- Email: [email protected]
Effects of freeze-thaw cycles on fatigue performance of asphalt mixture and development of fatigue-freeze-thaw (FFT) uniform equation
Construction and Building Materials 242 (2020) 118043
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Effects of freeze-thaw cycles on fatigue performance of asphalt mixture and development of fatigue-freeze-thaw (FFT) uniform equation Zepeng Fan a,b, Huining Xu a,⇑, Jiazhe Xiao a, Yiqiu Tan a a b
School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150090, China Institute of Highway Engineering, RWTH Aachen University, Aachen 52074, Germany
h i g h l i g h t s Fatigue life N f decreases with increase of saturation and number of freeze-thaw cycle. Decrease rate of fatigue life N f becomes more pronounced at higher stress levels. The fatigue-freeze-thaw (FFT) uniform equation was established.
a r t i c l e
i n f o
Article history: Received 5 August 2019 Received in revised form 21 December 2019 Accepted 2 January 2020
Keywords: Asphalt mixture Freeze-thaw cycles Fatigue life Water saturation Fatigue-freeze-thaw uniform equation
a b s t r a c t Although it is widely recognized that freeze-thaw cycles can accelerate the performance deterioration and lead to premature failures of asphalt pavements, a quantitative understanding of how it affects the fatigue life is so far still lacking. This study aims to identify the effects of freeze-thaw cycles on fatigue performance of asphalt mixture. For this, the indirect tensile fatigue tests were performed up on the specimens to measure the fatigue life of the freeze-thaw damaged specimens. Results suggest that fatigue life Nf decreases with the increase of saturation and number of freeze-thaw cycles and the decrease rate of fatigue life Nf becomes more pronounced at higher stress levels. The effects of freeze-thaw cycles on fatigue performance of asphalt mixture were quantified by establishing fatigue-freeze-thaw (FFT) uniform equation through two different strategies: the equivalent damage principle-based approach and the direct modification approach. A comparison study indicates that the FFT uniform equation based on equivalent damage principle and exponential shift factor function can best describe the coupling effect between freeze-thaw cycles and fatigue. Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction Freeze-thaw cycles has long been recognized as one of the major causes of premature failures of asphalt pavements in cold regions. The damage effect of freeze-thaw cycles was caused by the expansion of water that exists in asphalt mixture when the temperatures are below freezing point. Depending on the region, the asphalt pavements may experience multiple freeze-thaw cycles in one single year [16]. The infiltration of water in asphalt mixtures combined with alternating positive and negative ambient temperature alters the internal structure of asphalt mixture [26–28,30] and leads to performance deterioration of asphalt pavements [23,24].
⇑ Corresponding author. E-mail address: [email protected] (H. Xu). https://doi.org/10.1016/j.conbuildmat.2020.118043 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.
The mechanical properties of asphalt mixture under vehicle loading and/or environmental impacts are closely related to the complicated internal structure [8,17,28,31,32,35]. For purpose of capturing the internal structure evolution of asphalt mixture subjected to freeze-thaw cycles, the X-ray computed tomography (X-CT) technology has been reported to be a powerful tool [9,10,26,29]. Xu et al. [26] employed X-CT technology to obtain the internal structure information of three different types of asphalt mixtures before and after the freeze-thaw cycles. Their results indicate the existence of three structural evolution mechanisms: (1) expansion of existing individual voids; (2) coalescing of two separated air voids and (3) formation of new voids. Xu et al. [29] introduced the information entropy theory to describe the internal structural characteristics of asphalt mixture when subjected to freeze-thaw cycles. Gong et al. [9] investigated the air voids and morphological properties of nano-TiO2/CaCO3 and basalt fiber modified asphalt mixtures under freeze-thaw cycles. It is
2
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
found that the macro voids in the asphalt mixture under 15 freezethaw cycles began to connect gradually, and the number and shape of the air voids were changed. Besides, considerable research efforts were devoted to identifying the effect of freeze-thaw cycles on multiple mechanical performances of asphalt mixture [6,23,30,28,12,14,15,9,11,25,33]. Feng et al. [6] measured the tensile strengths of asphalt mixtures subjected to salt and freeze-thaw cycle conditionings and found that salt has a more significant effect on tensile strength when the percentage of salt is larger than 3% while freeze-thaw cycle shows greater impact when it is smaller than 3%. Lachance-Tremblay et al. [14] evaluated the moisture susceptibility and degradation due to freeze-thaw cycles of asphalt mixture with glass aggregates based on the complex modulus. Results showed that the freezethaw cycles damaged the mixtures and glass asphalt mixture was damaged faster than base mixture before 10 freeze-thaw cycles. In another research conducted by Lachance-Tremblay et al. [15], the improvement effect of hydrated lime on the dynamic mechanical property of asphalt mixture with glass aggregates subjected to water conditioning and freeze-thaw cycles were validated. Though the numerous literature reports, very few have concerned the impact of freeze-thaw cycles on the fatigue performance of asphalt mixture, whereas it is of great importance to asphalt pavement structural design [5,3,34,4,2]. Fatigue behavior of asphalt mixtures is dependent upon a number of variables which can be divided into three categories: load, environmental and mixture. In order to consider the effects of temperature, loading frequency, and mixture type, Monismith and Epps [21] expanded the fatigue equation by incorporating HMA stiffness. Finn et al. [7] further calibrated this model by using the field date from the American Association of State Highway Officials (AASHO) road test sections and the introduced calibration factor accounts for the effects of boundary difference between field and laboratory. Al-Khateeb and Ghuzlan [2] investigate the combined effect of the loading frequency, temperature and stress level on the fatigue life of asphalt paving mixtures. Kestler et al. [13] identified statistically the contributions of specific winter season characteristics (e.g. freeze season length, thaw depth, and depth to water table) to cumulative pavement damage and found that the combination of the surface freezing season length and corresponding average pavement surface temperature appears significant for fatigue performance. To date, a quantitative understanding of how freezethaw cycle affects the fatigue performance of asphalt mixture is so far still lacking. This study was initiated to clarify the effects of freeze-thaw cycles on fatigue performance of asphalt mixture. The specimens were firstly exposed to different combinations of saturation and number of freeze-thaw cycle conditionings after which the indirect tensile fatigue tests were performed to measure the fatigue life of the freeze-thaw damaged specimens. Analyses were then carried out on basis of the test results to investigate the effects of saturation and number of freeze-thaw cycles on fatigue performance deterioration. Lastly, two approaches were adopted to establish the FFT uniform equation and a final recommendation was given based on a comparative study.
2. Objectives The objectives of this study presented in this paper were: Analyze the effects of freeze-thaw cycle conditions (including water saturation and number of freeze-thaw cycles) on the fatigue performance of asphalt mixture; Establish the FFT uniform equation by coupling the effects of freeze-thaw cycle into the conventional fatigue equation.
3. Materials and methods 3.1. Raw materials and mixture design 3.1.1. Asphalt binder In this research, the 60/80 penetration graded SBS modified asphalt was used to fabricate the asphalt mixture specimens. The basic technical properties of the selected asphalt binder were shown in Table 1. 3.1.2. Aggregates and filler The coarse and fine aggregates used in this research were andesite. The technical properties of the coarse and fine aggregates were tested according to the Chinese technical specification Test Methods of Aggregate for Highway Engineering (JTG F42-2005) [19] and results were shown in Tables 2 and 3, respectively. The technical properties of the mineral filler were shown in Table 4. 3.1.3. Mixture design and specimen preparation The conventional dense graded asphalt mixture AC-13 was selected according to the Technical Specifications for Construction of Highway Asphalt Pavements in China (JTG F40-2004) [18] and the detailed aggregate gradation was shown in Table 5. The determined optimal content of asphalt binder for AC-13 was 5.0%. The Superpave gyratory compactor was used to prepare the cylindrical specimens with an angle of gyration of 1.25°, vertical pressure stress of 0.6 MPa, and gyration speed of 30 rpm. The air void content of specimens was controlled as 6%. 3.2. Test methods 3.2.1. Freeze-thaw cycle test In order to investigate the effect of freeze-thaw cycles on the fatigue performance of asphalt mixture, the freeze-thaw cycle tests were performed on the prepared specimens firstly. The test procedure adopted here was obtained by modifying the Saturated Water Content Test of Bituminous Mixtures (T 0716-2011) and Freezethaw Splitting Test of Bituminous Mixtures (T 0729-2000) recommended by Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011) [20]. Four saturation degrees (20%, 50%, 70% and 90%) and six freeze-thaw cycles (5, 10, 15, 20, 25, 30 cycles) were adopted for purpose of studying the effect of saturation and number of freeze-thaw cycles, respectively. Within each FT cycle, the specimen was firstly processed in the solution of distilled water by vacuum saturation with a 98 kPa residual pressure for 15 min. Then the specimen was shaken once and weighted to calculate the saturation level every three minutes until the saturation level falls into the range of 50%±5%. Following this step, the specimen was frozen in the refrigerator 12 h at a temperature of 18 °C. Finally, the specimen was thawed in water bath at 60 °C for 12 h. The specimens were subjected to 5, 10, 15, 20, 25 and 30 cycles respectively. The specimens after different freezethaw cycles (5, 10, 15, 20, 25 and 30) at different saturation degrees (20%, 50%, 70%, and 90%) were to be employed for further tests.
