**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

*Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures*. Washington, DC: The National Academies Press. doi: 10.17226/26302.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

*Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures*. Washington, DC: The National Academies Press. doi: 10.17226/26302.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

*Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures*. Washington, DC: The National Academies Press. doi: 10.17226/26302.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

**Suggested Citation:**"CHAPTER 2. RESEARCH APPROACH." National Academies of Sciences, Engineering, and Medicine. 2021.

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23 CHAPTER 2. RESEARCH APPROACH MATERIALS Binders Sixteen binders were specifically selected for testing in NCHRP 9-59. These represented a wide range of binder types and grades, including seven polymer-modified binders, a binder modified with ground tire rubber, two modified with recycled engine oil bottoms (REOB), two oxidized binders, one modified with polyphosphoric acid (PPA), and four straight-run binders. General characteristics of these 16 binders are summarized in Table 3. Some details concerning these binders, including their source are not given here at the request of the suppliers. Throughout this report the specific identify of the binders have been hidden, again at the request of the suppliers, but also because the objective of NCHRP 9-59 was not to rank the performance of various binders, but to develop an improved binder specification for fatigue resistance. All tests performed during NCHRP 9-59 were done on laboratory aged binderâspecifically, aged in the rolling thin-film oven (RTFOT) followed by 40 hours in the pressure aging vessel (PAV). As discussed below, mixture tests were performed on materials loose-mix aged for five days at 95Â°C, which was selected to approximately match the binder aging regime. Table 3. Characteristics of NCHRP 9-59 Asphalt Binders. Binder Grade Modification/Additive Expected Fatigue Performance PG 88-22 SBS modified Good PG 76-28 SBS modified Good PG 76-22 SBS modified/PPA Good PG 64-28 SBS modified Good PG 70-22 SBR modified Good PG 76-22E SBS modified Good PG 58-34 Terpolymer-modified Good PG 58-28 Straight run Moderate PG 64-22 Straight run Moderate PG 64-22 Straight run Moderate PG 70-22 Ground tire rubber Moderate PG 70-22 Oxidized Poor PG 76-16 Oxidized Poor PG 58-28 REOB Poor PG 58-28 REOB Poor PG 70-22 PPA Poor

24 In addition to these 16 binders, the eight core asphalts from the Strategic Highway Research Program (SHRP) were also tested (University of California, Berkeley, 1994). These binders, however, were aged only using the RTFOT. The SHRP core asphalts were included in this research program so that use could be made of the substantial database of flexural fatigue tests performed with these binders. The mixtures used in these fatigue tests were aged only using short-term oven conditioning, and so these binders were aged only using the RTFOT in order to match the conditioning of the mixtures. Including both the SHRP and NCHRP 9-59 binders in the fatigue analysis provided both a wide range of binders of different types and a great range of aging conditions. Table 4 includes a list of the SHRP core asphalts. There was no need to blind the SHRP core asphalts, so in some of the analyses some of the binders have been identified. Some readers may not be familiar with the older grades listed in Table 4. The 150/200 pen grade is a relatively soft asphalt graded using the penetration system. The AC-8 and AC-10 grades are also soft asphalts but are graded using the old viscosity system. The AC-20 was a widely used viscosity graded asphalt of intermediate stiffness, similar to a PG 64-22. The AC-30, also viscosity graded, was a slightly harder asphalt grade widely used in the Southeastern U.S. It is very similar to the PG 67-22 grade currently used in the same region. The AR-4000 asphalts were also viscosity graded, but the grading was based on the aged (âresidualâ) asphalt. The AR- 4000 grade was similar to the AC-20. The AAK-1 asphalt was traditionally known for exhibiting very good performance. Asphalts AAG-1 and AAM-1 both had a record of exhibiting premature fatigue cracking. Table 4. SHRP Core Asphalts (University of California, Berkeley, 1994) SHRP Code Grade Crude Source AAA-1 150/200 pen Canadian / Lloydminster AAB-1 AC-10 Wyoming sour AAC-1 AC-8 Canadian / Redwater AAD-1 AR-4000 California Coastal AAF-1 AC-20 West Texas Sour AAG-1 AR-4000 California Valley AAK-1 AC-30 Venezuela / Boscan AAM-1 AC-20 West Texas Intermediate Five binders from the second ALF fatigue experiments were included in this study for many of the binder tests. These included a PG 70-22, an air blown asphalt, a crumb-rubber modified binder, and two polymer-modified binders (Gibson et al., 2012). Properties of these binders are summarized in Table 5. As with the SHRP core asphalts, these were tested after RTFOT aging, to match the condition as tested in the ALF experiment. Occasional use was made of a fourth data set of asphalt binders. These were tested by AAT as part of NCHRP Project 1-19 (Pellinen, 2001), and were used in development of the original Hirsch model (Christensen and Bonaquist,

