Fatigue-Healing Performance Analysis of Warm-Mix Rubber Asphalt Mastic Using the Simplified Viscoelastic Continuum Damage Theory

Abstract

As a green and low-carbon road material, warm-mix rubber asphalt (WMRA) has received extensive attention from scholars for its road performance. In the in-depth study of its properties, the fatigue characteristics of WMRA are particularly critical. However, in current studies on asphalt fatigue performance, its self-healing ability is often underestimated or neglected. Furthermore, the simplified viscoelastic continuum damage theory (S-VECD), with its accuracy, speed, and convenience, provides a powerful tool for analyzing asphalt fatigue performance. Therefore, to analyze the fatigue and self-healing performances of WMRA in practical applications, four sample materials were selected in this study: virgin asphalt mastic (VAM), rubber asphalt mastic (RAM), Sasobit rubber asphalt mastic (SRAM), and Evotherm rubber asphalt mastic (ERAM). Subsequently, the samples were subjected to a comprehensive experimental design with frequency sweep tests, linear amplitude sweep tests, and multiple intermittent loading time sweep tests under different aging conditions. The fatigue and self-healing performances of different aging degrees and different types of WMRA were evaluated based on the S-VECD theory. The results show that aging reduces the fatigue and self-healing performances of asphalt mastic to a certain extent, and at a 7% strain, the fatigue life of SRAM after long-term aging is only 30.7% of the life of the unaged sample. The greater the aging degree, the more pronounced the effect. Under different aging levels, the warm-mix agent can significantly improve the fatigue and self-healing performances of rubber asphalt mastic. After undergoing ten fatigue intermittent loading tests, the recovery rate of the complex shear modulus for the long-term aged VAM was 0.65, which is lower than that of SRAM under the same conditions, and the warm mix can further extend the fatigue life of rubber asphalt by improving the self-healing properties of the asphalt. The role of Sasobit in enhancing the fatigue and self-healing performances of rubber asphalt mastic is more significant. This study can provide a theoretical basis for the promotion and application of WMRA pavements and contribute to the sustainable development of road construction.

1. Introduction

As the global economy grows and people’s consumption levels rise, the automotive industry and global tire production proliferate. Relevant studies show that about 4 billion tires are discarded globally every year [1]. Traditional waste rubber disposal methods, such as landfills and incineration, cause environmental pollution and damage human health [2,3]. Grinding waste tires into rubber powder and adding them to asphalt to make rubber asphalt pavement solves the above problems and significantly improves pavement performance [4,5]. Therefore, the technical means of rubber asphalt is increasing in attention and is gradually being used in road engineering. However, the production and construction of rubber asphalt produces a lot of harmful gases due to the high temperature, which limits its popularity and application.

At present, warm-mix technology mainly includes foaming warm-mix technology, emulsified asphalt warm-mix technology, and organic viscosity reduction warm-mix technology [6,7,8,9]; among them, the organic viscosity-reducing warm mix, represented by the Sasobit warm mix and the emulsified asphalt warm mix represented by Evotherm warm mix are widely used. Suppose waste tire rubber powder is added to asphalt using warm-mix technology. In that case, it not only reduces greenhouse gas emissions during the production and construction process but also reduces energy loss [10,11,12]. Not only that, but with further research scholars have found that the use of warm-mix technology can improve the performance of rubber asphalt. Guo et al. [10] found that warm-mix additives improved the low-temperature crack resistance of asphalt mixtures through freeze–thaw cycle tests. Shi et al. [13] used dynamic mechanical analysis (DMA) and found that an organic viscosity-reducing temperature mix improves the high-temperature performance of warm-mix rubber asphalt. Bilema et al. [14] found that Sasobit improves the stiffness and workability of rubber asphalt by comparing the effects of three warm mixes on the physical properties of rubber asphalt.

In addition to conventional performance studies, the fatigue performance of asphalt materials has emerged as a research priority and is aimed at enhancing the service life and road performance of asphalt pavements [15,16]. Under the long-term influence of vehicle loads, fatigue cracks develop in asphalt pavements, which seriously impacts their service life. Therefore, in recent years, scholars have successively carried out related research on the fatigue performance of warm-mix rubber asphalt and its mixtures. Wang et al. [17] found that the addition of a warm mix can effectively improve the long-term fatigue performance of rubber asphalt by testing the fatigue performance of warm-mix rubber asphalt after long-term aging. Xiao et al. [18] evaluated the effects of warm-mix asphalt additives on the fatigue characteristics of the rubber asphalt mixture from the perspectives of low temperature, aging, and fatigue. They found that warm-mix agents can effectively extend the fatigue life of rubber asphalt mixture. Kumar et al. [19] compared the fatigue performance of different types of warm-mix rubber asphalt and its mixtures through various fatigue testing methods and found that the chemical warm-mix asphalt (WMA) additive improved the fatigue resistance of rubber asphalt more than the organic WMA additive. Wang et al. [20] revealed the fatigue performance enhancement mechanism of warm asphalt rubber by removing crumb rubber modifier (CRM) particles through filtration, obtaining the liquid phases of asphalt rubber (AR) and four WAR binders, and performing fatigue tests and gel permeation chromatography (GPC) tests on them.

