Fatigue resistance of aged asphalt binders: An investigation of different analytical methods in linear amplitude sweep test

Construction and Building Materials 241 (2020) 118099

Contents lists available at ScienceDirect

Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Fatigue resistance of aged asphalt binders: An investigation of different analytical methods in linear amplitude sweep test Hanyu Zhang a, Kairen Shen a, Gang Xu a, Jusheng Tong a, Rui Wang a, Degou Cai b, Xianhua Chen a,⇑ a b

School of Transportation, Southeast University, 2 Southeast University Road, Nanjing, Jiangsu 211189, PR China Railway Engineering Research Institute, China Academy of Railway Sciences Group Co. Ltd., 2 Daliushu Road, Beijing 100081, PR China

h i g h l i g h t s
The peak shear stress is a better fatigue failure criterion and using the 20 hours PAV aged binder sample to conduct LAS test could obtain the more

accurate data.
The pseudo-strain energy-based analytical method is theoretically more accurate to represent the damage growth than the dissipated energy-based

method.
The effect of aging on asphalt binders fatigue resistance is material specific and depends on the loading strain, and the critical strain level for neat asphalt

binder is approximate 4.5%.

a r t i c l e

i n f o

Article history: Received 24 November 2019 Received in revised form 1 January 2020 Accepted 5 January 2020

Keywords: Asphalt binder Fatigue resistance Linear amplitude sweep Viscoelastic continuum damage Aging

a b s t r a c t This paper aims to investigate the fatigue resistance of asphalt binders using different analytical methods and fatigue failure criteria with the consideration of various aging conditions. Four different performance grade (PG) binders with and without modifiers were tested by Linear Amplitude Sweep (LAS) test to characterize their fatigue behavior. The fatigue failure strain was determined using three different definitions: peak value of shear stress, peak value of phase angle and the maximum stored pseudo-strain energy. The damage characteristic curves and fatigue life were obtained by two kinds of analytical methods: dissipated energy-based method and pseudo-strain energy-based method. Statistical analysis shows that there is no distinct difference between these three criteria of fatigue failure for aged and unaged asphalt binders. However, for the modified asphalt binders at unaged condition, it is hard to observe the peak value of phase angle or stored pseudo-strain energy. The fatigue life determined by the pseudo-strain energy-based method is slightly higher than that of dissipated energy-based method across the entire loading strain range. In addition, the fatigue resistance of neat asphalt binder tested in this paper is deteriorated at high strain levels but improved at low strain levels and the critical strain level is approximate 4.5%. The effect of aging is asphalt specific and depends on the strain levels from the experimental results. Ó 2020 Elsevier Ltd. All rights reserved.

1. Introduction Fatigue cracking results from repeated traffic loading is one of the major distress in asphalt pavement. Numerous factors are influential to the occurrence of fatigue cracking including climate condition, materials property and design, pavement structure, construction and maintenance [1]. Although the proper mixture and pavement design could accommodate to a certain extent for a

⇑ Corresponding author. E-mail addresses: [email protected] (H. Zhang), [email protected] (K. Shen), [email protected] (J. Tong), [email protected] (R. Wang), [email protected] (X. Chen). https://doi.org/10.1016/j.conbuildmat.2020.118099 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.

non-ideal binder fatigue resistance, it is still recognized that the fatigue resistance of asphalt binders significantly affects the fatigue performance of asphalt pavements [2], because the fatigue cracking can generally initiate and propagate in the binder phase that is the weakest part of asphalt concrete. Besides, the aging phenomenon of asphalt pavement during its construction and service also affects asphalt binders fatigue resistance. Hence, the investigation on fatigue resistance of aged asphalt binders is of great importance to the design, construction, and maintenance of asphalt pavements, especially for the perpetual pavements. A large number of experimental and analytical methods have been utilized to evaluate the fatigue resistance of asphalt binders up to now. The fatigue parameter |G*|∙sin d which can be obtained

