# Effects of Test Conditions on APA Rutting and Prediction Modeling for Asphalt Mixtures

Authors: Hui Wang; Haoqi Tan; Tian Qu; Jiupeng Zhang
Journal: Advances in Materials Science and Engineering
 (2017)

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## Abstract

APA rutting tests were conducted for six kinds of asphalt mixtures under air-dry and immersing conditions. The influences of test conditions, including load, temperature, air voids, and moisture, on APA rutting depth were analyzed by using grey correlation method, and the APA rutting depth prediction model was established. Results show that the modified asphalt mixtures have bigger rutting depth ratios of air-dry to immersing conditions, indicating that the modified asphalt mixtures have better antirutting properties and water stability than the matrix asphalt mixtures. The grey correlation degrees of temperature, load, air void, and immersing conditions on APA rutting depth decrease successively, which means that temperature is the most significant influencing factor. The proposed indoor APA rutting prediction model has good prediction accuracy, and the correlation coefficient between the predicted and the measured rutting depths is 96.3%.


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## Body

## 1. Introduction

Rutting prevention has become one of the most in-demand topics of study with more-extensive research on damage to asphalt pavement. Studies all over the world have established a variety of rutting test methods to analyze and evaluate the antirutting properties of asphalt mixtures. APA (Asphalt Pavement Analyzer) rutting test has gained much international attention in recent years for such advantages as the ability to simulate live load conditions. In 2001, NCAT (National Center for Asphalt Technology) evaluated the applicability of various methods for evaluating the antirutting performance, including APA, HWTD (Hamburg Wheel-tracking Device), FRT (French Pavement Rutting Tester), RLWT, and triaxial repeated load creep tests, and preferentially recommended APA rutting test. Subsequently, numbers of research have conducted the antirutting properties of asphalt mixtures by using APA test.Xie et al. researched moisture susceptibility through APA and analyzed the results of water-submerged rut testing, from which they presented an index of water submergence stability to assess water resistance of different asphalt mixtures [1]. Han et al. investigated the effects of water on permanent deformation potential by using APA and indicated that APA testing form, preconditioning conditions, and the freezing and thawing cycle times are the main universal reasons that cause a greater extent of deformation in wet rut compared with dry rut [2]. Zhang et al. presented a rule of the effect of different size aggregates on the high-temperature performance of asphalt mixtures on the basis of APA tests and indicated a reasonable percentage of different size aggregates, which could help to design both skeleton and dense-construction asphalt mixtures [3]. Junbiao et al. used digital image-processing to analyze the loading modes of the RLWT (Rotary Loaded Wheel Tester) and APA rutting tests, by comparing the angle between the long axis and the x-axis of coarse aggregates in RLWT testing specimens, APA testing specimens, and untested specimens; they found that the loading modes of RLWT and APA rutting tests differ notably [4]. Cao et al. studied the deformation property of asphalt mixtures at constant and varying temperatures through APA and determined that deformation curves have two phases: delayed elastic deformation and viscous deformation [5]. Xue et al. performed APA tests on SAWI (Stress-Absorbing Waterproof Interlayers) to analyze the fatigue properties and indicated that the fatigue life of SAWI is 3.32 times that of common asphalt concrete [6]. Xiao et al. researched the compaction properties of different asphalt mixtures and analyzed their abilities to resist rutting and water damage by using APA [7, 8]. Rushing and Little assessed rutting sensitivity through APA, triaxial static creep, and triaxial repeated load creep tests and found that the increasing rate of permanent strain and the flow time value determined via triaxial static creep tests has the strongest correlation to APA rutting depth [9]. Ali et al. assessed antirutting properties of WMA (Warm Mix Asphalt) by using APA, pointing out that reducing the production temperature of foamed WMA might result in the increasing potential of permanent deformation and moisture-induced damage [10]. Xie and Shen researched the rutting resistance, moisture susceptibility, and fatigue resistance of rubberized SMA (Stone Matrix Asphalt), analyzing the incorporation of CRM (Crumb Rubber Modifier) by using APA [11]. Malladi et al. researched moisture and rutting susceptibility of WMA by using APA and indicated that WMA performance is on a par with that of HMA and good potential for the widespread use of WMA [12].Numbers of achievements have been obtained on APA test in the last decades, and most of the previous research focused on the evaluation of asphalt mixture antirutting performance by using APA test. Few attempts have reported the effects of testing conditions on APA rutting depth and are not sufficient in understanding the results of APA rutting tests influenced by test conditions. Therefore, in this paper, the APA experiments were performed under different test conditions for further understanding the influences of load, temperature, and other conditions on rutting depth, and an APA rutting prediction model was established to provide reference for further popularization and application of APA rutting tests.