Based on the above literature analysis, current research on the fatigue performance of WMRA pavements by scholars mainly focuses on two directions: Firstly, the use of macroscale testing to analyze the influence of the type and dosage of warm-mix additives on the fatigue performance of WMRA and its mixtures, and secondly, the employment of microscale testing to explore the mechanisms by which warm-mix additives enhance the fatigue performance of modified asphalt. However, there has been relatively little research on the impact of asphalt material’s self-healing properties on the fatigue damage process. The asphalt material has a certain self-healing function (i.e., self-healing performance). Under certain conditions, the generated microcracks can be gradually recovered [21,22]. As the microcrack surface undergoes reconstruction, contact, and wetting, the stiffness of the asphalt begins to recover and the cracks gradually close. After the cracks close, the asphalt molecules begin to diffuse into each other, and eventually, the stiffness and strength of the asphalt become comparable to their original state [23,24,25]. This lack of research contributes to the specific differences between fatigue life measured in the laboratory and fatigue life observed under actual pavement conditions. Moreover, asphalt mastic is the basis for forming asphalt mixtures, a key factor affecting the road performance of asphalt mixtures [26,27,28]. In addition, the aging effect on the performance of asphalt pavement is unavoidable in practical applications. Therefore, to more accurately assess the service life of warm-mix rubber asphalt materials, it is necessary to carry out a systematic study on the fatigue performance and self-healing performance of asphalt mastic under different aging effects.

In summary, the aim of this paper is to analyze and compare the fatigue and self-healing properties of virgin asphalt mastic (VAM), rubber asphalt mastic (RAM), Sasobit rubber asphalt mastic (SRAM), and Evotherm rubber asphalt mastic (ERAM) under different degrees of aging, in order to assess the fatigue durability and self-healing capacity of warm-mixed rubber asphalt pavements in practical applications. To achieve this objective, four materials were aged in this study through short-term and long-term aging tests simulating everyday aging environments. The frequency scanning test, linear amplitude test, and multiple intermittent loading time scanning test were further carried out by a dynamic shear rheometer, and theoretical analyses were carried out by using the simplified viscoelastic continuum damage theory to provide theoretical basis and technical support for the application of warm-mix rubber asphalt pavements.

2. Materials and Methods

2.1. Materials

In this paper, 70# petroleum asphalt was selected, and the property indicators are shown in

Table 1. Technical indicators of asphalt.

Technical Indicator	Test Value	Technical Requirement	Unit
Penetration (25 °C, 100 g, 5 s)	70.9	60–80	0.1 mm
Softening point	54.6	≥46	°C
Ductility (15 °C, 5 cm/min)	>100	≥100	cm

.

In this paper, a 60-mesh fine rubber powder type of rubber powder was selected, as shown in Figure 1. The dosage was 20% of the weight of asphalt. Its main technical parameters are shown in

Table 2. Main technical parameters of rubber.

Technical Indicators	Test Value	Unit
Particle size	60	mesh
Moisture content	0.69	%
Relative density	1.35	-

.

In this paper, two warm mixes were selected: one is organic viscosity-reducing warm-mix Sasobit, as shown in Figure 2a, developed by Sasol, Johannesburg, South Africa, with a dosage of 3% of the weight of asphalt. The other is Evotherm, an emulsified asphalt warm mix developed by MeadWestvaco, Richmond, Virginia, USA, as shown in Figure 2b. In this paper, the third generation of Evotherm is used, and the dosage is 0.6% of the weight of asphalt. Due to the different modification mechanisms, the dosage of Sasobit and Evotherm is different. The dosage in this paper is the optimum dosage based on relevant studies and manufacturer recommendations [29,30,31]. The main basic properties of the two warm mixes are shown in

Table 3. The main basic properties of Sasobit warm mixes.

Technical Indicators	Test Value	Unit
Melting point	101	°C
Density (25 °C)	0.94	g/cm3
Flash point	293	°C
Brinell rotational viscosity (135 °C)	5.46 × 10−3	Pa·s

and

Table 4. The main basic properties of Evotherm warm mixes.

Technical Indicators	Test Value	Unit
Density (25 °C)	8.07	lbs/gal
Proportion (25 °C)	0.968	-
Viscosity (20 °C)	660–1225	mPa·s

.

The filler of the mastic is limestone mineral powder, as shown in Figure 3, with a density of 2.7429/cm³, hydrophilic coefficient of 0.83, particle size of 0.075 mm through the rate of 100%, and no agglomeration phenomenon.

