# Influence of Compaction, Gradations, and Stress Levels on Fatigue Performance of SMA-13 Mixtures

Authors: Jinshun Xue; Yingjun Jiang
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

The fatigue characteristics of the stone-mastic asphalt (SMA) mixture and pavement structure are the basis of SMA mixture pavement design. However, the fatigue performance of the SMA mixture compacted by a vertical vibration compaction method (VTM) has been rarely studied. This paper presents the indirect tensile fatigue test results of a laboratory investigation focused on the influence of compaction methods (Marshall compaction method, vertical vibration compaction method, and Superpave gyration compaction method), gradations (specification gradation and skeleton dense gradation), and stress levels on the fatigue performance of the SMA mixture with the nominal maximum particle size of 13.2 mm (SMA-13 mixture). Results showed that the fatigue life of the SMA-13 mixtures decreases linearly with the increase of the stress level under the same failure probability. The fatigue life of the SMA-13 mixture was 156% and 310% higher than that of the SGC and Marshall methods under the same loading stress, respectively. Furthermore, the fatigue life of the SMA-13 mixture with skeleton dense gradation was 55% higher than that of specification gradation. Through comparing the fatigue life of SMA-13 mixtures prepared under different compaction methods and gradations, the compaction methods of VTM and the skeleton dense gradation were recommended for SMA-13 mixture design.


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## Body

## 1. Introduction

With the intensifying trend of China’s traffic toward “large flow, large-scale vehicles, heavy load, and overload” [1] and the frequent occurrence of extreme weather, asphalt pavements should meet higher performance requirements [2]. New road-paving technologies, such as stone-mastic asphalt mixture (SMA) [3], fiber asphalt mixture [4], and high-modulus asphalt mixture [5], are gradually being applied in China. Among these, the SMA mixture is formed by the gap-graded coarse aggregates inlaid into a skeleton and has been applied in China for nearly 30 years [6].As the SMA mixture pavement is increasingly widely applied, the influence of the performance of the SMA mixture on the pavement construction quality has been attracting more attention [7–9]. Masri et al. [10, 11] pay attention on the physical characteristic and mechanical properties of SMA mixture incorporating nanomaterials, which concluded that the addition of nanomaterials in the asphalt binder improved its overall properties. Muniandy et al. [12] used a crack meander technique to evaluate the fatigue of modified and unmodified asphalt binders in SMA mixtures. The fracture energy and low-temperature performance of asphalt mortar with polyolefin–aramid fibers and polyacrylonitrile was investigated by Slebi-Acevedo et al. [13, 14]. The results show that the performance improvement of the asphalt binder can contribute positively to the performance of the SMA mixture [14]. The coarse aggregate composition plays an important role in the SMA mixture, which has an effect on the volume parameter and mechanical properties of the mixture, so the relative content of the coarse aggregates must be reasonable [15–17].The aforementioned studies mostly focused on the influence of SMA mixture composition on fatigue performance, such as asphalt binder and aggregate composition. However, the performance of the SMA mixture is affected by the compaction methods, such as Marshall compaction method (Marshall method) and Superpave gyratory compaction method (SGC method) [18, 19]. The SGC method is more representative of the field conditions compared with the Marshall method [18], and the mixture compacted by the SGC method performs better than the Marshall method [19]. As the Marshall method cannot effectively simulate the field compaction situation and the expensive equipment of the SGC method, Jiang et al. [20, 21] suggested asphalt mixture compaction through the vertical vibration compaction method (VTM) to investigate the performance of mixtures. However, the influence of compaction methods on the performance of the SMA-13 mixture based on the Marshall, SGC, and VTM methods has yet to be explored.SMA mixture fatigue is a phenomenon caused by the accumulation of unrecoverable strength attenuation of the material under cyclic loading [22], and the fatigue characteristics of asphalt mixture and pavement structure are the basis of asphalt pavement design [23]. Therefore, studying the influencing factors of the SMA mixture fatigue characteristics is important, and improving the fatigue durability of the SMA mixture is crucial to the development of asphalt pavements. The influence of mixture composition, test temperature, water, and loading frequency on the fatigue performance of the SMA mixture was investigated [24–26]. Laboratory fatigue tests, such as trabecular bending fatigue [27], indirect tensile fatigue [28], and semicircular bending fatigue [29] tests, were used for the fatigue performance evaluation of the SMA mixture. Promising results have been found in investigating the fatigue performance of the SMA mixture; however, limited research has been conducted on the fatigue performance of the SMA mixture compacted by the VTM method.Pre-existing research has initially proved that the asphalt binder and aggregate composition of the SMA mixture have a significant influence on its fatigue performance. However, the fatigue performance SMA mixture compacted by the vertical vibration compaction method (VTM) has been rarely studied. Therefore, in this paper, the methodology was conducted according to the flowchart as shown in Figure1. The objective of this study is to investigate the compaction methods, gradations, and stress levels, especially the VTM, on the fatigue performance of the SMA-13 mixtures based on the indirect tensile fatigue test method, which has a positive influence on the development of SMA pavement design.Figure 1
Flowchart of methodology.