2

H. Zhang et al. / Construction and Building Materials 241 (2020) 118099

by using a Dynamic Shear Rheometer (DSR) was proposed by the Strategic Highway Research Program (SHRP) to characterize the fatigue resistance of asphalt binders. The relatively lower value of fatigue parameter corresponds to the lower dissipated energy and thus, asphalt binders ability to resist fatigue cracking is better. However, many researchers argued that |G*|∙sin d is not a reliable indicator to characterize the fatigue performance of asphalt binders, especially for modified asphalt binders [3–5]. One key issue is that the fatigue parameter is tested under a small shear strain and with only a few cycles of non-damaged loading condition, which is far from the actual fatigue phenomenon. To better simulate the damage accumulation of asphalt binders under repeated traffic loading, the Time Sweep test was introduced to assess the binders fatigue resistance [6]. In a Time Sweep test, the asphalt binder is subjected to a constant shear strain under repeated cyclic loading until a specific fatigue failure occurs. Existing studies illustrated its reliability when using Time Sweep to evaluate asphalt binders fatigue resistance [7–9]. Nevertheless, the main drawback of Time Sweep test is time-consuming, and it is therefore difficult to be applied as a standard test method. In recent years, a new accelerated fatigue experiment named Linear Amplitude Sweep (LAS) test was developed to be a substitute for Time Sweep test [10,11]. In this test, the binder sample is subjected to a cyclic loading where strain amplitudes are increased linearly from zero to 30% to accelerate the rate of damage accumulation. This loading scheme successfully avoided the compliance issue of making abrupt changes in strain amplitude between loading steps [12]. Then, the viscoelastic continuum damage (VECD) theory is applied to analyze the results of LAS test. This theory has achieved much success in characterizing the complex fatigue behavior of asphalt binders and mixtures [13–16]. The primary benefit of using VECD theory is that results from a single test run at a specific set of conditions can be used to predict the behavior of that material under any variety of alternate conditions [11]. However, there exists different analytical methods and models based on the VECD theory for the analysis of LAS test results, and the main issue is how to define and determinate the fatigue failure during the test process. On the other hand, some phenomenon maybe also interact with fatigue damage during cyclic loading of asphalt binders, such as thixotropy, self-healing and steric hardening [17,18]. Hence, it is necessary to investigate the different analytical methods for LAS test results. In addition, aging is also a vital factor that could not be neglected when assessing the fatigue resistance of asphalt binders. Laboratory aging appeared to improve neat binders fatigue resistance at low strain levels but deteriorate fatigue resistance at high levels, and it was noteworthy that these changes are highly asphalt specific [19]. Besides, in spite of the fact that modified binders could provide better fatigue resistance than neat binders, the effect of aging could cause the mechanical response of modified and unmodified binders to be similar [20]. Such a conclusion excluded the effect of temperature on asphalt binders fatigue resistance, because at a certain test temperature, the presence of viscoelastic phenomenon that co-exists with fatigue damage could lead to a misunderstanding of the effect caused by aging. Therefore, all these analytical methods in LAS test need to be reassessed with the consideration of asphalt binders aging. This paper presents an investigation of two analytical methods and three fatigue failure criteria used to assess the fatigue resistance of asphalt binders in LAS test, and the aging effects on fatigue resistance are also taken into consideration. Four kinds of asphalt binders were subjected to laboratory aging including short-term aging and long-term aging, and all the asphalt binders were conducted to LAS test. The experimental results were analyzed by two methods based on VECD theory respectively. This research focuses on selecting a suitable method to evaluate the fatigue resistance of aged asphalt binders in LAS test.

2. Objectives The objectives of this paper are to:
Evaluate different fatigue failure criteria and analytical methods in LAS test.
Investigate the evolution of asphalt binders fatigue resistance with laboratory aging.
Identify a suitable fatigue failure criterion and an analytical method for aged asphalt binders in LAS test. 3. Background The most important part of using VECD theory to characterize the fatigue resistance of asphalt materials is to establish the damage characteristic curve (DCC), which is a function of material integrity (C) and damage intensity (D). The DCC specifies the path of materials losing structural integrity caused by the damage accumulation under cyclic loading. In addition, this relationship is unique because it is independent of the test conditions (e.g., temperature, loading level, frequency, and control mode) [21]. These advantages make VECD theory widely used in fatigue damage analysis of asphalt materials. 3.1. Analytical method based on dissipated energy The damage evolution is based on the Schapery’s work potential theory [22]:

dD ¼ dt




@W @D

a

ð1Þ

where D is the damage intensity; t is time; W represents the work performed; a is the material constant related to the rate at which damage progresses. The quantification of work performed was proposed by using the dissipated energy [23].

W ¼ pc20 jG jsind

ð2Þ

where c0 denotes the shear strain of a cycle in interest; |G*| is the damaged complex shear modulus; d is the phase angle. Substitute Eq. (2) into Eq. (1) and integrated numerically to obtain the following equation to calculate the damage intensity (D):

DðtÞ ffi

N X 

pc20 ðjG jsindi1  jG jsindi Þ

1þa a

1

ðt i  t i1 Þ1þa

ð3Þ

i¼1

The relationship between |G*|∙sin d and D(t) is proposed to be fitted using the power law: C jG jsind ¼ C 0  C 1 ðDÞ 2

ð4Þ

where C0 is the initial value of C (1.0 if |G*|∙sin d is normalized); C1 and C2 are model coefficients which can be derived through linearization of the power law. Researchers usually use normalized |G*|∙sin d to represent the material integrity (C), therefore, Eq. (4) can be rewritten as follows:

C ðt Þ ¼ C 0  C 1 ðDÞC2

ð5Þ

where C(t) is the normalized value of |G*|∙sin d. Combining Eqs. (1), (2) and (4) allows for the derivation of a fatigue model between fatigue life (Nf) and maximum strain amplitude (cmax):

