Influence of binder grade, gradation, temperature and loading rate on R-curve of asphalt concrete

Construction and Building Materials 154 (2017) 780–790

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

Influence of binder grade, gradation, temperature and loading rate on R-curve of asphalt concrete Shu Yang a,⇑, Andrew F. Braham b a b

Department of Civil Engineering, Hunan University, Changsha 410082, China University of Arkansas, 4190 Bell Engineering Center, Fayetteville, AR 72701, USA

h i g h l i g h t s
Polymer modification impacts the crack initiation parameters of cohesive energy.
Testing temperature impacts fracture energy, cohesive energy and energy rate.
R-curve can be used to understand the performance of asphalt concrete.

a r t i c l e

i n f o

Article history: Received 6 April 2017 Received in revised form 25 July 2017 Accepted 4 August 2017 Available online 17 August 2017 Keywords: Asphalt concrete R-curve Fracture energy Cohesive energy Energy rate

a b s t r a c t The R-curve method is widely applied in characterizing a vast range of materials. However, research on Rcurves in asphalt concrete is very limited. In previous research, the R-curve method was developed to characterize and quantify the fracture resistance of asphalt concrete. In this paper, a more comprehensive experimental matrix for R-curve research was performed to enlarge the potential envelope of R-curve in asphalt concrete. Thus, this research studied the influence of binder grade, aggregate size, testing temperature, and loading rate on R-curve extractions: fracture energy, cohesive energy, and energy rate. In conclusion, it is found that R-curve method can benefit the fracture analysis of asphalt concrete. This method can differentiate the fracture resistance of the materials in terms of crack initiation and propagation. Significant findings include the polymer modification only influences cohesive energy; the loading rate only influences the energy rate; and both the NMAS and testing temperature influence the facture energy, energy rate, and cohesive energy. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Irwin and Kies [12] developed a concept to quantify the crack growth resistance called the Resistance Curve, or R-curve. Krafft et al. [15] postulated and verified the concept of R-curve. An Rcurve considers fracture resistance as a function of crack extension. A plot of resistance versus crack length extension can be defined as R-Curve, crack extension occurs when energy release rate equals to the material resistance [25]. R-curve has been widely and successfully applied in vast range of materials such as Ceramic [23], human tooth enamel [4], human bone [9], epoxy adhesives [2], alloy [19], dental porcelain [8], rock [18], and Concrete [22]. The information that R-curve provides to characterize and quantify the fracture resistance can be abundant compare to single number. For example, R-curve can not only predict the life expectancy of ⇑ Corresponding author. E-mail Braham).

addresses:

[email protected] (S. Yang), [email protected] (A.F.

http://dx.doi.org/10.1016/j.conbuildmat.2017.08.019 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

materials [20], but can also explain the mechanism of crack initiation and propagation [13] and identify the contribution of crack resistance [27]. R-curve method, in theory, can quantify the fracture resistance of materials that vary from linear elastic material, plastic-elastic material to time-dependent material [3]. In this large range of materials, fracture resistance can be considered as crack driving force, J-integral, or C⁄ integral corresponding to linear elastic fracture, plastic-elastic fracture and time-dependent fracture. However, according to literature, there is limited research to fully investigate R-curve method for the fracture analysis of asphalt concrete. The earliest literature found that utilized Rcurve for asphalt concrete was Mobasher et al. [17]. This research used R-curve method to evaluate the crack propagation properties of asphalt concrete and indicated that R-curve approach provided good measurement of fracture resistance of asphalt concrete. Recently, however, there has been preliminary research on Rcurve to further study the fracture resistance of asphalt concrete. Braham and Mudford [6] applied the R-curve for asphalt concrete to evaluate the fracture resistance. Multiple R-curves at

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different testing temperatures for the same mixture were established. By shifting the curves at different temperature, a master R- Curve was constructed. This study used the master R-curve to quantify and characterize the cracking resistance of asphalt concrete, which evaluated the cracking resistance more comprehensively than a single number parameter. However, this research used CMOD as the crack extension rather than crack length, which was a deviation from traditional R-curve methods in other materials. Yang and Braham [26] constructed R-curve for asphalt concrete using crack length and CMOD respectively and compared the resulting R-curve generated by these two protocols. The crack length protocol captured different shape of R-curve as the CMOD protocol, which indicated that perhaps the relationship between crack length and CMOD was not well understood. Ghafari and Nejad [11] constructed R-curve in asphalt concrete by using SE (B) test to characterize the crack propagation. J-integral was utilized as the fracture resistance to construct R-curve which characterized the elastic-plastic property in fracture of asphalt concrete. Yang and Braham [25] establish R-curve for three types of asphalt concrete considering aging, moisture condition, and temperature. It is found that R-curve can be powerful to characterize and quantify the crack initiation and propagation in asphalt concrete. Because R-curve is a function of crack resistance, it records the whole process of crack development including crack initiation and crack propagation. The crack initiation was quantified by cohesive energy, while the propagation was quantified with fracture energy, which was the combination of both cohesive energy and propagation energy. The research found that the cohesive energy was relatively unchanged between mixtures and external factors, while the overall fracture energy was more sensitive. While previous study of R-curve for asphalt concrete provides a first glimpse to the potential benefits of utilizing R-curves, it did not explore common variables and test conditions in mix design of asphalt concrete. In this paper, a non-linear parameter, fracture energy is used as the fracture resistance to construct R-curve. This study further investigated the influence of mix-design variables on R-curve in asphalt concrete. There are two considerations to compliment the previous research of R-curve for asphalt concrete. First, this expanded research of R-curve intends to investigate the most fundamental variables in asphalt concrete: asphalt binder Performance Grade (PG) and Nominal Maximum Aggregate Size (NMAS). Second, as asphalt concrete is a viscoelastic material, the testing temperature and loading rate impact the crack behavior significantly. Viscous deformation always associates with the fracture process, know that the energy dissipated in the system is used to create crack, or creep deformation. Therefore, a wide range of temperatures and loading rates were also explored.