## 2. Experimental Design

### 2.1. Asphalt Mixture Design and Specimen Preparation

Four kinds of AC-20 (Asphalt Concrete whose nominal maximum size of aggregate is 20 mm) asphalt mixtures and two kinds of AC-13 (Asphalt Concrete whose nominal maximum size of aggregate is 13 mm) asphalt mixtures (namely, AC-20 coarse-type modified asphalt, AC-20 coarse-type matrix asphalt, AC-20 fine-type modified asphalt, AC-20 fine-type matrix asphalt, AC-13 modified asphalt, and AC-13 matrix asphalt) were designed according to highway project to research the influence of experimental conditions on APA rutting tests. Shell 70 matrix asphalt and SBS modified asphalt were used in the experiments. Their technical properties are given in Table1, and Table 2 conforms to the technical requirements published inTechnical Specification for Construction of Highway Asphalt Pavement (JTG F40-2004).Table 1
Technical properties of Shell 70 matrix asphalt.
Test index
Unit
Test result
Technical requirement
Penetration (100 g, 5 s, 25°C)
0.1 mm
76.83
60~80
Penetration index
—
−1.2
−1.5~1.0
Softening point
°C
46.2
≥45
Ductility (5 cm/min, 10°C)
cm
79.5
>25
Ductility (5 cm/min, 15°C)
cm
138.0
>100
Wax content (distillation method)
%
1.9
≤2.2
Flash point
°C
316.3
≥260
Solubility
%
99.58
≥99.5
Density (15°C)
g/cm3
1.036
Measured records
Density (25°C)
g/cm3
1.033
—
Quality loss after RTFOT
%
0.170
±0.8
Residual penetration after RTFOT (100 g, 5 s, 25°C)
0.1 mm
52.83
—
Penetration ratio after RTFOT (25°C)
%
68.76
≥61
Residual ductility after RTFOT (5 cm/min, 10°C)
cm
10.4
>6
Residual ductility after RTFOT (5 cm/min, 15°C)
cm
46.8
>15Table 2
Technical properties of SBS modified asphalt.
Test index
Unit
Test result
Technical requirement
Penetration (100 g, 5 s, 25°C)
0.1 mm
65.67
60~80
Penetration index
—
0.1
≥−0.4
Softening point
°C
83.1
≥55
Ductility (5 cm/min, 5°C)
cm
33.8
≥30
Flash point
°C
272
≥230
Solubility
%
99.7
≥99
Elastic recovery (25°C)
%
99.67
≥65
Segregation of storage stability, difference of softening point after 48 h
°C
1.6
≤2.5
Density (15°C)
g/cm3
1.034
—
Relative density (15°C)
—
1.037
—
Density (25°C)
g/cm3
1.030
—
Relative density (25°C)
—
1.033
—
Quality loss after RTFOT
%
−0.2
±1.0
Residual penetration after RTFOT (100 g, 5 s, 25°C)
0.1 mm
48.7
—
Penetration ratio after RTFOT (25°C)
%
74.16
≥60
Residual ductility after RTFOT (5 cm/min, 5°C)
cm
21.46
≥20Three kinds of aggregate gradations (namely, AC-20 coarse-type, AC-20 fine type, and AC-13) were selected to mix with two kinds of asphalt binders, respectively, to prepare six kinds of asphalt mixtures. Optimal asphalt contents of asphalt mixtures were determined by the Marshall method; the results are presented in Table3.Table 3
Design gradations and optimal asphalt contents of asphalt mixtures.
Gradation type
Mass percentage (%) through the following mesh (mm)
OAC (%)
26.5
19
16
13.2
9.5
4.75
2.36
1.18
0.6
0.3
0.15
0.075
Matrix asphalt
Modified asphalt
AC-20 C-type
100
92.3
82.9
69.6
58.2
39.9
27.3
18.7
13.7
10.9
6.9
4.7
4.0
4.2
AC-20 F-type
100
95.1
88.9
79.7
68.5
53.3
40.9
31.1
21.6
16.3
8.9
5.4
4.3
4.3
AC-13
100
100
100
97.3
75.4
45.6
27.1
20.3
14.2
10.7
8.2
5.1
5.1
4.9Cylinder specimens (Φ 150 × 75 mm) were molded by using SGC (Superpave Gyratory Compactor) according to the results of the material composition designs given previously, and the target air voids were 4 and 7%.


### 2.2. APA Rutting Test Schemes

APA rutting tests using SGC cylinder specimens (as shown in Figure1) were conducted in both dry and immersion conditions, respectively. Under dry conditions, the specimens with 4% air voids were selected for APA rutting tests, and the test temperatures were 40, 50, and 60°C. The APA rutting test was the force of a concave wheel applied indirectly on the specimen through an inflatable rubber hose. In this paper, standard load was 445±22 N; standard air pressure of the rubber hose was 690±22 kPa; and running frequency of the wheel was 60 Hz, that is, 60 times back and forth per minute. To analyze the effect of overloading on APA rutting, two combinations of load and tire pressure (533 N/827 kPa and 889 N/827 kPa) were increased to test at 60°C.Figure 1
Cylinder specimens in APA testing.Under immersion conditions, the specimens with the air voids of 4 and 7% were tested, respectively; test temperatures were 50 and 60°C, respectively; load was 445 N; and tire pressure was 690 kPa. All the specimens were placed in APA test machines at the test temperature for 6–24 h before testing to ensure that the specimens would reach the test temperature and maintain temperature equalizing.