Table 1 Technical properties of the SBS modified asphalt. Indexes
Test value
Technical requirements
Penetration@25 , 5 s, 100 g /0.1 mm Ductility@15 /cm Softening point(R&B)/
66.1 32.8 64.9
60–80 30 55
3
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043 Table 2 Technical properties of the coarse aggregates. Indexes
Screen size (mm)
Bulk specific gravity Apparent specific gravity Water absorption (%) Crushed stone value (%) Weared stone value (%) Flat- elongated particle content (%) Adhesion level
13.2
9.5
4.75
2.36
2.760 2.780 0.53 15.2 13.4 6.1 5
2.754 2.772 0.55 15.1 13.6 9.4 5
2.720 2.760 0.76 14.8 15.9 10.9 5
2.815 2.820 0.78 15.1 16.1 9.5 5
Table 3 Technical properties of the fine aggregates. Indexes
Screen size (mm)
Apparent specific gravity Angularity
1.18
0.6
0.3
0.15
0.075
2.776 41
2.770
2.755
2.758
2.705
Table 4 Technical properties of the mineral filler. Apparent specific gravity
Water content (%)
2.705
0.92
Passing percentage (%) 0.6 mm
0.3 mm
0.15 mm
0.075 mm
100
100
97.5
84.3
Table 5 Gradation of asphalt mixture AC-13. Size (mm)
Percent passing/% 16
13.2
9.5
4.75
2.36
1.18
0.6
0.3
0.15
0.075
AC-13
100
95
76.5
53
37
28
19
13.5
10
6
RT ¼ 0:006287PT =h
ð1Þ
where P T is the maximum applied load (N); h is the height of the specimen (mm). 3.2.3. Indirect tensile fatigue test The indirect tensile fatigue test was performed on both the undamaged and freeze-thaw damaged specimens. The stresscontrol mode was adopted at four stress levels of 30, 40, 50 and 60% of the splitting strength RT . The load applied on the specimens was half-sinusoidal repeated load with the frequency of 10 Hz and the test temperature was 15 . The total number of the repeated load was defined as the fatigue life N f when the specimen cracks completely. Considerable researches have been devoted to fatigue performance of asphalt mixture (Monismith et al., 2000; [34]). It has been demonstrated that the fatigue response of asphalt mixture to repeated load can be defined by relationship of the following form
Nf ¼ k1
k2 1
r
ð2Þ
where N f is number of repetitions to failure; r is magnitude of the stress repeatedly applied; k1 and k2 are fitting coefficients. On the
dual logarithmic coordinate diagram, this relationship is shown as a straight line through
lgNf ¼ lgk1 k2 lgr
ð3Þ
where k2 and lgk1 are the slope and intercept, respectively. This straight line is referred to as the fatigue curve and the fatigue performance of asphalt mixture was to be described in the form of fatigue curve in what follows.
20% saturation 50% saturation 70% saturation 90% saturation
1,6
Splitting strength (MPa)
3.2.2. Splitting test The splitting test was adopted in this study to measure the splitting strength of the undamaged as well as the freeze-thaw cycle damaged specimens. The test was conducted according to the Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011) [20]. The splitting strength RT was calculated through
1,2
0,8
0,4
0
5
10
15
20
25
30
Number of freeze-thaw cycles Fig. 1. The measured splitting strengths of asphalt mixtures subjected to freezethaw cycles.
4
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
Fig. 2. Fatigue curves of asphalt mixtures at different saturations after (a) 5, (b) 10, (c) 15, (d) 20, (e) 25 and (f) 30 freeze-thaw cycles.
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
5
4. Results and discussion 4.1. Effects of freeze-thaw cycles on fatigue performance 4.1.1. Splitting test results The measured splitting strengths of both the undamaged and freeze-thaw cycle damaged asphalt mixtures were shown in Fig. 1. It could be found that the splitting strength of asphalt mixture decreases rapidly with the increase of the number of freezethaw cycles. The reduction effect becomes more significant as the saturation increases. This can be attributed to the fact that the asphalt mixture accumulates more damage when exposed to higher saturation level and more times of freeze-thaw cycles. 4.1.2. Effects of saturation The fatigue Eq. (3) was used to fit the indirect tensile fatigue test results of the undamaged and freeze-thaw cycle damaged specimens. To investigate the effects of saturation on the fatigue performance of asphalt mixture, the fitted fatigue curves of the damaged asphalt mixtures under the condition of varying saturation were compared to that of the undamaged one. The comparisons were grouped by the number of freeze-thaw cycles as shown in Fig. 2. In these comparisons a difference in location of the fatigue curves is indicated. It is easy to see that the location changes comprise two mechanisms: translation in the left direction and rotation in the clockwise direction. The left translation induces a decrease in fatigue life while the clockwise rotation implies a more stress-sensitive fatigue behavior. Fig. 2 shows that the increase in saturation results in a decrease in fatigue life N f regardless of the number of freeze-thaw cycles. Besides, the decrease in fatigue life N f was found to be larger at higher stress levels. It was also found that the location movement of the fatigue curve caused by the increase of saturation becomes more pronounced as the number of freeze-thaw cycles increases. Furthermore, the location changes of the fatigue curves were quantitatively illustrated in Fig. 3 by plotting the intercept versus saturation and slope versus saturation, respectively. It shows that both intercept and slope of the fatigue curves decrease with the increase of saturation. They decrease linearly with the increase of saturation when subjected to fewer freeze-thaw cycles. But for the high freeze-thaw cycle cases, a sharp decline of intercept and slope were observed at low saturations (up to 20%) and the decline rate tends to be constant as the saturation continually increases. Considering that the intercept decrease corresponds to the decrease of fatigue life while the slope decrease represents a more stress-sensitive fatigue behavior, conclusion can be drawn that the increase in saturation results in a decrease in fatigue life N f regardless of the number of freeze-thaw cycles and the decrease in fatigue life N f was found to be larger at higher stress levels. 4.1.3. Effects of number of freeze-thaw cycles Similarly, comparisons were also made to investigate the effects of the number of freeze-thaw cycle on the fatigue performance of asphalt mixture. The comparisons here were grouped by saturation as shown in Fig. 4, and location changes similar to Fig. 2 were observed. It indicates that the increase in number of freeze-thaw cycles resulted in a decrease in the fatigue life N f regardless of saturation and this decrease was found to be larger at higher stress levels. Fig. 4 also shows that the damage caused by the increase of the number of freeze-thaw cycles becomes more pronounced as the saturation increases. Fig. 5 quantified the impact of number of freeze-thaw cycles on location changes of the fatigue curves by plotting the intercept versus number of freeze-thaw cycles and slope versus number of freeze-thaw cycles, respectively. It could be found that both
Fig. 3. Plots of (a) intercept and (b) slope versus saturation.
intercept and slope of the fatigue curves decrease linearly with the increase of number of freeze-thaw cycles. In consideration of the meanings of the intercept and slope parameters, Fig. 5 implies that asphalt mixtures exhibit shorter fatigue lives and become more stress-sensitive when subjected to a higher number of freeze-thaw cycles. Besides, the decreasing rates of intercept and slope of the fatigue curves increase with saturation. 4.2. Establishment of the FFT uniform equation In order that effects of freeze-thaw cycles on fatigue performance of asphalt mixture can be quantitatively considered, this study attempted to establish the FFT uniform equation by means of modifying the conventional fatigue equation. For this, two different kinds of modifying schemes were proposed, as detailed in what follows. 4.2.1. Equivalent damage principle-based approach The equivalent damage principle-based approach begins with reviewing the influence laws of freeze-thaw cycles on fatigue behavior of asphalt mixtures, as schematically illustrated in Fig. 6. In the figure, the damaged curve represents that the test specimens itre exposed to any given degree of freeze-thaw cycles before the fatigue tests were conducted. On basis of the fatigue curve, the fatigue life of the undamaged asphalt mixture at any given stress level r can be calculated to be N f . But for the damaged asphalt mixture, the fatigue life at the same stress level decreases 0
to N f . Then, the damage effect of the employed degree of
6
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
Fig. 4. Fatigue curves of asphalt mixtures after different freeze-thaw cycles under (a) 20%, (b) 50%, (c) 70% and (d) 90% saturation.