25 1999); these binders are referred to in this report as the âNCHRP 1-19 binders.â These binders are listed in Table 6. They were tested in three conditions: the unaged or âtankâ condition; after RTFOT aging; and after RTFOT and PAV aging. The testing done on these binders including frequency sweeps with the DSR over a wide range of temperatures, BBR testing at three temperature and direct tension tests at three temperatures. This data set is useful because of the wide range of data available on the binders at various aging conditions. Table 5. Binders from ALF II Fatigue Experiment (Gibson et al., 2012). Binder Grade Description PG 70 PG 79-22 Straight run Air blown PG 70-28 Oxidized CR-TB PG 76-28 Crumb rubber modified SBS-LG PG 70-28 SBS modified Terpolymer PG 70-28 Terpolymer-modified Table 6. NCHRP 1-19 Binders (Pellinen, 2001). Project Binder Description FHWA ALF AC-5 AC-20 Polyethylene modified SBS modified MNRoad 120/150 pen AC-20 Westrack PG 64-22 NCHRP 9-59 Mixtures A 9.5-mm nominal maximum aggregate size (NMAS) mix design with all virgin materials was used for mixture testing in this project. The NCHRP 9-59 binders (Table 3 above) were used in making these mixtures. The mix was designed at a design compaction effort (Ndesign) of 80 gyrations. The aggregate blend in the mix consisted of four individual aggregates, including granite 89, natural sand, limestone 8910 and granite M10. The asphalt binder content in the mix design was 6.0%. The same gradation and asphalt binder content were used to evaluate all the binders in this study. A liquid anti-stripping agent (LOF 6500) was used in the mix design and pre-blended with the hot binder at a rate of 0.5% by weight of virgin binder before mixing. After mixing, each loose mix sample was short-term conditioned in an oven at 135Â°C for 4 hours in accordance with AASHTO R30. The loose mix sample was then spread out in large pans and conditioned in another oven at 95Â°C for 5 days prior to compaction for preparing test specimens.

26 SHRP Mixtures The mixture used in the SHRP flexural fatigue test program were designed using the Hveem method, with a minimum Hveem stability of 35. In the main experiment, called the expanded test program or the 8 Ã 2 test program, all eight core asphalts were used in combination with two aggregatesâa limestone aggregate and a graywacke gravel aggregate, both with a nominal maximum aggregate size (NMAS) of 12.5 mm. The asphalt content for the limestone mix was 4.5 % by aggregate weight, while the asphalt content for the graywacke gravel mix was 5.2 % by aggregate weight. Specimens were prepared using two different air void contents, 4 % and 7 %. Measured air void contents were typically within one percent of these targets. All mixes were short termed aged at 135Â°C for four hours prior to specimen preparation. The primary focus of the analyses in this report is on the SHRP 8 Ã 2 experiment, in conjunction with the NCHRP 9-59 fatigue tests. This is because the SHRP 8 Ã 2 experiment is balanced with respect to the variables. Data from two other experiments were made limited use of in NCHRP 9-59: the mix design study, and the temperature equivalency factors experiment. In the mix design study one asphalt (AAG-1) with a granite aggregate (NMAS of 12.5 mm) was used. Two asphalt contents were used: 4.5 and 6.0 % by aggregate weight. Specimens were prepared at three air void contents: 4 to 5 %, 5 to 6 % and 7 to 9 %. These mixes were also short-term oven aged at 135Â°C for four hours. In the temperature equivalency factors experiment, a single asphalt (AAD-1) was combined with the graywacke gravel aggregate (12.5 mm NMAS). The asphalt content was 5.2 % by aggregate weight, and the air void content of the specimens was 4 Â± 1 %. LABORATORY TEST PROGRAM Binders The binders studied as part of NCHRP 9-59 were tested using a variety of procedures. Frequency sweep tests were conducted using the dynamic shear rheometer (DSR) at temperatures of 10, 22, 34 and 46Â°C, at frequencies ranging from 0.1 to 100 rad/s. The procedures used follow AASHTO T 315, although the minimum frequency of 0.1 rad/s is lower than the 1 rad/s given in the standard. The SHRP core asphalts were also tested using this procedure, but they were tested after RTFOT aging, while the NCHRP 9-59 binders were tested after RTFOT and 40 hours PAV conditioning. All of the binders were also tested using the simplified single-edge notched tension (SDENT) test, in essence a tension test run on an asphalt ductility test device using force-ductility specimens with notches in their centers. The procedure followed was as described in FHWA- HRT-11-45, found in an appendix in the report on the second FHWA ALF fatigue experiment (Gibson et al., 2012), with several changes. The loading rate is 50 mm/min, rather than 100 mm/min was used. This change was made to ensure that any standard method developed from NCHRP 9-59 could be run on a standard ductilometer. The other change is that instead of using three sets of two specimensâeach with a different notch sizeâthe simplified version uses one