The flow diagram of the research in this paper is shown in Figure 4.

2.2. Sample Preparation

2.2.1. Modified Asphalt

Firstly, the asphalt was heated to flow dynamically at 150 °C, and the corresponding mass of rubber powder was added to it at 170 °C. Then, it was sheared with a high-speed shear at 4500 rad/min for 60 min to produce rubber asphalt. After that, we maintained 160 °C, added the corresponding mass of warm mix to the already prepared rubber asphalt, and continued to shear at 4500 rad/min for 10 min to obtain warm-mix rubber asphalt.

2.2.2. Asphalt Mastic

We weighed the limestone mineral powder according to the powder rubber ratio of 1:1 and placed the weighed mineral powder and asphalt into the oven, heated at 150 °C for 2 h. Then, we added the mineral powder to the asphalt in batches, maintained the temperature at 150 °C, and sheared it with a high-speed shearer at a rotational speed of 3000 rad/min for 35 min to make asphalt mastic.

2.3. Methods

2.3.1. Aging Test

(1) The rolling thin film oven test (RTFOT) in JTG E20-2011 [32] was used to simulate the short-term aging of asphalt during transport, storage, and paving.

(2) To simulate the long-term aging of asphalt pavements during long-term use, the pressurized aging vessel (PAV) test from JTG E20-2011 [32] was used in this study for the asphalt after short-term aging.

The short-term aging (RTFOT) and long-term aging (PAV) test specimens are shown in Figure 5 and Figure 6. The summary of asphalt mastic samples is shown in

Table 5. The summary of asphalt mastic samples.

Type of Asphalt Mastic	Aging Status
VAM	Unaged
	RTFOT
	PAV
RAM	Unaged
	RTFOT
	PAV
SRAM	Unaged
	RTFOT
	PAV
ERAM	Unaged
	RTFOT
	PAV

.

2.3.2. Frequency Sweep Test

When using the S-VECD model to characterize the fatigue properties of asphalt, it is necessary to comprehensively consider three main elements: the linear viscoelastic response, damage characteristic curve (DCC), and fatigue failure criterion (${\mathrm{G}}^{\mathrm{R}}$) [33,34].

The dynamic shear rheometer used in this study is shown in Figure 7.

Specimens were made using molds of 8 mm diameter and 2 mm height. The standard molds and asphalt mastic specimens are shown in Figure 8. To ensure the accuracy of the test data, three parallel tests were carried out for each asphalt mastic specimen, and the average of the data was taken for analysis.

In this study, according to a standard testing procedure (AASHTO T 315-19 [35]), the frequency sweep test (FS) was used to obtain the parameters of the materials’ linear viscoelastic properties [36]. The test temperatures were 15 °C, 25 °C, and 35 °C, and the sweep frequencies ranged from 0.1 to 100 rad/s. The test was conducted in the strain control mode with a strain level of 0.1%. The master curve was obtained by translating the frequency (time) at different test times through the principle of time-temperature equivalence.

The reduced angular frequency coordinates are used in the master curve, Equation (1):

$$\log {\mathsf{\omega }}_{\mathrm{r}}=\log \mathsf{\omega }+\log {\mathsf{\phi }}_{\mathrm{T}}$$

(1)

where $\mathsf{\omega }$ is the angular frequency (rad/s), ${\mathsf{\omega }}_{\mathrm{r}}$ is the reduced angular frequency (rad/s), and ${\mathsf{\phi }}_{\mathrm{T}}$ is the shift factor.

2.3.3. Linear Amplitude Sweep Test

According to the standard testing procedure (AASHTO TP 101-14 [37]), the linear amplitude sweep (LAS) test was conducted using a dynamic shear rheometer [38,39]. A strain loading mode was applied at a test temperature of 25 °C, a loading frequency of 10 Hz, and a standard loading time of 5 min (300 s). During the test, the amplitude of the sinusoidal load applied to the asphalt material increased linearly from 0.1% to 30%.

Based on the simplified viscoelastic continuum damage (S-VECD) theory, the relationship between the damage modulus S of asphalt material and the corresponding virtual modulus C is established, as shown in Equation (2):

$$\mathrm{C}\left(\mathrm{S}\right)={\displaystyle \frac{{\mathsf{\tau }}_{\mathrm{P}}}{{\mathsf{\gamma }}_{\mathrm{P}}^{\mathrm{R}}\cdot \mathrm{D}\mathrm{M}\mathrm{R}}}$$

(2)

where ${\mathsf{\tau }}_{\mathrm{P}}$ is the peak shear stress, ${\mathsf{\gamma }}_{\mathrm{P}}^{\mathrm{R}}$ is the peak virtual strain, and DMR is the ratio of the initial dynamic shear modulus to the linear viscoelastic dynamic shear modulus of the asphalt material.