freeze-thaw cycles on the fatigue performance of asphalt mixture at stress level
the other hand, for the undamaged asphalt mixture, the fatigue life 0
of N f corresponds to a stress level of
r . This means that for any 0
stress level r, there exists an increased stress level r at which the fatigue life lost due to the test stress increase is equal to that of exposure to the given degree of freeze-thaw cycles. In other words, the damage caused by freeze-thaw cycles can be equivalented to that of increasing the fatigue test stress. Based on this equivalent damage principle, it came to the first approach of coupling the effects of freeze-thaw cycles on fatigue performance of asphalt mixture by establishing the functional relation between freeze-thaw cycle variables and stress increase. In practical terms, this study referenced the theory of TimeTemperature Superposition Principle (TTSP) [1,22] and introduced a shift factor a as 0
r ¼ra 0
ð4Þ
The shift factor a depends on the freeze-thaw cycle variables (i.e. saturation S and number of freeze-thaw cycles n). For the fatigue test specimens experienced no freeze-thaw cycles, the shift factor a is equal to 1. For the specimens subjected to freeze-thaw cycles before fatigue test, the shift factor a > 1 considering the damage effect of freeze-thaw cycles on fatigue performance. Once the functional expression of shift factor a was obtained, one can easily obtain the FFT uniform equation with the expression of
Nf ¼ k1
k2 1
r0
or
0
r can be defined as the fatigue life lost Nf Nf . On
ð5Þ
lgNf ¼ lgk1 k2 lgr
0
ð6Þ
It should be noted that the relations above apply to any two cases in which the specimens were subjected to different degrees of freeze-thaw cycles damage. However, for convenience of description, this research selected the undamaged situation as the reference freeze-thaw cycles state. The follow-up works were based on this assumption in the absence of special explanation. So far, the original issue of establishing the FFT uniform equation has been transformed to the determination of the function of shift factor a with saturation S and number of freeze-thaw cycles n. For this, the influence laws of different freeze-thaw cycle variables on shift factor a were firstly analyzed based on the experiment results before which kind of functional form can be finally determined to use. The concrete steps were: (1) Select the fitted fatigue equation of the undamaged asphalt mixtures as the standard fatigue equation; 0
(2) Substitute the measured fatigue life N f of the damaged asphalt mixtures into the standard fatigue equation and 0 backcalculate the corresponding increased stress r ; (3) Calculate the values of the shift factor according to 0 lga ¼ lgr lgr. The effect of number of freeze-thaw cycles n on shift factor a was investigated firstly as shown in Fig. 7. Considering that lga ¼ 0 holds at n ¼ 0 regardless of the saturationS, function y ¼ f x was employed to conduct the linear fitting and results
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
7
Fig. 7. Linear fittings between logarithm shift factor lga and number of freeze-thaw cycles n.
Furthermore, the relationship between saturation S and slope f was plotted in Fig. 8 for purpose of determining the function form of f ðSÞ. In light of the physical fact that f ¼ 0 when S ¼ 0, the selected function for f ðSÞ should pass through the origin. Therefore, two different kinds of function forms were adopted in this study. The first was the linear function with the expression of f ðSÞ ¼ a S and the second was the exponential function S f ðSÞ ¼ a 1 b . The corresponding fitting results were shown in Fig. 8. It indicates that both of the two functions can well describe the relation between slope f and saturation S with high determination coefficients, and the exponential function is the better one. On basis of the above analysis, the final expression for the shift factor a can be naturally achieved. Corresponding to the two different forms of f ðSÞ, two function expressions were introduced in this approach for shift factor a which were expressed respectively as (I) Linear function Fig. 5. Plots of (a) intercept and (b) slope versus number of freeze-thaw cycles.
were included in the figure. In view of the high determination coefficients, conclusion can be drawn that the logarithm of shift factor lga increases linearly with the number of freeze-thaw cycles n for any given saturation S while the slope f depends on saturation S. Thus, the shift factor a can be expressed as
lga ¼ f ðSÞ n
lga ¼ a n S (II) Exponential function
S lga ¼ a n 1 b
ð9Þ
Eqs. (4) and (5) together with Eqs. (8) or (9) form the final FFT uniform equation for asphalt mixture.
ð7Þ
Fig. 6. Schematic diagram of fatigue curves for undamaged and damaged asphalt mixtures.
ð8Þ
Fig. 8. Curve fitting results between slope f and saturation S.
8
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
Table 6 Summary of the fitting results for established FFT uniform equations. Method
FFT uniform equation
Equivalent damage principle approach
I II
Direct approach
I II III
1 2:82
N f ¼ 1457 r ; lga ¼ 0:238 n S 3:528 ; lga ¼ 0:018 n 1 0:006S N f ¼ 1470 r1 1 2:255þ0:115nS
N f ¼ 103:3430:12nS r
3:4260:018n7:842S
N f ¼ 10
4.2.2. Direct modification approach The desired FFT uniform equation can also be established by modifying the original fatigue Eq. (3) directly. It has been proven in Figs. 3 and 5 that both intercept and slope of the fitted fatigue curve decrease with saturation S and number of freeze-thaw cycles n. Once the functional relations between the freeze-thaw cycle variables and the fatigue curve parameters were established, they can be substituted into the equation to obtain the FFT uniform equation. According to the depicted influence laws of saturation S and number of freeze-thaw cycles n on intercept lgk1 and slope k2 in Figs. 3 and 5, three different kinds of functional forms were selected which were expressed respectively as
lgk1 ¼ a þ b n S
ð10Þ
k2 ¼ c þ d n S
ð11Þ
(II) Exponential function
k2 ¼ d þ e n f
S
5:9 1 2:516þ0:003nð1þSÞ
r
R2
3
0.695
4
0.884
4
0.796
6
0.780
6
0.808
tion coefficient R2 ¼ 0:884. To summarize, the FFT uniform equation II based on the equivalent damage principle is the top recommendation FFT with both good fitting precision and simple function form. The established FFT uniform equation in this study is of great meaning in at least two aspects: firstly, it provides a way to quantitatively identify the effects of freeze-thaw cycles on the fatigue behavior of asphalt mixture; secondly, it makes it possible for the designers to fully grasp the complicated coupling effects of freeze-thaw cycle and fatigue damage across the broad conditional domain with limited experimental results. This is important especially considering that both freeze-thaw cycle and fatigue tests are time-consuming.
5. Conclusions
(I) Linear function
lgk1 ¼ a þ b n cS
r
3:3420:017nð1þSÞ2:98
N f ¼ 10
S 1 2:452þ0:003n68:75
Parameter number
ð12Þ ð13Þ
(III) Power function
lgk1 ¼ a þ b n ð1 þ SÞc
ð14Þ
k2 ¼ d þ e n ð1 þ SÞf
ð15Þ
Then, the final FFT uniform equation can be obtained by substituting the above equations into Eq. (3), respectively. 4.2.3. Summary and review In this study, five FFT uniform equations were proposed in total, among which two were based on the equivalent damage approach and three were based on the direct modification approach. To validate the applicability and compare the advantages and disadvantages of these FFT uniform equations, the nonlinear curve fitting method was adopted to obtain the equation parameters in use of the experimental results and the fitting results were detailed in Table 6. It could be found from Table 6 that the FFT uniform equation I based on the equivalent damage principle has the simplest function form with only three parameters. However, its determination coefficient R2 ¼ 0:695 indicates that it has the worst fitting precision. The three FFT uniform equations based on the direct approach have almost the same fitting precisions while the equation I owns the simplest function form with four parameters. The parameter number of the FFT uniform equation II based on the equivalent damage principle was also four, but it has the highest determina-