27 set of three specimens, each with the same notch size. Analyses of several tests has shown that there is an excellent correlation between crack tip opening displacement (CTOD) determined using the standard DENT procedure and extension to failure using the simplified test. Initially, a specimen with two 2.5-mm deep notches were used, creating a rather large 15-mm wide ligament (neck) in the center of the specimen. However, after completing tests on the SHRP core asphalts, the ALF binders and several of the NCHRP 9-59 binders, it was discovered that some heavily modified and aged binders could not be tested with this specimen geometryâthe specimen would pull away from the end pieces prior to failing. After evaluating the data already gathered, it was decided to test all the NCHRP 9-59 binders using specimens with larger notchesâ7.5 mm on each side of the specimen, creating a much smaller 5-mm ligament. This greatly reduced stresses generated during the test, so that even heavily modified and aged binders could be tested to failure without pulling away from the end pieces. Unfortunately, project resources did not allow retesting of the SHRP core asphalts and the ALF binders using the specimens with the smaller ligament. However, as described later in this chapter, it was possible to develop an accurate conversion for converting the results of the earlier tests to equivalent results for the specimens with the 5-mm ligament. The LAS test was performed according to AASHTO TP 101-14, although a different criterion was used for selecting the test temperature. Initial testing showed that many specimens were either delaminating during the test or losing integrity of the specimen edges. It is believed that the heavy binder aging makes delamination more likely, reducing the useful range for the test. The final protocol for selecting LAS temperature was to use the DSR frequency sweep data to determine the temperature at which Gâ = 17.5 MPa at a frequency of 10 Hz. Only one test temperature was run using this protocol, as it appeared that problems occurred at temperatures much higher or lower than this value. The LAS test, as explained in the literature review, involves applying a regime of gradually increasing strains to a 4-mm diameter DSR parallel plate specimen. Three different specimens are tested, each at a different strain rate. In the standard procedure, a continuum damage type analysis is done to obtain predicted cycles to failure at several different strain levels. This analysisâapplied to the NCHRP 9-59 specimensâproduced highly variable and often inconsistent results. An alternative approach that provides better results is explained later in this report. NCHRP 9-59 Mixtures Three test procedures were used to characterize the NCHRP 9-59 mixes: flexural fatigue, uniaxial fatigue, and a healing test. The flexural fatigue testing was performed on 9 of the 16 NCHRP 9-59 binders; the uniaxial fatigue tests were done on all 16. Eight of the 16 NCHRP 9- 59 binders were tested in the healing experiment. The procedures used in these three tests are described below

28 Binder Beam Fatigue Testing The bending beam fatigue test (BBFT) was conducted in accordance with AASHTO T321- 14. Six to eight specimens were tested for each mix as additional specimens were tested in case of variable test results. The target air voids for the specimen were 7 Â± 1% after trimming. Testing were conducted at 10Â°C and 20Â°C to determine the effect of test temperature on the fatigue life of each mixture. In this test procedure, a 380-mm by 50-mm by 63-mm beam was held by four equally- spaced clamps, and sinusoidal loading at a frequency of 10 Hz was applied at the two inner clamps (Figure 6). The magnitude of the load applied by the actuator and the deflection measured at center of beam were recorded and used to calculate the flexural stiffness. The stiffness at the 50th loading cycle was defined as the initial stiffness of each beam specimen. The failure point was the number of cycles where the peak of the product of flexural stiffness times number of cycles occurred. This concept is illustrated graphically in Figure 7. More detailed information about this test is included in Appendix C. Figure 6. IPC Global BBF Testing Apparatus with Fixed Reference Retrofit.

29 Figure 7. Example of Bending Beam Fatigue Failure Point Dynamic Modulus and Uniaxial Cyclic Fatigue Test Two tests were conducted in the Asphalt Mixture Performance Tester (AMPT) to characterize the fatigue cracking resistance of each asphalt mixture using the simplified viscoelastic continuum damage (S-VECD) model. The dynamic modulus test was done to quantify the linear viscoelastic (LVE) characteristics, and the uniaxial cyclic fatigue test was performed to determine the damage characteristic curve of each mixture. The dynamic modulus test was performed in accordance with AASHTO T378-17. Specimens for this test were prepared in accordance with AASHTO R83-17. The Superpave gyratory compactor (SGC) specimens were compacted 180 mm high and 150 mm in diameter, then cut and cored to make the test specimens (150 mm high and 100 mm in diameter). Three replicate specimens were prepared for each mix. The temperatures and frequencies used for testing the mixtures were selected in accordance with AASHTO R84-17. The high test temperature was varied depending on the high performance grade (PG) of the binder utilized in the mixture. All dynamic modulus testing was performed unconfined, and test results were screened for data quality in accordance with the limits set in AASHTO T378-17. The uniaxial cyclic fatigue test was performed in accordance with AASHTO TP 107-14. Three specimens of 100 mm in diameter and 130 mm in height were prepared at target air voids of 7 Â± 0.5% according to AASHTO R83-17, glued to the top and bottom platens (Figure 8), and tested for each mix. In case of variable test results, another test specimen was tested. Testing was conducted at two temperatures based on the PG of the binder in the mixture: [(high PG + low PG)/2 â 3] and [(high PG + low PG)/2 + 3]. For each test temperature, three strain levels were 0.0E+0 1.0E+9 2.0E+9 3.0E+9 4.0E+9 0 2,000 4,000 6,000 8,000 10,000 0 300,000 600,000 900,000 1,200,000 M od ul us x C yc le s Fl ex ur al S tif fn es s (M Pa ) Number of Cycles Flexural Stiffness Modulus x Cycles Failure Point