## 2.1. Asphalt Mixture Design and Specimen Preparation

Four kinds of AC-20 (Asphalt Concrete whose nominal maximum size of aggregate is 20 mm) asphalt mixtures and two kinds of AC-13 (Asphalt Concrete whose nominal maximum size of aggregate is 13 mm) asphalt mixtures (namely, AC-20 coarse-type modified asphalt, AC-20 coarse-type matrix asphalt, AC-20 fine-type modified asphalt, AC-20 fine-type matrix asphalt, AC-13 modified asphalt, and AC-13 matrix asphalt) were designed according to highway project to research the influence of experimental conditions on APA rutting tests. Shell 70 matrix asphalt and SBS modified asphalt were used in the experiments. Their technical properties are given in Table1, and Table 2 conforms to the technical requirements published inTechnical Specification for Construction of Highway Asphalt Pavement (JTG F40-2004).Table 1
Technical properties of Shell 70 matrix asphalt.
Test index
Unit
Test result
Technical requirement
Penetration (100 g, 5 s, 25°C)
0.1 mm
76.83
60~80
Penetration index
—
−1.2
−1.5~1.0
Softening point
°C
46.2
≥45
Ductility (5 cm/min, 10°C)
cm
79.5
>25
Ductility (5 cm/min, 15°C)
cm
138.0
>100
Wax content (distillation method)
%
1.9
≤2.2
Flash point
°C
316.3
≥260
Solubility
%
99.58
≥99.5
Density (15°C)
g/cm3
1.036
Measured records
Density (25°C)
g/cm3
1.033
—
Quality loss after RTFOT
%
0.170
±0.8
Residual penetration after RTFOT (100 g, 5 s, 25°C)
0.1 mm
52.83
—
Penetration ratio after RTFOT (25°C)
%
68.76
≥61
Residual ductility after RTFOT (5 cm/min, 10°C)
cm
10.4
>6
Residual ductility after RTFOT (5 cm/min, 15°C)
cm
46.8
>15Table 2
Technical properties of SBS modified asphalt.
Test index
Unit
Test result
Technical requirement
Penetration (100 g, 5 s, 25°C)
0.1 mm
65.67
60~80
Penetration index
—
0.1
≥−0.4
Softening point
°C
83.1
≥55
Ductility (5 cm/min, 5°C)
cm
33.8
≥30
Flash point
°C
272
≥230
Solubility
%
99.7
≥99
Elastic recovery (25°C)
%
99.67
≥65
Segregation of storage stability, difference of softening point after 48 h
°C
1.6
≤2.5
Density (15°C)
g/cm3
1.034
—
Relative density (15°C)
—
1.037
—
Density (25°C)
g/cm3
1.030
—
Relative density (25°C)
—
1.033
—
Quality loss after RTFOT
%
−0.2
±1.0
Residual penetration after RTFOT (100 g, 5 s, 25°C)
0.1 mm
48.7
—
Penetration ratio after RTFOT (25°C)
%
74.16
≥60
Residual ductility after RTFOT (5 cm/min, 5°C)
cm
21.46
≥20Three kinds of aggregate gradations (namely, AC-20 coarse-type, AC-20 fine type, and AC-13) were selected to mix with two kinds of asphalt binders, respectively, to prepare six kinds of asphalt mixtures. Optimal asphalt contents of asphalt mixtures were determined by the Marshall method; the results are presented in Table3.Table 3
Design gradations and optimal asphalt contents of asphalt mixtures.
Gradation type
Mass percentage (%) through the following mesh (mm)
OAC (%)
26.5
19
16
13.2
9.5
4.75
2.36
1.18
0.6
0.3
0.15
0.075
Matrix asphalt
Modified asphalt
AC-20 C-type
100
92.3
82.9
69.6
58.2
39.9
27.3
18.7
13.7
10.9
6.9
4.7
4.0
4.2
AC-20 F-type
100
95.1
88.9
79.7
68.5
53.3
40.9
31.1
21.6
16.3
8.9
5.4
4.3
4.3
AC-13
100
100
100
97.3
75.4
45.6
27.1
20.3
14.2
10.7
8.2
5.1
5.1
4.9Cylinder specimens (Φ 150 × 75 mm) were molded by using SGC (Superpave Gyratory Compactor) according to the results of the material composition designs given previously, and the target air voids were 4 and 7%.


## 2.2. APA Rutting Test Schemes

APA rutting tests using SGC cylinder specimens (as shown in Figure1) were conducted in both dry and immersion conditions, respectively. Under dry conditions, the specimens with 4% air voids were selected for APA rutting tests, and the test temperatures were 40, 50, and 60°C. The APA rutting test was the force of a concave wheel applied indirectly on the specimen through an inflatable rubber hose. In this paper, standard load was 445±22 N; standard air pressure of the rubber hose was 690±22 kPa; and running frequency of the wheel was 60 Hz, that is, 60 times back and forth per minute. To analyze the effect of overloading on APA rutting, two combinations of load and tire pressure (533 N/827 kPa and 889 N/827 kPa) were increased to test at 60°C.Figure 1
Cylinder specimens in APA testing.Under immersion conditions, the specimens with the air voids of 4 and 7% were tested, respectively; test temperatures were 50 and 60°C, respectively; load was 445 N; and tire pressure was 690 kPa. All the specimens were placed in APA test machines at the test temperature for 6–24 h before testing to ensure that the specimens would reach the test temperature and maintain temperature equalizing.