Nf ¼

 k f Df ðc Þ2a kðpC 1 C 2 Þa max

ð6Þ

H. Zhang et al. / Construction and Building Materials 241 (2020) 118099

where f and Df represent experimental loading frequency and damage accumulation at failure; k ¼ 1 þ ð1  C 2 Þa. For the above analytical method, it has a major drawback that Eq. (2) neglects the fact that only a portion of the dissipated energy serves as the driving force for damage growth and the dissipated energy is also responsible for viscous dissipation [21]. Therefore, whether this method is really applicable for the analysis of asphalt binders fatigue resistance remains to be investigated. 3.2. Analytical method based on pseudo-strain energy It should be noticed that the VECD theory is founded on the pseudo-strain based elastic-viscoelastic correspondence principle [22]. The damage evolution law previously introduced can be expressed as follows, which uses the pseudo-strain energy to be the corresponding physical variable [24].

dD ¼ dt



@W R @D

!a ð7Þ

where WR is pseudo-strain energy. Pseudo-strain energy density was proposed to quantify the work performed [25]:

WR ¼

1  R 2 C c 2

ð8Þ

where C is the material integrity which is represented by pseudostiffness; cR is pseudo-strain. Then, C and cR can be expressed as follows:

sP cRP  DMR

C¼

ð9Þ

cRP ¼ cP  jG jLVE

ð10Þ

R P

where sP, c and cP are measured peak shear stress, peak pseudostrain, and measured peak strain, respectively; DMR is the complex shear modulus ratio (=|G*|fingerprint/|G*|LVE) which is introduced to eliminate sample-to-sample variability, where |G*|fingerprint is the initial |G*| from the amplitude sweep test and |G*|LVE is the linear viscoelastic |G*| at a given temperature and loading frequency from the frequency sweep test. Eqs. (7)–(10) are combined and Eq. (7) is numerically integrated to obtain the damage D:

D¼

1þa a N  X 1 DMR  R 2 cP ðC i1  C i Þ ½ti  ti1 1þa 2 i¼1

ð11Þ

For a cyclic fatigue test, the relationship between C and D can be fitted with a power law model:

C ¼ 1  C 1 ðDÞC 2

ð12Þ

where C1 and C2 are the model parameters which best fit the data. Combining Eqs. (7)–(10), and (12), the fatigue model between fatigue life (Nf) and any given loading strain (cp) can be obtained:

Nf ¼

aC 2 þa f  2a  D1 f

ð1  aC 2 þ aÞðC 1 C 2 Þa ðjG jLVE  cP Þ

2a

ð13Þ

where f and Df represent experimental loading frequency and damage accumulation at failure. This pseudo-strain energy-based method separates the viscoelastic properties of asphalt materials from the damage test so that the development of damage can be analyzed alone. Therefore, the fatigue life of asphalt binders calculated by this method is more accurate than the dissipated energy-based method theoretically.

3

3.3. Fatigue failure criteria The fatigue failure criterion in AASHTO TP101 is the measured peak stress in the stress-strain curve. This peak stress is defined as the yield stress of tested asphalt, and the corresponding shear strain is defined as the yield strain. Fig. 1(a) shows the typical curve and the definition. This is a simple and practical phenomenological indicator and is therefore widely used. However, authors argue that yield stress or strain seems to indicate the stress or strain bearing capacity of asphalt binders under repeated loading, whether it can be a definition of fatigue failure is needed more investigation. Besides, current study has shown that the phase angle of asphalt binders also appears a peak value similar to the peak stress during the LAS test process [26]. Fig. 1(b) shows this phenomenon. It has also been found that the peak phase angle always appears behind the peak stress during the test process [26]. Therefore, if the peak shear stress is regarded as the occurrence of materials yielding, it is logically feasible to regard the peak phase angle as the final failure of asphalt materials. In other words, asphalt binders have undergone the first yielding and then failure in LAS test. In addition, recent studies proposed that the maximum pseudostrain energy (PSE) is a more suitable fatigue failure criterion for the LAS experiment [27]. Because this approach can quantify the damage effect separately according to the elastic-viscoelastic correspondence principle which eliminates the effects of viscoelasticity of asphalt materials. The total PSE (W Rt ) (Eq. (14)) includes two parts: the stored PSE (W RS ) and the released PSE (W Rr ). The W RS and W Rr can be calculated by Eqs. (15) and (16). The typical diagrams of PSE are shown in Fig. 1(c) and (d). It can be seen that at the beginning of the test, the material stores almost all the energy input, and the released energy is near zero. With the increase of the loading level, the stored energy increases, however, the released energy also increases gradually, and the release of energy indicates the generation and development of damage. Then there is an obvious peak point in W RS curve, and the W RS will dramatically decrease after reaching that peak value which indicates that more energy is released from the input material. Therefore, the peak value of W RS represents the maximum energy that materials can store, and it can be used as a new definition for asphalt fatigue failure.