The damage intensity (S) changes with time (t), and the relationship is shown in Equation (3):

$$\mathrm{S}\left(\mathrm{t}\right)={\sum }_{\mathrm{i}=1}^{\mathrm{N}}{\left[{\displaystyle \frac{\mathrm{D}\mathrm{M}\mathrm{R}}{2}}{\left({\mathsf{\gamma }}_{\mathrm{P}}^{\mathrm{R}}\right)}^2\left({\mathrm{C}}_{\mathrm{i}-1}-{\mathrm{C}}_{\mathrm{i}}\right)\right]}^{{\displaystyle \frac{\mathsf{\alpha }}{1+\mathsf{\alpha }}}}{({\mathrm{t}}_{\mathrm{R}\mathrm{i}}-{\mathrm{t}}_{\mathrm{R}\mathrm{i}-1})}^{{\displaystyle \frac{1}{1+\mathsf{\alpha }}}}$$

(3)

$${\mathrm{t}}_{\mathrm{R}\mathrm{i}}={\displaystyle \frac{{\mathrm{t}}_{\mathrm{i}}}{{\mathsf{\phi }}_{\mathrm{T}}}}$$

(4)

$${\gamma }_P^R={\displaystyle \frac{1}{G_R}}\cdot \left({\left|G^{\mathrm{*}}\right|}_{LVE}\cdot {\gamma }_P\right)$$

(5)

where ${\gamma }^R$ is the virtual strain; $G_R$ is the reference modulus of the material, which is taken as 1 MPa in this study; ${\left|G^{\mathrm{*}}\right|}_{LVE}$ is the linear viscoelastic dynamic shear modulus of the asphalt material; ${\mathsf{\phi }}_{\mathrm{T}}$ is the temperature shift factor of asphalt material; α is the damage evolution rate of the asphalt material, α = 1 + 1/m; m is the slope of the master curve of the dynamic shear modulus in the linear viscoelastic range of the asphalt material; i is the loading cycle; and ${\mathrm{t}}_{\mathrm{R}}$ is the curtailment time.

Fitting the imaginary modulus (C) and the damage variable (S) obtained based on the S-VECD theory, the Damage Characteristic Curve (DCC) of the asphalt material can be obtained as shown in Equation (6):

$$\mathrm{C}\left(\mathrm{t}\right)=1-{\mathrm{K}}_1\cdot \mathrm{S}{\left(\mathrm{t}\right)}^{{\mathrm{K}}_2}$$

(6)

where ${\mathrm{K}}_1$ and ${\mathrm{K}}_2$ are the best fitting parameters for the DCC curve of asphalt materials.

Based on the theory of virtual strain energy and the processing of the data obtained from the LAS test, the amount of virtual strain energy stored in the asphalt specimen by the applied load can be calculated by Equation (7):

$${\mathrm{W}}_{\mathrm{S}}^{\mathrm{R}}={\displaystyle \frac{1}{2}}{\mathsf{\tau }}_{\mathrm{P}}{\mathsf{\gamma }}_{\mathrm{P}}^{\mathrm{R}}∕\mathrm{D}\mathrm{M}\mathrm{R}={\displaystyle \frac{1}{2}}\cdot \mathrm{C}\cdot {\left({\mathsf{\gamma }}_{\mathrm{P}}^{\mathrm{R}}\right)}^2$$

(7)

where ${\mathrm{W}}_{\mathrm{S}}^{\mathrm{R}}$ is the stored virtual strain energy.

As the load level gradually increases, the released virtual strain energy gradually increases, and the stored virtual strain energy first increases and then decreases. A gradual increase in the released virtual strain energy indicates that the asphalt material is gradually being destroyed. When the stored virtual strain energy reaches the peak value, the maximum value of the asphalt material can store the applied load. Therefore, the peak value of stored virtual strain energy is chosen as the fatigue failure point in the LAS test.

In this paper, ${\mathrm{G}}^{\mathrm{R}}$ (the average release rate of the virtual strain energy) is chosen as the fatigue failure criterion to predict the fatigue life of asphalt materials under different strains [40]. Non-standard linear amplitude tests with sweep times of 500 s and 800 s were added as a way to change the sweep time to adjust the constant strain rate for calculation.