30 selected to produce a wide range of fatigue life (from 1,000 to 100,000 cycles). Controlled actuator displacements were applied at a frequency of 10 Hz on each test specimen. Figure 8. Uniaxial Fatigue Test Setup. In accordance with AASHTO TP 107-14, uniaxial cyclic fatigue testing was conducted in two steps: fingerprint dynamic modulus and cyclic fatigue. The fingerprint test was performed to obtain the fingerprint dynamic modulus. The dynamic modulus ratio (DMR) of the fingerprint dynamic modulus results to the corresponding dynamic modulus results determined in the dynamic modulus test was used as a quality control indicator, and test results were accepted when the DMR was between 0.9 and 1.1. The uniaxial cyclic fatigue test was conducted at three strain levels (by controlling the maximum displacement of the actuator) at each test temperature to produce a wide range of fatigue life (from 1,000 to 100,000). Loading cycles, applied loads, actuator displacements and on-specimen strains were recorded. The software also computed and recorded the tensile stress, tensile strain, phase angle and stiffness data. The failure point was the number of cycles where a sharp sudden decrease in the phase angle occurred (Figure 9). The dynamic modulus and cyclic fatigue test data were imported into the FlexMAT software to determine the damage characteristic curve and cracking resistance for each mixture based on the S-VECD model. More detailed information about the dynamic modulus and uniaxial cyclic fatigue are included in Appendix C.

31 Figure 9. Example of Failure Point in Uniaxial Fatigue Test. SHRP Flexural Fatigue Testing SHRP flexural fatigue testing was done on beams 6.35 wide by 5.1 cm high by 38.1 cm long. The testing frequency was 10 Hz. Continuous haversine loading was used, with the intent of keeping all of the loading in tension. However, it is now generally accepted that it is difficult or impossible to maintain haversine loading during continuous fatigue testing, and the loading tends to gradually revert to fully the fully reversed condition. The testing was strain controlled, with strain levels generally at 400 and 700 Ã 10-6 m/m. Most of the tests were performed at 20Â°C. In the mix design study, lower strains of 200 and 300 Ã 10-6 m/m were included in the test program. A wider range of both temperature and strains were used in the temperature equivalency factors experiment, with temperatures of 5, 10, 20 and 25Â°C, and strains ranging from 300 to 1,200 Ã 10- 6 m/m. Details of the test procedure and sample preparation methods can be found in reports SHRP-A-404 (University of California, Berkeley, 1994) and in Harveyâs technical memorandum (Harvey, 1991), respectively. Healing Experiment The healing experiment involved performing uniaxial, stress-controlled fatigue tests on asphalt concrete specimens prepared as for dynamic modulus tests (AASHTO TP 378-17), 100 mm diameter by 150 mm high specimens cored from large gyratory specimens. Companion tests were done on sets of specimens, with one test consisting of continuous loading, and the other of pulse loading. The objective of the experiment was to determine (1) if the pulse loading resulted in healing compared to the continuous loading; and (2) if healing was observed, could it be correlated to one or more asphalt binder rheological properties? In the continuously loaded 0 5 10 15 20 25 30 35 0 2,000 4,000 6,000 8,000 10,000 0 5,000 10,000 15,000 Ph as e A ng le , d eg re e D yn am ic M od ul us , M Pa Loading Cycles Dynamic Modulus Phase angle Failure Point

32 specimens, completely reversed, sinusoidal stress-controlled loading was used, at a frequency of 10 Hz. Pulse loading was performed using a single, fully reversed sinusoidal stress cycle followed by 6.9 seconds of recovery. A slight compressive stress was applied during this recovery to ensure that any damaged surfaces remained in contact. A variety of temperatures and strain levels were used to provide a wide range of data for examining if relationships exist between asphalt mixture healing properties and asphalt binder rheological characteristics. DATA ANALYSIS Model Used in Analyzing Mixture Fatigue and Binder Test Data It has historically been difficult to correlate mixture fatigue tests to field performance and also to a variety of binder test data, and that this might be due to problems with traditional ways of analyzing fatigue data rather than because of shortcomings in the test method. In order to help make more effective comparisons between fatigue tests, fracture tests and other mechanical tests on both asphalt concrete mixtures and asphalt binders, a novel theoretical framework was developed during NCHRP 9-59 to explain fatigue and fracture phenomena in asphalt mixtures and binders. The research team has coined the term general failure theory for asphalt binders (GFTAB) for this new framework. Appendix D of this report is a detailed discussion of the data analysis methods used in NCHRP 9-59, including a description of the GFTAB model. Below is a summary of the primary features of this approach to analyzing asphalt mixture and binder fatigue and fracture data. The GFTAB model is relatively simple and intuitive. It states that the fatigue life of an asphalt mixture is proportional to the ratio of the fatigue strain capacity to the applied binder strain, raised to an exponent proportional to the inverse of the phase angle (as a fraction): ð = Ã â â (3) Where: Nf = number of cycles to failure FFPR = fatigue/fracture performance ratio, equal to the ratio of the strain capacity of a given binder to the average or typical strain capacity FSC* = Average or typical fatigue strain capacity (%), analogous to failure strain = 4.45Ã106 |G*|-0.806 Îµ = effective strain in binder (%) = mix strain / (VBE/100) k1 = constant determined through statistical analysis to be 2 Î´ = binder phase angle, degrees