W Rt ¼

1 1  2  sundamaged  cRP ¼  cRP 2 2

ð14Þ

W Rs ¼

 2 1 1  sP  cRP =DMR ¼  C  cRP 2 2

ð15Þ

 2 1  ð1  C Þ  cRP 2

ð16Þ

W Rr ¼ W Rt  W Rs ¼

4. Materials and experimental plan A wide range of asphalt binders was selected in this study including both neat and modified asphalt binders. To investigate the effect of aging on asphalt binders fatigue behavior, all the asphalt binders were conducted Rolling Thin Film Oven (RTFO) test and Pressure Aging Vessel (PAV) test according to AASHTO T240 and AASHTO R28, respectively. The application of RTFO and PAV test aimed to simulate the short-term and long-term aging phenomenon during asphalt mixtures production and service. In addition, to investigate the evolution of asphalt binders fatigue behavior with long-term laboratory aging, two kinds of the selected asphalt binders with relatively good fatigue resistance were subjected to the extended PAV aging. The details of studied asphalt binders and their aging conditions are shown in Table 1. Each asphalt binder at each aging conditions was subjected to LAS test according to AASHTO TP101 using a HAAKE MARS 40 model Dynamic Shear Rheometer (DSR). Experiments in advance found that the sample binder and the parallel plate were not bonded well enough when the fatigue test was carried out at 15 °C or 20 °C, and this issue would impact the accuracy of test results. Therefore, the test

4

H. Zhang et al. / Construction and Building Materials 241 (2020) 118099

0.6

70

65

Defined Fatigue Failure

0.4

Phase angle (°)

Shear stress (MPa)

0.5

0.3 0.2

Defined Fatigue Failure

60

55 0.1 0

50 0

5

10 15 20 Shear strain (%)

25

30

0

5

10

(a)

30

Released PSE

0.25

Defined Fatigue Failure

5

1

4

0.8

0.2 3 0.15 2 0.1 1

0.05

Shear stress (MPa)

0.3

Stored PSE

25

(b)

Released PSE

Stored PSE

15 20 Shear strain (%)

Released PSE WrR

0.6 Undamaged Line 0.4

0.2

Stored PSE WSR

0

0 0

5

10

15 20 Shear strain (%)

25

30

(c)

0

0

0.2

0.4 0.6 0.8 Pseudo-strain (mm/mm)

1

(d)

Fig. 1. (a) Shear stress-based failure criterion; (b) Phase angle-based failure criterion; (c) PSE-based failure criterion; (d) Typical diagram of PSE distribution.

Table 1 Details of tested asphalt binders. Binder type

Dosage of modifier

Performance grade

Aging condition

Neat CR SBS SR

– 18% crumb rubber 5.5% SBS 5.5% SBS + 18% crumb rubber

PG PG PG PG

Original, RTFO, 20 h PAV

64-22 64-28 76-28 76-28

Original, RTFO, 20 h PAV, 40 h PAV, 60 h PAV

temperature was held at 25 °C. The parallel plate geometry of 8 mm diameter and 2 mm gap was used. The LAS test comprises two parts: frequency sweep and amplitude sweep. The frequency sweep test data is used to obtain the a parameter. It applies oscillatory shear loading at constant amplitude (0.1%) over a range of loading frequencies (0.2, 0.4, 0.6, 0.8, 1.0, 2.0, 4.0, 6.0, 8.0, 10, 20, and 30 Hz). Complex shear modulus and phase angle are recorded at each frequency. The amplitude sweep test is a strain-control mode at 10 Hz using an oscillatory shear. The strain amplitude increases linearly from 0.1% to 30% over the course of 3100 cycles of loading. Complex shear modulus, phase angle, peak shear stress, and peak shear strain are measured every 10 cycles. The test time is 5 min.

5. Results and discussion 5.1. Comparison of fatigue failure criteria Table 2 shows the different failure strain calculated by the three fatigue failure criteria. In general, the value of failure strain based on peak phase angle is the highest compared with the other two

definitions for the neat and CR asphalt binders. For the SBS and SR modified asphalt binders, the value of failure strain based on maximum W Rs is the highest except for the 60 h PAV aged SBS asphalt binder. Besides, the addition of modifiers significantly reduced the values of peak stress and maximum W Rs of Neat asphalt at the original condition, especially the addition of crumb rubber. This may be explained by that the rubber particles can play a certain role in stress absorption. It is noteworthy that some of the failure strain of SBS and SR modified asphalt binders are approaching 30% before the 20 h PAV aging condition, which is the maximum strain level of LAS test. This is because there is no obvious peak values of these three definitions in the process of determining fatigue failure, in other words, the binder specimen still does not appear fatigue failure when the applied strain reaches the maximum value. Therefore, for the modified asphalt binders with relatively good fatigue resistance, the definition of fatigue failure is of vital importance. According to the experimental results of Table 2, it is obvious to observe the peak value of shear stress than the other two failure definitions for modified asphalt binders. In addition, the fatigue failure strain of asphalt binders decreases with the increase of aging degrees, which implies that if the LAS test stipulates to use binder specimen after 20 h PAV aging for testing, the definition of fatigue failure could be more accurate. For these four asphalt binders at original, RTFO and 20 h PAV aging conditions, the Analysis of Variance (ANOVA) test was applied to identify the significant level of the fatigue failure criterion as an independent variable. The dependent variables are the

5

H. Zhang et al. / Construction and Building Materials 241 (2020) 118099 Table 2 Comparison of different fatigue failure criteria. Binder code

Peak stress (MPa)