2. Objective The motivation of this research is to fully evaluate the functionality of the R-curve method for agencies to quantify the crack resistance of asphalt concrete in terms of crack initiation and propagation. To achieve this motivation, this paper aims to investigates internal and external factors of R-curve for asphalt concrete including binder grade, aggregate size, testing temperature, and loading rate.

3. Material and methods To maximize the envelope of R-curve in asphalt concrete, this paper uses the experimental matrix shown in Table 1. The factors (including binder grade, Nominal Maximum Aggregate Size, testing temperature, and loading rate) and levels are chosen to expect significant difference in R-curve behavior of asphalt concrete.

Table 1 Experimental matrix. Factors

# of Levels

Level

Binder Grade NMAS Test Temperature Loading Rate

2 2 3 2

PG 64-22, PG 76-22 9.5 mm, 25 mm 24 °C*, 0 °C, 24 °C 0.03 mm/min, 1.0 mm/min

* The test result at 24 °C is not included in discussion and the reason will be given in Section 4.3.

3.1. Materials In this study, the factor of binder grade had two levels, PG 76-22 and PG 64-22. PG76-22 binder used in this research is a SBS polymer modified binder on a neat binder PG64-22. Thermal cracking is usually an issue at low temperature and these two asphalt binders to have the same lower limit of their binder grade. However, fracture behavior of these two binders in asphalt concrete could be different for two reasons. First, the low temperature grading in a Superpave PG is graded by the DSR fatigue test and the Bending Beam Rheometer (BBR) test on binder only. Second, the PG 76-22 was polymer modified with styrene-butadienestyrene (SBS), whereas PG 64-22 was a neat binder without any modification. The purpose of the addition of polymer in the binder is the toughness increment at high temperature, but the polymer may also influence the fracture behavior at low temperature. The second factor, aggregate, can be influenced by the size of the gradation. A NMAS 9.5 mm is usually applied in surface course, whereas a NMAS 25 mm is usually placed in field as the binder course between surface course and base course. As known, the finer aggregate gradation has more surface area than the courser gradation, thus the binder content is usually higher in finer aggregate gradation to cover the surface area. In asphalt concrete, the matrix between aggregate and asphalt binder is usually the weak point compare to the tensile strength of aggregate itself, so cracks often form at either the interface of the aggregate and matrix or in the matrix itself, not generally in the aggregate. It is usually observed crack growing in the asphalt binder filled voids of the asphalt concrete. Finally, the gradation structures in the asphalt concrete can be very different due to the NMAS, which may result in significant fracture toughness and fracture behavior. A Superpave mix design was performed for the NMAS 9.5 mm, and NMAS 25 mm gradation, using PG 64-22 binder and targeting 4% air voids. In order to control the viable of binder content that could have added a confounding factor on the cracking behavior of asphalt concrete, this research uses the same binder contents for PG 76-22 binder and PG 64-22 binder. The binder contents determined by the mix design are 5.70% for the 9.5 mm NMAS mixture, and 4.02% for the 25 mm NMAS mixture. The compaction data is recorded during the compaction, the percentage of theoretical maximum specific gravity (Gmm) is plotted versus gyration numbers. The testing sample compaction reduced the gyrations according to the compaction curve when compacting to achieve 7% air void to mimic the field air void immediately after the construction and as per standard practice. All the samples experienced two hours aging at the compaction temperature before the compaction. In addition to the asphalt binder type and aggregate gradation, external factors are also important in asphalt concrete behavior. Due to the viscoelastic nature of asphalt concrete, time and temperature are vital in fracture behavior. This paper used three testing temperatures: 24 °C, 0 °C and 24 °C. The temperature of 24 °C was chosen because of the lower limit of the PG grade for both binder is 22. 24 °C is 2 °C below the lower PG limit. This test temperature for fracture test is established by Braham et al. [7] and is intended to capture the glass transition temperature of the asphalt cement. 24 °C is usually the ambient temperature and significant amount of research is found to perform fracture test at ambient temperature. For example, Faruk et al. [10] at Texas A&M Transportation Institute, found that the room temperature at 25 °C, was the better suited for low binder content asphalt concrete in SCB) test. Wu et al. [21] at Louisiana Transportation Research Center performed the SC(B) test at 25 °C, for the asphalt concrete contains the binder for PG 76-22 and PG70-22. However, since the energy dissipated in the specimen during a fracture tests can be separated into three parts: fracture energy, recoverable strain energy, and creep strain energy [5], fracture testing at ambient temperatures include more than just the energy associated with separating fracture faces. This indicates that fracture is associated with the elastic deformation recoverable) and viscous deformation creep). Li and Marasteanu [16] found that it takes higher external work in a fracture test at higher testing temperature. This may indicate that the creep deformation is larger at higher testing temperature. In other words, the creep energy increases in the system as the increment of the testing temperature. This research did not separate the three types of energy, but the three levels of testing temperature promoted a trend of the change of creep energy and elastic energy. Thus, 24 °C, 0 °C, and 24 °C are chosen to expect to detect the trend. It is known that the effect of time and temperature can be converted by the law of time-temperature superposition. Loading rate is the form of time in a fracture test, a faster loading rate at higher temperature may be equivalent to a slower loading rate at lower temperature. In this paper, two loading rates are considered in the