In this study, the AC-13 asphalt mixture specimens were fabricated and exposed to different combinations of saturation (20, 50, 70, and 90%) and number (5, 10, 15, 20, 25, and 30 cycles) of freezing-thawing conditioning. The indirect tensile fatigue tests were then performed to measure the fatigue life of the freezethaw damaged specimens and the fatigue curves were established. By comparing the fatigue curves, it is found that the effects of freeze-thaw cycles on fatigue performance of asphalt mixture can be characterized by the location changes of fatigue curves in two mechanisms: translation in the left direction and rotation in the clockwise direction. The left translation induces a decrease in fatigue life while the clockwise rotation implies a more stresssensitive fatigue behavior. The effects of saturation and number of freeze-thaw cycles on location changes of the fatigue curves were quantified, respectively. The intercept and slope of the fatigue curves decrease linearly with the increase of saturation when subjected to fewer freeze-thaw cycles. But for the high freeze-thaw cycle cases, a sharp decline of intercept and slope were observed at low saturations (up to 20%) and the decline rate tends to be constant as the saturation continually increases. However, their values decrease linearly with the increase of number of freeze-thaw cycles regardless of saturation. In consideration of the physical meanings of intercept and slope, this suggests that asphalt mixtures exhibit shorter fatigue lives and become more stress-sensitive when subjected to a higher saturation and number of freeze-thaw cycles. Two different approaches, which are the equivalent damage principle-based approach and direct modification approach, were proposed to establish the FFT uniform equation. In the former, we borrowed techniques from the Time-Temperature Superposition Principle theory and a shift factor function was introduced to associate the freeze-thaw cycle parameters to stress. Among the five developed equations, the one based on equivalent damage principle with an exponential shift factor function is the most recommended since it has relatively few unknown parameters but the highest coefficient of determination. The conclusions obtained in this study were based on the experimental tests of AC-13, and further researches are needed to verify
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
the effects of freeze-thaw cycles on fatigue performance of other types of asphalt mixture. Moreover, the fundamental mechanisms underlying the damage effect of freeze-thaw cycles on fatigue performance of asphalt mixture (e.g. the microstructure evolution of asphalt mixture when subjected to freeze-thaw cycles as well as its relationship with fatigue performance) remain to be further explored in the future work. CRediT authorship contribution statement Zepeng Fan: Data curation, Writing - original draft. Huining Xu: Conceptualization, Methodology, Writing - review & editing. Jiazhe Xiao: Formal analysis, Methodology, Writing - original draft. Yiqiu Tan: Supervision. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the National Natural Science Funds of China (Grant No. 51678207) and Fundamental Research Funds for the Central Universities (Grant No. HIT.BRETIII.201511). The authors gratefully acknowledge their financial support. References [1] G.D. Airey, R. Behzad, Combined bituminous binder and mixture linear rheological properties, Constr. Build. Mater. 18 (2004) 535–548. [2] G.G. Al-Khateeb, K.A. Ghuzlan, The combined effect of loading frequency, temperature, and stress level on the fatigue life of asphalt paving mixtures using the IDT test configuration, Int. J. Fatigue 59 (2014) 254–261. [3] H.D. Benedetto, C.D.L. Roche, H. Baaj, A. Pronk, R. Lundström, Fatigue of bituminous mixtures, Mater. Struct. 37 (3) (2004) 202–216. [4] M. Boudabbous, A. Millien, C. Petit, J. Neji, Energy approach for the fatigue of thermoviscoelastic materials: application to asphalt materials in pavement surface layers, Int. J. Fatigue 47 (1) (2013) 308–318. [5] J. Epps, C. Monismith, Fatigue of Asphalt Concrete Mixtures-Summary of Existing Information. In Gallaway, B. (Ed.), STP508-EB Fatigue of Compacted Bituminous Aggregate Mixtures, (1972), (pp. 19–45). [6] D. Feng, J. Yi, D. Wang, L. Chen, Impact of salt and freeze-thaw cycles on performance of asphalt mixtures in coastal frozen region of China, Cold Reg. Sci. Technol. 62 (1) (2010) 34–41. [7] F.N. Finn, C. Saraf, R. Kulkarni, K. Nair, W. Smith, A. Abdullah, The use of distress prediction subsystems for the design of pavement structures, Proceedings of the 4th International Conference on the Structural Design of Asphalt Pavements, Vol. 1, University of Michigan, Ann Arbor, MI, 1977, pp. 3– 38. [8] X. Gao, Z. Fan, J. Zhang, S. Liu, Micromechanical model for asphalt mixture coupling inter-particle effect and imperfect interface, Constr. Build. Mater. 148 (2017) 696–703. [9] Y. Gong, H. Bi, Z. Tan, G. Tan, Pavement performance investigation of NanoTiO2/CaCO3 and basalt fiber composite modified asphalt mixture under freeze-thaw cycles, Appl. Sci. 8 (2018) 2581, https://doi.org/10.3390/ app8122581. [10] Y. Gong, H. Bi, C. Liang, S. Wang, Microstructure analysis of modified asphalt mixtures under freeze-thaw cycles based on CT Scanning technology, Appl. Sci. 8 (2018) 2191, https://doi.org/10.3390/app8112191. [11] T. Huang, Shuai Qi, M. Yang, S. Lv, H. Liu, J. Zheng, Strength criterion of asphalt mixtures in three-dimensional stress states under freeze-thaw conditions, 8 (2018) p. 1302, doi: 10.3390/app8081302.
9
[12] M.R. Islam, R.A. Tarefder, Effects of large freeze-thaw cycles on stiffness and tensile strength of asphalt concrete, J. Cold Reg. Eng. 30 (1) (2016) 06014006. [13] M.A. Kestler, R.L. Berg, S.R. Bigl, Statistical significance of freeze-thaw related factors on cumulative damage to flexible pavements, Transp. Res. Rec. 2232 (1) (2011) 55–67. [14] E. Lachance-Tremblay, D. Perraton, M. Vaillancourt, H.D. Benedetto, Degradation of asphalt mixtures with glass aggregates subjected to freezethaw cycles, Cold Reg. Sci. Technol. 141 (2017) 8–15. [15] E. Lachance-Tremblay, D. Perraton, M. Vaillancourt, H.D. Benedetto, Effect of hydrated lime on linear viscoelastic properties of asphalt mixtures with glass aggregates subjected to freeze-thaw cycles, Constr. Build. Mater. 184 (2018) 58–67. [16] S. Lamothe, D. Perraton, H. Di. Benedetto, Degradation of hot mix asphalt samples subjected to freeze-thaw cycles and partially saturated with water or brine, Road Mater. Pavement Design 18 (4) (2017) 849–864. [17] E. Masad, V.K. Jandhyala, N. Dasgupta, N. Somadevan, N. Shashidhar, Characterization of air void distribution in asphalt mixes using x-ray computed tomography, J. Mater. Civ. Eng. 14 (2) (2002) 122–129. [18] Ministry of Transport, Technical Specification for Construction of Highway Asphalt Pavements (JTG F40-2004), Chine Communication Press, 2004. [19] Ministry of Transport, Chinese technical specification Test Methods of Aggregate for Highway Engineering (JTG F42-2005), Chine Communication Press, 2005. [20] Ministry of Transport, Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011), Chine Communication Press, 2011. [21] C.L. Monismith, J.A. Epps, Asphalt mixture behavior in repeated flexure, Transportation and Traffic Engineering, University of California at Berkeley, California, 1969. [22] H.M. Nguyen, S. Pouget, H.D. Benedetto, C. Sauzéat, Time-temperature superposition principle for bituminous mixtures, Eur. J. Environ. Civ. Eng. 13 (9) (2009) 1095–1107. [23] E. Ozgan, S. Serin, Investigation of certain engineering characteristics of asphalt concrete exposed to freeze-thaw cycles, Cold Reg. Sci. Technol. 85 (2013) 131–136. [24] N. Tang, C. Sun, S. Huang, S. Wu, Damage and corrosion of conductive asphalt concrete subjected to freeze-thaw cycles and salt, Mater. Res. Innovat. 17 (S1) (2013) 240–245. [25] R. Tarefder, H. Faisal, G. Barlas, Freeze-thaw effects on fatigue LIFE of hot mix asphalt and creep stiffness of asphalt binder, Cold Reg. Sci. Technol. 153 (2018) 197–204. [26] H. Xu, Y. Tan, W. Guo, Internal structural evolution of asphalt mixtures during freeze-thaw cycles, Mater. Des. 86 (2015) 436–446. [27] H. Xu, W. Guo, Y. Tan, Permeability of asphalt mixtures exposed to freeze-thaw cycles, Cold Reg. Sci. Technol. 123 (2016) 99–106. [28] H. Xu, X. Yao, Y. Tan, X-ray computed tomography in hydraulics of asphalt mixtures: Procedure, accuracy, and application, Constr. Build. Mater. 108 (2016) 10–21. [29] H. Xu, H. Li, Y. Tan, L. Wang, Y. Hou, A micro-scale investigation on the behaviors of asphalt mixtures under freeze-thaw cycles using entropy theory and a computerized tomography scanning technique, Entropy 20 (2) (2018) 68. [30] K. Yan, D. Ge, L. You, X. Wang, Laboratory investigation of the characteristics of SMA mixtures under freeze-thaw cycles, Cold Reg. Sci. Technol. 119 (2015) 68–74. [31] J. Yi, S. Shen, B. Muhunthan, D. Feng, Viscoelastic–plastic damage model for porous asphalt mixtures: application to uniaxial compression and freeze-thaw damage, Mech. Mater. 70 (2014) 67–75. [32] Z. You, S. Adhikari, M.E. Kuta, Dynamic modulus simulation of the asphalt concrete using the X-ray computed tomography images, Mater. Struct. 42 (5) (2009) 617–630. [33] L. You, Z. You, Q. Dai, S. Guo, J. Wang, M. Schultz, Characteristics of waterfoamed asphalt mixture under multiple freeze-thaw cycles: laboratory evaluation, J. Mater. Civ. Eng. 30 (11) (2018) 04018270. [34] J. Yu, B. Tsai, X. Zhang, C. Monismith, Development of asphalt pavement fatigue cracking prediction model based on loading mode transfer function, Road Mater. Pavement Des. 13 (3) (2012) 501–517. [35] J. Zhang, Z. Fan, H. Wang, W. Sun, J. Pei, D. Wang, Prediction of dynamic modulus of asphalt mixture using micromechanical method with radial distribution functions, Mater. Struct. 52 (2019) 49.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Effects of freeze-thaw cycles on fatigue performance of asphalt mixture and development of fatigue-freeze-thaw (FFT) uniform equation Zepeng Fan a,b, Huining Xu a,⇑, Jiazhe Xiao a, Yiqiu Tan a a b
School of Transportation Science and Engineering, Harbin Institute of Technology, Harbin 150090, China Institute of Highway Engineering, RWTH Aachen University, Aachen 52074, Germany
h i g h l i g h t s Fatigue life N f decreases with increase of saturation and number of freeze-thaw cycle. Decrease rate of fatigue life N f becomes more pronounced at higher stress levels. The fatigue-freeze-thaw (FFT) uniform equation was established.
