Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures (2022)

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19   Research Approach Binders Sixteen binders were selected specifically for testing in NCHRP 09-59. These represented a wide range of binder types and grades: • Six polymer-modified binders, • One binder modified with ground-tire rubber, • Two modified with recycled engine oil bottoms (REOB), • Two oxidized binders, • One modified with polyphosphoric acid (PPA), • One modified with both polymer and PPA, and • Three straight-run binders. General characteristics of these 16 performance-graded (PG) 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 identity of the binders has been hidden, again at the request of the suppliers, but also because the objective of NCHRP 09-59 was not to rank the performance of various binders but to develop an improved binder specification for fatigue resistance. All tests performed during NCHRP 09-59 were done on laboratory-aged binders—specifically, RTFOT aging followed by 40 hours in a PAV. As will be discussed, mixture tests were performed on materials loose-mix aged for 5 days at 95°C, which was selected to approximately match the binder-aging regime. In addition to these 16 binders, the eight core asphalts from SHRP were also tested (University of California, Berkeley, 1994). These binders, however, were aged using only 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 in these fatigue tests were aged using only short-term oven conditioning; these binders were therefore aged using only the RTFOT to match the conditioning of the mixtures. Including both the SHRP and the NCHRP 09-59 binders in the fatigue analysis provided a wide range of binders and a great range of aging conditions. Table 4 lists the SHRP core asphalts. There was no need to blind the SHRP core asphalts, so some analyses have identified some of the binders. 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-10 and AC-8 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 United States. It is 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 C H A P T E R 2

20 Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures aged (“residual”) asphalt. The AR-4000 grade was similar to the AC-20. The AAK-1 asphalt was traditionally known for good performance. Asphalts AAG-1 and AAM-1 both had a record of premature fatigue cracking. Five binders from the second ALF fatigue experiments were included in this study for many of the binder tests. These were (1) a PG 70-22, (2) an air-blown asphalt, (3) a crumb rubber– modified binder, and (4 and 5) 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 first ALF experiment. Occasional use was made of a fourth data set of asphalt binders. These were tested by Advanced Asphalt Technologies as part of NCHRP Project 01-19, “Development of a System for Nationwide Evaluation of PCC Pavements” (see also Pellinen, 2001), and were used in development of the original Hirsch model (Christensen et al., 2003); these binders are referred to in this report as the NCHRP 01-19 binders. The fourth set of binders, listed in Table 6, was tested in three conditions: (1) the unaged or “tank” condition, (2) after RTFOT aging, and (3) after RTFOT and PAV aging. The testing done on these binders included frequency sweeps with the DSR over a wide range of temperatures, BBR testing at three temperatures, and DT tests at three temperatures. This data set is useful because a wide range of data is available on the binders at various aging conditions. 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 Table 3. Characteristics of NCHRP 09-59 asphalt binders. 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 Table 4. SHRP core asphalts (University of California, Berkeley, 1994).

Research Approach 21   NCHRP 09-59 Mixtures A 9.5-millimeter (mm) nominal maximum aggregate size (NMAS) mix design with all virgin materials was used for mixture testing in this project. The NCHRP 09-59 binders (Table 3) 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: (1) granite 89, (2) natural sand, (3) limestone 8910, and (4) 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 binders in this study. A liquid anti-stripping agent (LOF 6500) was used in the mix design and preblended 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 135°C for 4 hours in accordance with AASHTO R 30. The loose-mix sample was then spread in large pans and conditioned in another oven at 95°C for 5 days before compaction for preparing test specimens. SHRP Mixtures The mixture used in the SHRP flexural fatigue test program was designed using the Hveem method, with a minimum Hveem stability of 35. In the main experiment, called the expanded test program or the 8 × 2 test program, all eight core asphalts were used in combination with two aggregates—a limestone aggregate and a graywacke gravel aggregate, both with an 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 air void contents of 4% and 7%. Measured air void contents were typically within 1% of these targets. All mixes were short-term aged at 135°C for 4 hours before specimen preparation. The primary focus of the analyses in this report is on the SHRP 8 × 2 experiment, in con- junction with the NCHRP 09-59 fatigue tests. This is because the SHRP 8 × 2 experiment is balanced with respect to the variables. Data from two other experiments, the mix design study and the temperature equivalency factors experiment, were made limited use of in NCHRP 09-59. 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 5. Binders from ALF II fatigue experiment (Gibson et al., 2012). Project Binder Description FHWA ALF AC-5 AC-20 Polyethylene modified SBS modified MnRoad 120/150 pen AC-20 Westrack PG 64-22 Table 6. NCHRP 01-19 binders (Pellinen, 2001).