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Fig. 1. Dynamic modulus in indirect tensile (IDT) mode.

experimental matrix, 0.03 mm/min, and 1.0 mm/min, in the control of CMOD, these two loading rates are selected to enlarge the difference of R-curve shape due to loading rate. Four replicates are performed for each factor at each level. Finally, as the stiffness is an indicator to the viscoelastic behavior, dynamic modulus was tested for the material listed in the test matrix. In order to achieve the stiffness at SC(B) testing temperature of 24 °C, it was decided to add a dynamic modulus testing temperature of 24 °C instead of extrapolation values from the dynamic modulus master curve.

can be used for the SC(B) fracture testing as well. In addition, the dynamic modulus in tensile mode also provides the same orientation for the IDT sample and SCB sample is the same. This is important because the loading direction of the IDT dynamic modulus test and SC(B) test is perpendicular to the sample compaction direction, whereas the loading direction in uniaxial dynamic modulus test is parallel to the sample compaction direction. The IDT samples were tested in a MTS load frame with a 5 kip load cell. Two pair of 38 mm extensometers were attached to each surface of the IDT sample to measure the vertical and horizontal strain. Five testing temperature were selected: 24 °C, 10 °C, 4 °C, 21 °C, 37 °C and 54 °C. Recall that 24 °C was selected because of one of the SC(B) testing temperature is 24 °C, and the other five temperatures are from the specification of uniaxial dynamic modulus, AASHTO T 342. Five frequencies selected per specification as well: 25 Hz, 10 Hz, 5 Hz, 1 Hz, 0.5 Hz, and 0.1 Hz, all from AAHTO T 342. The IDT samples were cut from Superpave gyratory compactor (SGC) samples. The samples were targeting 40 mm thickness slice, with a single sample extracted from the middle of each SGC sample. All the samples targeted 7% air voids. After completing all the tests for dynamic modulus, it was observed that at the testing temperature of 54 °C, the strain level was not able to be controlled within the range of linear elastic, 50–150 mm. Thus, the data collected at 54 °C was not applied to construct the master curves. In addition, the data collected at 25 Hz, and 10 Hz saw an abnormally high level of scatter, so these data were not applied to construct master curve as well. The master curves of dynamic modulus for the four types of asphalt concrete are constructed by following AASHTO R62-13, using Eqs. (1)–(4). An improved method that restricts initial coefficient of a, b, c, a1 and a2 was applied to construct rational smoother master curves [24]

log jE j ¼ d þ

ð1Þ

f r ¼ f  aT

ð2Þ

logaT ¼ a1 ðT R  TÞ2 þ a2 ðT R  TÞ

ð3Þ

SSE ¼

3.2. Dynamic modulus test configuration

a

1 þ ebþclogðf r Þ

N X ^ j  log jE j Þ2 ðlog jE i i

ð4Þ

i¼1

Dynamic modulus of asphalt concrete provides the constitutive characterization over a wide temperature and frequency range. This study performed the dynamic modulus test of the materials that used in the test matrix of fracture test to investigate is the if the results from dynamic modulus test and R-curve test have the same trend. As seen in Fig. 1, the dynamic modulus in indirect tensile IDT) mode was utilized for the four types of asphalt concrete in the SCB) experimental matrix: PG 76-22 with NMAS 25 mm; PG 76-22 with NMAS 9.5 mm; PG 64-22 with NMAS 25 mm; PG 64-22 with NMAS 9.5 mm. This testing geometry, developed by Kim et al. [14], is beneficial because the samples used in the IDT dynamic modulus test

where; jE ji = average measured dynamic modulus for each testing temperature and testing frequency combination, i, (MPa), ^ j = predicted dynamic modulus by Eq. (1) for each testing temperature and jE i testing frequency combination, i, (MPa), N = total number of testing temperature and frequency combination, SSE = square sum of error between measured and predicted dynamic modulus, and a; b; c; a1 ; a2 = coefficient for best fitted curve to have lowest SSE.