## 2. Materials and Experimental Methods

### 2.1. Materials

SBS-modified asphalt was obtained from a local manufacturer and a property test was conducted based on the specifications of Standard Test Methods for Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011) [30]. The characteristics of SBS-modified asphalt are shown in Table 1.Table 1
Properties of the SBS-modified asphalt.
PropertiesTest methodsRequirementTest values25°C Penetration, 0.1 mmT 0604-201160 min, and 80 max71Penetration indexT 0604-2011−0.4 min0.47Softening point, °CT 0606-201155 min825°C ductility, cmT 0605-201130 min42.5Mineral aggregates (such as coarse and fine aggregates and mineral powder) were obtained from Shangluo City, Shaanxi Province in China, and lignin fiber was provided by a local manufacturer from Jiangsu Province. The characteristics of these mineral aggregates are shown in Table2.Table 2
Properties of the mineral aggregates.
PropertiesTest methodsRequirementTest valuesCoarse aggregatesCrushed stone value, %14.126 maxT 0316-2005Los angeles abrasion, %15.328 maxT 0317-2005Polished stone value4340 minT 0321-2005Fine aggregatesSand equivalent, %89.560 minT 0334-2005Angularity, s32.830 minT 0345-2005Mineral powderBulk specific gravity, g/cm32.7062.5 minT 0352-2000Plasticity index0.581.0 maxT 0354-2000


### 2.2. Mixture Gradations

Table3 presents the specification gradation and skeleton dense gradation adopted in this study. The specification gradation is the mid-value of the gradation of SMA-13 mixture according to Technical Specifications for Construction of Highway Asphalt Pavements (JTG F40–2004) [31]. The skeleton dense gradation is optimized based on the mortar theory through previous research, which has more coarse aggregate content than the specification gradation.Table 3
Aggregate gradations of the SMA-13 mixtures.
GradationsMass percentage (%) passing the following sieve size (mm)1613.29.54.752.361.180.60.30.150.075Specification gradation10095.062.527.020.519.016.013.012.010.0Skeleton dense gradation10095.058.025.020.517.515.513.511.59.0


### 2.3. Fatigue Test Method

At present, the commonly used laboratory fatigue tests are trabecular bending, indirect tensile, and semicircular bending fatigue tests. In this study, a radar chart was used to analyze the advantages and disadvantages of different laboratory fatigue test methods from five angles: sensitivity, data reliability, simulation reality, sample preparation, and instrument operation (Figure2). The advantage gap widened as the value of influence factors decreased, that is, a smaller area of the fatigue test method in the radar chart indicates that the method is recommended.Figure 2
Comparison of advantages and disadvantages of laboratory fatigue test methods.Figure2 shows that the trabecular bending fatigue test ranks first among the three fatigue test methods, but the samples of different compacted methods used in the trabecular bending fatigue test cannot reflect the difference of compaction methods because the density of samples compacted by various compaction methods has a minimal difference under the same compaction work [21]. Sample preparation and instrument operation of the semicircular bending fatigue test are difficult, and the correlation between the laboratory test and actual pavement mechanics case is poor. The indirect tensile fatigue test (Figure 3) somewhere in between the aforementioned methods in terms of simulation reality, data reliability, and sample preparation is easy. Therefore, to study the fatigue performance of the SMA-13 mixtures with different compaction methods, an indirect tensile fatigue test was selected as the fatigue test method in this study.Figure 3
Schematic diagram of the indirect tensile fatigue test.The indirect tensile fatigue test method is tested using an MTS810 fatigue testing machine as shown in Figure4(a), and the installation of the test specimen is shown in Figure 4(b).Figure 4
Indirect tensile fatigue test method. (a) MTS810 fatigue testing machine. (b) Installation of test specimen.
(a)(b)The test was performed in stress control mode, which has an accurate definition of failure and data reliability. Then, the specimens were subjected to a 10 Hz repeated half sinusoidal wave. The cyclic eigenvalue was 0.1, in which the ratio of maximum load to minimum load is 10 (σmax/σmin = 10).The stress level is a key parameter during the fatigue test process, which was calculated as follows:(1)S=σmaxσS,where S is the stress level, σmax is the maximum cyclic stress (MPa), and σs is the ultimate splitting strength.With the increase of the stress level, the fatigue life of the asphalt mixture shows a decreasing trend. Therefore, the selection of the stress level determines the fatigue life of the SMA-13 mixture. If the stress level is low, then the fatigue life is extremely long, which is not only time-consuming but also data discrete; whereas, if the stress level is extremely high, then the fatigue life becomes small and fatigue test becomes meaningless. Thus, five stress levels were adopted in this study: 0.3, 0.4, 0.5, 0.6, and 0.7. The test temperature was 15°C. The performance tests were conducted four times, and the results were examined and averaged through Grubbs’ method.


### 2.4. Specimen Compaction Methods

In this paper, Marshall, VTM, and SGC methods are used to prepare specimens for the fatigue test. The Marshall method as the uncomplicated and inexpensive compaction method is widely adopted for the SMA mixture in the world, but the Marshall compactor hammer drop impact resulting in the breakage of aggregate during the compaction process, which cannot effectively simulate the actual pavement compaction [15]. However, the SGC method can better simulate the stress state of the pavement surface under the action of loading, and the specimens compacted by the SGC method had good correlation with the field core samples from the pavement. The instrument adopted by the VTM method was vertical vibratory testing equipment, which used only vertical force during the compaction procedure. The parameters of various compaction methods are listed in Tables 4–6, and the design results of different compaction methods are listed in Table 7.Table 4
Working parameters of the Marshall method.
Compaction hammer, gDrop height of hammer, cmWorking frequency, times·min−1Specimen size, mm453647.560Φ101.6 × h63.5Table 5
Working parameters of the SGC method.
Vertical pressure, kPaCompaction rotation angle, kgRotation speed, r·min−1Specimen size, mm6001.2530Φ100 × h63.5Table 6
Working parameters of the VTM method.
Working frequency, HzUpper equipment weight, °Nether equipment weight, kgStatic eccentricity, kg·mSpecimen size, mm371671080.109Φ100 × h63.5Table 7
Design results of different compaction methods.
GradationsCompaction methodsOptimal asphalt aggregate ratio, %Density, g·cm−3Volume of air voids, %Specification gradationMarshall method5.72.5294.1SGC method5.32.5524.0VTM method5.42.5822.9Skeleton dense gradationMarshall method5.62.5354.0SGC method5.22.5604.0VTM method5.22.5912.9