The average released virtual strain energy for each loading cycle from the start of the test until the asphalt material reaches the point of fatigue failure is calculated and noted as $\overline{{\mathrm{W}}_{\mathrm{R}}^{\mathrm{R}}}$. Therefore, ${\mathrm{G}}^{\mathrm{R}}$ can be calculated using Equation (8):

$${\mathrm{G}}^{\mathrm{R}}={\displaystyle \frac{\overline{{\mathrm{W}}_{\mathrm{R}}^{\mathrm{R}}}}{{\mathrm{N}}_{\mathrm{f}}}}={\displaystyle \frac{\mathrm{A}}{{\left({\mathrm{N}}_{\mathrm{f}}\right)}^2}}$$

(8)

where A is the area of integration of the curve corresponding to the released virtual strain energy when the asphalt material reaches the peak value of stored virtual strain energy and ${\mathrm{N}}_{\mathrm{f}}$ is the number of cyclic loading cycles of asphalt material.

Fitting ${\mathrm{G}}^{\mathrm{R}}$ to the fatigue life (${\mathrm{N}}_{\mathrm{f}}$), as shown in Equation (9):

$${\mathrm{G}}^{\mathrm{R}}=\mathrm{a}{\left({\mathrm{N}}_{\mathrm{f}}\right)}^{\mathrm{b}}$$

(9)

where a and b are the best fit parameters.

By combining the above relationship between ${\mathrm{G}}^{\mathrm{R}}$ and ${\mathrm{N}}_{\mathrm{f}}$ with the S-VECD theory and the virtual strain energy theory, the relationship between fatigue life ${\mathrm{N}}_{\mathrm{f}}$ and the strain amplitude ${\gamma }_P$ in the test can be obtained, which finally constitutes the fatigue failure criterion based on ${\mathrm{G}}^{\mathrm{R}}$, as shown in Equation (10), and thus, the fatigue life of the asphalt material can be calculated under different strains.

$$N_f={\left[{\displaystyle \frac{X}{\mathrm{a}}}\cdot {\left({\gamma }_P\right)}^{2+2\alpha \left({\displaystyle \frac{K_2}{Q}}\right)}\right]}^{{\displaystyle \frac{1}{b+1-\frac{K_2}{Q}}}}$$

(10)

where the parameters X and Q are calculated by Equations (11)–(13).

$$X={\displaystyle \frac{1}{2}}\cdot K_1\cdot {\left({\left|G^{\mathrm{*}}\right|}_{LVE}\right)}^2\cdot Y^{\left(-K_2∕Q\right)}\cdot {\displaystyle \frac{1}{\left(K_2∕Q\right)+1}}$$

(11)

$$Q=1-\alpha \cdot K_2+\alpha$$

(12)

$$Y={\displaystyle \frac{f\cdot 2^{\alpha }}{Q{\left(K_1{K}_2\right)}^{\alpha }{\left({\left|G^{\mathrm{*}}\right|}_{LVE}\right)}^{2\alpha }}}$$

(13)

2.3.4. Time Sweep Test

This study used time sweep (TS) to conduct the self-healing research on asphalt mastic [41]. Furthermore, to more realistically simulate actual asphalt pavement loading conditions, this paper selected multiple fatigue intermittent loading modes. Ten fatigue intermittent loading tests were conducted under strain-controlled conditions, with a strain level of 1.25%, a loading frequency of 10 Hz, and a temperature of 25 °C. The loading was halted when the complex shear modulus decreased to 55% of its initial value, followed by an intermittent period of 30 min, after which the test was resumed.

As shown in Figure 9, ${\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ is the number of self-healing loading cycles increased from the previous one after the i-th interval.

$\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ is the cumulative increase in the number of self-healing loading cycles after the i-th interval, as shown in Equation (14):

$$\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)={\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$$

(14)

As the number of intervals increases, the complex shear modulus also changes. The change in the dynamic shear modulus of the asphalt material with the increase in the number of intervals can be quantified by the following Equation (15):

$$\mathrm{R}\mathrm{C}\mathrm{M}={\displaystyle \frac{{\mathrm{G}}_{\mathrm{i}}^{\mathrm{*}}}{{\mathrm{G}}_0^{\mathrm{*}}}}$$

(15)

where RCM is the recovery rate of the complex shear modulus, ${\mathrm{G}}_{\mathrm{i}}^{\mathrm{*}}$ is the complex shear modulus after the i-th healing process, and ${\mathrm{G}}_0^{\mathrm{*}}$ is the initial complex shear modulus.

3. Results and Analysis

3.1. Results and Analysis of Fatigue Performance Tests

The Ishikawa cause-and-effect diagram is the evaluation of the fatigue performance of asphalt mastic based on the S-VECD theory and is shown in Figure 10.

3.1.1. Dynamic Modulus Master Curve

The viscoelastic performance of asphalt is closely related to its fatigue performance, and high-quality viscoelastic performance helps to reduce the amount of deformation of asphalt during repeated loading, which effectively reduces fatigue damage, thus enhancing its durability and service life [42].

Figure 11 shows the dynamic modulus master curves of the four asphalt mastics at different degrees of aging. As can be seen from Figure 11, the SRAM and ERAM show high dynamic shear moduli in the whole frequency range, both in the unaged, short-term aging, and long-term aging states. Moreover, the complex shear moduli of all four asphalt mastics increased to a certain extent after both the short-term and long-term aging effects.