Fig. 2. SC(B) test configuration, before (left) and after (right) test.

Fig. 3. SC(B) sample fabrication.

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S. Yang, A.F. Braham / Construction and Building Materials 154 (2017) 780–790 Replicate 1

Replicate 2

Replicate 3

Replicate 4

Average Curve

1400

Fracture Energy: y-value at the end point

1200 1000 800

Crack propagaon: energy rate

600 400 200 0

Crack iniaon: cohesive energy 0

5

10

15

20

25

30

35

40

Crack Length Extention (mm) Fig. 4. Sample R-curves for 25 mm, PG 64-22 HMA, at loading rate of 0.03 mm/min.

3.3. SC(B) test configuration SC(B) test was utilized in this research to construct the R-curve for asphalt concrete as illustrated in Fig. 2. The SC(B) samples were tested on a MTS load frame with a 5 kip load cell. A clip gauge was attached to the bottom center of the SC (B) to control the opening of the crack mouth, the load control was CMOD (Crack Mouth Opening Displacement) control at different levels of rate. A Basler camera setup was used in the test to capture the images of one surface of the sample for determining crack length. The images captured were 18 megapixels, eight-bit monochrome grey scale, which means each pixel in the image has a grey value that ranges from 0 to 256. For the tests at loading rate of 1.00 mm/min, the frame rate of 14 frame per second(fps) was applied, and a slower 0.2 fps is applied to the tests at loading rate 0.03 mm/min due to the ram memory of the equipment and the longer

testing times. Tests run at 1.0 mm/min were often completed in as little as 30 s, whereas the 0.03 mm/min tests were typically 20–30 min, and even longer for the higher testing temperatures. The illumination of the sample face for a more accurate capture of the images was two 60 w, 60 Hz LED bulbs, as shown in Fig. 2. LED lights had cold light that did not radiate and heat the face of the SC(B) sample. This ensured that the sample was consistently maintained at the proper temperature during testing. A bulb level was used to ensure that the camera was level during each test and can be seen on top of the camera in Fig. 2. Samples were cut from the IDT samples used in dynamic modulus. The thickness of the sample is 25 mm and the notch is 1 mm wide and 15 mm deep at the bottom center of the sample. In the preliminary research, samples were cut from three slices of the cylinder sample and then cut into halves, thus the six samples have three orientations from the cylinder height. As the air voids vary in cylinder height, the SC(B) samples in preliminary research may have air void variation because of the orientation of the sample. As shown in Fig. 3, the samples discussed in this paper, are all cut from the middle height of the cylinder, so only one slice is cut from the cylinder and the slide is cut into two SC(B) samples. 3.4. R-curve method This research generated R-curve of asphalt concrete based on the data collected from the SCB) test. The R-curve construction method and the following parameters’ analysis protocol are developed from the preliminary research by Yang and Braham [25]. Fig. 4 illustrates a set of four R-curve from a single asphalt concrete mixture and the average R-curve from the four replicates. Each R-curve is constructed by plotting the cumulative fracture energy as a function of the crack extension There are three parameters can be extracted from the R-curve: fracture energy, cohesive energy, and energy rate [25]. First, fracture energy can be found from the right end point of the R-curve, which measures the total energy dissipated in the process of fracture. In the SC(B) test the cumulative fracture energy is the external work calculated by the axial external load on the center top of SC(B) sample and the load line displacement(LLD). This external work is a storage energy that may dissipate in sample as recoverable strain energy, creep energy and fracture energy. For this research, this external work is considered as the fracture energy.

100000

10000

10000

|E*|( Mpa)

100000

-24°C -10°C 4.4°C 21.1°C 37.8°C Master Curve

1000

|E*|( Mpa)

Cumulatvie Fracture Energy (J/m2)

1600

1000

100 1.00E-04 1.00E+00 1.00E+04 1.00E+08 1.00E+12

100 1.00E-04 1.00E+00 1.00E+04 1.00E+08 1.00E+12

Reduced Frequency

Reduced Frequency

(a)

(b)

10000

10000

-24°C -10°C 4.4°C 21.1°C 37.8°C Master Curve

100 1.00E-04 1.00E+00 1.00E+04 1.00E+08 1.00E+12

|E*|( Mpa)

100000

|E*|( Mpa)

100000

1000

-24°C -10°C 4.4°C 21.1°C 37.8°C Master Curve

-24°C -10°C 4.4°C 21.1°C 37.8°C Master Curve

1000

100 1.00E-04 1.00E+00 1.00E+04 1.00E+08 1.00E+12

Reduced Frequency (Hz)

(c)

Reduced Frequency

(d)

*SSE = sum of square error; TR = reference temperature in °C Fig. 5. Master curves of mixture with: (a) NMAS 9.5 mm, PG 64-22; (b) NMAS 9.5 mm, PG 76-22; (c) NMAS 25 mm, PG 64-22; (d) NMAS 25 mm, PG 76-22. *SSE = sum of square error; TR = reference temperature in °C.

