Value	Standard Value	Test Value	Standard Value
Penetration (25 °C, 100 g, 5 s)		65.2	60–80	16.8	10–20	59.1	60–80
Softening point	°C	55.6	≥43	69.6	≥60	80.6	≥55
Ductility (5 cm/min, 15 °C)	cm	>100	≥40	10.6	/	>100	/
Relative density (15 °C)	g/cm3	1.033	/	1.042	/	1.039	/
After Rotating Thin-Film Oven Test (RTFOT)
Mass loss on heating	%wt.	0.32	≤0.8	0.03	≤0.6	0.10	≤1.0
Retained penetration after RTFOT	%	78.5	≥54	85.0	≥65	84.1	≥60
Retained ductility after RTFOT	cm	59.2	≥15	4.6	/	21.3	≥20

Note: “/” means no specification in the standard.

.

2.1.2. Composite High-Modulus Agent

A composite high-modulus agent (CHMA) was selected as the modifier in this study, as illustrated in Figure 1. It is dark brown particles synthesized by natural rock asphalt, nanopolymer material, and stabilizer. It requires storage in a moisture-proof condition. Natural rock asphalt has good compatibility with petroleum asphalt and is less prone to aging and corrosion. Its interaction with nanopolymer material leads to the formation of an organic compound that plays an important role in enhancing the high-temperature performance of asphalt mixture. Silicon-like stabilizer ensures the storage stability of CHMA during transportation and construction. The basic properties of CHMA are presented in

Table 2. Basic properties of CHMA.

Index	Test Value	Standard Value	Test Standard
Appearance	Powder	/	Visual inspection
Color	Brown	Brown or black	Visual inspection
Density (g/cm3)	1.40	/	T0603-2011
Flash point (°C)	307	/	T0611-2011
Water content (%)	0.82	≤2.0	T0612-2011
Natural rock bitumen content (%)	51	/	T0735-2011
Mass loss on heating after thin-film oven test (%)	0.5	≤1.0	T0609-2011

Note: “/” means no specification in the standard.

.

2.1.3. Aggregate Gradation

EME of France prefers continuous gradation with a smooth curve in the logarithmic coordinate system. In French standards, the passing rates of 0.063 mm, 2 mm, 4 mm, and 6 mm sieves are specified, respectively. The maximum size (D) of aggregate indicates a 100% passing rate at the sieve with 2D size, 98~100% passing rate at sieve with 1.4D size, and 85~98% passing rate at the sieve with D size. As shown in

Table 3. Requirements on passing rate of AC-20 and EME-14.

AC-20	Sieve size (mm)	26.5	19	16	13.2	9.5	4.75	2.36	1.18	0.6	0.075
	Passing rate (%)	100	90~100	78~92	62~80	50~72	26~56	16~44	12~33	8~24	3~7
EME-14	Sieve size (mm)	28 (2D)	19.6 (1.4D)	14 (D)		6	4	2		/	0.063
	Passing rate (%)	100	98~100	85~98		50~70	40~60	25~38		/	5.4~7.7

, the requirements on passing rate of key sieve size of AC-20 gradation and EME-14 gradation are very close. Hence, AC-20 asphalt mixture has been widely applied in the construction of high-modulus asphalt pavement in China. In this study, the gradation curve of AC-20 was designed as shown in Figure 2, which also met the requirements of EME14.

2.2. Specimen Preparation

2.2.1. CHMA-Modified Asphalt Binder

The optimal content of CHMA was determined as 22% of the asphalt binder by mass according to previous research results [39]. The preparation process is briefly introduced here. First, the 70# asphalt binder was heated to 135 °C for a few hours to make it fully melted. Then, the CHMA modifier was added to the melted asphalt binder and manually mixed with a glass rod at 175 °C. Finally, the mixture was stirred for 1 h using the high-speed shear mixer at a speed of 3000 r/min to make the CHMA modifier uniformly dispersed in the base asphalt binder.