## 3. Results and Discussion

### 3.1. Influence of Temperature on APA Rutting under Dry Conditions

Under dry conditions, the APA rutting depth development trends for different types of asphalt mixtures under three different temperatures are shown in Figures2–4. Results show the high-temperature performances of the asphalt mixtures according to rutting depth-size order, under three different temperatures reaching unanimity, namely, AC-20 fine-type matrix asphalt mixture > AC-13 matrix asphalt mixture > AC-20 coarse-type matrix asphalt mixture > AC-20 fine-type modified asphalt mixture > AC-13 modified asphalt mixture > AC-20 coarse-type modified asphalt mixture. Thus, it shows that modified bitumen can improve the high-temperature performance of asphalt mixtures. At a test temperature of 40°C, the growth of rutting of different asphalt mixtures is moderate with small degree rutting. At 50°C, rutting is 2-3 times bigger than rutting at 40°C; rutting at 60°C is approximately 1.5 times bigger than rutting at 50°C and 3–5 times bigger than rutting at 40°C. Comparisons of APA rutting test results indicate that temperature appears to significantly affect the development of rutting, which has been confirmed by Zhang et al. [13–15].Figure 2
APA rutting depths of asphalt mixtures at 40°C under air-dry conditions.Figure 3
APA rutting depths of asphalt mixtures at 50°C under air-dry conditions.Figure 4
APA rutting depths of asphalt mixtures at 60°C under air-dry conditions.Results show that rutting depth changes with the number of loads and the temperature, according to the APA rutting test results under different temperatures. Thus, the temperature-effects regression model shown in (1) was established.(1)RR0=TT0αNN0β,where R is the predicted rutting depth (mm); R0 is the benchmark rutting depth under temperature T0 and at loading times N0 on the basis of the rutting test (mm); T,N are the test temperature and the loading times corresponding to the predicted rutting depth; and α,β are the regression coefficients of the materials.For the asphalt mixtures, many factors, such as asphalt properties, asphalt content, air void, aggregate gradation, and others could influence rutting depthR and the performance coefficient of the materials α,β. The model would be greatly complicated if these factors were considered in the temperature-effects regression model of rutting depth. Therefore, to simplify the model, R0 is introduced into formula (1) to standardize the influence of the asphalt mixture type for predicting rutting depth. Benchmark rutting depth R0 is the result of the APA rutting test under various conditions of temperature T0 and loading times N0. Groups of data (324) from 54 times rutting tests were used in the regression analysis. Eight benchmark depths were selected to regress, respectively, and each of them corresponded to different test temperatures and loading times. The regression analyses show the following: a correlation coefficient of R≥0.94, high correlations exist between both the independent and the dependent variables; standard error ≤ 0.2 mm, the fitting degree of regression equation is good; and significance F<0.01, the established regression equation is very significant. The average values α=3.062 and β=0.246 were applied in the regression equation because a negligible difference exists between the regression coefficients α,β obtained from the eight benchmark depths. Thus, (2) can be obtained.(2)RR0=TT03.062NN00.246.


### 3.2. Influence of Load on APA Rutting under Dry Conditions

Under dry conditions, the influence from combinations of different loads and tire pressures on the APA rutting depth of asphalt mixtures is shown in Figure5. The results show that the orders of asphalt mixtures under three combinations of load and tire pressure (namely, 690 kPa/445 N, 827 kPa/533 N, and 827 kPa/889 N) are the same, from excellent to poor for AC-20 coarse-type modified asphalt, AC-13 modified asphalt, AC-20 fine-type modified asphalt, AC-20 coarse-type matrix asphalt, AC-13 matrix asphalt, and AC-20 fine-type matrix asphalt, respectively.Figure 5
APA rutting depths of asphalt mixtures at different combinations of load and tire pressure.
(a)
Matrix asphalt mixture
(b)
Modified asphalt mixtureThe testing results are consistent with research results of Gu et al., which indicate rutting depths all tend to increase with increases in load and tire pressure [16, 17]. Little difference exists among rutting test results under combinations of 690 kPa/445 N and 827 kPa/533 N; rutting depths under combinations of 827 kPa/533 N were approximately 1.08 times that of the rutting depths under combinations of 690 kPa/445 N. Comparing combinations of 690 kPa/445 N revealed that the load of 827 kPa/533 N increased 20% and tire pressure increased 20%, however, tire ground pressure increased by only 6%, that is, 42 kPa. A large difference exists between the rutting test results under combinations of 827 kPa/889 N and two other combinations. For matrix asphalt mixtures, rutting deeper than 12 mm appeared under far fewer than 8000 load times. For modified asphalt mixtures, the rutting depths under combinations of 827 kPa/889 N were approximately 2.72 times that of rutting depths under combinations of 690 kPa/445 N and approximately 2.45 times that of rutting depths under combinations of 827 kPa/533 N. Thus, overloading requires more attention for its significant effect on the rutting depth of asphalt mixtures.