33 For most binders, the phase angle used in Equation 3 is simply the value measured at the temperature and frequency of interest. However, for some heavily modified binders the phase angle is significantly altered by the polymer network. Put another way, the phase angle used in Equation 3 for polymer-modified binders is the value for the continuous, asphalt phase of the material. Although determining this value precisely is difficult (or even impossible), an estimate can be made by determining the Christensen-Anderson R-value at a high modulus value and then estimating the binder modulus using the relationship between phase angle, modulus and R-value. A simple approach to calculating R-valueâand the one used in this NCHRP project for determining the phase angle value for use in fatigue analysisâinvolves determining the modulus and phase angle at a single point, where the modulus is at least 10 MPa, and using the following equation to estimate R: ð = ððð 2 | â| Ãâ â (4) Where R = Christensen-Anderson R (rheologic index) |G*| = dynamic complex modulus, Pa Î´ = binder phase angle, degrees (at same temperature and frequency as |G*|) The phase angle is then calculated from the R-value along with the modulus at the desired temperature and frequency: ð¿ = 90 1 â ðð¥ð Ã | â| Ãâ (5) Where the variables are as defined above. In the discussion below, where the phase angle is mentioned or used in an equation, it refers to the phase angle as determined above. Equation 3 allows the fatigue performance of binders and mixtures to be understood and analyzed over a wide range of conditions. It must be emphasized that the FSCâfatigue strain capacityâis analogous to the binder failure strain, and theoretically represents the strain at which the fatigue life is exactly one. The average/typical FSC is designated as FSC*, while the actual observed strain capacity for a given binder is designated as FSC. They are related through FFPR; the strain capacity for a given binder (FSC) is given as FFPR Ã FSC*. As explained in Appendix D, testing during NCHRP 9-59 suggests that binder FSC and mix FSC are not identical but are very close over the range of data analyzed during NCHRP 9-59. The difference may be due to the complex state of stress existing in the asphalt binder in a mixture as compared to the uniaxial stress typically used in binder testing. As modulus increases, FSC* dramatically decreases, decreasing the fatigue life of the mixture if the applied strain is held constant. This relationship between FSC* and modulus can be thought of as a failure envelope, defining at a given modulus value what the failure strain of a binder is. Figure 10 is a plot showing several such failure envelopes: (1) the asphalt binder failure envelope proposed by Heukelom (1966); (2)

34 the asphalt binder failure envelope (with measured data points) determined as part of NCHRP 9- 59; and (3) the FSC failure enveloped determined fatigue NCHRP 9-59 mixture fatigue tests. These are all reasonably close together, the differences probably resulting from the behavior of binders versus mixtures, from differences in monotonic and fatigue tests, and from differences in the specific test procedures used. Figure 10. Failure Envelopes as Reported by Heukelom (1966), and as Determined During NCHRP 9-59 from Binder Tests and Mixture Fatigue Tests, along with Data Points from Binder Testing. The decrease in strain capacity as modulus increases is one of the most important aspects of the fracture and fatigue behavior of asphalt binders and mixes. The phase angle of the binder also plays an important role in the fatigue performance of these materials. Specifically, as the phase angle decreases the fatigue exponent increases, which tends to increase fatigue life when the applied strain is significantly lower than the FSC. Because phase angle tends to decrease with increasing modulus, this effect is in direct opposition to the decrease in FSC with increasing modulus. This explains why interpreting mixture fatigue data can be so difficult, often providing results that seem to contradict observed field performance or laboratory binder tests. To understand the fatigue behavior of asphalt mixtures and binders, one needs to understand how both the FSC and the fatigue exponent are changing. The GFTAB model provides a way of understanding these changes, and a way of comparing mixture fatigue performance and binder 0.01 0.10 1.00 10.00 100.00 1,000.00 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 1.E+11 Fa ilu re St ra in o r F SC , % Stiffness/3 or G*, Pa From binder tests From mix fatigue Heukelom SHRP DENT ALF DENT NCHRP 9-59 DENT Direct tension

35 test data in a meaningful way. The relationship between the fatigue exponent and binder phase angle is a key feature of this theory and represents a major departure from standard models for asphalt mixture fatigue behavior and ideally should be verified. Most asphalt mixture fatigue tests are performed over a narrow range of temperaturesâmany test programs are only done at one temperature (20Â°C), so there is typically a narrow range in phase angle making analysis of the relationship between fatigue exponent and phase angle difficult or impossible. Fortunately, as part of the SHRP fatigue test program, a temperature dependence experiment was done in which a mix made with a single binder (AAD-1) was tested at four different temperatures: 5, 10, 20 and 25Â°C, using a range of strains at each temperature. This allows the fatigue exponentâthe slope of cycles to failure versus strain plot on a log-log scaleâto be calculated at each temperature. Figure 11 below is a plot of calculated fatigue exponent as a function of binder phase angle for this data. The plot not only shows a good relationship between these parameters (r2 = 85%), but the regression line is close to the value determined in the GFTAB model. It is important to note that the data underlying Figure 11 was not included in the calibration of the GFTAB model and presents strong verification of the relationship between fatigue exponent and binder phase angle. Figure 11. Relationship Between Fatigue Exponent and Phase Angle for SHRP Asphalt AAD-1 (University of California, Berkeley, 1994). Included is the line representing the relationship determined for the GFTAB model. One of the most important features of Equation 3 is the fatigue/fracture performance ratio, FFPR. This represents the ratio of the failure strain of a binder at a given modulus value to the average or typical failure strain at that modulus value. It represents the inherent strain tolerance of an asphalt binder and is probably the most important characteristic defining fatigue performance. FFPR values much above 1.0 indicate good fatigue/fracture performance, while values much below 1.0 suggest poor fatigue/fracture performance. FFPR values for the asphalt y = 2.21x RÂ² = 0.85 2.0 3.0 4.0 5.0 6.0 1.0 1.5 2.0 2.5 3.0 Fa tig ue e xp on en t 90/phase angle Exp = 2 x 90/phase