a r t i c l e
i n f o
Article history: Received 5 August 2019 Received in revised form 21 December 2019 Accepted 2 January 2020
Keywords: Asphalt mixture Freeze-thaw cycles Fatigue life Water saturation Fatigue-freeze-thaw uniform equation
a b s t r a c t Although it is widely recognized that freeze-thaw cycles can accelerate the performance deterioration and lead to premature failures of asphalt pavements, a quantitative understanding of how it affects the fatigue life is so far still lacking. This study aims to identify the effects of freeze-thaw cycles on fatigue performance of asphalt mixture. For this, the indirect tensile fatigue tests were performed up on the specimens to measure the fatigue life of the freeze-thaw damaged specimens. Results suggest that fatigue life Nf decreases with the increase of saturation and number of freeze-thaw cycles and the decrease rate of fatigue life Nf becomes more pronounced at higher stress levels. The effects of freeze-thaw cycles on fatigue performance of asphalt mixture were quantified by establishing fatigue-freeze-thaw (FFT) uniform equation through two different strategies: the equivalent damage principle-based approach and the direct modification approach. A comparison study indicates that the FFT uniform equation based on equivalent damage principle and exponential shift factor function can best describe the coupling effect between freeze-thaw cycles and fatigue. Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction Freeze-thaw cycles has long been recognized as one of the major causes of premature failures of asphalt pavements in cold regions. The damage effect of freeze-thaw cycles was caused by the expansion of water that exists in asphalt mixture when the temperatures are below freezing point. Depending on the region, the asphalt pavements may experience multiple freeze-thaw cycles in one single year [16]. The infiltration of water in asphalt mixtures combined with alternating positive and negative ambient temperature alters the internal structure of asphalt mixture [26–28,30] and leads to performance deterioration of asphalt pavements [23,24].
⇑ Corresponding author. E-mail address: [email protected] (H. Xu). https://doi.org/10.1016/j.conbuildmat.2020.118043 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.
The mechanical properties of asphalt mixture under vehicle loading and/or environmental impacts are closely related to the complicated internal structure [8,17,28,31,32,35]. For purpose of capturing the internal structure evolution of asphalt mixture subjected to freeze-thaw cycles, the X-ray computed tomography (X-CT) technology has been reported to be a powerful tool [9,10,26,29]. Xu et al. [26] employed X-CT technology to obtain the internal structure information of three different types of asphalt mixtures before and after the freeze-thaw cycles. Their results indicate the existence of three structural evolution mechanisms: (1) expansion of existing individual voids; (2) coalescing of two separated air voids and (3) formation of new voids. Xu et al. [29] introduced the information entropy theory to describe the internal structural characteristics of asphalt mixture when subjected to freeze-thaw cycles. Gong et al. [9] investigated the air voids and morphological properties of nano-TiO2/CaCO3 and basalt fiber modified asphalt mixtures under freeze-thaw cycles. It is
2
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
found that the macro voids in the asphalt mixture under 15 freezethaw cycles began to connect gradually, and the number and shape of the air voids were changed. Besides, considerable research efforts were devoted to identifying the effect of freeze-thaw cycles on multiple mechanical performances of asphalt mixture [6,23,30,28,12,14,15,9,11,25,33]. Feng et al. [6] measured the tensile strengths of asphalt mixtures subjected to salt and freeze-thaw cycle conditionings and found that salt has a more significant effect on tensile strength when the percentage of salt is larger than 3% while freeze-thaw cycle shows greater impact when it is smaller than 3%. Lachance-Tremblay et al. [14] evaluated the moisture susceptibility and degradation due to freeze-thaw cycles of asphalt mixture with glass aggregates based on the complex modulus. Results showed that the freezethaw cycles damaged the mixtures and glass asphalt mixture was damaged faster than base mixture before 10 freeze-thaw cycles. In another research conducted by Lachance-Tremblay et al. [15], the improvement effect of hydrated lime on the dynamic mechanical property of asphalt mixture with glass aggregates subjected to water conditioning and freeze-thaw cycles were validated. Though the numerous literature reports, very few have concerned the impact of freeze-thaw cycles on the fatigue performance of asphalt mixture, whereas it is of great importance to asphalt pavement structural design [5,3,34,4,2]. Fatigue behavior of asphalt mixtures is dependent upon a number of variables which can be divided into three categories: load, environmental and mixture. In order to consider the effects of temperature, loading frequency, and mixture type, Monismith and Epps [21] expanded the fatigue equation by incorporating HMA stiffness. Finn et al. [7] further calibrated this model by using the field date from the American Association of State Highway Officials (AASHO) road test sections and the introduced calibration factor accounts for the effects of boundary difference between field and laboratory. Al-Khateeb and Ghuzlan [2] investigate the combined effect of the loading frequency, temperature and stress level on the fatigue life of asphalt paving mixtures. Kestler et al. [13] identified statistically the contributions of specific winter season characteristics (e.g. freeze season length, thaw depth, and depth to water table) to cumulative pavement damage and found that the combination of the surface freezing season length and corresponding average pavement surface temperature appears significant for fatigue performance. To date, a quantitative understanding of how freezethaw cycle affects the fatigue performance of asphalt mixture is so far still lacking. This study was initiated to clarify the effects of freeze-thaw cycles on fatigue performance of asphalt mixture. The specimens were firstly exposed to different combinations of saturation and number of freeze-thaw cycle conditionings after which the indirect tensile fatigue tests were performed to measure the fatigue life of the freeze-thaw damaged specimens. Analyses were then carried out on basis of the test results to investigate the effects of saturation and number of freeze-thaw cycles on fatigue performance deterioration. Lastly, two approaches were adopted to establish the FFT uniform equation and a final recommendation was given based on a comparative study.
2. Objectives The objectives of this study presented in this paper were: Analyze the effects of freeze-thaw cycle conditions (including water saturation and number of freeze-thaw cycles) on the fatigue performance of asphalt mixture; Establish the FFT uniform equation by coupling the effects of freeze-thaw cycle into the conventional fatigue equation.
3. Materials and methods 3.1. Raw materials and mixture design 3.1.1. Asphalt binder In this research, the 60/80 penetration graded SBS modified asphalt was used to fabricate the asphalt mixture specimens. The basic technical properties of the selected asphalt binder were shown in Table 1. 3.1.2. Aggregates and filler The coarse and fine aggregates used in this research were andesite. The technical properties of the coarse and fine aggregates were tested according to the Chinese technical specification Test Methods of Aggregate for Highway Engineering (JTG F42-2005) [19] and results were shown in Tables 2 and 3, respectively. The technical properties of the mineral filler were shown in Table 4. 3.1.3. Mixture design and specimen preparation The conventional dense graded asphalt mixture AC-13 was selected according to the Technical Specifications for Construction of Highway Asphalt Pavements in China (JTG F40-2004) [18] and the detailed aggregate gradation was shown in Table 5. The determined optimal content of asphalt binder for AC-13 was 5.0%. The Superpave gyratory compactor was used to prepare the cylindrical specimens with an angle of gyration of 1.25°, vertical pressure stress of 0.6 MPa, and gyration speed of 30 rpm. The air void content of specimens was controlled as 6%. 3.2. Test methods 3.2.1. Freeze-thaw cycle test In order to investigate the effect of freeze-thaw cycles on the fatigue performance of asphalt mixture, the freeze-thaw cycle tests were performed on the prepared specimens firstly. The test procedure adopted here was obtained by modifying the Saturated Water Content Test of Bituminous Mixtures (T 0716-2011) and Freezethaw Splitting Test of Bituminous Mixtures (T 0729-2000) recommended by Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011) [20]. Four saturation degrees (20%, 50%, 70% and 90%) and six freeze-thaw cycles (5, 10, 15, 20, 25, 30 cycles) were adopted for purpose of studying the effect of saturation and number of freeze-thaw cycles, respectively. Within each FT cycle, the specimen was firstly processed in the solution of distilled water by vacuum saturation with a 98 kPa residual pressure for 15 min. Then the specimen was shaken once and weighted to calculate the saturation level every three minutes until the saturation level falls into the range of 50%±5%. Following this step, the specimen was frozen in the refrigerator 12 h at a temperature of 18 °C. Finally, the specimen was thawed in water bath at 60 °C for 12 h. The specimens were subjected to 5, 10, 15, 20, 25 and 30 cycles respectively. The specimens after different freezethaw cycles (5, 10, 15, 20, 25 and 30) at different saturation degrees (20%, 50%, 70%, and 90%) were to be employed for further tests.