By further comparison, SRAM has the highest complex shear modulus in the case of unaged and short-term aging. This is consistent with previous findings [29]. This may be due to the fact that Sasobit is capable of forming a network-like crystalline structure within asphalt, which enhances the asphalt’s shear resistance and, as a result, elevates its complex shear modulus [29]. In contrast, ERAM has the highest complex modulus in the case of long-term aging. In actual pavement applications, asphalt will inevitably be subjected to a variety of aging effects. Therefore, when using rubber asphalt pavement, incorporating Sasobit and Evotherm warm-mix additives can enhance the complex shear modulus of the asphalt, thereby improving resistance to deformation of the asphalt pavement during its actual use.

3.1.2. Stress–Strain Curves

Figure 12 presents the stress–strain curves of the four asphalt mastics under different aging degrees, with the endpoints corresponding to the shear stress and strain at the fatigue failure point. It can be seen from Figure 12 that all four asphalt mastics have peak stresses under different aging conditions, but the locations and widths have changed. The wider peak stress of asphalt mastic represents the larger shear strain it can withstand. The changes in the locations and widths of the peak stresses are due to the differences in the warm mixes and the degree of aging. Under different aging conditions, SRAM has the highest peak stress, and ERAM has the second-highest peak stress, indicating that the addition of a warm mix enhances the fatigue damage resistance of RAM to a certain extent. Comparing the stress–strain curves under different aging conditions, it was found that the Sasobit warm mix had a more noticeable effect on the fatigue resistance of rubber asphalt mastic.

Further comparison shows that the peak stresses of the same asphalt mastic have increased with the aging degree. This is because aging causes the light components of the asphalt to volatilize and the internal components to oxidize with oxygen, making the asphalt mastic harder. The deeper the aging, the more pronounced the effect.

3.1.3. Damage Characterization Curves

The damage characteristic curve (DCC), i.e., the relationship between the virtual modulus C and the damage variable S, was fitted for the four asphalt mastics at different aging levels, as shown in Figure 13, where the endpoints of the curves correspond to the fatigue failure point of each asphalt mastic. As shown in Figure 13, all the DCC curves have the same trend of a decreasing virtual modulus C from 1 and increasing S from 0. This indicates that fatigue damage is produced in the asphalt mastic as the LAS test proceeds, demonstrating the damage evolution process of asphalt materials.

By comparison, the S values of SRAM and ERAM are greater than those of RAM when the asphalt mastic reaches the fatigue damage failure point, regardless of the aging action. This indicates that under the same load, the warm-mix rubber asphalt mastic can withstand greater damage, reaching fatigue damage when the time required is longer. Therefore, in practice, Sasobit and Evotherm can be added to improve the fatigue resistance of rubber asphalt pavements.

3.1.4. Fatigue Life Analysis

Typically, each asphalt material possesses a different DCC curve, and the cumulative fatigue damage and virtual modulus analysis can only provide a qualitative understanding of the fatigue behavior of asphalt materials. To quantitatively evaluate the fatigue performance of different asphalt mastics, this paper employs Equations (9)–(13) to calculate the fatigue life of various asphalt mastics under various aging conditions and at different strain levels (4%, 7%, and 10%). The fatigue life of asphalt mastic at 7% strain is shown in Figure 14. Subsequently, a linear fitting of the strain and N_f (fatigue life) is performed using a double logarithmic coordinate system, as depicted in Figure 15, which offers a more intuitive comparison of the fatigue life performance of asphalt mastic under different strain conditions [43].

From Figure 15, it can be seen that the fatigue life of the four asphalt pastes shows a decreasing trend with an increase in the strain amplitude. In addition, regardless of the aging state and strain amplitude, the fatigue life curves of the asphalt mastics with the addition of warm-mix agents Sasobit and Evotherm are above those of RAM and VAM. This is consistent with previous findings [44]. For example, after long-term aging at 7% strain, the fatigue life of SRAM is 9.9 times the fatigue life of VAM, 2.4 times the fatigue life of RAM, and the fatigue life of ERAM is 8.7 times the fatigue life of VAM and 1.7 times the fatigue life of RAM. This shows that a warm-mix agent can significantly improve the fatigue life of asphalt mastic, and the improvement effect of Sasobit is more obvious. This is because Sasobit forms a network of crystalline structures in the asphalt. These structures make the asphalt more rigid at low and medium temperatures, which improves the deformation resistance of the asphalt [29]. On the other hand, Evotherm is able to increase the adhesion between asphalt and mineral powder, which makes the bonding interface between the two less prone to damage, thus reducing the generation and extension of fatigue cracks [45].