22 Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures 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 135°C for 4 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 ± 1 %. Laboratory Test Program Binders The binders studied as part of NCHRP 09-59 were tested using a variety of procedures. Frequency-sweep tests were conducted using the DSR at temperatures of 10°C, 22°C, 34°C, and 46°C, at frequencies ranging from 0.1 to 100 radian per second (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 after RTFOT aging, while the NCHRP 09-59 binders were tested after RTFOT and 40 hours PAV conditioning. All of the binders were also tested using the simplified double-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 the following changes: • A loading rate of 50 mm/min, rather than 100 mm/min, was used. This change was made to ensure that any standard method developed from NCHRP 09-59 could be run on a standard ductilometer. • Instead of using three sets of two specimens, each with a different notch size, the simplified version uses one set of three specimens, each with the same notch size. Analyses of several tests have shown an excellent correlation between crack tip opening displacement determined using the standard DENT procedure and extension to failure using the simplified test. Initially, a specimen with two 2.5-mm deep notches was used, creating a 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 09-59 binders, it was discovered that some heavily modified and aged binders could not be tested with this specimen geometry—the specimen would pull away from the end pieces before failing. After evaluating the data already gathered, it was decided to test all the NCHRP 09-59 binders using specimens with larger notches—7.5 mm on each side of the specimen—creating a 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. Heavy binder aging is believed to make 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

Research Approach 23   the temperature at which the loss modulus G′ = 17.5 MPa at a frequency of 10 Hz. Only one test temperature was run using this protocol, as problems seemed to occur 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 strain levels. This analysis, when applied to the NCHRP 09-59 specimens, produced highly variable and often inconsistent results. An alternative approach that provides better results is explained later in this report. NCHRP 09-59 Mixtures Three test procedures were used to characterize the NCHRP 09-59 mixes: (1) flexural fatigue, (2) uniaxial fatigue, and (3) a healing test. Flexural fatigue testing was performed on 9 of the 16 NCHRP 09-59 binders; uniaxial fatigue testing was done on all 16. Eight of the 16 NCHRP 09-59 binders were tested in the healing experiment. Bending Beam Fatigue Testing The bending beam fatigue test (BBFT) was conducted in accordance with AASHTO T 321-14. 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 ± 1% after trimming. Testing was conducted at 10°C and 20°C to determine the effect of test temperature on the fatigue life of each mixture. In the BBFT 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 Figure 6. IPC Global BBF testing apparatus with fixed reference retrofit.

24 Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures at the center of the 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 at which the peak of the product of flexural stiffness times the number of cycles occurred. This concept is illustrated graphically in Figure 7. More detailed information about this test is included in Appendix C. Dynamic Modulus and Uniaxial Cyclic Fatigue Test Two tests were conducted in the Asphalt Mixture Performance Tester 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 for each mixture to quantify its linear viscoelastic characteristics, and the uniaxial cyclic fatigue test was performed to determine its damage characteristic curve. The dynamic modulus test was performed in accordance with AASHTO T 378-17. Specimens for this test were prepared in accordance with AASHTO R 83-17. The Superpave gyratory compactor 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 R 84-17. The high-test temperature was varied depending on the high PG of the binder used in the mixture. All dynamic modulus test- ing was performed unconfined, and test results were screened for data quality in accordance with the limits set in AASHTO T 378-17. 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 ± 0.5% according to AASHTO R 83-17, glued to the top and bottom platens (Figure 8), and tested for each mix. In the 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 – 3] and [(high PG + low PG)/2 + 3]. For each test temperature, three strain levels were 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. In accordance with AASHTO TP 107-14, uniaxial cyclic fatigue testing was conducted in two steps: (1) fingerprint dynamic modulus and (2) cyclic fatigue. The fingerprint test was performed to obtain the fingerprint dynamic modulus. The dynamic modulus ratio (DMR) 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 F le xu ra l S ti ff ne ss ( M P a) Number of Cycles Flexural Stiffness Modulus x Cycles Failure Point Figure 7. Example of bending beam fatigue failure point.