Corresponding failure strain (%)

Peak phase angle (°)

Corresponding failure strain (%)

Maximum W Rs

Corresponding failure strain (%)

Neat-Original Neat-RTFO Neat-20 h PAV CR-Original CR-RTFO CR-20 h PAV SBS-Original SBS-RTFO SBS-20 h PAV SBS-40 h PAV SBS-60 h PAV SR-Original SR-RTFO SR-20 h PAV SR-40 h PAV SR-60 h PAV

0.338 0.390 0.483 0.142 0.162 0.213 0.222 0.242 0.318 0.324 0.327 0.154 0.188 0.195 0.255 0.359

10.91 10.62 10.12 14.87 14.54 14.42 21.55 18.85 18.21 15.03 14.82 29.99 19.41 18.73 16.67 15.93

67.93 65.51 63.89 68.68 67.25 65.55 64.67 64.65 64.50 63.08 62.89 65.53 65.53 64.57 64.55 63.82

14.90 14.55 13.77 18.35 18.24 17.93 28.03 27.48 25.74 17.72 17.41 29.99 21.25 18.22 18.21 17.53

7.821 15.886 26.507 1.909 2.678 5.427 7.795 8.523 12.479 13.126 15.323 2.958 4.985 6.279 10.173 18.098

12.34 12.24 12.05 18.16 16.75 16.66 30.02 29.05 26.04 17.85 15.75 30.02 29.99 29.25 26.05 21.96

failure strain levels obtained by the three criteria, and the significance level (a) is 0.05. The analysis results are detailed in Table 3. The ANOVA analysis indicates that the F-value is smaller than the F crit, and the P-value is greater than 0.05. That means there is no significant difference between the failure strain levels by using these three fatigue failure criteria. However, the phase angle value can hardly predict the fatigue performance of asphalt binders due to there is no information related to phase angle in the current VECD theory. Besides, the maximum W Rs is still essentially a parameter derived from the shear stress, and using this fatigue failure criterion seems difficult to capture the peak value for the modified asphalt binders with excellent fatigue performance (as can be seen in Table 2). Therefore, the authors maintain that the peak stress-based failure criterion is more applicable and accurate compared with the other two definitions. 5.2. Damage characteristic curves and fatigue curves The DCCs of original asphalt binders through the previous reviewed two analytical methods are shown in Fig. 2. As we can see, the total value of damage intensity D are quite different between the two analytical methods, this is due to the difference  R 2 cP that lead to the different between the coefficients pc20 and DMR 2 D values of asphalt binders according to Eqs. (3) and (11), especially for these binders with high initial modulus. In addition, the relative position of DCCs is also different by using these two analytical methods. Current study considered that the relative position of DCC is primarily controlled by the materials modulus, and lower modulus typically produces a lower curve [28,29]. The authors have noticed that the changes of materials integrity C are equivalent of asphalt binders at the same strain level, and the distinction of D values impacts the relative position of DCCs. The clear diagram of this phenomenon can be found in Fig. 3. In Fig. 3(a) and (b), the changes of C values of unaged Neat and SBS asphalt binder, and the loading strain level are all equal. Therefore, the evaluation and comparison of fatigue performance of asphalt binders cannot be judged by using DCCs alone because of the involvement of

modulus and the different coefficients in the calculation process of damage intensity [29]. Fatigue curves of original asphalt binders are shown in Fig. 4. It should be pointed out that the fatigue curves and fatigue life of asphalt binders in the following text are all calculated according to the peak stress-based failure criterion. It can be found that there is no significant difference in fatigue curves obtained by the two analytical methods. The SR compound modified asphalt binder shows the best fatigue resistance, followed by SBS and CR modified asphalt binders, and the Neat asphalt has the worst fatigue performance. According to the existed research [30], the fatigue life were calculated at both a low and high strain levels represented by 2.5% and 5%, respectively, as shown in Fig. 5. The MD represents the method of dissipated energy, and the MP represents the method of pseudo-strain energy. According to Fig. 5, almost all the fatigue life determined by the pseudo-strain energy approach are higher than those of the dissipated energy method at any aging condition except for the CR asphalt, while especially for the SBS and SR modified asphalt. Besides, the addition of SBS can effectively improve the fatigue resistance of Neat asphalt binder at both low and high strain levels. In general, the rank of fatigue performance of studied asphalt binders is: SR > SBS > CR > Neat. On the other hand, Fig. 5 also indicates the different aging effects on different asphalt binders. For the Neat asphalt and CR modified asphalt, increasing in the aging degree is seen to improve the fatigue resistance at the condition of 2.5% strain level because of the slight increasing of fatigue life. The similar experimental results occur in CR modified asphalt binder at the condition of 5% strain level. This phenomenon was also found by other researchers [19,31]. However, for SBS modified asphalt and SR compound modified asphalt, their fatigue life at both 2.5% and 5% strain levels decline with the increase of aging intensity. Such a different influence of aging on asphalt binders fatigue life indicates that the aging effect is asphalt specific and depends on the loading strain levels. 5.3. Effect of aging on fatigue resistance Fig. 6 represents the fatigue curves of selected asphalt binders at different aging conditions by using the two analytical methods.