Comparing the fatigue life of the same asphalt mastic, it can be found that aging will reduce the fatigue life of asphalt mastic to a certain extent, and the deeper the aging level, the greater the reduction. For example, at 7% strain, the fatigue life of SRAM after long-term aging is only 30.7% of the fatigue life in the unaged state and 49.4% of the fatigue life in the short-term aging state. This shows that aging has a certain adverse effect on the fatigue performance of asphalt mastic.

3.2. Results and Analysis of Self-Healing Performance Tests

3.2.1. Cumulative Increase in the Number of Self-Healing Loading Cycles

Based on the experimental results of the multiple intermittent test method, the values of $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ for the four asphalt mastics at different levels of aging were obtained, as shown in Figure 16. By analyzing Figure 16, the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of each asphalt mastic increases gradually with the increase in loading and the number of intervals, but its growth rate slows down gradually. This indicates that although the intervals are the same, multiple loadings gradually decrease the recovery of the asphalt mastic. The self-healing capacity of the asphalt mastic decreases continuously and tends to zero.

By further comparing the changes in $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of the four asphalt mastics under the effects of unaged, short-term aging, and long-term aging, it can be found that aging decreases the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of each asphalt mastic. For example, after ten fatigue intermittent loads in the long-term aging state, the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of the SRAM is only 53.2% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ in the unaged state and 58.8% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ in the short-term aging state. This indicates that aging decreases the self-healing ability of asphalt mastic, and the deeper the aging, the greater the decrease.

However, the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of SRAM and ERAM are higher than those of VAM and RAM, regardless of the aging condition. For example, after ten fatigue intermittent loads in a long-term aging condition, the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of VAM is only 43.2% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of SRAM and, 48.2% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of ERAM, and the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of RAM is only 76.1% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of SRAM and 84.8% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of ERAM. This indicates that the warm mix can significantly enhance the self-healing ability of rubber asphalt mastic.

3.2.2. The Recovery Rate of Complex Shear Modulus

The complex shear modulus of asphalt mastic can be recovered to a certain extent after fatigue loading and the introduction of intervals. Therefore, the self-healing ability of the four asphalt mastics can be observed by the recovery rate of the complex shear modulus (RCM) under different aging degrees and multiple loading intervals. As depicted in Figure 17, the RCM values of the four asphalt mastics under the three aging conditions exhibit a decreasing trend, signifying the gradual weakening of their self-healing ability.

A further comparison can show that the RCM values of SRAM and ERAM were higher than those of VAM and RAM under different aging conditions. For example, the values of RCM for long-term aging VAM and RAM after ten fatigue intermittent loading tests are 0.65 and 0.70, respectively, which are lower than the values of RCM for SRAM and ERAM in the same state. This shows that the warm mix can significantly improve the self-healing performance of RAM, among which the improvement effect of the Sasobit warm mix is more satisfactory. The enhancement mechanisms of Sasobit and Evotherm on the self-healing performance of asphalt have not been clarified, probably because the long-chain aliphatic alkane structure of Sasobit forms reticulated crystals in asphalt, which slows down crack expansion and promotes self-healing. Evotherm reduces the viscosity of asphalt and improves the low-temperature fluidity, which is conducive to the filling and healing of microcracks. These hypotheses require further investigation, research, and validation.

3.3. Fatigue Life Analysis Considering the Effect of Self-Healing

From the above self-healing tests, it is evident that the introduction of the intervals increases the loading cycles of the asphalt mastic, which affects its fatigue life to a certain extent. Therefore, to more accurately predict the fatigue life of warm-mix rubber asphalt mastic, the fatigue life conversion factor μ was used in this study to calculate the fatigue life after self-healing [46]. μ is calculated as shown in (16):

$$\mu ={\displaystyle \frac{{\mathrm{N}}_0+{\mathrm{N}}_{\mathrm{H}}\left(1\right)}{{\mathrm{N}}_0}}$$

(16)

where ${\mathrm{N}}_0$ is the number of initial loading cycles, and ${\mathrm{N}}_{\mathrm{H}}\left(1\right)$ is the number of self-healing loading cycles increased from the previous one after the first interval. The μ values of various asphalt mastics are shown in

Table 6. Fatigue life conversion factor before and after asphalt healing μ.

Type of Asphalt	Unaged	RTFOT	PAV
VAM	1.500896	1.469959	1.370156
RAM	1.527895	1.500586	1.449185
ERAM	1.529193	1.515128	1.474655
SRAM	1.535672	1.529622	1.491847

.