Research Approach 25   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 in which 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 Figure 8. Uniaxial fatigue test setup. 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 P ha se A ng le , de gr ee D yn am ic M od ul us , M P a Loading Cycles Dynamic Modulus Phase Angle Failure Point Figure 9. Example of failure point in uniaxial fatigue test. An asphalt mixture performance tester sample glued with steel epoxy to rigidly mounted end platens.

26 Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures characteristic curve and cracking resistance for each mixture on the basis of the S-VECD model. More detailed information about the dynamic modulus and uniaxial cyclic fatigue is included in Appendix C. 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 maintaining haversine loading during continuous fatigue testing is difficult or impossible, and the loading tends to gradually revert to the fully reversed condition. The testing was strain controlled, with strain levels generally at 400 and 700 × 10−6 meters per meter (m/m). Most tests were performed at 20°C. In the mix design study, lower strains of 200 and 300 × 10−6 m/m were included in the test program. A wider range of both temperature and strains was used in the temperature equivalency factors experiment, with temperatures of 5°C, 10°C, 20°C, and 25°C, and strains ranging from 300 to 1,200 × 10−6 m/m. Details of the test procedure and sample preparation methods can be found in SHRP-A-404 (University of California, Berkeley, 1994) and Harvey’s 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 two objectives of the experiment were to determine (1) whether pulse loading resulted in healing compared with continuous loading, and if healing was observed, whether it was correlated to one or more asphalt binder rheological properties. In the continuously loaded 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. Several temperatures and strain levels were used to provide a wide range of data that could be evaluated to determine whether relationships exist between asphalt mixture healing properties and asphalt binder rheological characteristics. Data Analysis Model for Analyzing Mixture Fatigue and Binder Test Data It has historically been difficult to correlate mixture fatigue tests to field performance as well as to a variety of binder test data. This might be caused by problems with traditional ways of analyzing fatigue data rather than by shortcomings in the test method. For more-effective comparisons between fatigue tests, fracture tests, and other mechanical tests on both asphalt concrete mixtures and asphalt binders, the NCHRP 09-59 research team developed a novel theoretical framework to explain fatigue and fracture phenomena in asphalt mixtures and binders, coining the term general failure theory for asphalt binders (GFTAB). Appendix D is a detailed discussion of the data analysis methods used in NCHRP 09-59, including a descrip- tion of the GFTAB model. Following is a summary of the primary features of this approach to analyzing asphalt mixture and binder fatigue and fracture data. The GFTAB model is simple and intuitive. It states that the fatigue life of an asphalt mixture is proportional to the ratio of the FSC to the applied binder strain, raised to an exponent propor- tional to the inverse of the phase angle (as a fraction):

Research Approach 27   = × ε     ( )δ* (3) 901 N FFPR FSC f k 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 = 4.45 × 106 |G*|−0.806, ε = effective strain in binder (%), = mix strain/(effective binder content by volume, or Vbe/100), k1 = constant determined through statistical analysis to be 2, and δ = binder phase angle (degrees). 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 precisely determining this value 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-value—and the one used in this NCHRP project for determining the phase angle value for use in fatigue analysis—involves 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: 2 * 1 10 1 90 (4) 9 R log log G log ( ) ( )( )= × − δ where R = Christensen-Anderson R-value (rheologic index), |G*| = dynamic complex modulus, in pascal (Pa), and δ = 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: 90 1 2 * 1 10 (5)10 9 exp log log G R{ }( )( )δ = − × ×  where the variables are as defined. In the following discussion, where the phase angle is mentioned or used in an equation, it refers to the phase angle as previously determined. 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 FSC is analogous to the binder failure strain and theoretically represents the strain at which the fatigue life is exactly 1. The average or 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 × FSC*.