Table 3 ANOVA test results. Variable

Fatigue failure criteria

Original

RTFO

20 h PAV

F-value

F crit

P-value

F-value

F crit

P-value

F-value

F crit

P-value

0.23

4.26

0.79

0.97

4.26

0.42

0.93

4.26

0.43

6

H. Zhang et al. / Construction and Building Materials 241 (2020) 118099

Neat

CR

SBS

Neat

SR

1

CR

SBS

SR

1 Original

Original

0.8

0.6

0.6 C

C

0.8

0.4

0.4

0.2

0.2

0

0 0

100

200

300 D

400

500

600

0

100

200

300 D

(a)

400

500

600

(b)

Fig. 2. Damage characteristic curves: (a) Dissipated energy-based method; (b) Pseudo-strain energy-based method.

Neat

Neat

SBS 1

0.8

0.8

0.6

0.6

SBS

C

C

1

0.4

0.4

0.2

0.2

0

0 0

100

200

300 D

400

500

0

600

100

(a)

200

300 D

400

500

600

(b)

Fig. 3. Schematic diagram of different positions of DCCs obtained from two methods: (a) Dissipated energy-based method; (b) Pseudo-strain energy-based method.

Neat

CR

SBS

SR

Neat

1.E+07

CR

SBS

Original

Original

1.E+06

1.E+06

Fatigue life

Fatigue life

SR

1.E+07

1.E+05

1.E+04

1.E+03

1.E+05

1.E+04

1.E+03

1.E+02

1.E+02 1

10 Strain level (%)

(a)

1

10 Strain level (%)

(b)

Fig. 4. Fatigue curves of four asphalt binders: (a) Dissipated energy-based method; (b) Pseudo-strain energy-based method.

7

H. Zhang et al. / Construction and Building Materials 241 (2020) 118099

Original-MD

Original-MP

RTFO-MD

RTFO-MP

20 hr PAV-MD

20 hr PAV-MP

40 hr PAV-MD

40 hr PAV-MP

60 hr PAV-MD

60 hr PAV-MP

1.E+06

2.5%

Fatigue life

1.E+05

1.E+04

1.E+03 Neat

CR

SBS

SR

(a) Original-MD

Original-MP

RTFO-MD

RTFO-MP

20 hr PAV-MD

20 hr PAV-MP

40 hr PAV-MD

40 hr PAV-MP

60 hr PAV-MD

60 hr PAV-MP

1.E+05

Fatigue life

5%

1.E+04

1.E+03 Neat

CR

SBS

SR

(b) Fig. 5. Fatigue life at different strain levels using two analytical methods: (a) 2.5%; (b) 5%.

It shows that the fatigue life calculated by pseudo-strain energy method is slightly higher than that of the dissipated energy method, especially for the unaged binders at the low strain levels. This indicates that the total damage input is different when calculating the fatigue life of asphalt binders according to the two methods. As discussed previously, only a part of dissipated energy is responsible for the damage growth, and the pseudo-strain energy is more accurate when regarded as the input damage. For the SBS modified asphalt and SR compound modified asphalt, aging exerts the similar effect which decreases the fatigue life of asphalt binders. The difference of fatigue life between two aging conditions decreases with the increase of strain level. For the Neat asphalt, however, the effect of aging on asphalt binders fatigue resistance relies on the loading strain. As can be seen from Fig. 6(a) and (b), aging is detrimental to fatigue life at high strain levels but beneficial at low strain levels. The critical strain level is approximate 4.5%. For the CR modified asphalt binder, it is interesting to find that the fatigue life increases across the entire strain range, especially at the relatively low strain levels. The cause of this phenomenon is not clear. Authors consider that it may be due to the crumb rubber has not been well-stabilized during the production of CR modified asphalt used in this paper, and the rubber particles are further pyrolyzed under the condition of thermal-oxidative aging which forms a better physical network structure, finally resulting in the binders fatigue performance improvement.

6. Conclusions A comprehensive review of two fatigue analytical methods and three fatigue failure criteria in LAS test were investigated in this paper. Fatigue failure strain obtained by the three definitions for both unaged and aged asphalt binders were statistically compared. The fatigue curves were also evaluated considering the effect of aging. The main conclusions can be drawn from the experimental and analytical results of this study are as follows:
Statistical analysis of the fatigue failure strain shows there is no significant difference between the three criteria of fatigue failure. However, for the modified asphalt binder at unaged condition, it is hard to observe the peak value of phase angle or maximum W RS . Besides, some of the failure strain of SBS and SR modified asphalt binders are approaching 30% which is the maximum strain level of LAS test before the 20 h PAV aging condition. Therefore, to accurately determine the fatigue failure and obtain the further calculated parameters, the authors suggest to use the peak shear stress as the fatigue failure criterion and use the 20 h PAV aged binder sample to conduct the LAS test.
The damage characteristic curves obtained by the two different analytical methods are quite different due to the difference of calculating coefficients of damage intensity (D), although the