### 2.5. Failure Process of SMA-13 Mixture Samples

Previous research shows that the failure process of the asphalt mixture includes three stages: fatigue crack initiating, crack expansion, and sample failure. The failure process of the SMA-13 mixture samples is shown in Figure5. According to the failure characteristics of the SMA-13 mixture based on the indirect tensile fatigue test, the failure process is divided into the following four stages:(1)
Full stress, in which the SMA-13 mixture samples are under no stress or a few stress cycles, and the samples are well-structured.(2)
Fatigue crack initiation, in which the fatigue crack appears in the center of the cylinder samples of the SMA-13 mixture with the increase of stress cycles due to excessive horizontal tensile stress, and the microfatigue crack is located in the range of the upper and lower strips and the center of the circle is along the radial direction.(3)
Fatigue crack expansion, in which the microcrack gradually expands under the action of continuous stress cycles, and the fatigue crack becomes perceptible to human eyes. The load-bearing of the SMA-13 mixture sample decreases obviously, and the peak load applied on the SMA mixture sample shows a decaying state. The crack expansion mainly follows the range of the upper and lower strips and the center of the circle is along the radial direction.(4)
Sample failure stage, in which the crack propagates from bottom to top until the sample is completely destroyed.Figure 5
The failure process of SMA-13 mixture samples. (a) Full stress stage. (b) Fatigue crack initiating stage. (c) Fatigue crack expansion stage. (d) Sample failure stage.
(a)(b)(c)(d)


## 2.1. Materials

SBS-modified asphalt was obtained from a local manufacturer and a property test was conducted based on the specifications of Standard Test Methods for Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011) [30]. The characteristics of SBS-modified asphalt are shown in Table 1.Table 1
Properties of the SBS-modified asphalt.
PropertiesTest methodsRequirementTest values25°C Penetration, 0.1 mmT 0604-201160 min, and 80 max71Penetration indexT 0604-2011−0.4 min0.47Softening point, °CT 0606-201155 min825°C ductility, cmT 0605-201130 min42.5Mineral aggregates (such as coarse and fine aggregates and mineral powder) were obtained from Shangluo City, Shaanxi Province in China, and lignin fiber was provided by a local manufacturer from Jiangsu Province. The characteristics of these mineral aggregates are shown in Table2.Table 2
Properties of the mineral aggregates.
PropertiesTest methodsRequirementTest valuesCoarse aggregatesCrushed stone value, %14.126 maxT 0316-2005Los angeles abrasion, %15.328 maxT 0317-2005Polished stone value4340 minT 0321-2005Fine aggregatesSand equivalent, %89.560 minT 0334-2005Angularity, s32.830 minT 0345-2005Mineral powderBulk specific gravity, g/cm32.7062.5 minT 0352-2000Plasticity index0.581.0 maxT 0354-2000


## 2.2. Mixture Gradations

Table3 presents the specification gradation and skeleton dense gradation adopted in this study. The specification gradation is the mid-value of the gradation of SMA-13 mixture according to Technical Specifications for Construction of Highway Asphalt Pavements (JTG F40–2004) [31]. The skeleton dense gradation is optimized based on the mortar theory through previous research, which has more coarse aggregate content than the specification gradation.Table 3
Aggregate gradations of the SMA-13 mixtures.
GradationsMass percentage (%) passing the following sieve size (mm)1613.29.54.752.361.180.60.30.150.075Specification gradation10095.062.527.020.519.016.013.012.010.0Skeleton dense gradation10095.058.025.020.517.515.513.511.59.0