36 binders studied as part of NCHRP 9-59 ranged from about 0.4 to 2.0. FFPR values decrease significantly with binder aging. FFPR values can be determined from mixture fatigue tests, from binder fatigue tests such as the linear amplitude sweep (LAS) test, or from binder tension tests such as the double-edged notched tension (DENT) test. The sections below summarize the results of the analysis of mixture fatigue test data and binder test data, and then compares FFPR values and related data for mixtures and binders. Details of these analyses can be found in Appendix D. Analysis of Mixture Fatigue Data Statistical methods were used to determine FFRP values for the flexural fatigue data experiment, including mixtures made with 8 of 16 NCHRP 9-59 binders and the eight SHRP core asphalts. FFRP (fatigue/fracture performance ratio) represents the ratio of a given binderâs strain tolerance to that of a typical binder and provide a good indication of the overall strain tolerance of an asphalt binder. This is the main characteristic used to related mixture fatigue performance to binder properties. Determining the FFPR values from fatigue data involved fitting the observed fatigue data to the GFTAB model, as explained in Appendix D. Microsoft Excel solver was used, which employs non-linear least squares to determine model parameters. As explained in Appendix D, statistical parameters not provided by Excel Solver were calculated using standard methods for such calculations in non-linear least squares analysis. The resulting calibrated model was then used to analyze the results of the uniaxial fatigue tests on mixes made using all 16 NCHRP 9-59 binders. In analyzing the uniaxial data, the GFTAB model was used to estimate the FFRP value for each test; the entire data set was then treated as a simple analysis of variance problem to develop statistics for the model, including confidence limits on FFRP values. The results of these analyses are given in Chapter 3 and in Appendix D. Traditional Analysis of Bending Beam Fatigue Data A traditional analysis approach was used to evaluate bending beam fatigue data. A power model (Equation 6) was fitted to the test data to develop a correlation between the number of cycles to failure (Nf) and the applied strain level (Îµ) for each mixture at 10Â°C and 20Â°C. ð = ð (1ð) (6) where Nf = number of cycles to failure Îµ = applied stain on sample k1, k2 = material constants. Simplified Viscoelastic Continuum Damage Analysis of Uniaxial Fatigue Data The Simplified Viscoelastic Continuum Damage (S-VECD) analysis of the uniaxial fatigue data was performed using the FlexMAT spreadsheet developed by the pavement research group at North Carolina State University. The S-VECD analysis included the following steps:

37 1. First, a storage modulus master curve was created based on the dynamic modulus test results by simultaneously optimizing sigmoidal model parameters and time-temperature shift factors. The master curve model was used to generate data that is used to determine the Prony series coefficients. The E(t) Prony series coefficients were used to determine Î± value which is a critical parameter for the damage calculation. Additionally, the dynamic modulus data were also used to determine the DMR value which is used for the calculation of pseudo secant modulus (C). 2. Uniaxial fatigue data were analyzed in two steps. The first part consisted of the data for the first half of the first loading path (from zero to first peak stress). The second part consisted of the rest of the data. For the first cycle of loading, full time history data was used to calculate the pseudo strain (ÎµR) up until the peak tensile load. Then, pseudo stiffness (C) calculated based on the stress divided by the pseudo strain and DMR and damage parameter (S) was computed using DMR, pseudo stiffness and Î± value. For the rest of the loading history, pseudo stiffness and damage were computed using peak-to- peak stress and strain values in each cycle. Additionally, the fatigue life for the tested specimen was determined based on the peak in the phase angle data from the uniaxial fatigue test. 3. The C-S curve was developed for each specimen based on the calculated C and S values. The C-S curve could be fitted using a power law function (Equation 7). The C-S curve is an important output of S-VECD analysis, which illustrates how fatigue damage evolves in the mix during the uniaxial fatigue test. ð¶ = 1 â ð¶ ð (7) where C = pseudo stiffness S = damage parameter c11, c12 = material constants. 4. Another important output of S-VECD analysis was GR failure criterion. GR is defined as the rate of change of the averaged released pseudo strain energy (per cycle) throughout the test. GR could be calculated using Equation 8. The relationship between GR and the fatigue life can be used to compare fatigue property between mixes. For a given GR, a higher fatigue life indicates a better fatigue cracking resistance. ðº = ðð (8) where, ð is the released pseudo strain energy and Nf is the number of cycles to failure.