8

H. Zhang et al. / Construction and Building Materials 241 (2020) 118099

Original

RTFO

Original

20 hr PAV

RTFO

20 hr PAV Neat

Neat

2.E+05 Fatigue life

Fatigue life

2.E+05

2.E+04

2.E+03

2.E+03

2.E+02

2.E+02 1

10

Original

(a)

(b)

RTFO

Original

20 hr PAV

RTFO

20 hr PAV

5.E+05

CR

5.E+04

CR

5.E+04

5.E+03

5.E+03

5.E+02

5.E+02

1

Original

1

10

RTFO

10

Strain level (%)

Strain level (%)

(c)

(d)

20 hr PAV

40 hr PAV

5.E+06

60 hr PAV

Original

RTFO

20 hr PAV

40 hr PAV

60 hr PAV

5.E+06

SBS

5.E+05

SBS

5.E+05 Fatigue life

Fatigue life

10 Strain level (%)

Fatigue life

Fatigue life

1

Strain level (%)

5.E+05

5.E+04

5.E+04

5.E+03

5.E+03

5.E+02

5.E+02

1

Original

1

10

RTFO

10

Strain level (%)

Strain level (%)

(e)

(f)

20 hr PAV

40 hr PAV

5.E+06

Original

60 hr PAV SR

RTFO

20 hr PAV

40 hr PAV

60 hr PAV SR

5.E+06

Fatigue life

5.E+05 Fatigue life

2.E+04

5.E+04

5.E+03

5.E+05

5.E+04

5.E+03

5.E+02

5.E+02

1

10

1

10

Strain level (%)

Strain level (%)

(g)

(h)

Fig. 6. Fatigue curves: (a, c, e, g) Dissipated energy-based method; (b, d, f, h) Pseudo-strain energy-based method.

H. Zhang et al. / Construction and Building Materials 241 (2020) 118099

changes in material integrity (C) are equal. The analytical method of pseudo-strain energy is more promising and is theoretically more accurate to represent the damage growth than the dissipated energy-based method, and the calculated fatigue life of asphalt binders at all the aging conditions are slightly higher than the fatigue life calculated by the method of dissipated energy.
The effect of aging on asphalt binders fatigue resistance is material specific and depends on the loading amplitude (strain level). For the Neat asphalt, aging is detrimental to fatigue life at high strain levels but beneficial at low strain levels. The critical strain level is approximate 4.5%. For the CR modified asphalt, the fatigue life increases across the entire strain range, especially at the low strain level. For the SBS and SR modified asphalt, aging exerts a similar effect, which decreases the fatigue life of asphalt binders.
The addition of modifiers, particularly the SBS modifier, effectively improves the fatigue performance of Neat asphalt at the undamaged condition. Moreover, the fatigue life of SBS and SR modified asphalt are much higher than the Neat asphalt and CR modified asphalt even at the 60 h PAV aging condition. CRediT authorship contribution statement Hanyu Zhang: Conceptualization, Methodology, Formal analysis, Investigation, Writing - original draft. Kairen Shen: Methodology, Investigation. Gang Xu: Formal analysis, Investigation. Jusheng Tong: Writing - review & editing. Rui Wang: Formal analysis, Investigation. Degou Cai: Writing - review & editing, Supervision. Xianhua Chen: Writing - review & editing, 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. Acknowledgment The authors would like to acknowledge the financial support of the National Natural Science Foundation of China (No. 51778136). References [1] R.L. Lytton, J. Uzan, E.G. Fernando, R. Roque, D. Hiltunen, S.M. Stoffels, Development and Validation of Performance Prediction Models and Specifications for Asphalt Binders and Paving Mixes: SHRP-A-357, National Research Council, 1993. [2] M.N. Partl, H.U. Bahia, F. Canestrari, C. Roche, H. Benedetto, H. Piber, D. Sybilski, Advances in Interlaboratory Testing and Evaluation of Bituminous Materials. RILEM State-of-the-Art Reports, 2013. [3] H.U. Bahia, H. Zhai, K. Bonnetti, S. Kose, Non-linear viscoelastic and fatigue properties of asphalt binders, J. Assoc. Asphalt Paving Technol. 68 (1999) 1–34. [4] B. Tsai, C.L. Monismith, Influence of asphalt binder properties on the fatigue performance of asphalt concrete pavements, J. Assoc. Asphalt Paving Technol. 74 (2005) 733–790. [5] R. Hajj, A. Bhasin, The search for a measure of fatigue cracking in asphalt binders – a review of different approaches, Int. J. Pavement Eng. 19 (3) (2018) 205–219.