28 Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures As explained in Appendix D, testing during NCHRP 09-59 suggests that binder FSC and mix FSC are not identical but are close over the range of data analyzed during NCHRP 09-59. The difference may arise from the complex state of stress existing in the asphalt binder in a mixture as compared with 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 the failure strain of a binder. Figure 10 is a plot showing several such failure envelopes: (1) the asphalt binder failure envelope (with measured data points) determined as part of NCHRP 09-59; (2) the FSC failure enveloped determined fatigue NCHRP 09-59 mixture fatigue tests; and (3) the asphalt binder failure envelope proposed by Heukelom (1966). These are all reasonably close together, the differences probably resulting from the behavior of binders versus mixtures, differences in monotonic and fatigue tests, and differences in the specific test procedures used. The decrease in strain capacity as modulus increases is an important aspect 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 under- stand how both the FSC and the fatigue exponent are changing. The GFTAB model provides a way of understanding these changes, and a way of meaningfully comparing mixture fatigue performance and binder test data. The relationship between the fatigue exponent and binder phase angle is a key feature of this theory, representing a major departure from standard models for asphalt mixture fatigue behavior that, ideally, should be verified. Most asphalt mixture fatigue tests are performed over a narrow range of temperatures—many test programs are only done at one temperature (20°C). Phase angle is therefore typically within a narrow range, making 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 S tr ai n or F SC , % Stiffness/3 or G*, Pa From binder tests From mix fatigue Heukelom SHRP DENT ALF DENT NCHRP 9-59 DENT Direct tension Figure 10. Failure envelopes as determined during NCHRP 09-59 from binder tests and mixture fatigue tests and as reported by Heukelom (1966), along with data points from binder testing.

Research Approach 29   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 temperatures, 5°C, 10°C, 20°C, and 25°C, using a range of strains at each temperature. This allowed the fatigue exponent—the slope of cycles to failure versus strain plot on a log-log scale—to be calculated at each temperature. Figure 11 is a plot of calculated fatigue exponent as a function of binder phase angle for these 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. The data underlying Figure 11 were not included in the calibration of the GFTAB model, and the figure presents strong verification of the relationship between fatigue exponent and binder phase angle. An important feature of Equation 3 is 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 decrease significantly with binder aging. 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 binders studied as part of NCHRP 09-59 ranged from about 0.4 to 2.0. FFPR values can be determined from mixture fatigue tests, from binder fatigue tests such as the LAS test, or from binder tension tests such as the DENT test. The following sections summarize the results of the analysis of mixture fatigue test data and binder test data and then compare FFPR values with 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 FFPR values for the flexural fatigue data experi- ment, including mixtures made with 8 of the 16 NCHRP 09-59 binders and the eight SHRP core asphalts. FFPR represents the ratio of a given binder’s strain tolerance to that of a typical binder and indicates the overall strain tolerance of an asphalt binder. FFPR is the main characteristic used to relate mixture fatigue performance to binder properties. y = 2.21x R² = 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 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.

30 Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures Determining the FFPR values from fatigue data involved fitting the observed fatigue data to the GFTAB model, as explained in Appendix D. The research team used Microsoft Excel Solver, 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 09-59 binders. In analyzing the uniaxial data, the GFTAB model was used to estimate the FFPR 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 FFPR values. The results of these analyses are given in Chapter 3 and 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 (ε) for each mixture at 10°C and 20°C. = ε     1 (6)1 2 N kf k where Nf = number of cycles to failure, ε = applied stain on sample, and k1, k2 = material constants. Simplified Viscoelastic Continuum Damage Analysis of Uniaxial Fatigue Data 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 had four steps: 1. A storage modulus master curve was created on the basis of 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 for determining the Prony series coefficients. The E(t) Prony series coefficients were used to determine α value, a critical parameter for the damage calculation. Additionally, the dynamic modulus data were also used to determine the DMR value used for the calculation of pseudo secant modulus (C). 2. Uniaxial fatigue data were analyzed in two steps. The first consisted of the data for the first half of the first loading path (from zero to first peak stress). The second consisted of the rest of the data. For the first cycle of loading, full time-history data were used to calculate the pseudo strain (εR) up until the peak tensile load. Then, pseudo stiffness (C) calculated on the basis of the stress divided by the pseudo strain and the DMR and damage parameter (S) was computed using DMR, pseudo stiffness, and α 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 on the basis of the peak in the phase angle data from the uniaxial fatigue test. 3. The C-S curve was developed for each specimen on the basis of 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.