## 2.3. Fatigue Test Method

At present, the commonly used laboratory fatigue tests are trabecular bending, indirect tensile, and semicircular bending fatigue tests. In this study, a radar chart was used to analyze the advantages and disadvantages of different laboratory fatigue test methods from five angles: sensitivity, data reliability, simulation reality, sample preparation, and instrument operation (Figure2). The advantage gap widened as the value of influence factors decreased, that is, a smaller area of the fatigue test method in the radar chart indicates that the method is recommended.Figure 2
Comparison of advantages and disadvantages of laboratory fatigue test methods.Figure2 shows that the trabecular bending fatigue test ranks first among the three fatigue test methods, but the samples of different compacted methods used in the trabecular bending fatigue test cannot reflect the difference of compaction methods because the density of samples compacted by various compaction methods has a minimal difference under the same compaction work [21]. Sample preparation and instrument operation of the semicircular bending fatigue test are difficult, and the correlation between the laboratory test and actual pavement mechanics case is poor. The indirect tensile fatigue test (Figure 3) somewhere in between the aforementioned methods in terms of simulation reality, data reliability, and sample preparation is easy. Therefore, to study the fatigue performance of the SMA-13 mixtures with different compaction methods, an indirect tensile fatigue test was selected as the fatigue test method in this study.Figure 3
Schematic diagram of the indirect tensile fatigue test.The indirect tensile fatigue test method is tested using an MTS810 fatigue testing machine as shown in Figure4(a), and the installation of the test specimen is shown in Figure 4(b).Figure 4
Indirect tensile fatigue test method. (a) MTS810 fatigue testing machine. (b) Installation of test specimen.
(a)(b)The test was performed in stress control mode, which has an accurate definition of failure and data reliability. Then, the specimens were subjected to a 10 Hz repeated half sinusoidal wave. The cyclic eigenvalue was 0.1, in which the ratio of maximum load to minimum load is 10 (σmax/σmin = 10).The stress level is a key parameter during the fatigue test process, which was calculated as follows:(1)S=σmaxσS,where S is the stress level, σmax is the maximum cyclic stress (MPa), and σs is the ultimate splitting strength.With the increase of the stress level, the fatigue life of the asphalt mixture shows a decreasing trend. Therefore, the selection of the stress level determines the fatigue life of the SMA-13 mixture. If the stress level is low, then the fatigue life is extremely long, which is not only time-consuming but also data discrete; whereas, if the stress level is extremely high, then the fatigue life becomes small and fatigue test becomes meaningless. Thus, five stress levels were adopted in this study: 0.3, 0.4, 0.5, 0.6, and 0.7. The test temperature was 15°C. The performance tests were conducted four times, and the results were examined and averaged through Grubbs’ method.


## 2.4. Specimen Compaction Methods

In this paper, Marshall, VTM, and SGC methods are used to prepare specimens for the fatigue test. The Marshall method as the uncomplicated and inexpensive compaction method is widely adopted for the SMA mixture in the world, but the Marshall compactor hammer drop impact resulting in the breakage of aggregate during the compaction process, which cannot effectively simulate the actual pavement compaction [15]. However, the SGC method can better simulate the stress state of the pavement surface under the action of loading, and the specimens compacted by the SGC method had good correlation with the field core samples from the pavement. The instrument adopted by the VTM method was vertical vibratory testing equipment, which used only vertical force during the compaction procedure. The parameters of various compaction methods are listed in Tables 4–6, and the design results of different compaction methods are listed in Table 7.Table 4
Working parameters of the Marshall method.
Compaction hammer, gDrop height of hammer, cmWorking frequency, times·min−1Specimen size, mm453647.560Φ101.6 × h63.5Table 5
Working parameters of the SGC method.
Vertical pressure, kPaCompaction rotation angle, kgRotation speed, r·min−1Specimen size, mm6001.2530Φ100 × h63.5Table 6
Working parameters of the VTM method.
Working frequency, HzUpper equipment weight, °Nether equipment weight, kgStatic eccentricity, kg·mSpecimen size, mm371671080.109Φ100 × h63.5Table 7
Design results of different compaction methods.
GradationsCompaction methodsOptimal asphalt aggregate ratio, %Density, g·cm−3Volume of air voids, %Specification gradationMarshall method5.72.5294.1SGC method5.32.5524.0VTM method5.42.5822.9Skeleton dense gradationMarshall method5.62.5354.0SGC method5.22.5604.0VTM method5.22.5912.9


## 2.5. Failure Process of SMA-13 Mixture Samples

Previous research shows that the failure process of the asphalt mixture includes three stages: fatigue crack initiating, crack expansion, and sample failure. The failure process of the SMA-13 mixture samples is shown in Figure5. According to the failure characteristics of the SMA-13 mixture based on the indirect tensile fatigue test, the failure process is divided into the following four stages:(1)
Full stress, in which the SMA-13 mixture samples are under no stress or a few stress cycles, and the samples are well-structured.(2)
Fatigue crack initiation, in which the fatigue crack appears in the center of the cylinder samples of the SMA-13 mixture with the increase of stress cycles due to excessive horizontal tensile stress, and the microfatigue crack is located in the range of the upper and lower strips and the center of the circle is along the radial direction.(3)
Fatigue crack expansion, in which the microcrack gradually expands under the action of continuous stress cycles, and the fatigue crack becomes perceptible to human eyes. The load-bearing of the SMA-13 mixture sample decreases obviously, and the peak load applied on the SMA mixture sample shows a decaying state. The crack expansion mainly follows the range of the upper and lower strips and the center of the circle is along the radial direction.(4)
Sample failure stage, in which the crack propagates from bottom to top until the sample is completely destroyed.Figure 5
The failure process of SMA-13 mixture samples. (a) Full stress stage. (b) Fatigue crack initiating stage. (c) Fatigue crack expansion stage. (d) Sample failure stage.
(a)(b)(c)(d)