2.2.2. Asphalt Mixture Specimen

The CHMA modifier was added to the asphalt mixture through the dry process. Base asphalt mixture and SBS-modified asphalt mixture were prepared as the control group. The optimal asphalt content was 4.6% for CHMA-modified asphalt mixture, 5.2% for 20# asphalt mixture, and 5.0% for the SBS-modified asphalt mixture according to the Marshall test results. The preparation process of CHMA-modified asphalt mixture was as follows. First, the aggregates were heated to 180 °C and mixed in the pot for 30 s. The CHMA modifier was then added and mixed with the aggregate for 180 s. Next, the melted asphalt was poured into the mixing pot and mixed for 90 s. After that, the heated mineral powder was added and mixed for another 90 s. Finally, the CHMA-modified asphalt mixture was obtained, which was then transferred to the rotary compactor to prepare the cylindrical specimens with a radius of 15 cm and a height of 12 cm. It was then cut into two specimens with a height of 5 cm for FSCH and RSCH tests, as shown in Figure 3.

3. Methods

3.1. Rheological Property Tests

The frequency/temperature sweep tests were conducted to evaluate the viscoelastic properties of the CHMA-modified asphalt binders before and after the aging process using the dynamic shear rheometer (DSR) in accordance with T0628-2011 in China. For the CHMA-modified asphalt binders before and after RTFOT aged, a 25 mm parallel plate with a gap of 1 mm was used. The temperature sweep tests were performed in the range of 46–70 °C with an interval of 6 °C. The loading frequency was 10 rad/s. For the CHMA-modified asphalt binders after PAV aging, an 8 mm parallel plate with a gap of 2 mm was used. The loading frequency was 10 rad/s. Complex modulus (G*), phase angle (δ), and rutting factor (G*/sinδ) were determined from the testing data.

3.2. Dynamic Modulus Test

Dynamic modulus is an important index of asphalt mixture, which greatly affects the performance of asphalt pavement when subjected to dynamic vehicle loadings during the service period. Generally speaking, the asphalt mixture with a higher dynamic modulus has better rutting resistance, owing to its excellent elastic property. The dynamic modulus test was conducted under various conditions according to T0738-2011 in China. The temperature was set as 0 °C, 15 °C, 30 °C, 45 °C, and 60 °C, respectively. The loading frequency was set as 0.1 Hz, 0.5 Hz, 1 Hz, 5 Hz, 10 Hz, 20 Hz, and 25 Hz, respectively. The cylindrical specimen was loaded with the compressive force on the top surface. Two extensometers were symmetrically installed on the middle of two sides of the cylinder specimen to collect deformation information. The dynamic modulus was calculated according to Formulas (1)–(3).

$$\left|E^{*}\right|=\frac{{\sigma }_0}{{\epsilon }_0}$$

(1)

$${\sigma }_0=\frac{P_i}{A}$$

(2)

$${\epsilon }_0=\frac{{\Delta }_i}{l_0}$$

(3)

where E* represents the dynamic modulus, MPa; ${\sigma }_0$ represents the axis stress amplitude, MPa; ${\epsilon }_0$ represents the axial strain amplitude, mm/mm; P_i represents the average amplitude of compressive force during the last five loading cycles, N; A represents the radial cross-sectional area of the specimen, mm²; ${\Delta }_i$ represents the average amplitude of recoverable axial deformation, mm; l₀ represents the measuring length of the extensometer, mm.

3.3. Wheel Tracking Test

Asphalt concrete (AC) consists of coarse aggregates, fine aggregates, mineral fillers, asphalt binders, and air voids. AC exhibits more viscous-like characteristics under the action of vehicle loadings, especially at high-temperature conditions, which is prone to cause rutting phenomenon. In order to evaluate the high-temperature performance of asphalt mixtures, the wheel tracking test was conducted according to T0719 (JTJE20-2011). The square slab specimens (300 mm × 300 mm× 50 mm) were fabricated and loaded with a special solid rubber tire whose contacting pressure was 0.7 MPa in a constant temperature chamber at 60 °C. The tire ran on the slab for 1 h at the speed of 42 ± 1 cycles/min during the test process. The variation of rutting depth with running time was measured and recorded, and the dynamic stability (DS) could be expressed as Formula (4).

$$DS=\frac{15\times 42}{d_{60}-d_{45}}=\frac{630}{d_{60}-d_{45}}$$

(4)

where d₄₅ and d₆₀ are the rutting depth at 45 min and 60 min, respectively.