9

[6] H.U. Bahia, D.I. Hanson, M. Zeng, H. Zhai, M.A. Khatri, R.M. Anderson, Characterization of Modified Asphalt Binders in Superpave Mix Design: NCHRP Report 459, National Research Council, 2001. [7] K.S. Bonnetti, K. Nam, H.U. Bahia, Measuring and defining fatigue behavior of asphalt binders, Transp. Res. Rec. 1810 (2002) 33–43. [8] J.P. Planche, D.A. Anderson, G. Gauthier, Y.M. Le Hir, D. Martin, Evaluation of fatigue properties of bituminous binders, Mater. Struct. 37 (5) (2004) 356–359. [9] S. Shen, G.D. Airey, S.H. Carpenter, H. Huang, A dissipated energy approach to fatigue evaluation, Road Mater. Pavement Des. 7 (1) (2006) 47–69. [10] C.M. Johnson, Estimating Asphalt Binder Fatigue Resistance Using an Accelerated Test Method (Ph.D. Dissertation), University of WisconsinMadison, 2010. [11] C. Hintz, R. Velasquez, C. Johnson, H. Bahia, Modification and validation of linear amplitude sweep test for binder fatigue specification, Transp. Res. Rec. 2207 (2011) 99–106. [12] C. Hintz, H. Bahia, Simplification of linear amplitude sweep test and specification parameter, Transp. Res. Rec. 2370 (2013) 10–16. [13] Z. Zhou, X. Gu, Q. Dong, F. Ni, Y. Jiang, Rutting and fatigue cracking performance of SBS-RAP blended binders with a rejuvenator, Constr. Build. Mater. 203 (2019) 294–303. [14] F. Safaei, C. Castorena, Y.R. Kim, Linking asphalt binder fatigue to asphalt mixture fatigue performance using viscoelastic continuum damage modeling, Mech. Time-Dependent Mater. 20 (3) (2016) 299–323. [15] R. Lundstrom, U. Isacsson, Asphalt fatigue modelling using viscoelastic continuum damage theory, Road Mater. Pavement Des. 4 (1) (2003) 51–75. [16] B.S. Underwood, C. Baek, Y.R. Kim, Simplified viscoelastic continuum damage model as platform for asphalt concrete fatigue analysis, Transp. Res. Rec. 2296 (2012) 36–45. [17] F.E. Pérez-Jiménez, R. Botella, R. Miró, Differentiating between damage and thixotropy in asphalt binder’s fatigue tests, Constr. Build. Mater. 31 (2012) 212–219. [18] E. Santagata, O. Baglieri, L. Tsantilis, D. Dalmazzo, Evaluation of self healing properties of bituminous binders taking into account steric hardening effects, Constr. Build. Mater. 41 (2013) 60–67. [19] C. Hintz, R. Velasquez, Z. Li, H. Bahia, Effect of oxidative aging on binder fatigue performance, J. Assoc. Asphalt Paving Technol. 80 (2011) 527–548. [20] R. Miró, A.H. Martínez, F. Moreno-Navarro, M. Rubio-Gámez, Effect of ageing and temperature on the fatigue behaviour of bitumens, Mater. Des. 86 (2015) 129–137. [21] W. Cao, C. Wang, A new comprehensive analysis framework for fatigue characterization of asphalt binder using the linear amplitude sweep test, Constr. Build. Mater. 171 (2018) 1–12. [22] R.A. Schapery, Correspondence principles and a generalized J integral for large deformation and fracture analysis of viscoelastic media, Int. J. Fract. 25 (1984) 195–223. [23] Y.R. Kim, H.J. Lee, D. Little, Y. Kim, N. Gibson, G. King, T. Pellinen, F. Fee, A simple testing method to evaluate fatigue fracture and damage performance of asphalt mixtures, J. Assoc. Asphalt Paving Technol. 75 (2006) 755–788. [24] S.W. Park, Y.R. Kim, R.A. Schapery, A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete, Mech. Mater. 24 (1996) 241–255. [25] J.S. Daniel, Development of a Simplified Fatigue Test and Analysis Procedure Using a Viscoelastic, Continuum Damage Model and its Implementation to WesTrack Mixtures (Ph.D. Dissertation), North Carolina State University, 2001. [26] C. Wang, Rheological Characterization on Paving Performance of Asphalt Binders (in Chinese) (Ph.D. Dissertation), Beijing University of Technology, 2015. [27] C. Wang, C. Castorena, J. Zhang, Y.R. Kim, Unified failure criterion for asphalt binder under cyclic fatigue loading, Road Mater. Pavement Des. 16 (Suppl. 2) (2015) 125–148. [28] W. Cao, C. Wang, Fatigue performance characterization and prediction of asphalt binders using the linear amplitude sweep based viscoelastic continuum damage approach, Int. J. Fatigue 119 (2019) 112–125. [29] W. Cao, L.N. Mohammad, M. Elseifi, Assessing the effects of RAP, RAS, and warm-mix technologies on fatigue performance of asphalt mixtures and pavements using viscoelastic continuum damage approach, Road Mater. Pavement Des. 18 (Suppl. 4) (2017) 353–371. [30] H. Bahia, H.A. Tabatabaee, T. Mandal, A. Faheem, Field, Evaluation of Wisconsin Modified Binder Selection Guidelines – Phase II, Wisconsin Department of Transportation, 2013. [31] W. Cao, Y. Wang, C. Wang, Fatigue characterization of bio-modified asphalt binders under various laboratory aging conditions, Constr. Build. Mater. 208 (2019) 686–696.