## 3. Fatigue Test Results

### 3.1. Splitting Test Results

To ensure the accuracy of splitting fatigue test results, the reliable and accurate splitting strength maximum value of the SMA-13 mixture is necessary for the splitting fatigue test. Thus, the splitting strength of the mixture was tested using a MTS810 material testing machine. The test results are listed in Table8.Table 8
Splitting strength of SMA-13 mixture.
GradationsSpecification gradationSkeleton dense gradationDesign methodsMarshall methodSGC methodVTM methodMarshall methodSGC methodVTM methodSplitting strength (MPa)1.011.101.201.091.221.35Table8 shows that compared with the SMA-13 mixture with specification gradation, the splitting strength of the SMA-13 mixture with skeleton dense gradation are increased by 7%–12%, with an average increase of 10%. The reason is that the skeleton dense gradation proposed in a previous study can improve the embedding force of the aggregate in the SMA-13 mixture, resulting in improvement of the splitting strength of the SMA-13 mixture. Compared with the SMA-13 mixture designed using the Marshall method, the splitting strength of the SMA-13 mixture designed using the SGC and VTM methods is increased by 10% and 22%, respectively. This result means that the compaction work of VTM method is significantly greater than that of Marshall and SGC methods. Thus, the splitting strength of the SMA-13 mixture designed through the VTM method is better than that of the Marshall and SGC methods. Therefore, the compaction method plays a key role in the internal aggregate positioning and arrangement of SMA-13 mixture and the VTM is more conducive to the rearrangement of internal aggregates and the formation of stable structure than SGC and MCM [32].


### 3.2. Results of the Fatigue Test

In this study, four test samples for each test condition were fabricated (Table9), but the discreteness of the fatigue test data adds difficulty in fatigue performance evaluation. Replacing the original data with the average cannot effectively reflect the fatigue performance of various types of SMA-13 mixtures. Therefore, the Weibull distribution, which is widely used in data processing of various fatigue life tests, is adopted in this study to deal with the fatigue data [33, 34]. The Weibull fitting curves of various types of SMA-13 mixtures are shown in Figures 6 and 7, where ρ is the probability of failure and N is the measured equivalent fatigue life of the SMA-13 mixture.Table 9
Measured equivalent fatigue life of the SMA-13 mixture with different gradations and compaction methods.
GradationsDesign methodsThe measured equivalent fatigue life of SMA-13 mixture at different stress levels0.30.40.50.60.7Specification gradationMarshall method6462157459837117273711831965450226832120171079515243847224241286597353SGC method72081645734426233833219951107572258856724471349667287963425661511734356VTM method757818458145022619183255311515943039555275815387093831015329561634764410Skeleton dense gradationMarshall method66641842966425188815020641168531302933621811273601325954726361379784440SGC method75551891989541256810422171171654317913124531424723366978427851483770379VTM method7749218510046163178994244312007813619803275316168194051011029051711900416Figure 6
Weibull fitting results of the SMA-13 mixture with specification gradation. (a) Marshall method. (b) SGC method. (c) VTM method.
(a)(b)(c)Figure 7
Weibull fitting results of the SMA-13 mixture with skeleton dense gradation. (a) Marshall method. (b) SGC method. (c) VTM method.
(a)(b)(c)Figures6 and 7 show the variation ln ln1/(1 − ρ) and ln N among the various stress levels and compaction methods. The ln ln1/(1 − ρ) count showed a linear correlation of the ln N, and the correlation coefficients of the Weibull fitting curves were greater than 0.90, which indicate a good correlation between the two parameters. This result further confirms that the Weibull distribution was an operational and effective assumption for the fatigue life distribution of the SMA-13 mixture with various stress levels and compaction methods.


### 3.3. Equivalent Fatigue Life

The equivalent fatigue life of the SMA-13 mixture with various stress levels and compaction methods can be calculated by the linear relationship between ln ln1/(1 −ρ) and ln N, which are listed in Table 10.Table 10
Equivalent fatigue life of the SMA-13 mixture with different stress levels and compaction methods.
GradationsDesign methodsProbability of failure (%)The equivalent fatigue life of SMA-13 mixture at different stress levels0.30.40.50.60.7Specification gradationMarshall method551841121346260965077051971977485247SGC method55836114643228615450848821721170601287VTM method56132129846836017650917625411277645341Skeleton dense gradationMarshall method55018135974826410350847521941204585310SGC method56045141870741818950869623491273676331VTM method56338174362547025750922125871384784378


## 3.1. Splitting Test Results

To ensure the accuracy of splitting fatigue test results, the reliable and accurate splitting strength maximum value of the SMA-13 mixture is necessary for the splitting fatigue test. Thus, the splitting strength of the mixture was tested using a MTS810 material testing machine. The test results are listed in Table8.Table 8
Splitting strength of SMA-13 mixture.
GradationsSpecification gradationSkeleton dense gradationDesign methodsMarshall methodSGC methodVTM methodMarshall methodSGC methodVTM methodSplitting strength (MPa)1.011.101.201.091.221.35Table8 shows that compared with the SMA-13 mixture with specification gradation, the splitting strength of the SMA-13 mixture with skeleton dense gradation are increased by 7%–12%, with an average increase of 10%. The reason is that the skeleton dense gradation proposed in a previous study can improve the embedding force of the aggregate in the SMA-13 mixture, resulting in improvement of the splitting strength of the SMA-13 mixture. Compared with the SMA-13 mixture designed using the Marshall method, the splitting strength of the SMA-13 mixture designed using the SGC and VTM methods is increased by 10% and 22%, respectively. This result means that the compaction work of VTM method is significantly greater than that of Marshall and SGC methods. Thus, the splitting strength of the SMA-13 mixture designed through the VTM method is better than that of the Marshall and SGC methods. Therefore, the compaction method plays a key role in the internal aggregate positioning and arrangement of SMA-13 mixture and the VTM is more conducive to the rearrangement of internal aggregates and the formation of stable structure than SGC and MCM [32].