3.4. Frequency Sweep Test at a Constant Height

The FSCH test was conducted on the specimen to investigate the influence of vehicle speed on the rutting behavior of asphalt mixtures. The operating details were specified in AASHTO T 320. The strain control mode was adopted, as illustrated in Figure 4. The horizontal strain was selected as a sine wave with an amplitude of 50 μm. The loading frequency was determined as 10 Hz, 5 Hz, 2 Hz, 1 Hz, 0.5 Hz, 0.2 Hz, 0.1 Hz, 0.05 Hz, 0.02 Hz, and 0.01 Hz. The loading cycles varied with the loading frequency, namely 50 loading cycles for 10 Hz and 5 Hz, 20 loading cycles for 2 Hz and 1 Hz, 7 loading cycles for 0.5 Hz, 0.2 Hz and 0.1 Hz, and 4 loading cycles for 0.05 Hz, 0.02 Hz, and 0.01 Hz. Test temperature was set as 60 °C. During the FSCH test, the vertical force was provided to keep the specimen height constant, and the horizontal loads with different frequencies were provided to simulate the effect of different driving speeds on the asphalt pavement. The stress and strain of the specimen were recorded during the test period.

The complex shear modulus G* at different frequencies can be calculated using the stress and strain data, as shown in Formula (5).

$$G^{*}=\frac{{\tau }_0}{{\gamma }_0}$$

(5)

where G* represents the shear modulus; ${\tau }_0$ represents the peak value of dynamic shear stress; ${\gamma }_0$ represents the recoverable deformation.

Shear stress and strain at time t can be calculated according to Formulas (6) and (7).

$${\tau }_t={\tau }_0\sin \left(\omega t\right)$$

(6)

where τ_t represents the shear stress at time t; ω represents the angular velocity; t represents time.

$${\gamma }_t={\gamma }_0\sin \left(\omega t-\phi \right)$$

(7)

where ${\gamma }_t$ represents the shear strain at time t; ${\gamma }_0$ represents the recoverable strain; φ represents phase angle.

The phase angle is used to characterize the viscoelastic properties of materials. It is 0 for pure elastic materials, while it is 90 for pure viscous materials. The complex shear modulus is closely related to the deformation ability of asphalt concrete. Therefore, the phase angle and complex shear modulus were adopted to evaluate the resistance of asphalt concrete to shear deformation.

3.5. Repeated Shear Test at a Constant Height

The RSCH test is a shear dynamic modulus test for measuring the stress–strain relationship of the specimen under shear loadings at a constant shear strain in accordance with AASHTO T 320.

During the test process, the specimen height was kept constant, and a half sine wave of 69 ± 5 kPa was applied to the specimen for 0.1 s and then resting for 0.6 s in each loading cycle, as shown in Figure 5. The test temperature was set as 60 °C. The variation of strain with the number of repeated loadings was recorded, which simulated the response of asphalt pavement to repeated vehicle loadings. The regression equation was obtained as Formula (8) based on the cumulative strain curve. The antishear performance of asphalt mixture at high temperatures could be characterized by the shear slope.

$$\mathit{\epsilon }\left(\mathrm{N}\right)=\mathsf{\epsilon }(\mathrm{N}=1)+\mathrm{S}\times \mathrm{N}$$

(8)

where ε(N) represents the permanent strain after the Nth loading cycle; ε(N = 1) represents the permanent strain after the first loading cycle; S represents the shear slope; N represents the number of loading cycles.

4. Results and Discussions

4.1. Rheological Propery of Asphalt Binders

The rheological property of the asphalt binders was investigated by the frequency sweep test and the temperature sweep test, respectively. The variation of the complex shear modulus G*, phase angle δ, and rutting factor G*/sinδ with the frequency was calculated and presented in Figure 6a–c, respectively. G*/sinδ is used to reflect the ability of the asphalt binder to resist deformation. The higher value of G* indicates smaller deformation and better performance at a high-temperature condition. With the increase of frequency, G* went up quickly, while δ dropped down gradually. It should be noted that the changing rates of the 20# asphalt binder and CHMA-modified asphalt binder was obviously higher than that of SBS-modified asphalt binder. CHMA-modified asphalt binder was close to 20# asphalt binder in G* value, and their rutting factor showed the same tendency, demonstrating its strong ability to resist deformation.