38 Analysis of Binder Test Data Three binder test parameters were evaluated for comparison with mixture fatigue FFPR: the Christensen-Anderson R-value; FFPR values calculated from the LAS test; and FFPR values calculated from the SDENT test. The GRP is considered separately, as it is not an indicator of inherent strain tolerance like R or FFPR, but instead is a surrogate for failure strain or FSC at a given loading rate and temperature. Therefor GRP is compared with mixture FSC (FFPR x FSC*) at the fatigue loading rate of 10 Hz and the selected test temperature. The nature of the GRP will be discussed more thoroughly in Chapter 3 of this report. The R-values for the binders were calculated from LAS data at 10 Hz using Equation 4 presented previously. This approach was used because it was a relatively high modulus level, ensuring that for polymer-modified binders, the effect of the polymer on the phase angle was minimal. The LAS data also had the advantage of consisting of the average of three separate determinations, so the R-value would represent the average of three measurements. The LAS data was analyzed as a fatigue test, using an equation derived from the GFTAB model and similar to the approach used in analyzing mixture uniaxial fatigue data: ð¹ð¹ðð = . â â ð (ð¾ ) ( â )â ( â )â (9) FFPR = fatigue/fracture performance ratio, equal to the ratio of the strain capacity of a given binder to the average or typical strain capacity FSC* = Average or typical fatigue strain capacity (%), analogous to failure strain = 3.21Ã106 |G*|-0.788 nf = number of cycles to failure Ni = number of loading cycles in loading step i Î³i = shear strain in binder (%) k1 = constant determined through statistical analysis to be 2 Î´ = binder phase angle, degrees The FFPR in this case represents the ratio of the measured fatigue strain capacity (FSC) of the binder in the LAS test to the expected, or typical value (FSC*). The factor 4.8 in Equation 9 includes a factor of 3 for converting from shear strain to extensional strain, and a calibration factor of 1.6 for the LAS test geometry. This calibration factor was determined empirically and the fact that it differs from 1.0 is probably because the stresses and strains in the LAS test are not uniform but increase from the center of the specimen to the outer edge. Analysis of the SDENT data is complicated by the fact that the heavily notched specimen cannot be analyzed as if it were a tension test, using calculated stresses, strains and modulus. The procedure used instead relied upon comparing measured specimen extension and initial specimen stiffness (Equation 10). Extension in this case was the extension to the post peak point where the load was 20 % of the peak load. This approach was used, rather than trying to determine total extension, in order to avoid the high variability potentially associated with extreme extensions.

39 Specimen initial stiffness was calculated as the specimen load divided by the extension at 3 seconds loading time. Specimen extension was plotted against specimen stiffness, and Microsoft Excel solver was used to fit the extension data to the model shown in Equation 10. ð¸ = ð¹ð¹ðð ð´ð (10) Where Ei = extension of ith specimen, mm FFPRi = fatigue/fracture performance ratio of ith specimen (dimensionless) A, B = power law coefficients for relationship between extension and stiffness Si = initial stiffness of ith specimen, N/m FFPR values for this model were defined so that a non-polymer-modified binder with an R-value of 2.0 would have an FFPR of 1.0. For the standard SDENT geometryâwith the small, 5 mm ligamentâthe constants A and B were found to be 17.4 and -0.334, respectively, and the fit of the model was excellent with r2 = 99 %. Some early SDENT tests were run with a different geometryâthe large, 15 mm ligament. In this case, the constants A and B were found to be 176 and -0.359, respectively. The fit for this model was also excellent, with an r2 of over 99 %. For calculating FFPR values from SDENT tests using the standard geometry with the 5 mm ligament, Equation 11 should be used: ð¹ð¹ðð = . . (11) Where the extension is in mm and S is the specimen stiffness at 3 seconds, in N/m. For best results, the initial specimen stiffness should be between about 15 and 35 N/m. It should be emphasized that the FFPR parameter represents the SDENT extension normalized for stiffness and is a representation of the inherent strain tolerance of a binder, independent of stiffness. FFPR values for the SDENT were also calculated based on extension to maximum force and total energy to failure, but these FFPR values showed significantly weaker relationships to mixture fatigue FFPR values and are not considered in the body of this report in the interest of conciseness and clarity. Values for SDENT extension to maximum force, SDENT total energy to failure and FFPR values based on these parameters are included in Appendix E, which is a summary of pertinent data for NCHRP 9-59. The GRP was calculated using an equation suggested by Rowe (2011): ðºð ð = |ðºâ| (cos ð¿) sinð¿â (12) Where |G*| is dynamic complex modulus (in Pa) and Î´ is the phase angle. For reasons that will become clear in Chapter 3, the GRP in this report has been calculated at the loading time and temperature of interest. For example, in comparing GRP to FSC values calculated from the