Table 1 Technical properties of the SBS modified asphalt. Indexes
Test value
Technical requirements
Penetration@25 , 5 s, 100 g /0.1 mm Ductility@15 /cm Softening point(R&B)/
66.1 32.8 64.9
60–80 30 55
3
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043 Table 2 Technical properties of the coarse aggregates. Indexes
Screen size (mm)
Bulk specific gravity Apparent specific gravity Water absorption (%) Crushed stone value (%) Weared stone value (%) Flat- elongated particle content (%) Adhesion level
13.2
9.5
4.75
2.36
2.760 2.780 0.53 15.2 13.4 6.1 5
2.754 2.772 0.55 15.1 13.6 9.4 5
2.720 2.760 0.76 14.8 15.9 10.9 5
2.815 2.820 0.78 15.1 16.1 9.5 5
Table 3 Technical properties of the fine aggregates. Indexes
Screen size (mm)
Apparent specific gravity Angularity
1.18
0.6
0.3
0.15
0.075
2.776 41
2.770
2.755
2.758
2.705
Table 4 Technical properties of the mineral filler. Apparent specific gravity
Water content (%)
2.705
0.92
Passing percentage (%) 0.6 mm
0.3 mm
0.15 mm
0.075 mm
100
100
97.5
84.3
Table 5 Gradation of asphalt mixture AC-13. Size (mm)
Percent passing/% 16
13.2
9.5
4.75
2.36
1.18
0.6
0.3
0.15
0.075
AC-13
100
95
76.5
53
37
28
19
13.5
10
6
RT ¼ 0:006287PT =h
ð1Þ
where P T is the maximum applied load (N); h is the height of the specimen (mm). 3.2.3. Indirect tensile fatigue test The indirect tensile fatigue test was performed on both the undamaged and freeze-thaw damaged specimens. The stresscontrol mode was adopted at four stress levels of 30, 40, 50 and 60% of the splitting strength RT . The load applied on the specimens was half-sinusoidal repeated load with the frequency of 10 Hz and the test temperature was 15 . The total number of the repeated load was defined as the fatigue life N f when the specimen cracks completely. Considerable researches have been devoted to fatigue performance of asphalt mixture (Monismith et al., 2000; [34]). It has been demonstrated that the fatigue response of asphalt mixture to repeated load can be defined by relationship of the following form
Nf ¼ k1
k2 1
r
ð2Þ
where N f is number of repetitions to failure; r is magnitude of the stress repeatedly applied; k1 and k2 are fitting coefficients. On the
dual logarithmic coordinate diagram, this relationship is shown as a straight line through
lgNf ¼ lgk1 k2 lgr
ð3Þ
where k2 and lgk1 are the slope and intercept, respectively. This straight line is referred to as the fatigue curve and the fatigue performance of asphalt mixture was to be described in the form of fatigue curve in what follows.
20% saturation 50% saturation 70% saturation 90% saturation
1,6
Splitting strength (MPa)
3.2.2. Splitting test The splitting test was adopted in this study to measure the splitting strength of the undamaged as well as the freeze-thaw cycle damaged specimens. The test was conducted according to the Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011) [20]. The splitting strength RT was calculated through
1,2
0,8
0,4
0
5
10
15
20
25
30
Number of freeze-thaw cycles Fig. 1. The measured splitting strengths of asphalt mixtures subjected to freezethaw cycles.
4
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
Fig. 2. Fatigue curves of asphalt mixtures at different saturations after (a) 5, (b) 10, (c) 15, (d) 20, (e) 25 and (f) 30 freeze-thaw cycles.
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
5
4. Results and discussion 4.1. Effects of freeze-thaw cycles on fatigue performance 4.1.1. Splitting test results The measured splitting strengths of both the undamaged and freeze-thaw cycle damaged asphalt mixtures were shown in Fig. 1. It could be found that the splitting strength of asphalt mixture decreases rapidly with the increase of the number of freezethaw cycles. The reduction effect becomes more significant as the saturation increases. This can be attributed to the fact that the asphalt mixture accumulates more damage when exposed to higher saturation level and more times of freeze-thaw cycles. 4.1.2. Effects of saturation The fatigue Eq. (3) was used to fit the indirect tensile fatigue test results of the undamaged and freeze-thaw cycle damaged specimens. To investigate the effects of saturation on the fatigue performance of asphalt mixture, the fitted fatigue curves of the damaged asphalt mixtures under the condition of varying saturation were compared to that of the undamaged one. The comparisons were grouped by the number of freeze-thaw cycles as shown in Fig. 2. In these comparisons a difference in location of the fatigue curves is indicated. It is easy to see that the location changes comprise two mechanisms: translation in the left direction and rotation in the clockwise direction. The left translation induces a decrease in fatigue life while the clockwise rotation implies a more stress-sensitive fatigue behavior. Fig. 2 shows that the increase in saturation results in a decrease in fatigue life N f regardless of the number of freeze-thaw cycles. Besides, the decrease in fatigue life N f was found to be larger at higher stress levels. It was also found that the location movement of the fatigue curve caused by the increase of saturation becomes more pronounced as the number of freeze-thaw cycles increases. Furthermore, the location changes of the fatigue curves were quantitatively illustrated in Fig. 3 by plotting the intercept versus saturation and slope versus saturation, respectively. It shows that both intercept and slope of the fatigue curves decrease with the increase of saturation. They decrease linearly with the increase of saturation when subjected to fewer freeze-thaw cycles. But for the high freeze-thaw cycle cases, a sharp decline of intercept and slope were observed at low saturations (up to 20%) and the decline rate tends to be constant as the saturation continually increases. Considering that the intercept decrease corresponds to the decrease of fatigue life while the slope decrease represents a more stress-sensitive fatigue behavior, conclusion can be drawn that the increase in saturation results in a decrease in fatigue life N f regardless of the number of freeze-thaw cycles and the decrease in fatigue life N f was found to be larger at higher stress levels. 4.1.3. Effects of number of freeze-thaw cycles Similarly, comparisons were also made to investigate the effects of the number of freeze-thaw cycle on the fatigue performance of asphalt mixture. The comparisons here were grouped by saturation as shown in Fig. 4, and location changes similar to Fig. 2 were observed. It indicates that the increase in number of freeze-thaw cycles resulted in a decrease in the fatigue life N f regardless of saturation and this decrease was found to be larger at higher stress levels. Fig. 4 also shows that the damage caused by the increase of the number of freeze-thaw cycles becomes more pronounced as the saturation increases. Fig. 5 quantified the impact of number of freeze-thaw cycles on location changes of the fatigue curves by plotting the intercept versus number of freeze-thaw cycles and slope versus number of freeze-thaw cycles, respectively. It could be found that both
Fig. 3. Plots of (a) intercept and (b) slope versus saturation.
intercept and slope of the fatigue curves decrease linearly with the increase of number of freeze-thaw cycles. In consideration of the meanings of the intercept and slope parameters, Fig. 5 implies that asphalt mixtures exhibit shorter fatigue lives and become more stress-sensitive when subjected to a higher number of freeze-thaw cycles. Besides, the decreasing rates of intercept and slope of the fatigue curves increase with saturation. 4.2. Establishment of the FFT uniform equation In order that effects of freeze-thaw cycles on fatigue performance of asphalt mixture can be quantitatively considered, this study attempted to establish the FFT uniform equation by means of modifying the conventional fatigue equation. For this, two different kinds of modifying schemes were proposed, as detailed in what follows. 4.2.1. Equivalent damage principle-based approach The equivalent damage principle-based approach begins with reviewing the influence laws of freeze-thaw cycles on fatigue behavior of asphalt mixtures, as schematically illustrated in Fig. 6. In the figure, the damaged curve represents that the test specimens itre exposed to any given degree of freeze-thaw cycles before the fatigue tests were conducted. On basis of the fatigue curve, the fatigue life of the undamaged asphalt mixture at any given stress level r can be calculated to be N f . But for the damaged asphalt mixture, the fatigue life at the same stress level decreases 0
to N f . Then, the damage effect of the employed degree of
6
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
Fig. 4. Fatigue curves of asphalt mixtures after different freeze-thaw cycles under (a) 20%, (b) 50%, (c) 70% and (d) 90% saturation.