The rutting factors of neat, RTFOT aged, and PAV aged asphalt binders are illustrated in Figure 7. The temperature had a significant effect on the properties of the asphalt binders. With the temperature increasing, the complex modulus declined, and the phase angle increased. Meanwhile, the rutting factor also decreased, indicating that the viscous characteristic of asphalt binders gradually increased, negatively affecting its high-temperature stability. For the RTFOT and PAV aged asphalt binders, the variation of rutting factor with temperature also presented a similar regular pattern. In addition, the value of rutting factor kept growing with the aggravation of aging. This can be explained by the increase of elastic response and the decrease of viscous response due to the hardening of the asphalt binder during the aging process.

4.2. Dynamic Mechanical Performance

4.2.1. Dynamic Modulus

The dynamic modulus and phase angle of the asphalt mixtures at various testing temperatures are shown in Figure 8. The dynamic modulus increased with the raising frequency and decreased with the elevating temperature. That is to say, the lower vehicle speed and higher temperature led to a lower dynamic modulus, which was consistent with the phenomenon that asphalt pavement was prone to suffer rutting distress when subjected to low-speed vehicle loadings, especially at high temperatures. This indicated that the high-modulus asphalt mixtures could effectively alleviate rutting at high temperatures and low vehicle speed conditions. Among the three types of asphalt mixtures, AC-20(20#) had the highest dynamic modulus, and AC-20(CHMA) was slightly lower than AC-20(20#), while AC-20(SBS) presented the worst performance. At 15 °C and 10 Hz conditions (Figure 8b), the dynamic modulus of AC-20(20#), AC-20(CHMA), and AC-20(SBS) were 22,915 Mpa, 19,568 Mpa, and 12,497 Mpa, respectively. The first two types of mixtures exceeded 14,000 Mpa, which met the specification requirement.

The phase angle mainly showed decreasing tendency with the increase of frequency. This could be attributed to the increase in elastic response of the asphalt binder in the high-frequency range. It should be noted that, in Figure 8e, the phase angle of AC-20(SBS) exhibited different characteristics compared with the other two types of asphalt mixtures, which went up gradually with the increase in the frequency. It could be explained by the stress-dependent behaviors of the aggregate skeleton and the viscosity changes. When the temperature reached a certain value, the asphalt binder behaved as a viscous material, which affected the performance of mixtures significantly. Therefore, the phase angle of AC-20(SBS) was the largest and exhibited a fluctuating tendency. The other two types of asphalt mixtures did not show obvious viscous characteristics, implying stronger resistance to rutting at high temperatures.

4.2.2. Dynamic Modulus Master Curve

Due to the limitation of the testing device, time, and other causes, the results of the dynamic modulus could be tested only in a certain condition. In order to predict the dynamic modulus under various temperatures, frequencies, and extreme conditions, it is necessary to establish the dynamic modulus master curve. First, the sigmoidal function was selected as the fitting model to fit the test results at different temperature conditions. Then, for a certain reference temperature, the shift factors at various test temperatures were calculated based on the principle of time–temperature equivalence. Finally, the dynamic modulus curves at different temperatures and loading frequencies were shifted to the reference temperature, and superimposed into a smooth curve, namely the master curve [40].

Figure 9a shows the scatter diagram of dynamic modulus of CHMA-modified asphalt mixture under different frequencies after being shifted from other test temperatures to 30 °C. The sigmoidal function, as shown in Formula (9), was used to fit the data in Figure 9a using the simple surface climbing method. The values of the fitting coefficients were obtained, as shown in

Table 4. Fitting coefficients for dynamic modulus master curve.

Fitting Coefficient		δ	φ	$\mathit{\beta }$	$\mathit{\gamma }$	C1	C2
Estimated value	AC-20(CHMA)	1.772	4.574	−1.051	−0.493	17.9	193.5
	AC-20(SBS)	1.120	3.269	−0.864	−0.532	23.3	248.6
	AC-20(20#)	1.793	4.627	−1.266	−0.395	362.7	3055.6

. The dynamic modulus at different temperatures and the corresponding master curves of the control groups are depicted in Figure 10 and Figure 11. Similarly, their fitting coefficients were also obtained, as shown in Table 4.

$$log\left(E^{*}\right)=\delta +\frac{\phi -\delta }{1+e^{\beta +\gamma ·log{\omega }_r}}$$

(9)

where $E^{*}$ is the dynamic modulus; ${\omega }_r$ is the reduced frequency at corresponding temperatures; $\delta$ is the logarithm of the minimum value of dynamic modulus; φ, β, and γ are the fitting coefficients.