## 3.2. Results of the Fatigue Test

In this study, four test samples for each test condition were fabricated (Table9), but the discreteness of the fatigue test data adds difficulty in fatigue performance evaluation. Replacing the original data with the average cannot effectively reflect the fatigue performance of various types of SMA-13 mixtures. Therefore, the Weibull distribution, which is widely used in data processing of various fatigue life tests, is adopted in this study to deal with the fatigue data [33, 34]. The Weibull fitting curves of various types of SMA-13 mixtures are shown in Figures 6 and 7, where ρ is the probability of failure and N is the measured equivalent fatigue life of the SMA-13 mixture.Table 9
Measured equivalent fatigue life of the SMA-13 mixture with different gradations and compaction methods.
GradationsDesign methodsThe measured equivalent fatigue life of SMA-13 mixture at different stress levels0.30.40.50.60.7Specification gradationMarshall method6462157459837117273711831965450226832120171079515243847224241286597353SGC method72081645734426233833219951107572258856724471349667287963425661511734356VTM method757818458145022619183255311515943039555275815387093831015329561634764410Skeleton dense gradationMarshall method66641842966425188815020641168531302933621811273601325954726361379784440SGC method75551891989541256810422171171654317913124531424723366978427851483770379VTM method7749218510046163178994244312007813619803275316168194051011029051711900416Figure 6
Weibull fitting results of the SMA-13 mixture with specification gradation. (a) Marshall method. (b) SGC method. (c) VTM method.
(a)(b)(c)Figure 7
Weibull fitting results of the SMA-13 mixture with skeleton dense gradation. (a) Marshall method. (b) SGC method. (c) VTM method.
(a)(b)(c)Figures6 and 7 show the variation ln ln1/(1 − ρ) and ln N among the various stress levels and compaction methods. The ln ln1/(1 − ρ) count showed a linear correlation of the ln N, and the correlation coefficients of the Weibull fitting curves were greater than 0.90, which indicate a good correlation between the two parameters. This result further confirms that the Weibull distribution was an operational and effective assumption for the fatigue life distribution of the SMA-13 mixture with various stress levels and compaction methods.


## 3.3. Equivalent Fatigue Life

The equivalent fatigue life of the SMA-13 mixture with various stress levels and compaction methods can be calculated by the linear relationship between ln ln1/(1 −ρ) and ln N, which are listed in Table 10.Table 10
Equivalent fatigue life of the SMA-13 mixture with different stress levels and compaction methods.
GradationsDesign methodsProbability of failure (%)The equivalent fatigue life of SMA-13 mixture at different stress levels0.30.40.50.60.7Specification gradationMarshall method551841121346260965077051971977485247SGC method55836114643228615450848821721170601287VTM method56132129846836017650917625411277645341Skeleton dense gradationMarshall method55018135974826410350847521941204585310SGC method56045141870741818950869623491273676331VTM method56338174362547025750922125871384784378


## 4. Influence of the Stress Level on Fatigue Performance of the SMA-13 Mixture

To investigate the influences of stress level on the fatigue performance of the SMA-13 mixture under different probabilities of failure, we considered the results in Table10 to draw the fitted fatigue curves of the mixture under the condition of varying stress levels. The comparisons of fatigue life were grouped by the probability of failure as shown in Figures 8 and 9.Figure 8
Fatigue life of the SMA-13 mixture with specification gradation versus stress level under different probabilities of failure. (a) Probability of failure is 5%. (b) Probability of failure is 50%.
(a)(b)Figure 9
Fatigue life of the SMA-13 mixture with skeleton dense gradation versus stress level under different probabilities of failure. (a) Probability of failure is 5%. (b) Probability of failure is 50%.
(a)(b)Figures8 and 9 show a clear trend in which the fatigue life of the SMA-13 mixture decreases with the increase of stress level, and this trend is particularly obvious when the stress level increases from 0.3 to 0.4. The reason is that when the stress level is large, the maximum value of the cyclic stress acting on the specimen is correspondingly large, and the damage caused by the increase of the cyclic stress becomes more pronounced. An interesting phenomenon is that the decrease of fatigue life slows down after the stress level reached 0.5. The reason is that when the stress level is greater than 0.5, the fatigue life is small, resulting in a minimal difference in fatigue life under various stress levels.The relevant literature suggests the existence of a linear relationship between the fatigue life of the asphalt mixture and the stress level in double logarithmic coordinates as shown in (2). Therefore, we considered taking the logarithm of fatigue life and stress level for linear fitting to discuss the influences of the stress level on the fatigue performance of the SMA-13 mixture. The fitting results under specification gradation and skeleton dense gradation are shown in Figure 10.(2)lgN¯=a−blgS,where N¯ is the equivalent fatigue life, S is the stress level, and a and b are the fatigue equation parameters.Figure 10
Equivalent fatigue life versus stress level at different gradation. (a) Specification gradation. (b) Skeleton dense gradation.
(a)(b)Figure10 presents the results of the relationship between the equivalent fatigue life of the SMA-13 mixture under probability of failure, which is 5% and stress level. The results indicated that the fatigue life of the SMA-13 mixture decreases linearly with the increase of the stress level under the same failure probability. We can conclude that when the loading on the SMA-13 mixture is constant, the greater the ultimate splitting strength of SMA-13 mixture, the lower is the stress level and the greater is the fatigue life. Therefore, the splitting strength should be considered during the SMA-13 mixture composition design. In the present section, the splitting strength of the SMA-13 mixture designed using the VTM method is better than that of the Marshall and SGC methods. Thus, the fatigue resistance of the SMA-13 mixture compacted by the VTM method is better than that of the Marshall and SGC methods under the current traffic conditions of “large flow, large-scale vehicles, heavy load, and overload” [35].The results in Figure10 also show that (2) can be used to determine the fatigue performance in SMA-13 mixture analysis. Thus, the linear regression was adopted between the equivalent fatigue life of the SMA-13 mixture and stress level to obtain the fatigue equation parameters, which are listed in Table 11. The parameter a in the fatigue equation is the intercept of the fatigue curve and the fatigue life increases with the increase of a value, which indicates that a larger value of the fatigue curve of the SMA-13 mixture shows better fatigue life of the corresponding mixture. The parameter b is the slope of the fatigue curve of the SMA-13 mixture, which reflects the sensitivity of the fatigue life of this mixture to the change of stress level. The smaller b indicates that the mixture has better fatigue resistance performance.Table 11
Fitting results of different types of SMA-13 mixtures.
GradationsCompaction methodsFatigue equation parametersFatigue equation parameters under different probability of failure5%50%Specification gradationMarshall methodB4.5303.956a1.2921.786R20.9820.996SGC methodb4.1933.844a1.4811.885R20.9780.992VTM methodb4.0583.799a1.5781.949R20.9730.996Skeleton dense gradationMarshall methodb4.4323.792a1.4121.910R20.9840.993SGC methodb3.9033.713a1.6881.966R20.9880.993VTM methodb3.7283.618a1.7922.042R20.9810.992The fitting results showed that the linear-regression coefficients (R2) of the fatigue curve of various types of SMA-13 mixtures were greater than 0.97, which indicated that the linear-regression results were considered acceptable.