Research Approach 31   = −1 (7)11 12C C SC where C = pseudo stiffness, S = damage parameter, and 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 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. ∫= (8)0 2 G W N R N C R f f where GR = change of averaged released pseudo strain energy per cycle, Nf = number of cycles to failure, and WRC = released pseudo strain energy. Analysis of Binder Test Data Three binder test parameters were evaluated for comparison with mixture fatigue FFPR: (1) the Christensen-Anderson R-value, (2) FFPR values calculated from the LAS test, and (3) FFPR values calculated from the SDENT test. The GRP is considered separately, as it does not indicate inherent strain tolerance like R-value or FFPR, but instead is a surrogate for failure strain or FSC at a given loading rate and temperature. Therefore, GRP is compared with mixture FSC (FFPR × 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. The R-values for the binders were calculated from LAS data at 10 Hz using Equation 4. This approach was used because the binders had a 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 being the average of three separate determinations, so the R-value would represent the average of three measurements. The LAS data were analyzed as a fatigue test, using an equation derived from the GFTAB model and similar to the approach toward analyzing mixture uniaxial fatigue data: ∑{ }( )= γ ( ) ( )δ= δ14.8 * (9) 90 1 90 1 1FFPR FSC Ni i ki Nf k where 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 = 3.21 × 106 |G*|-0.788 Nf = number of cycles to failure,

32 Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures Ni = number of loading cycles in loading step i, γi = shear strain in binder (%), k1 = constant determined through statistical analysis to be 2, and δ = binder phase angle (degrees). The FFPR in this case represents the ratio of the measured FSC of the binder in the LAS test to the expected or typical value (FSC*). The factor 4.8 in Equation 9 represents a factor of 3 for converting from shear strain to extensional strain multiplied by a calibration factor of 1.6 for the LAS test geometry. This calibration factor was determined empirically, and it probably differs from 1.0 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 in that the heavily notched specimen cannot be analyzed as if it were a tension test, using calculated stresses, strains, and modulus. The procedure instead relied on comparing measured specimen extension with initial specimen stiffness (Equation 10). Extension in this case was the extension to the post peak point for which the load was 20% of the peak load. This approach was used, rather than determination of total extension, to avoid the high variability sometimes associated with extreme extensions. 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 fit the extension data to the model shown in Equation 10. = (10)E FFPR ASi i iB 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, and Si = initial stiffness of ith specimen in Newtons per meter (N/m). FFPR values for this model were defined so that a binder that was not polymer modified (a non-polymer-modified binder) with an R-value of 2.0 would have an FFPR of 1.0. For the standard SDENT geometry—with the small 5-mm ligament—the constants A and B were found to be 48.0 and −0.371, respectively, and the fit of the model was excellent, with a standard error of 2.4%. Some early SDENT tests were run with a different geometry—the large 15-mm ligament. In this case, the constants A and B were found to be 176.0 and −0.359, respectively. The fit for this model was also excellent, with a standard error of 3.5%. For calculating FFPR values from SDENT tests using the standard geometry with the 5-mm ligament, Equation 11 should be used, with extension in mm and S is specimen stiffness at 3 seconds, in N/m: 17.4 (11) 0.334 FFPR Extension S = − For best results, the initial specimen stiffness should be between about 15 and 35 N/m. The FFPR parameter represents the SDENT extension normalized for stiffness and represents the inherent strain tolerance of a binder, independent of stiffness. FFPR values for the SDENT were also calculated on the basis of 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 based on these parameters are included in Appendix E, a summary of pertinent data for NCHRP 09-59.