40 mixture flexural fatigue tests, it was calculated at a frequency of 10 Hz and at temperatures of 10 and 20Â°C. Many pavement engineers and researchers have recently correlated pavement crackingâboth transverse and fatigue crackingâto the parameter ÎTc, which is the difference between critical temperatures based on stiffness and based on m-value, as determined using the bending beam rheometer (BBR). In consultation with the panel, it was decided that BBR testing would not be done as part of NCHRP 9-59, and so ÎTc is not considered in this analysis. However, as it is pointed out in Chapter 3, ÎTc is directly related to R-value, and the relationships developed here between fatigue performance and R-value would in all probability also exist if ÎTc were to be substituted for R, although the relationship would perhaps not be as strong. Comparison of Mixture Fatigue Data and Binder Test Data Before comparing mixture and binder fatigue and fracture properties, the accuracy of the analytical approach must be verified. That is done in Chapter 3 by verifying several important relationships: (1) The predicted and observed cycles to failure for the fatigue model should be reasonably good, keeping in mind the that mixture fatigue test data is notoriously variable; (2) The FFPR values determined from flexural fatigue data and from uniaxial fatigue data should be in reasonably close agreement; (3) The failure envelope determined from the analysis (fatigue strain capacity as a function of modulus) should agree with the failure envelope presented by Heukelom, and with failure data for asphalt binders, such as shown in Figure 10 above; and (4) Fatigue exponents for the mixture should be inversely related to the binder phase angle, as indicated in the GFTAB model. Probably the most important part of the analysis in this project was the comparison of mixture fatigue FFPR values to binder FFPR values and binder R-value. A good correlation between mixture FFPR and binder FFPR or R-value would suggest that an improved binder fatigue specification can be developed using the parameter that best correlates to mixture fatigue FFPR. In this part of the NCHRP 9-59 analysis, simple regression methods are used to evaluate the relationship between mixture FFPR values and binder FFPR values and R-values. Confidence limits are included on plots to provide information on the variability associated with the various parameters. The objective of this analysis is to determine which if any of the binder tests/parameters are suitable for use in an improved binder fatigue specification, and if more than one appear suitable, to determine which is best suitable for this purpose. As mentioned at the beginning of this section, the GRP is a somewhat different sort of binder parameter compared to FFPR values or R-value. The GRP is an indicator of binder failure strain at a given temperature and loading frequency, rather than an indicator of inherent overall strain tolerance. For this reason, to evaluate GRP it should be compared with FSC (FFPR x FSC*) to determine if it is potentially useful in a specification. It should be understood, however, that

41 specifying GRP does not control overall fatigue performance in the way that specifying FFPR or R-value does, it controls fatigue/fracture performance at a given point. This is possibly even more important than controlling R or FFPR, as proper control of FSC at a given temperature helps ensure that a binder has adequate strain tolerance in a given climate. In some ways GRP can be seen as an alternative to |G*| sin Î´ in the current binder specification. The nature of the relationship between the GRP and pavement performance is discussed in more detail in Chapter 3 of this report. Analysis of Data from Healing Experiment The healing experiment involved performing healing tests under continuous loading and using pulse loading with rest periods between single loading events. The analysis was done by comparing the loss in modulus at failure under continuous loading to the estimated loss in modulus at failure under pulse loading, the estimated loss in modulus was made using the GFTAB model described above. Almost always the loss in modulus at failure under pulse loading was significantly less than under continuous loading. This is an indication of healing under intermittent loading. It was hypothesized at the start of NCHRP 9-59 that such healing would be related to binder rheologyâeither to the loss modulus Gâ or the phase angle. The general approach to analyzing healing data was to estimate the amount of healing for each mix and test temperature, and then compare this to Gâ and phase angle for the binder, along with a variety of other rheological parameters. The damage during mixture fatigue loading in the healing experiment was estimated using a relationship based on Equation 3: D= â ð â ( â ) (13) Where: D = damage index for fatigue loading, theoretically = 1.00 at failure (dimensionless) i = step number in loading/calculation; the selection of the size and number of steps in the calculation is somewhat arbitrary and a matter of convenience. A step in this calculation will generally contain many loading cycles. Nf = cycles to failure Ni = number of cycles in the ith step of the damage calculation Îµi = average mixture strain during ith step of damage calculation (%) VBE = effective binder content by volume (%) k1 = constant determined through statistical analysis to be 2 Î´ = binder phase angle, degrees The damage for both continuous and pulse loading was calculated using Equation 13, along with the damage ratioâthe ratio of the damaged modulus at a given point in the loading to the initial, undamaged modulus. The damage ratio was then plotted against the calculated damage, as shown in Figure 12. The continuous loading damage curve is then shifted upward until it matches the damage curve for pulse loading, using the following relationship:

42 ð¶ = 1 â (1 â ð¶)(1 âð ) (14) Where: CH = damage ratio after healing C = damage ratio before considering healing RH = healing ratio = 0 for no healing, 1 for complete healing Figure 12. Results of Fatigue Healing Experiment for Binder P at 30Â°C. Failure under continuous loading occurred at a damage index of 4.97 Ã 10-9. In addition to the vertical shifting, the damage calculated for the continuous loading using Equation 13 is adjusted by multiplying the strain by the damage ratio after healing (CH). There were numerous problems in conducting the healing experiment. The data was often noisy, in some cases possibly due to loosen LVDTs. Some specimens failed outside the gage length. Equipment malfunctions in several cases resulted in lost data. As a result, shifting the continuously loaded data to match the pulse loading at times involved substantial judgement. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.E+00 5.E-09 1.E-08 |E *| /| E| in iti al Fatigue Damage Index (dimensionless) pulse loading continuous loading continuous loading (shifted)