Furthermore, the WLF (Williams–Landel–Ferry) empirical equation, as shown in Formula (10), was used to fit the shift factors at different temperatures. It can be seen from Figure 9b that the correlation coefficient of the WLF fitted curve was above 0.99. It implies that the shift factor could be well fitted by the WLF empirical equation, and it is feasible to analyze the interlayer dynamic modulus using the time–temperature equivalent principle. The values of C₁ and C₂ were obtained in Table 4.

$$\lg {\alpha }_{30}\left(T\right)=\frac{-C_1\left(T-30\right)}{C_2+\left(T-30\right)}$$

(10)

where T is the test temperature; ${\alpha }_{30}\left(T\right)$ is the shift factor of test temperature T relative to the reference temperature (30 °C); C₁ and C₂ are the fitting coefficients.

The dynamic modulus curve at any other temperatures can be obtained by constructing the master curve combined with the shift factor, and the changing trend of dynamic modulus in a wider range of loading frequencies can also be known. This lays the foundation for the mechanical analysis of asphalt pavement with a high modulus.

The logarithmic value of the dynamic modulus approaches the minimum value (δ) at the tail end of the master curve, reflecting the mechanical property of asphalt mixture at high-temperature and low-frequency conditions. It approaches the maximum value (φ) at the head end of the master curve, reflecting the mechanical property of asphalt mixture at low-temperature and high-frequency conditions. Hence, the two ends of the master curve can be used to explain the mechanical properties of asphalt mixture under extreme conditions. From Figure 9, Figure 10 and Figure 11 and Table 4, it can be found that the dynamic modulus gradually increased with increasing frequency. Under the testing conditions, AC-20(20#) exhibited the best mechanical performance regardless of whether it was at the high-temperature, low-frequency condition or the low-temperature, high-frequency condition. AC-20(CHMA) was only slightly weaker than AC-20(20#) in mechanical strength, and obviously superior to AC-20 (SBS), indicating that it had potentially good application in constructing high modulus asphalt pavement.

4.3. Rutting Resistance Performance

Figure 12 illustrates the results of the wheel tracking test. The dynamic stability of AC-20(SBS), AC-20(CHMA), and AC-20(20#) was 6698 times/mm, 8094 times/mm, and 10,624 times/mm, respectively. Although they all met the requirement of JTG F40-2004, which requires more than 3000 times/mm, they showed different resistance abilities to the rutting deformation. Among these mixtures, AC-20(20#) had the best rutting performance, whose dynamic stability was 1.31 times and 1.59 times that of the AC-20(CHMA) and AC-20(SBS), respectively. In addition, the final deformations of three asphalt mixtures were 1.957 mm, 1.425 mm, and 1.082 mm, which were consistent with the results of dynamic stability. This could be ascribed to the viscoelastic characteristic of asphalt binder. Since the higher elastic characteristic of CHMA-modified asphalt binder compared with SBS-modified asphalt binder, CHMA-modified asphalt mixture had better permanent deformation resistance than SBS-modified asphalt mixture. Advantages of CHMA-modified asphalt at high temperatures was due to the compound high-modulus modifier HRMA enriched with natural rock asphalt. Natural rock asphalt has the characteristics of a high softening point and high nitrogen content. Its addition improved the softening point and cohesion of the matrix asphalt. Therefore, the high-temperature performance of the asphalt mixture was improved.

4.4. Shear Resistance Performance

4.4.1. FSCH Test Results

The FSCH test results are presented in Figure 13. In the low-frequency range (0.01–0.1 Hz), there was no obvious difference among these mixtures. With the increase in frequency, the mixtures showed different development trends of complex shear modulus. AC-20(20#) had the highest complex shear modulus and increasing rate, indicating that it was sensitive to the frequency. It should be mentioned that the complex shear modulus usually exhibited a small value in the low-frequency range, which indicated that low velocity affected the pavement performance significantly. According to the investigation in China, 80 km/h is the most probable velocity in the highway, which corresponds to 10 Hz. At the frequency of 10 Hz, the complex shear modulus of AC-20(20#), AC-20(CHMA), and AC-20(SBS) were 241.5 MPa, 185.3 Mpa, and 65.5 MPa, respectively. Thus, AC-20(20#) and AC-20(CHMA) both showed good performance according to the FSCH test results.