### 3.3. Development Trend of Immersion APA Rutting

Development trends of APA rutting depth of asphalt mixtures with the air voids of 4% and 7% under different temperature and humidity conditions are shown in Figures6–9. Cracking, asphalt exfoliating, and stripping appeared at the interface of aggregate and asphalt under the water bath condition in the APA rutting test. A decline in the adhesion of aggregate and asphalt also results in the reduction of the structural stability of the asphalt mixture. The larger rutting appeared under the drier conditions in the APA rutting test.Figure 6
APA rutting depths of asphalt mixtures with 4% air voids at 60°C under immersing conditions.Figure 7
APA rutting depths of asphalt mixtures with 7% air voids at 60°C under immersing conditions.Figure 8
APA rutting depths of asphalt mixtures with 4% air voids at 50°C under immersing conditions.Figure 9
APA rutting depths of asphalt mixtures with 7% air voids at 50°C under immersing conditions.The rutting depth ratio is defined as the ratio of dry rutting depth and immersion rutting depth, and the water stability of asphalt mixture with greater rutting ratio is better [18]. The rutting depth ratios were calculated according to APA rutting depths under different immersing conditions, and the results are shown in Figures 10–13.Figure 10
Rutting depth ratio of specimens with 4% air void at 60°C under different rolling times.
(a)
Matrix asphalt mixture
(b)
Modified asphalt mixtureFigure 11
Rutting depth ratios of specimens with 7% air void at 60°C under different rolling times.
(a)
Matrix asphalt mixture
(b)
Modified asphalt mixtureFigure 12
Rutting depth ratios of specimens with 4% air void at 50°C under different rolling times.
(a)
Matrix asphalt mixture
(b)
Modified asphalt mixtureFigure 13
Rutting depth ratios of specimens with 7% air void at 50°C under different rolling times.
(a)
Matrix asphalt
(b)
Modified asphaltAnalyses show that the rutting depth ratio of the modified asphalt mixture is greater which means that the water stability is better considering the viscosity of modified asphalt is greater than that of matrix asphalt, more polar materials exist in the matrix asphalt, and the matrix asphalt has good wettability. The water stabilities of the AC-13 modified asphalt mixture and the AC-13 matrix asphalt mixture are worse than those of the other limestone mixtures because of the use of acidic stone granite. The AC-13 matrix asphalt mixture is obvious, its rutting depth ratio is the smallest, and the specimens were spilled at the test temperature of 60°C.Comparisons of the rutting depth ratios at different loading times show that the rutting depth ratios increases, whereas the influence of water decreases gradually with the increase in loading times. The air void of asphalt mixtures decreases and the aggregate skeleton resistance increases with the repeated action of the loading wheel. The increasing amplitude of pore-water pressure is smaller compared to that of the increasing amplitude of the aggregate skeleton resistance, although pore-water pressure also increases. Thus, the influence of water decreases gradually. The results also show that the order of the water stability of the asphalt mixture ordered by rutting depth ratios under 25 or by 4000 loading times is not stable, whereas the order of the water stability of the asphalt mixture ordered by rutting depth ratios under 8000 loading times is more stable. Therefore, 8000 loading times of APA equipment should be ensured when evaluating tests of water stability performance, and test results from loading times under 25 or 4000 are not recommended for evaluating water stability of asphalt mixtures.


### 3.4. Grey Correlation Analyses of Influencing Factors in APA Rutting Tests

Numbers of researchers analyzed influencing factors of rutting deformation characteristics on asphalt pavement. Peilong et al. analyzed the correlation of influencing factors of rut resistance using grey theory, indicating that rut deformation rate has the maximum grey correlation with rate rut depth among five influencing factors of void ratio, graduation index, rut deformation rate, passing rate at 4.75 mm in middle layer, and filler/asphalt ration [19]. But few attempts have been reported about effects of test conditions on APA rutting using grey theory. Therefore, the correlation degrees of temperature, combinations of load and tire pressure, and water on APA rutting depths were researched by using the grey correlation method on the basis of the tests described previously [20]. The grey correlation method orders correlation degrees and identify the main factor influencing the target value by calculating their target values and influence factors.Firstly, pinpoint both the reference sequence and the compared sequence when using the grey correlation method for analysis. Assume that the reference sequence isX0, X0=X0k∣k=1,2,…,n; the comparison sequence is Xii=1,2,…,m, Xi=Xik∣k=1,2,…,n. Establish an average value for each of these sequences; namely, each sequence is divided by the average value, and a new sequence is obtained.(3)Y0=Y0k=X0k/∣k=1,2,…,n.In (3), X0-=∑k=1nX0k/N.(4)Yi=Yik=Xik/∣k=1,2,…,n.In (4), Xi-=∑k=1nXik/N,(i=1,2,…,m).Y
0 is new reference sequence; Yi is a new compared sequence. The correlation of the reference curve and the compared curve at time K (indicator and space) is(5)ζik=mini⁡mink⁡Y0k-Yik+ζmaxi⁡maxk⁡Y0k-YikY0k-Yik+ζmaxi⁡maxk⁡Y0k-Yik.In (5), ζ is the distinguish coefficient; its value is between 0 and 1; mini⁡mink⁡Y0(k)-Yi(k) is the smallest difference between two poles; maxi⁡maxk⁡Y0(k)-Yi(k) is the biggest difference between two poles; k=1,2,…,n; i=1,2,…,m.The expression of the correlation degree isγi=1/N∑Nnζi(k); γi is the correlation degree of the curve Xi(Yi) and the reference sequence X0(Y0). When the correlation degrees are ordered, the results show that the bigger γi leads to the steadier development trend of Xi and X0 and the greater influence of Xi on X0. The calculation results of the grey correlation degree of different factors are shown in Figure 14. The Abscissas 1 to 6 corresponded to the AC-20 coarse-type matrix asphalt mixture, AC-20 coarse-type modified asphalt mixture, AC-20 fine-type matrix asphalt mixture, AC-20 fine-type modified asphalt mixture, AC-13 matrix asphalt mixture, and the AC-13 modified asphalt mixture.Figure 14
Grey correlation degrees of temperature, air void, load, and immersing condition.The results show that the order of correlation degree is temperature, load, air void, and immersing condition. Thus, temperature is the closest correlation associated with asphalt mixture rutting depth. The main reason is that the asphalt binder in the asphalt mixture is temperature-sensitive, and the deformation depends significantly on temperature. Under high-temperature conditions, the asphalt is prone to flow, and rutting appears. This finding also verifies that asphalt pavement rutting forms mainly under high temperatures. Also, load is closely associated with asphalt mixture rutting depth. Increasing the load might damage the interlock structure between the aggregates in the asphalt mixture, which might affect the temperature of the pavement structure and lead to rutting. The relationship between air void and rutting is that the existence of air voids might cause supplementary compaction under loading. However, the air voids of asphalt mixtures are limited. Hence, the correlation degree of air voids is relatively low. Meanwhile, rutting should be weak. Water damage to the asphalt mixture is mainly attributable to water entering the interface of the asphalt and the aggregate and causing asphalt and aggregate spalling. However, mixtures with dense gradation are mainly used in this research while the water that could enter the interface of the asphalt to aggregate is limited. Thus, water has a relatively low influence on the stability of mixtures.