## 5. Influence of the Compaction Method on Fatigue Performance of the SMA-13 Mixture

In this section, the influence of the compaction method on the fatigue performance of the SMA-13 mixture was analyzed. Furthermore, the fatigue curve of the SMA-13 mixture with various compaction methods under the probability of failure is 50% as shown in Figure11.Figure 11
Fatigue curve of the SMA-13 mixture with different compaction methods. (a) Specification gradation. (b) Skeleton dense gradation.
(a)(b)According to Figure11, when the probability of failure and gradation is known, the fatigue curve of the SMA-13 mixture compacted by the VTM method had the highest line position. The SGC method came second, followed by the Marshall method. This phenomenon is also confirmed by Table 11, where the fatigue curve of the SMA-13 mixture compacted by the VTM method had the largest a value 1.949 (specification gradation) or 2.042 (skeleton dense gradation). The SGC method had the second smallest a value (1.885 or 1.966) and the Marshall method had the smallest a value (1.786 or 1.910). These results show that the fatigue performance of the SMA-13 mixture compacted by the VTM method is better than that of the other two methods in the same stress level, which may be due to the greater compaction work of the VTM method. Thus, the samples compacted by the VTM method had higher density and the contact among aggregates of the mixture was denser, which showed better fatigue performance.The relevant studies showed that the stress level of the asphalt pavement under vehicle loading generally does not exceed 0.45. Therefore, the fatigue life analysis of various types of SMA-13 mixtures was carried out with a stress level of 0.45 as shown in Table12. Meanwhile, the stress level is the ratio of the loading stress of the asphalt pavement and the ultimate strength of the asphalt mixture. Thus, the comparison of fatigue life under the same stress level cannot reflect the influence of the ultimate strength of various asphalt mixtures on the fatigue life. Then, the same loading stress was used for comparison of the fatigue performance of various types of SMA-13 mixture. Assuming that the stress level was 0.45, the loading stress of the SMA-13 mixture compacted by the Marshall method was 0.456 MPa (0.45 × 1.014 MPa), and the same loading stress (0.456 MPa) was more reasonable to adopt in evaluating the fatigue life of various types of SMA-13 mixtures. Based on the same loading stress, the fatigue life analysis results of the SMA-13 mixtures compacted by different compaction methods are shown in 2Tables 12 and 13.Table 12
Fatigue life of SMA-13 mixture with different compaction methods and gradations.
GradationsCompaction methodsCorresponding fatigue life under 0.45 stress levelCorresponding fatigue life under 0.456 MPa loading550550Specification gradationMarshall method72914387291438SGC method861165212152265VTM method967184719203511Skeleton dense gradationMarshall method88916798891679SGC method1100179322713572VTM method1216198035425590Table 13
Comparison of fatigue life of the SMA-13 mixture under different compaction methods.
ItemStress level is 0.45Loading stress is 0.456 MPaρ (%)550550NG−V/NG−M1.331.282.632.44NG−V/NG−S1.121.121.581.55NS−V/NS−M1.371.183.983.33NS−V/NS−S1.101.101.561.56NG−V is the fatigue life of the SMA-13 mixture with specification gradation compacted by the VTM method, and the NS−V is the fatigue life of the SMA-13 mixture with skeleton dense gradation compacted by the VTM method.Table12 shows that the fatigue life of the SMA-13 mixture difference between the two conditions (0.45 stress level and 0.456 MPa loading stress) is larger under the same compaction method and gradation. As shown in Table 13, at a stress level of 0.45, the fatigue life of the SMA-13 mixture compacted by the VTM method increased by an average of 11% and 29% compared with that of the SGC and Marshall methods, respectively. When the loading stress was 0.456 Mpa, the fatigue life of the SMA-13 mixture was 156% and 310% higher than that of the SGC and Marshall methods, respectively. The fatigue damage of the SMA-13 mixture is due to local nonuniformity of the mixture microstructure, which induces stress concentration and microdamage in the internal structure of the SMA-13 mixture. The microdamage gradually accumulates and expands under the action of repeated stress, resulting in the structural damage of mixture. Compared with the SMA-13 mixture compacted by the Marshall and SGC methods, the air voids of the SMA-13 mixture compacted by the VTM method was reduced by approximately 30%, which can decrease the local heterogeneity of the material microstructure and is conducive to improving the fatigue resistance of the SMA-13 mixture. Furthermore, compared with the SMA-13 mixture compacted by the Marshall method, the asphalt aggregate ratio of the SMA-13 mixture compacted by the VTM method was reduced by approximately 7%, the maximum density was increased by 2%, voids filled with binder was significantly improved, and the flexural tensile strength was increased by 20%. The stress level of the SMA-13 mixture compacted by the VTM method was reduced by 20% under the same repeated stress, and the fatigue resistance of the mixture was significantly improved [32].