Figure 14 presents the variation of phase angle with the frequency in the FSCH test. The phase angle of AC-20(CHMA) was always between the other two mixtures. With the increase of frequency, the phase angle gradually increased until a peak value was reached around 1Hz, and then it experienced a downward trend. In the low-frequency range, the phase angle of AC-20(CHMA) was slightly higher than that of AC-20(20#), while AC-20(SBS) had the highest phase angle. In the high-frequency range, mixtures showed different levels. Among these mixtures, AC-20(20#) had the lowest phase angle, indicating that it was dominated by elastic characteristics.

4.4.2. RSCH Test Results

Asphalt pavement usually suffers rutting distress due to inadequate shear resistance under repeated vehicle loadings, especially at high-temperature condition. The RSCH test was adopted to evaluate the shear resistance ability of asphalt mixture. Test results are presented in Figure 15 and Figure 16. With the number of loading cycles increasing, the shear strain experienced a rapid increase in the primary stage, and then its growth rate slowed down gradually, finally reaching a constant growth rate. The final strain of AC-20(SBS) was the highest, followed by AC-20(CHMA) and AC-20(20#). It means that the high-modulus asphalt mixtures had a distinct advantage. The strain variation trend of AC-20(CHMA) was similar to that of AC-20(20#), and its growth rate was a little higher than AC-20(20#). Hence, AC-20(CHMA) was recognized to be excellent in resisting shear deformation. Based on the shear strain curve, the shear slopes of AC-20(SBS), AC-20(CHMA), and AC-20(20#) were calculated as 2.26 × 10⁻⁴, 1.45 × 10⁻⁴, and 6.89 × 10⁻⁵, respectively. The smaller the shear slope is, the better the shear resistance ability is. AC-20(20#) had the smallest shear slope, while AC-20(SBS) had the largest shear slope. Although the shear slope of AC-20(CHMA) was higher than AC-20(20#), it was obviously lower than AC-20(SBS), demonstrating that the CHMA-modified asphalt binder contributed a lot to the antirutting performance of asphalt mixture.

AC-20(CHMA) has excellent high-temperature shear resistance, which is due to the modification of matrix asphalt by compound high-modulus modifier HRMA. The modifier contains a certain proportion of natural rock asphalt. Natural rock asphalt is a kind of natural solid asphalt with relatively large molecular weight. Its molecular weight is about three times that of ordinary asphalt, and the content of carbon, hydrogen, sulfur, oxygen, and nitrogen is relatively high. Almost every asphalt macromolecule contains the above impurities. The polar functional groups of each element make it have strong adsorption capacity on the rock surface. In other words, the addition of HRMA modifier improves the cohesion and shear deformation resistance of asphalt mortar.

5. Conclusions

In this paper, a new high-modulus asphalt mixture, namely the CHMA-modified asphalt mixture, was prepared and investigated, aiming to improve the antirutting performance of asphalt pavement. The dynamic characteristics of CHMA-modified asphalt binder and mixture were investigated by the frequency/temperature sweep test, dynamic modulus test, wheel tracking test, FSCH test, and RSCH test to analyze its deformation-resisting ability. The main conclusions were obtained as follows:

(1)

The rheological property of the CHMA-modified asphalt binder was similar to that of low-graded asphalt binder, demonstrating that it has a strong ability to resist deformation.

(2)

The dynamic modulus of AC-20(CHMA) was 19,568 MPa at 15 °C and 10 Hz conditions, higher than 14,000 MPa, meeting the requirement for the high-modulus asphalt mixture. It had potentially good application in alleviating the rutting problems.

(3)

The dynamic stability of AC-20(CHMA) was 8094 times/mm, lower than that of AC-20(20#), but obviously higher than that of AC-20(SBS). Meanwhile, it was much higher than the specification requirement in China.

(4)

The asphalt mixture had a low complex shear modulus in the low-frequency range, implying that low velocity affected the pavement performance significantly. AC-20(20#) and AC-20(CHMA) both showed strong shear resistance according to the FSCH test results.

(5)

Under the repeated shear loadings, the growth rate of shear strain increased rapidly in the primary stage, and then slowed down gradually, finally reaching a constant growth rate. The shear slope of AC-20(CHMA) was higher than AC-20(20#), and obviously lower than AC-20(SBS).