## 3.1. Influence of Temperature on APA Rutting under Dry Conditions

Under dry conditions, the APA rutting depth development trends for different types of asphalt mixtures under three different temperatures are shown in Figures2–4. Results show the high-temperature performances of the asphalt mixtures according to rutting depth-size order, under three different temperatures reaching unanimity, namely, AC-20 fine-type matrix asphalt mixture > AC-13 matrix asphalt mixture > AC-20 coarse-type matrix asphalt mixture > AC-20 fine-type modified asphalt mixture > AC-13 modified asphalt mixture > AC-20 coarse-type modified asphalt mixture. Thus, it shows that modified bitumen can improve the high-temperature performance of asphalt mixtures. At a test temperature of 40°C, the growth of rutting of different asphalt mixtures is moderate with small degree rutting. At 50°C, rutting is 2-3 times bigger than rutting at 40°C; rutting at 60°C is approximately 1.5 times bigger than rutting at 50°C and 3–5 times bigger than rutting at 40°C. Comparisons of APA rutting test results indicate that temperature appears to significantly affect the development of rutting, which has been confirmed by Zhang et al. [13–15].Figure 2
APA rutting depths of asphalt mixtures at 40°C under air-dry conditions.Figure 3
APA rutting depths of asphalt mixtures at 50°C under air-dry conditions.Figure 4
APA rutting depths of asphalt mixtures at 60°C under air-dry conditions.Results show that rutting depth changes with the number of loads and the temperature, according to the APA rutting test results under different temperatures. Thus, the temperature-effects regression model shown in (1) was established.(1)RR0=TT0αNN0β,where R is the predicted rutting depth (mm); R0 is the benchmark rutting depth under temperature T0 and at loading times N0 on the basis of the rutting test (mm); T,N are the test temperature and the loading times corresponding to the predicted rutting depth; and α,β are the regression coefficients of the materials.For the asphalt mixtures, many factors, such as asphalt properties, asphalt content, air void, aggregate gradation, and others could influence rutting depthR and the performance coefficient of the materials α,β. The model would be greatly complicated if these factors were considered in the temperature-effects regression model of rutting depth. Therefore, to simplify the model, R0 is introduced into formula (1) to standardize the influence of the asphalt mixture type for predicting rutting depth. Benchmark rutting depth R0 is the result of the APA rutting test under various conditions of temperature T0 and loading times N0. Groups of data (324) from 54 times rutting tests were used in the regression analysis. Eight benchmark depths were selected to regress, respectively, and each of them corresponded to different test temperatures and loading times. The regression analyses show the following: a correlation coefficient of R≥0.94, high correlations exist between both the independent and the dependent variables; standard error ≤ 0.2 mm, the fitting degree of regression equation is good; and significance F<0.01, the established regression equation is very significant. The average values α=3.062 and β=0.246 were applied in the regression equation because a negligible difference exists between the regression coefficients α,β obtained from the eight benchmark depths. Thus, (2) can be obtained.(2)RR0=TT03.062NN00.246.


## 3.2. Influence of Load on APA Rutting under Dry Conditions

Under dry conditions, the influence from combinations of different loads and tire pressures on the APA rutting depth of asphalt mixtures is shown in Figure5. The results show that the orders of asphalt mixtures under three combinations of load and tire pressure (namely, 690 kPa/445 N, 827 kPa/533 N, and 827 kPa/889 N) are the same, from excellent to poor for AC-20 coarse-type modified asphalt, AC-13 modified asphalt, AC-20 fine-type modified asphalt, AC-20 coarse-type matrix asphalt, AC-13 matrix asphalt, and AC-20 fine-type matrix asphalt, respectively.Figure 5
APA rutting depths of asphalt mixtures at different combinations of load and tire pressure.
(a)
Matrix asphalt mixture
(b)
Modified asphalt mixtureThe testing results are consistent with research results of Gu et al., which indicate rutting depths all tend to increase with increases in load and tire pressure [16, 17]. Little difference exists among rutting test results under combinations of 690 kPa/445 N and 827 kPa/533 N; rutting depths under combinations of 827 kPa/533 N were approximately 1.08 times that of the rutting depths under combinations of 690 kPa/445 N. Comparing combinations of 690 kPa/445 N revealed that the load of 827 kPa/533 N increased 20% and tire pressure increased 20%, however, tire ground pressure increased by only 6%, that is, 42 kPa. A large difference exists between the rutting test results under combinations of 827 kPa/889 N and two other combinations. For matrix asphalt mixtures, rutting deeper than 12 mm appeared under far fewer than 8000 load times. For modified asphalt mixtures, the rutting depths under combinations of 827 kPa/889 N were approximately 2.72 times that of rutting depths under combinations of 690 kPa/445 N and approximately 2.45 times that of rutting depths under combinations of 827 kPa/533 N. Thus, overloading requires more attention for its significant effect on the rutting depth of asphalt mixtures.