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The second parameter that can be extracted from the R-curve is cohesive energy. At the beginning of the fracture test, the energy dissipates in the sample, not creating a macro-crack but developing a cohesive zone ahead the notch tip. The energy dissipates in the fracture test before any crack occurs is defined as cohesive energy. Cohesive energy is a parameter that can characterize crack initiation. In R-curve, the cohesive energy can be seen in the left side of each R-curve when the macro-crack begins to form. Thus, the y-value of the vertical line at the left side of each R-curve is the cohesive energy. The crack extension remains zero until the cumulative fracture energy reach to a certain point and the external work starts to create crack growth. Al-Qadi et al. [1] from the university of Illinois proposed a flexibility index (FI). FI is the ratio of fracture energy to the absolute value of slope at inflection of the post-peak part of the load-displacement. The research concluded that FI is strongly related to the crack velocity, or crack growth. However, this FI parameter only derived by using one point from load-displacement curve, which cannot represent the whole crack growth. In this research, a similar concept is extracted from Rcurve, by applying energy rate: energy rate. Energy rate is a crack propagation parameter that measures the amount of energy to create a unit length of crack after crack initiation. In R-curve, the energy rate can be defined as the average slope rate from the cohesive energy point on the left to the end of R-curve on the right. Eq. (5) defines is the calculation of the energy rate:

energy rate ¼

fracture energy  cohesiv e energy total crack extension

ð5Þ

where; Energy rate – unit energy dissipated in crack propagation, (J/m3), Fracture energy – the total energy dissipated in both crack initiation and propagation, (J/m2),

|E*|( Mpa)

100000

10000

NMAS25 PG76-22 NMAS25 PG64-22

1000

NMAS9.5 PG76-22 NMAS9.5 PG64-22 100 1.00E-04

1.00E+00

1.00E+04

1.00E+08

1.00E+12

Reduced Frequency Fig. 6. Comparison of dynamic modulus master curve.

Total crack extension – the crack length on the surface of SCB sample from image analysis, (mm).

4. Results and discussion 4.1. Dynamic modulus The master curves for the four types of asphalt concrete, NMAS9.5mm with PG 64-22; NMAS9.5mm with PG 76-22; NMAS25mm with PG 64-22; NMAS25mm with PG 76-22; are illustrated in Fig. 5(a)–(d). To have a clear view that how the dynamic modulus varies among these four mixtures, these four master curves are plotted in Fig. 6. As can be seen in the upper right corner the figure, the modulus of the two mixtures with the NMAS25mm is higher than the other two mixtures with the NMAS9.5mm, while the difference in modulus between PG 76-22 and PG 64-22 are much smaller. In other words, at low temperature or high frequency, mixtures with NMAS25mm observed higher modulus than mixtures with NMAS9.5mm, while the binder PG 76-22 and PG 64-22 do not differentiate the modulus at low temperature. This trend is as expected because larger aggregate size is expected to increase the modulus, or stiffness, as the aggregate is playing a larger role. Since both binders are graded as 22 for the lower limit, as the binder approaches elastic behavior, the two mixtures are expected to perform in a similar fashion. In the lower left corner of Fig. 6, it can be seen that the two mixtures with binder of PG 76-22 show higher modulus than the mixtures with binder of PG 64-22. In other words, mixtures with binder of PG 76-22 show higher modulus compare to mixtures with binder of PG 64-22. This trend is expected as well because polymer modification bump up two grades of the higher limit, and PG 76-22 is expected to be stiffer at high temperature. Comparing the two mixtures with binder of PG 64-22 at higher temperature area, the mixture with NMAS25mm indicates higher modulus than NMAS 9.5 mm, which is also as expected. However, comparing the two mixtures with binder of PG 76-22 at higher temperature area, the mixture with NMAS9.5mm indicates higher modulus. This is not expected because smaller aggregate size should result in lower modulus. But this unexceptional trend may indicate that at extreme high temperature, binder is more dominated in modulus compare to aggregate size.