freeze-thaw cycles on the fatigue performance of asphalt mixture at stress level
the other hand, for the undamaged asphalt mixture, the fatigue life 0
of N f corresponds to a stress level of
r . This means that for any 0
stress level r, there exists an increased stress level r at which the fatigue life lost due to the test stress increase is equal to that of exposure to the given degree of freeze-thaw cycles. In other words, the damage caused by freeze-thaw cycles can be equivalented to that of increasing the fatigue test stress. Based on this equivalent damage principle, it came to the first approach of coupling the effects of freeze-thaw cycles on fatigue performance of asphalt mixture by establishing the functional relation between freeze-thaw cycle variables and stress increase. In practical terms, this study referenced the theory of TimeTemperature Superposition Principle (TTSP) [1,22] and introduced a shift factor a as 0
r ¼ra 0
ð4Þ
The shift factor a depends on the freeze-thaw cycle variables (i.e. saturation S and number of freeze-thaw cycles n). For the fatigue test specimens experienced no freeze-thaw cycles, the shift factor a is equal to 1. For the specimens subjected to freeze-thaw cycles before fatigue test, the shift factor a > 1 considering the damage effect of freeze-thaw cycles on fatigue performance. Once the functional expression of shift factor a was obtained, one can easily obtain the FFT uniform equation with the expression of
Nf ¼ k1
k2 1
r0
or
0
r can be defined as the fatigue life lost Nf Nf . On
ð5Þ
lgNf ¼ lgk1 k2 lgr
0
ð6Þ
It should be noted that the relations above apply to any two cases in which the specimens were subjected to different degrees of freeze-thaw cycles damage. However, for convenience of description, this research selected the undamaged situation as the reference freeze-thaw cycles state. The follow-up works were based on this assumption in the absence of special explanation. So far, the original issue of establishing the FFT uniform equation has been transformed to the determination of the function of shift factor a with saturation S and number of freeze-thaw cycles n. For this, the influence laws of different freeze-thaw cycle variables on shift factor a were firstly analyzed based on the experiment results before which kind of functional form can be finally determined to use. The concrete steps were: (1) Select the fitted fatigue equation of the undamaged asphalt mixtures as the standard fatigue equation; 0
(2) Substitute the measured fatigue life N f of the damaged asphalt mixtures into the standard fatigue equation and 0 backcalculate the corresponding increased stress r ; (3) Calculate the values of the shift factor according to 0 lga ¼ lgr lgr. The effect of number of freeze-thaw cycles n on shift factor a was investigated firstly as shown in Fig. 7. Considering that lga ¼ 0 holds at n ¼ 0 regardless of the saturationS, function y ¼ f x was employed to conduct the linear fitting and results
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
7
Fig. 7. Linear fittings between logarithm shift factor lga and number of freeze-thaw cycles n.
Furthermore, the relationship between saturation S and slope f was plotted in Fig. 8 for purpose of determining the function form of f ðSÞ. In light of the physical fact that f ¼ 0 when S ¼ 0, the selected function for f ðSÞ should pass through the origin. Therefore, two different kinds of function forms were adopted in this study. The first was the linear function with the expression of f ðSÞ ¼ a S and the second was the exponential function S f ðSÞ ¼ a 1 b . The corresponding fitting results were shown in Fig. 8. It indicates that both of the two functions can well describe the relation between slope f and saturation S with high determination coefficients, and the exponential function is the better one. On basis of the above analysis, the final expression for the shift factor a can be naturally achieved. Corresponding to the two different forms of f ðSÞ, two function expressions were introduced in this approach for shift factor a which were expressed respectively as (I) Linear function Fig. 5. Plots of (a) intercept and (b) slope versus number of freeze-thaw cycles.
were included in the figure. In view of the high determination coefficients, conclusion can be drawn that the logarithm of shift factor lga increases linearly with the number of freeze-thaw cycles n for any given saturation S while the slope f depends on saturation S. Thus, the shift factor a can be expressed as
lga ¼ f ðSÞ n
lga ¼ a n S (II) Exponential function
S lga ¼ a n 1 b
ð9Þ
Eqs. (4) and (5) together with Eqs. (8) or (9) form the final FFT uniform equation for asphalt mixture.
ð7Þ
Fig. 6. Schematic diagram of fatigue curves for undamaged and damaged asphalt mixtures.
ð8Þ
Fig. 8. Curve fitting results between slope f and saturation S.
8
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
Table 6 Summary of the fitting results for established FFT uniform equations. Method
FFT uniform equation
Equivalent damage principle approach
I II
Direct approach
I II III
1 2:82
N f ¼ 1457 r ; lga ¼ 0:238 n S 3:528 ; lga ¼ 0:018 n 1 0:006S N f ¼ 1470 r1 1 2:255þ0:115nS
N f ¼ 103:3430:12nS r
3:4260:018n7:842S
N f ¼ 10
4.2.2. Direct modification approach The desired FFT uniform equation can also be established by modifying the original fatigue Eq. (3) directly. It has been proven in Figs. 3 and 5 that both intercept and slope of the fitted fatigue curve decrease with saturation S and number of freeze-thaw cycles n. Once the functional relations between the freeze-thaw cycle variables and the fatigue curve parameters were established, they can be substituted into the equation to obtain the FFT uniform equation. According to the depicted influence laws of saturation S and number of freeze-thaw cycles n on intercept lgk1 and slope k2 in Figs. 3 and 5, three different kinds of functional forms were selected which were expressed respectively as
lgk1 ¼ a þ b n S
ð10Þ
k2 ¼ c þ d n S
ð11Þ
(II) Exponential function
k2 ¼ d þ e n f
S
5:9 1 2:516þ0:003nð1þSÞ
r
R2
3
0.695
4
0.884
4
0.796
6
0.780
6
0.808
tion coefficient R2 ¼ 0:884. To summarize, the FFT uniform equation II based on the equivalent damage principle is the top recommendation FFT with both good fitting precision and simple function form. The established FFT uniform equation in this study is of great meaning in at least two aspects: firstly, it provides a way to quantitatively identify the effects of freeze-thaw cycles on the fatigue behavior of asphalt mixture; secondly, it makes it possible for the designers to fully grasp the complicated coupling effects of freeze-thaw cycle and fatigue damage across the broad conditional domain with limited experimental results. This is important especially considering that both freeze-thaw cycle and fatigue tests are time-consuming.
5. Conclusions
(I) Linear function
lgk1 ¼ a þ b n cS
r
3:3420:017nð1þSÞ2:98
N f ¼ 10
S 1 2:452þ0:003n68:75
Parameter number
ð12Þ ð13Þ
(III) Power function
lgk1 ¼ a þ b n ð1 þ SÞc
ð14Þ
k2 ¼ d þ e n ð1 þ SÞf
ð15Þ
Then, the final FFT uniform equation can be obtained by substituting the above equations into Eq. (3), respectively. 4.2.3. Summary and review In this study, five FFT uniform equations were proposed in total, among which two were based on the equivalent damage approach and three were based on the direct modification approach. To validate the applicability and compare the advantages and disadvantages of these FFT uniform equations, the nonlinear curve fitting method was adopted to obtain the equation parameters in use of the experimental results and the fitting results were detailed in Table 6. It could be found from Table 6 that the FFT uniform equation I based on the equivalent damage principle has the simplest function form with only three parameters. However, its determination coefficient R2 ¼ 0:695 indicates that it has the worst fitting precision. The three FFT uniform equations based on the direct approach have almost the same fitting precisions while the equation I owns the simplest function form with four parameters. The parameter number of the FFT uniform equation II based on the equivalent damage principle was also four, but it has the highest determina-