## 6. Influence of Gradation on Fatigue Performance of the SMA-13 Mixture

To investigate the influence of gradation on the fatigue performance of the SMA-13 mixture, 50% probability of failure was applied to the fatigue curves of all the SMA-13 mixtures. Figure12 shows the fatigue curves of the SMA-13 mixture with various gradations under different compaction methods. Tables 14 and 15 show a comparison of the fatigue life of the SMA-13 mixture under different gradations.Figure 12
Fatigue curve of SMA-13 mixture with different gradations. (a) Marshall method. (b) SGC method. (c) VTM method.
(a)(b)(c)Table 14
Fatigue life of SMA-13 mixture with different compaction methods and gradations.
GradationsCompaction methodsCorresponding fatigue life under 0.45 stress levelCorresponding fatigue life under 0.456 MPa loading550550Specification gradationMarshall method72914387291438SGC method861165212152265VTM method967184719203511Skeleton dense gradationMarshall method88916798891679SGC method1100179322713572VTM method1216198035425590Table 15
Comparison of fatigue life of the SMA-13 mixture under different gradations.
ItemStress level is 0.45Loading stress is 0.456 MPaρ (%)550550NS−M/NG−M1.221.171.221.17NS−S/NG−S1.281.091.871.58NS−V/NG−V1.261.071.851.59As shown in Figure12, for a given failure probability, the fatigue curve of the SMA-13 mixture with the skeleton dense gradation was at a higher line position, while the fatigue curve of the mixture with specification gradation was at a lower line position. This finding was related to the results shown in Table 11. Compared with the SMA-13 mixture with the specification gradation, the SMA-13 mixture with the skeleton dense gradation had a higher a value and a lower b value, indicating that the fatigue performance of the SMA-13 with skeleton dense gradation was better than that of the specification gradation at the same stress level. This phenomenon can be explained as follows: a slight difference exists in the fine aggregate content between skeleton dense gradation and specification gradation. However, the coarse aggregate content in the skeleton dense gradation is higher than that in the specification gradation. Compared with the aggregate structure of the specification gradation, the skeleton interlocking density structure in the SMA-13 mixture with the skeleton dense gradation formed by coarse aggregates can provide a greater intercalation force for the SMA-13 mixture and can effectively delay the crack propagation in the SMA-13 mixture under fatigue loading. Thus, it can bear more fatigue cycle loading, which shows that it has a long life.As shown in Tables14 and 15, at a stress level of 0.45, the fatigue life of the SMA-13 mixture with the skeleton dense gradation increased by an average of 18% compared with that of the specification gradation. When the loading stress was 0.456 MPa, the fatigue life of the SMA-13 mixture with skeleton dense gradation was 55% higher than that of the specification gradation. The results further illustrate that the fatigue performance of the SMA-13 mixture with skeleton dense gradation was better than that of the specification gradation. Thus, the aggregate’s composition of SMA-13 mixture dominates its mechanical properties. The skeleton dense gradation of SMA-13 mixture contain the certain coarse aggregates to formed the skeleton dense structure that having better fatigue resistance performance of SMA mixtures.


## 7. Conclusions

This study analyzed the influence of compaction methods, gradations, and stress levels on the fatigue performance of the SMA-13 mixtures by conducting the indirect tensile fatigue test. The conclusions are as follows:(i)
According to the failure characteristics of the SMA-13 mixture based on the indirect tensile fatigue test, the failure process is divided into four stages: full stress, fatigue crack initiation, fatigue crack expansion, and failure. Moreover, the Weibull distribution was an operational and effective assumption for the fatigue life distribution of the SMA-13 mixture with different stress levels and compaction methods.(ii)
After taking the logarithm of fatigue life and stress level, we found that the fatigue life of the SMA-13 mixtures decrease linearly with the increase of the stress level under the same failure probability.(iii)
Comparison of fatigue life under the same stress level cannot reflect the influence of the ultimate strength of various asphalt mixtures on the fatigue life. Then, the same loading stress was used for comparison of the fatigue performance of various types of SMA-13 mixture. When the loading stress was 0.456 MPa, the fatigue life of the SMA-13 mixture compacted by the VTM method was 56% and 210% higher than that of the SGC and Marshall methods, respectively.(iv)
Gradation significantly influences the fatigue performance of SMA-13 mixtures, when the loading stress was 0.456 MPa, the fatigue life of the SMA-13 mixture with skeleton dense gradation was 55% higher than that of the specification gradation.



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