Table 2 Summary of test results. Binder Grade

NMAS

Temp. °C

Loading Rate mm/min

F.E.* J/m2

COV* of F.E. %

C.E.* J/m2

COV of C. E. %

E. R.* J/m3

COV of E. R. %

64-22

9.5

24

0.03 1.00 0.03 1.00 0.03 1.00 0.03 1.00

357.5 409.8 981.2 539.3 461.4 393.0 1053.9 575.3

11.6 43.0 12.8 20.0 40.4 27.0 44.9 52.6

342.8 290.6 630.3 484.5 326.6 393.0 820.9 511.1

11.8 22.1 19.1 17.1 67.9 27.0 45.7 55.4

0.4 0.6 9.9 1.3 2.3 0.0 7.7 2.1

98.3 173.2 42.9 93.8 268.0 N/A 72.5 158.9

0.03 1.00 0.03 1.00 0.03 1.00 0.03 1.00

352.0 523.5 806.8 860.5 507.9 256.6 882.6 1079.9

13.4 13.6 26.1 8.5 29.1 20.0 37.5 28.0

338.3 521.6 658.4 786.4 484.7 256.6 620.9 907.8

13.3 14.3 26.8 8.5 34.1 20.0 54.8 27.1

0.4 0.0 26.8 2.1 0.6 0.0 9.1 5.9

58.0 200.0 7.5 37.8 214.4 N/A 41.7 57.8

0 25

24 0

76-22

9.5

24 0

25

24 0

C.E. = cohesive energy. E. R. = energy rate. COV=coefficient of variance. * F.E. = fracture energy.

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4.2. Fracture energy, cohesive energy and energy rate SC(B) tests discussed in this paper are performed at three testing temperatures: 24 °C, 0 °C, 24 °C. However, it is found that, the tests performed at 24 °C cannot be defined as fracture tests as crack Table 3 P-value summary of ANOVA for COVs. p-value

COV of F.E.

COV of C.E.

COV of E.R.

Temperature

0.4696

0.3572

0.0004

NMAS

0.0115 0.1053 0.944

0.0012 0.1702 0.1008

0.0089 0.0924

Performance grade Loading rate

0.0449

p-value <0.05

Table 4 P-value summary of ANOVA for fracture energy, cohesive energy and energy rate. p-value

F. E.

C. E.

E. R.

Temperature

0.0002 0.5639 0.4517 0.2560

0.0005 0.6032 0.1510 0.8896

0.0163 0.5324 0.3566 0.0584

NMAS Performance grade Loading Rate p-value <0.05

cannot be detected in many of the tests while significant creep damage can be seen in the sample. This finding reinforces the concept that fracture tests are not appropriate for high temperature testing at low loading rate. The intent of a fracture test is to drive the energy of the sample to the notch, but this did not happen with the majority of SC(B) fracture tests run at 24 °C. Since the majority of testing at 24 °C was not representative of fracture testing, this paper only covers the results at the temperature of 24 °C, and 0 °C. The test results of R-curve are summarized in Table 2. Due to the heterogeneous characterization, the coefficient of variance (COV) for some of the results are very high, an analysis of variance (ANOVA) is performed to test the hypothesis whether the factors of binder grade, NMAS, temperature or loading rate is statistically significant on COV with a 95% confidence. As seen in Table 3, it is found that there are five p-values are under 0.05: factor of temperature on COV of energy rate; factor of NMAS on COV of fracture energy, COV of cohesive energy, and COV of energy rate; factor of loading rate on COV of energy rate. In other words, testing temperature be the reason to increase the heterogeneous on crack growth, however, it is not the reason to increase the heterogamous on fracture energy or cohesive energy. This is reasonable: asphalt concrete becomes more brittle and less viscous as the temperature drops 0 °C to 24 °C, and crack at lower temperature imitates and grows in a much fast manner, which may increase uncertainty. Besides, the temperature change from 24 °C to 0 °C is not significant to cause the difference of variance for any form of energy

1200 Cohesive Energy(J/m2, PG 76-22)

Fracture Energy(J/m2, PG 76-22)

1200 1000 800 600 400 200 0

0

200

400

600

800

1000

1200

1000 800 600 400 200 0

0

200

400

600

800

1000

Cohesive Energy(J/m2, PG 64-22)

Fracture Energy(J/m2, PG 64-22)

(a)

(b)

Energy Rate (J/m3, PG 76-22)

30 25 20 15 10 5 0

0

5

10

15

20

25

30

Energy Rate (J/m3, PG 64-22)

(c) Fig. 7. Effect of performance grade on fracture energy (a), Cohesive energy (b), and energy rate (c).