## 3.3. Development Trend of Immersion APA Rutting

Development trends of APA rutting depth of asphalt mixtures with the air voids of 4% and 7% under different temperature and humidity conditions are shown in Figures6–9. Cracking, asphalt exfoliating, and stripping appeared at the interface of aggregate and asphalt under the water bath condition in the APA rutting test. A decline in the adhesion of aggregate and asphalt also results in the reduction of the structural stability of the asphalt mixture. The larger rutting appeared under the drier conditions in the APA rutting test.Figure 6
APA rutting depths of asphalt mixtures with 4% air voids at 60°C under immersing conditions.Figure 7
APA rutting depths of asphalt mixtures with 7% air voids at 60°C under immersing conditions.Figure 8
APA rutting depths of asphalt mixtures with 4% air voids at 50°C under immersing conditions.Figure 9
APA rutting depths of asphalt mixtures with 7% air voids at 50°C under immersing conditions.The rutting depth ratio is defined as the ratio of dry rutting depth and immersion rutting depth, and the water stability of asphalt mixture with greater rutting ratio is better [18]. The rutting depth ratios were calculated according to APA rutting depths under different immersing conditions, and the results are shown in Figures 10–13.Figure 10
Rutting depth ratio of specimens with 4% air void at 60°C under different rolling times.
(a)
Matrix asphalt mixture
(b)
Modified asphalt mixtureFigure 11
Rutting depth ratios of specimens with 7% air void at 60°C under different rolling times.
(a)
Matrix asphalt mixture
(b)
Modified asphalt mixtureFigure 12
Rutting depth ratios of specimens with 4% air void at 50°C under different rolling times.
(a)
Matrix asphalt mixture
(b)
Modified asphalt mixtureFigure 13
Rutting depth ratios of specimens with 7% air void at 50°C under different rolling times.
(a)
Matrix asphalt
(b)
Modified asphaltAnalyses show that the rutting depth ratio of the modified asphalt mixture is greater which means that the water stability is better considering the viscosity of modified asphalt is greater than that of matrix asphalt, more polar materials exist in the matrix asphalt, and the matrix asphalt has good wettability. The water stabilities of the AC-13 modified asphalt mixture and the AC-13 matrix asphalt mixture are worse than those of the other limestone mixtures because of the use of acidic stone granite. The AC-13 matrix asphalt mixture is obvious, its rutting depth ratio is the smallest, and the specimens were spilled at the test temperature of 60°C.Comparisons of the rutting depth ratios at different loading times show that the rutting depth ratios increases, whereas the influence of water decreases gradually with the increase in loading times. The air void of asphalt mixtures decreases and the aggregate skeleton resistance increases with the repeated action of the loading wheel. The increasing amplitude of pore-water pressure is smaller compared to that of the increasing amplitude of the aggregate skeleton resistance, although pore-water pressure also increases. Thus, the influence of water decreases gradually. The results also show that the order of the water stability of the asphalt mixture ordered by rutting depth ratios under 25 or by 4000 loading times is not stable, whereas the order of the water stability of the asphalt mixture ordered by rutting depth ratios under 8000 loading times is more stable. Therefore, 8000 loading times of APA equipment should be ensured when evaluating tests of water stability performance, and test results from loading times under 25 or 4000 are not recommended for evaluating water stability of asphalt mixtures.