Therefore, the predicted fatigue life equation considering asphalt healing is given as:

$$N_f\left(\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t}\right)=\mu \times N_f^{\prime }(\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{u}\mathrm{t} \mathrm{r}\mathrm{e}\mathrm{s}\mathrm{t})$$

(17)

According to the study, the strain of asphalt was estimated to be 50 times the strain in the bulk mixture, with the strain in strong pavements greater than 4 inches thick estimated to be 500 µm, which implies a strain of 2.5% in asphalt, and the strain in weak pavements less than 4 inches thick is estimated to be 1000 µm, resulting in a strain of 5% in the asphalt [47,48,49]. Therefore, the fatigue life of asphalt mastics at a 5% strain was used as an example [42,43]. After calculation, the fatigue life of the four asphalt mastics under 5% strain, considering the effect of self-healing and the fatigue life without self-healing, were obtained after undergoing different aging effects, as shown in Figure 18.

From Figure 18, including the interstitial period can effectively prolong the fatigue life of asphalt mastic, thus indicating that its self-healing behavior significantly affects its fatigue life. In addition, the fatigue life growth rate of asphalt mastic decreases after short-term and long-term aging, with the largest decrease after long-term aging, which is attributed to an increase in the asphalt’s hard components during long-term aging, which inhibits the healing of asphalt microcracks and leads to the deterioration of its ability to withstand the secondary loading. The fatigue life of asphalt mastic was significantly improved by both warm mixes in the unaged condition and the two aging conditions, with Sasobit providing the greatest improvement, which suggests that the Sasobit warm mix can not only positively affect the fatigue performance of asphalt but also further extend the fatigue life of asphalt by enhancing the self-healing performance of asphalt.

4. Conclusions

Through experimental tests and theoretical analyses, this paper evaluated the fatigue and self-healing performances of four asphalt mastics, VAM, RAM, SRAM, and ERAM, under simulated aging conditions, as well as the effect of self-healing behavior on fatigue performance. The following conclusions can be drawn:

(1)

Both Sasobit and Evotherm can significantly enhance the fatigue performance of asphalt mastics, thereby extending their fatigue life. This is due to the fact that the former can form a solid lattice structure in the bitumen, while the latter can effectively increase the bond between the bitumen and the mineral powder. Specifically, under the long-term aging condition of 7% strain, the fatigue life of SRAM is 9.9 times as long as that of VAM and 2.4 times as long as that of RAM; the fatigue life of ERAM is 8.7 times as long as that of VAM and 1.7 times as long as that of RAM. In addition, SRAM shows better fatigue performance.

(2)

The self-healing properties of four asphalt mastics under different aging states were tested and analyzed by multiple intermittent loading TS tests based on $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ and RCM. In particular, after ten fatigue intermittent loadings in the long-term aging condition, the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ for VAM is only 43.2% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ for SRAM and 48.2% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ for ERAM, while the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ for RAM is only 76.1% of the N for SRAM and 84.8% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ for ERAM. Moreover, the values of RCM for long-term aging VAM and RAM after ten fatigue intermittent loading tests are 0.65 and 0.70, respectively, which are lower than the values of RCM for SRAM. This indicates that adding a warm-mix agent can improve the self-healing properties of asphalt mastic.

(3)

The fatigue life of asphalt mastic at a 5% strain level before and after considering the effect of self-healing was calculated by the fatigue life conversion factor μ. A comparison reveals that the fatigue life of asphalt mastic is significantly prolonged after considering self-healing, which indicates that the self-healing property of asphalt mastic significantly enhances its fatigue performance.

(4)

This indicates that aging has some adverse effects on fatigue performance and self-healing performance, and the deeper the aging, the more pronounced the adverse effects. This is because aging hardens the asphalt and reduces its fluidity, which affects the road’s life and the asphalt’s self-healing performance. At a 7% strain, the fatigue life of SRAM after long-term aging is only 30.7% of the fatigue life in the unaged state and 49.4% of the fatigue life in the short-term aging state. Moreover, after ten fatigue intermittent loads in the long-term aging state, the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ of the SRAM is only 53.2% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ in the unaged state and 58.8% of the $\sum {\mathrm{N}}_{\mathrm{H}}\left(\mathrm{i}\right)$ in the short-term aging state.

(5)

The comprehensive results of the study concluded that Sasobit has a better effect on improving the fatigue and self-healing performances of rubber asphalt mastic. Therefore, Sasobit warm mix is preferable in practical applications to improve the performance of rubber asphalt pavements. This study can provide a theoretical basis for the promotion and application of WMRA pavements and contribute to the sustainable development of road construction.

Based on the S-VECD theoretical system, this study provides an in-depth analysis of the fatigue durability and self-healing capacity of warm-mix rubber asphalt mastic under different aging conditions. This paper not only systematically examines how aging affects the fatigue properties and self-healing potential of this material but also further explores the positive role of self-healing performance on fatigue performance. This paper aims to lay a theoretical foundation for the wide application of warm-mix rubber asphalt pavements through this series of studies and to help promote the wide application of warm-mix rubber asphalt technology in the field of road construction.