1200

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(fracture energy and cohesive energy), which may indicate that the creep energy associated with cracking are not significantly different at these two temperatures. NMAS is a significant factor that cause a higher COV for fracture energy, cohesive energy, and energy rate. A larger NMAS has a different structure in gradation compare to a smaller NMAS. The angularity of larger aggregate leads to more contract area thus more aggregate interlock, this may increase the uncertainty of crack growth, and the work that is need to initiate a crack, or cohesive energy. The performance grade of binder is not significant at all to the COV of either fracture energy, cohesive energy or energy rate. Loading rate is only significant on the COV of energy rate. This is the same as the effect of temperature because of the viscous characterization: lower temperature can be equivalent to faster loading rate. A loading rate of 1.00 mm/min can cause a significant different COV in energy rate compare to the loading rate of 0.03 mm/min. Also, ANOVA analysis is also performed to test the hypothesis whether these factors of binder grade, NMAS, temperature or loading rate is statistically significant on the crack initiation and propagation parameter: cohesive energy and energy rate. There are four replicates for each factor at each level. As seen in Table 4, there are three p-values are under 0.05: p-values from the factor of temperature on fracture energy, cohesive energy, and energy rate. This result indicate that temperature significantly impact on fracture energy, cohesive energy, and energy rate. According to the ANOVA results, the other factors of NMAS, performance grade, and loading rate are not statistically significant. However, a further discussion

of the results by using the technique of equality line figures is taken to expose the trend that is not statistically significant. 4.2.1. Effect of performance grade According to the statistical analysis, the performance grade of binder is not significant to impact on the fracture energy, cohesive energy and energy rate. The equality line figures are plotted to check if there is any trend can be found. Take Fig. 7(a) as an example, each point has an x-axis value of fracture energy for PG 64-22 binder, versus a y-value of fracture energy for PG 76-22 binder. All the other variables rather than binder type are fixed for each point. Thus, if the point falls below the equality line, the fracture energy of the PG 64-22 binder sample is higher; whereas if the point is above the equality line, the fracture energy of PG 76-22 binder sample is higher. In Fig. 7(a), four points are above the equality line, three points are below while one point is close to the equality line. This result agrees with the ANOVA result, there is not a significant difference found between these two binders in fracture energy. Take a further look at the cohesive energy in Fig. 7(b), there are less points fall below the equality line, which may indicate that the effect of the performance grade is stronger in impacting cohesive energy rather than fracture energy. The impaction of performance grade is not stronger in energy rate as seen in Fig. 7(c). Noticed that these two type of binder are all graded to 22 for the lower limit in PG, and these SC(B) tests are all performed at low temperature of 24 °C or 0 °C. PG 76-22 and PG 64-22 are graded different at the high limit due to the polymer modification

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eight points have the energy rate range from 0 to 2.1 J/m3, and one point has the energy rate of 9.9 J/m3, whereas there are five out of eight points have the energy rate range from 2.1 J/m3 to 9.1 J/m3. Although this is not proved by ANOVA, the equality line figure indicates that NMAS 25 mm may lead to higher energy rate. In Fig. 6, the results of dynamic modulus indicate influence of NMAS on modulus at low temperature are very clear: 25 mm NMAS results in higher modulus at low temperature. However, the influence of NMAS is not as clear in fracture energy, cohesive energy and energy rate. In summary, NMAS 25 mm indicates higher fracture energy, higher cohesive energy and higher energy rate in general. However, this conclusion needs to be verified with a larger amount of experiment.

4.2.2. Effect of NMAS The equality line figures are applied to detect the effect of NMAS on fracture energy, cohesive energy and energy rate. As seen in Fig. 8(a), six out of eight points are above the equality line, which means in most of the cases, bigger NMAS 25 mm results in higher fracture energy than NMAS 9.5 mm. This trend does not change much on cohesive energy, most of the five points out of eight are above the equality line while two points are close the line. Fig. 8(c) shows the effect of NMAS on energy rate. In this figure, there is one point far away from all the other points. This point is the case of NMAS 9.5 mm, PG 76-22, and loading rate 0.03 mm/min. If taken this point out, for NMAS 9.5 mm six out of

4.2.3. Effect of testing temperature The trend of effect of testing temperature is highly agreed with ANOVA: effect of testing temperature is significant on fracture energy, cohesive energy and energy rate. At the testing temperature of 0 °C, fracture energy, cohesive energy and energy rate are always higher than they are at the testing temperature of 24 °C. This can be a proof that at higher testing temperature, the total work may contain more creep dissipated energy. In this research, SC(B) tests are also performed at 24 °C. In most of those cases, crack cannot even be detected, because the work applied on the sample may be totally used to create creep damage rather than crack. This will be discussed later but it is also a proof that as the

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for the high temperature performance improvement such as rutting resistance, however, a slight effect of polymer modification on cohesive energy is detected. In Fig. 6, the dynamic modulus test results indicate that the modulus at low temperature are not effect by the polymer modification. The effect of polymer modification at low temperature cannot be differentiated by the dynamic modulus test but it can be differentiated by the R-curve. Five out of eight cases observed increase in cohesive energy. This is not statistically proved, but the sampling size in this research is relatively small, it is recommended to increase the statistical sample size in the future work. In summary, the polymer modification may have effect on cohesive energy despite the lower limit of the PG remains the same, but further research needs to be performed to verify.