## 3.4. Grey Correlation Analyses of Influencing Factors in APA Rutting Tests

Numbers of researchers analyzed influencing factors of rutting deformation characteristics on asphalt pavement. Peilong et al. analyzed the correlation of influencing factors of rut resistance using grey theory, indicating that rut deformation rate has the maximum grey correlation with rate rut depth among five influencing factors of void ratio, graduation index, rut deformation rate, passing rate at 4.75 mm in middle layer, and filler/asphalt ration [19]. But few attempts have been reported about effects of test conditions on APA rutting using grey theory. Therefore, the correlation degrees of temperature, combinations of load and tire pressure, and water on APA rutting depths were researched by using the grey correlation method on the basis of the tests described previously [20]. The grey correlation method orders correlation degrees and identify the main factor influencing the target value by calculating their target values and influence factors.Firstly, pinpoint both the reference sequence and the compared sequence when using the grey correlation method for analysis. Assume that the reference sequence isX0, X0=X0k∣k=1,2,…,n; the comparison sequence is Xii=1,2,…,m, Xi=Xik∣k=1,2,…,n. Establish an average value for each of these sequences; namely, each sequence is divided by the average value, and a new sequence is obtained.(3)Y0=Y0k=X0k/∣k=1,2,…,n.In (3), X0-=∑k=1nX0k/N.(4)Yi=Yik=Xik/∣k=1,2,…,n.In (4), Xi-=∑k=1nXik/N,(i=1,2,…,m).Y
0 is new reference sequence; Yi is a new compared sequence. The correlation of the reference curve and the compared curve at time K (indicator and space) is(5)ζik=mini⁡mink⁡Y0k-Yik+ζmaxi⁡maxk⁡Y0k-YikY0k-Yik+ζmaxi⁡maxk⁡Y0k-Yik.In (5), ζ is the distinguish coefficient; its value is between 0 and 1; mini⁡mink⁡Y0(k)-Yi(k) is the smallest difference between two poles; maxi⁡maxk⁡Y0(k)-Yi(k) is the biggest difference between two poles; k=1,2,…,n; i=1,2,…,m.The expression of the correlation degree isγi=1/N∑Nnζi(k); γi is the correlation degree of the curve Xi(Yi) and the reference sequence X0(Y0). When the correlation degrees are ordered, the results show that the bigger γi leads to the steadier development trend of Xi and X0 and the greater influence of Xi on X0. The calculation results of the grey correlation degree of different factors are shown in Figure 14. The Abscissas 1 to 6 corresponded to the AC-20 coarse-type matrix asphalt mixture, AC-20 coarse-type modified asphalt mixture, AC-20 fine-type matrix asphalt mixture, AC-20 fine-type modified asphalt mixture, AC-13 matrix asphalt mixture, and the AC-13 modified asphalt mixture.Figure 14
Grey correlation degrees of temperature, air void, load, and immersing condition.The results show that the order of correlation degree is temperature, load, air void, and immersing condition. Thus, temperature is the closest correlation associated with asphalt mixture rutting depth. The main reason is that the asphalt binder in the asphalt mixture is temperature-sensitive, and the deformation depends significantly on temperature. Under high-temperature conditions, the asphalt is prone to flow, and rutting appears. This finding also verifies that asphalt pavement rutting forms mainly under high temperatures. Also, load is closely associated with asphalt mixture rutting depth. Increasing the load might damage the interlock structure between the aggregates in the asphalt mixture, which might affect the temperature of the pavement structure and lead to rutting. The relationship between air void and rutting is that the existence of air voids might cause supplementary compaction under loading. However, the air voids of asphalt mixtures are limited. Hence, the correlation degree of air voids is relatively low. Meanwhile, rutting should be weak. Water damage to the asphalt mixture is mainly attributable to water entering the interface of the asphalt and the aggregate and causing asphalt and aggregate spalling. However, mixtures with dense gradation are mainly used in this research while the water that could enter the interface of the asphalt to aggregate is limited. Thus, water has a relatively low influence on the stability of mixtures.


## 4. Indoor Rutting Prediction Modeling and Validation Based on APA

With reference to the model of APA rutting depth-temperature-loading times in formula (1), the indoor APA rutting prediction model accounts for many factors such as temperature, loading time, loading level, and air void and presents these factors in (6)RR0=TT0αNN0βPP0γVV0ν,where T0, P0, N0, V0 are the benchmark parameters of the indoor APA rutting prediction model and R0 is the benchmark parameter showing the characterization of resistance to the permanent deformation of the material, which is obtained from the APA rutting depth under specific conditions. The specific conditions are that the test temperature is the reference temperature T0; the test loading time is the reference loading time N0; the test loading level is the reference loading level P0; and the test air void is the reference air void V0.The APA standard test conditions are as follows:T0=60°C; N0=8000 times; P0=0.714 MPa; and V0=4%. The data set (R/R0, T/T0, N/N0, P/P0, and V/V0) could be obtained from the rutting depth under other test conditions R divided by the rutting depth under standard test conditions R0 and other test conditions divided by the standard test conditions. By taking the logarithm of each data in the data set, lg(R/R0) is the dependent variable, while lg(T/T0), lg(N/N0), lg(P/P0), and lg(V/V0) are the independent variables. The regression index could be obtained after multiple regression analyses of the data set. By applying these results to (6), an APA rutting prediction model which could take into consideration any significant factors could be obtained.(7)RR0=TT02.960NN00.243PP01.625VV00.413.According to the predicted APA rutting depth in (7), the correlation coefficient of the predicted and measured APA rutting depths shown in the Figure 15 reaches 96.3%. Only seven data deviations exist, which are more than 1 mm among the measured and the predicted APA rutting depths in 1188 groups of experimental data. The biggest deviation is 2.392 mm.Figure 15
Comparison of measured and predicted APA rutting depths.


## 5. Conclusions

(1)
The orders of rutting depths for 6 kinds of asphalt mixtures under different temperatures and combinations of load and tire pressure are almost the same; that is, AC-20 type matrix asphalt mixture > AC-13 matrix asphalt mixture > AC-20 coarse-type matrix asphalt mixture > AC-20 fine-type modified asphalt mixture > AC-13 modified asphalt mixture > AC-20 coarse-type modified asphalt mixture. Compared with the matrix asphalt mixture, the APA rutting depth of the modified asphalt mixture is smaller. Besides he rutting resistance of the modified asphalt mixture is also better.
(2)
The effect of temperature on the development of rutting is nonnegligible. At a test temperature of 40°C, the development of rutting of different asphalt mixtures is relatively mild, and the rutting depth is small. Rutting depth at a test temperature of 50°C is 2 to 3 times as big as the rutting at 40°C, whereas rutting depth at 60°C is approximately 1.5 times as large as rutting at 50°C. The regression model of APA rutting depth-temperature-loading times was established and verified on the basis of rutting depth under different test temperatures and loading times.
(3)
The correlation degrees of temperature, combinations of load and tire pressure, and water on the APA rutting depth were researched through grey correlation method. The results show that temperature is the most significant influencing factor.
(4)
The indoor APA rutting prediction model considering several factors such as temperature, loading times, loading level, and air void was established. The prediction of this model is precise and convincing. Rutting depth under other conditions could be predicted on the basis of APA rutting depth under these benchmark conditions.



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*Source: 2062758-2017-11-06.xml*