In this study, the AC-13 asphalt mixture specimens were fabricated and exposed to different combinations of saturation (20, 50, 70, and 90%) and number (5, 10, 15, 20, 25, and 30 cycles) of freezing-thawing conditioning. The indirect tensile fatigue tests were then performed to measure the fatigue life of the freezethaw damaged specimens and the fatigue curves were established. By comparing the fatigue curves, it is found that the effects of freeze-thaw cycles on fatigue performance of asphalt mixture can be characterized by the location changes of fatigue curves in two mechanisms: translation in the left direction and rotation in the clockwise direction. The left translation induces a decrease in fatigue life while the clockwise rotation implies a more stresssensitive fatigue behavior. The effects of saturation and number of freeze-thaw cycles on location changes of the fatigue curves were quantified, respectively. The intercept and slope of the fatigue curves decrease linearly with the increase of saturation when subjected to fewer freeze-thaw cycles. But for the high freeze-thaw cycle cases, a sharp decline of intercept and slope were observed at low saturations (up to 20%) and the decline rate tends to be constant as the saturation continually increases. However, their values decrease linearly with the increase of number of freeze-thaw cycles regardless of saturation. In consideration of the physical meanings of intercept and slope, this suggests that asphalt mixtures exhibit shorter fatigue lives and become more stress-sensitive when subjected to a higher saturation and number of freeze-thaw cycles. Two different approaches, which are the equivalent damage principle-based approach and direct modification approach, were proposed to establish the FFT uniform equation. In the former, we borrowed techniques from the Time-Temperature Superposition Principle theory and a shift factor function was introduced to associate the freeze-thaw cycle parameters to stress. Among the five developed equations, the one based on equivalent damage principle with an exponential shift factor function is the most recommended since it has relatively few unknown parameters but the highest coefficient of determination. The conclusions obtained in this study were based on the experimental tests of AC-13, and further researches are needed to verify
Z. Fan et al. / Construction and Building Materials 242 (2020) 118043
the effects of freeze-thaw cycles on fatigue performance of other types of asphalt mixture. Moreover, the fundamental mechanisms underlying the damage effect of freeze-thaw cycles on fatigue performance of asphalt mixture (e.g. the microstructure evolution of asphalt mixture when subjected to freeze-thaw cycles as well as its relationship with fatigue performance) remain to be further explored in the future work. CRediT authorship contribution statement Zepeng Fan: Data curation, Writing - original draft. Huining Xu: Conceptualization, Methodology, Writing - review & editing. Jiazhe Xiao: Formal analysis, Methodology, Writing - original draft. Yiqiu Tan: Supervision. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported by the National Natural Science Funds of China (Grant No. 51678207) and Fundamental Research Funds for the Central Universities (Grant No. HIT.BRETIII.201511). The authors gratefully acknowledge their financial support. References [1] G.D. Airey, R. Behzad, Combined bituminous binder and mixture linear rheological properties, Constr. Build. Mater. 18 (2004) 535–548. [2] G.G. Al-Khateeb, K.A. Ghuzlan, The combined effect of loading frequency, temperature, and stress level on the fatigue life of asphalt paving mixtures using the IDT test configuration, Int. J. Fatigue 59 (2014) 254–261. [3] H.D. Benedetto, C.D.L. Roche, H. Baaj, A. Pronk, R. Lundström, Fatigue of bituminous mixtures, Mater. Struct. 37 (3) (2004) 202–216. [4] M. Boudabbous, A. Millien, C. Petit, J. Neji, Energy approach for the fatigue of thermoviscoelastic materials: application to asphalt materials in pavement surface layers, Int. J. Fatigue 47 (1) (2013) 308–318. [5] J. Epps, C. Monismith, Fatigue of Asphalt Concrete Mixtures-Summary of Existing Information. In Gallaway, B. (Ed.), STP508-EB Fatigue of Compacted Bituminous Aggregate Mixtures, (1972), (pp. 19–45). [6] D. Feng, J. Yi, D. Wang, L. Chen, Impact of salt and freeze-thaw cycles on performance of asphalt mixtures in coastal frozen region of China, Cold Reg. Sci. Technol. 62 (1) (2010) 34–41. [7] F.N. Finn, C. Saraf, R. Kulkarni, K. Nair, W. Smith, A. Abdullah, The use of distress prediction subsystems for the design of pavement structures, Proceedings of the 4th International Conference on the Structural Design of Asphalt Pavements, Vol. 1, University of Michigan, Ann Arbor, MI, 1977, pp. 3– 38. [8] X. Gao, Z. Fan, J. Zhang, S. Liu, Micromechanical model for asphalt mixture coupling inter-particle effect and imperfect interface, Constr. Build. Mater. 148 (2017) 696–703. [9] Y. Gong, H. Bi, Z. Tan, G. Tan, Pavement performance investigation of NanoTiO2/CaCO3 and basalt fiber composite modified asphalt mixture under freeze-thaw cycles, Appl. Sci. 8 (2018) 2581, https://doi.org/10.3390/ app8122581. [10] Y. Gong, H. Bi, C. Liang, S. Wang, Microstructure analysis of modified asphalt mixtures under freeze-thaw cycles based on CT Scanning technology, Appl. Sci. 8 (2018) 2191, https://doi.org/10.3390/app8112191. [11] T. Huang, Shuai Qi, M. Yang, S. Lv, H. Liu, J. Zheng, Strength criterion of asphalt mixtures in three-dimensional stress states under freeze-thaw conditions, 8 (2018) p. 1302, doi: 10.3390/app8081302.
9
[12] M.R. Islam, R.A. Tarefder, Effects of large freeze-thaw cycles on stiffness and tensile strength of asphalt concrete, J. Cold Reg. Eng. 30 (1) (2016) 06014006. [13] M.A. Kestler, R.L. Berg, S.R. Bigl, Statistical significance of freeze-thaw related factors on cumulative damage to flexible pavements, Transp. Res. Rec. 2232 (1) (2011) 55–67. [14] E. Lachance-Tremblay, D. Perraton, M. Vaillancourt, H.D. Benedetto, Degradation of asphalt mixtures with glass aggregates subjected to freezethaw cycles, Cold Reg. Sci. Technol. 141 (2017) 8–15. [15] E. Lachance-Tremblay, D. Perraton, M. Vaillancourt, H.D. Benedetto, Effect of hydrated lime on linear viscoelastic properties of asphalt mixtures with glass aggregates subjected to freeze-thaw cycles, Constr. Build. Mater. 184 (2018) 58–67. [16] S. Lamothe, D. Perraton, H. Di. Benedetto, Degradation of hot mix asphalt samples subjected to freeze-thaw cycles and partially saturated with water or brine, Road Mater. Pavement Design 18 (4) (2017) 849–864. [17] E. Masad, V.K. Jandhyala, N. Dasgupta, N. Somadevan, N. Shashidhar, Characterization of air void distribution in asphalt mixes using x-ray computed tomography, J. Mater. Civ. Eng. 14 (2) (2002) 122–129. [18] Ministry of Transport, Technical Specification for Construction of Highway Asphalt Pavements (JTG F40-2004), Chine Communication Press, 2004. [19] Ministry of Transport, Chinese technical specification Test Methods of Aggregate for Highway Engineering (JTG F42-2005), Chine Communication Press, 2005. [20] Ministry of Transport, Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011), Chine Communication Press, 2011. [21] C.L. Monismith, J.A. Epps, Asphalt mixture behavior in repeated flexure, Transportation and Traffic Engineering, University of California at Berkeley, California, 1969. [22] H.M. Nguyen, S. Pouget, H.D. Benedetto, C. Sauzéat, Time-temperature superposition principle for bituminous mixtures, Eur. J. Environ. Civ. Eng. 13 (9) (2009) 1095–1107. [23] E. Ozgan, S. Serin, Investigation of certain engineering characteristics of asphalt concrete exposed to freeze-thaw cycles, Cold Reg. Sci. Technol. 85 (2013) 131–136. [24] N. Tang, C. Sun, S. Huang, S. Wu, Damage and corrosion of conductive asphalt concrete subjected to freeze-thaw cycles and salt, Mater. Res. Innovat. 17 (S1) (2013) 240–245. [25] R. Tarefder, H. Faisal, G. Barlas, Freeze-thaw effects on fatigue LIFE of hot mix asphalt and creep stiffness of asphalt binder, Cold Reg. Sci. Technol. 153 (2018) 197–204. [26] H. Xu, Y. Tan, W. Guo, Internal structural evolution of asphalt mixtures during freeze-thaw cycles, Mater. Des. 86 (2015) 436–446. [27] H. Xu, W. Guo, Y. Tan, Permeability of asphalt mixtures exposed to freeze-thaw cycles, Cold Reg. Sci. Technol. 123 (2016) 99–106. [28] H. Xu, X. Yao, Y. Tan, X-ray computed tomography in hydraulics of asphalt mixtures: Procedure, accuracy, and application, Constr. Build. Mater. 108 (2016) 10–21. [29] H. Xu, H. Li, Y. Tan, L. Wang, Y. Hou, A micro-scale investigation on the behaviors of asphalt mixtures under freeze-thaw cycles using entropy theory and a computerized tomography scanning technique, Entropy 20 (2) (2018) 68. [30] K. Yan, D. Ge, L. You, X. Wang, Laboratory investigation of the characteristics of SMA mixtures under freeze-thaw cycles, Cold Reg. Sci. Technol. 119 (2015) 68–74. [31] J. Yi, S. Shen, B. Muhunthan, D. Feng, Viscoelastic–plastic damage model for porous asphalt mixtures: application to uniaxial compression and freeze-thaw damage, Mech. Mater. 70 (2014) 67–75. [32] Z. You, S. Adhikari, M.E. Kuta, Dynamic modulus simulation of the asphalt concrete using the X-ray computed tomography images, Mater. Struct. 42 (5) (2009) 617–630. [33] L. You, Z. You, Q. Dai, S. Guo, J. Wang, M. Schultz, Characteristics of waterfoamed asphalt mixture under multiple freeze-thaw cycles: laboratory evaluation, J. Mater. Civ. Eng. 30 (11) (2018) 04018270. [34] J. Yu, B. Tsai, X. Zhang, C. Monismith, Development of asphalt pavement fatigue cracking prediction model based on loading mode transfer function, Road Mater. Pavement Des. 13 (3) (2012) 501–517. [35] J. Zhang, Z. Fan, H. Wang, W. Sun, J. Pei, D. Wang, Prediction of dynamic modulus of asphalt mixture using micromechanical method with radial distribution functions, Mater. Struct. 52 (2019) 49.