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testing temperature increase, there are more creep dissipated energy associated with the fracture. In addition, as seen in Fig. 9(c), most of the points are above the equality line and closer to the y-axis. Compared to Fig. 9(a) and (b), in Fig. 9(c), the y-axis values at 0 °C, is even more significantly higher than the x-axis value 24 °C. This indicates that once the crack initiated, it consumes every small amount of energy to grow the crack, or the crack grows very fast after the initiation, most of the extern work applied on the sample dissipates into the cohesive energy. In other words, testing temperature has a larger impaction on crack propagation than crack initiation. Still, these extractions (fracture energy, cohesive energy and energy rate) from R-curve cannot separate the elastic portion, or recoverable strain energy, and viscous portion, or creep strain energy, from the fracture energy. But there is a trend of viscous portion increasing detected when testing temperature increases. Besides, this viscous portion increment may associate with crack propagation more than crack initiation, because testing temperature has a larger impaction on crack propagation than crack initiation. In summary, testing temperature significantly impacts on fracture energy, cohesive energy and energy rate. Higher testing temperature results in higher creep energy associated with fracture, and this higher creep energy associated with crack propagation more than crack initiation. Again, this finding needs to be verified with a large amount of experiment.

4.2.4. Effect of loading rate The effect of loading rate may interact with the effect of testing temperature due to the viscoelastic behavior of asphalt concrete, or the equivalency between temperature and loading rate. As seen in Fig. 10, the trend is not as clear as it is in Fig. 9. In Fig. 10(a) and (b), half of the points are above the equality line and half of the points are below the equality line. The effects of the loading rate on fracture energy and cohesive energy are hidden in equality line figures due to the interaction of temperature and loading rate. However, the trend of effect on energy rate is clear: Loading rate of 0.03 mm/min results in higher energy rate. In other words, if the crack propagates slower, the crack growth consumes more external work. The same trend can be found in Fig. 9(c): crack growth consumes more external work at higher testing temperature. The effects of fracture energy and cohesive energy can be hidden by equality line in Fig. 10(a) and (b), this effect of loading rate on energy rate is significant and cannot be hidden because of the interaction. Due to the equivalency of temperature and loading rate at some extends, this is another prove that viscous portion energy associates with crack propagation more than crack initiation. 4.3. Creep damage At the testing temperature of 24 °C, almost every SC(B) tests are not real fracture test because there is significant creep damage cap-

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Significant creep strain energy and creep damage increased as testing temperature increased. Fracture tests for R-curve construction are suggested to be performed at low temperature and not at ambient temperature. The above conclusions are made based on the results of ninetysix SC(B) tests, a further larger number of tests are suggested to be performed to prove those conclusions. These conclusions suggest that R-curve in asphalt concrete provides information of fracture behavior in terms of crack initiation and prorogation. Overall, the quantification of crack initiation and propagation can benefit the understanding the fracture mechanism in asphalt concrete. Acknowledgement The authors thank the generous support from the Fundamental Research Funds for the Central Universities. Fig. 11. Creep damage in SC(B) Test at 24 °C, 1.00 mm/min, NMAS 25 mm, PG 7622.

tured by the images. There are two types of creep damage observed in the SC(B) test at 24 °C. First, the creep deformation forms in a rate that leads to crack mouth open in a faster rate than the set loading rate. In this situation, usually no crack can be observed in the sample. This type of creep damage usually occurs at the loading rate of 0.03 mm/min. The second type of creep damage is shown as in the Fig. 11, the crack does not initiate form the notch tip, which means that the stress does not concentrate on the notch tip. The external work applied dominantly deforms the sample as permanent creep damage rather than create crack. Thus, the results of the testing at temperature of 24 °C was not included in section 4.2’s discussion. 5. Summary and conclusion SC(B) fracture tests were performed with an expanded experimental matrix to differentiate the crack characterization between different asphalt concrete mixtures. The factors of testing temperature (24 °C, 0 °C, 24 °C), loading rate (0.3 mm/min and 1.0 mm/ min), performance grade of binder (PG 64-22 and PG 76-22), and NMAS (9.5 mm and 25 mm) were considered in the experimental matrix. A new method of crack extension quantification using crack area was also initially developed. The propagation parameter energy rate was updated by using the crack area extension. The following conclusions can be made based on the results analysis:
Polymer modification impacted the crack initiation parameters of cohesive energy despite the lower limit of the PG remaining constant;
NMAS 25 mm provided higher fracture energy, higher cohesive energy and higher energy rate in general compared to 9.5 mm;
The R-curve results regarding binder type and NMAS does not completely agree with the dynamic modulus results, which reinforce that there are significant benefits to have both dynamic modulus and a form of cracking test to fully understand the performance of asphalt concrete;
Testing temperature significantly impacts on fracture energy, cohesive energy and energy rate. Higher testing temperature results in higher creep energy associated with fracture, and this higher creep energy associated with crack propagation more than crack initiation.
Loading rate of 0.03 mm/min resulted in higher energy rate as the slow crack propagation consumed more external work;

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