Research Approach 33   The GRP was calculated using an equation suggested by Rowe (2011): ( )= δ δ* cos sin (12)2GRP G where GRP = Glover-Rowe parameter, |G*| = dynamic complex modulus (in Pa), and δ = 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, to compare GRP with FSC values calculated from the mixture flexural fatigue tests, it was calculated at a frequency of 10 Hz and at temperatures of 10°C and 20°C. Many pavement engineers and researchers have recently correlated pavement cracking— both transverse and fatigue cracking—to the parameter ΔTc, the difference between critical temperatures based on stiffness and critical temperatures based on m-value, as determined using the BBR. In consultation with the panel, it was decided that BBR testing would not be done as part of NCHRP 09-59, and so ΔTc is not considered in this analysis. However, as pointed out in Chapter 3, ΔTc is directly related to R-value, and the relationships developed here between fatigue performance and R-value would in all probability also exist if ΔTc 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 mixture and binder fatigue and fracture properties can be compared, the accuracy of the analytical approach must be verified. Accuracy is determined in Chapter 3 by verifying several important relationships: 1. The predicted and observed cycles to failure for the fatigue model should be reasonably good, though that mixture fatigue test data are 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 (FSC as a function of modulus) should agree with the failure envelope presented by Heukelom (1966) and with failure data for asphalt binders, such as shown in Figure 10. 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 NCHRP 09-59 analysis was the comparison of mixture fatigue FFPR values with 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 09-59 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 and parameters is suitable for use in an improved binder fatigue specification and, if more than one appears suitable, to determine which is best. As mentioned at the beginning of this section, the GRP is a somewhat different binder parameter compared with FFPR values or R-value. The GRP indicates binder failure strain at

34 Relationships Between the Fatigue Properties of Asphalt Binders and the Fatigue Performance of Asphalt Mixtures a given temperature and loading frequency, rather than inherent overall strain tolerance. For this reason, GRP should be evaluated in comparison with FSC (FFPR × FSC*) to determine whether it is useful in a specification. Specifying GRP, however, does not control overall fatigue performance in the way that specifying FFPR or R-value does; rather, 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 δ in the current binder specification. The nature of the relationship between the GRP and pavement performance is discussed in more detail in Chapter 3. 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 compared the loss in modulus at failure under continuous loading with the estimated loss in modulus at failure under pulse loading; the loss in modulus was estimated using the GFTAB model described previously. Almost always, the loss in modulus at failure under pulse loading was significantly less than under continuous loading, indicating healing under intermittent loading. It was hypothesized at the start of NCHRP 09-59 that such healing would be related to binder rheology—either to the loss modulus G′ or the phase angle. The general approach to analyzing healing data was to estimate the amount of healing for each mix and test temperature, then compare this with G′ and phase angle for the binder along with a variety of other rheological parameters. Damage during mixture fatigue loading in the healing experiment was estimated using a relationship based on Equation 3: 100 (13)1 901 D N V i i be i N k f∑= ε   ( ) = δ where D = damage index for fatigue loading, theoretically = 1.00 at failure (dimensionless); i = step number in loading/calculation; Nf = number of cycles to failure; Ni = number of cycles in the ith step of the damage calculation; εi = average mixture strain during ith step of damage calculation (%); Vbe = effective binder content by volume (%); k1 = constant determined through statistical analysis to be 2; and δ = binder phase angle (degrees). The damage for both continuous and pulse loading was calculated using Equation 13, along with the damage ratio—the ratio of the damaged modulus at a given point in the load- ing to the initial, undamaged modulus. 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. 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: 1 1 1 (14)C C RH H( )( )= − − −

Research Approach 35   where CH = damage ratio after healing, C = damage ratio before considering healing, and RH = healing ratio (0 for no healing, 1 for complete healing). 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). Numerous problems emerged in conducting the healing experiment. The data were often noisy, in some cases possibly because of loose linear variable differential transducers. Some specimens failed outside the gauge length. Equipment malfunctions in several cases resulted in lost data. Shifting the continuously loaded data to match the pulse loading, therefore, at times involved substantial judgment. 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) Figure 12. Results of fatigue healing experiment for Binder P at 30°C. Failure under continuous loading occurred at a damage index of 4.97 × 10−9.