Validating the Fatigue Endurance Limit for Hot Mix Asphalt (2010)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

44 The testing performed at the University of New Hampshire (UNH) includes complex modulus, monotonic, and fatigue tests in uniaxial tension. Analysis of the data is done using viscoelastic and continuum damage mechanics principles to identify the fatigue endurance limit of the PG 67-22 opti- mum, PG 67-22 optimum plus, PG 76-22 optimum, and PG 76-22 optimum plus mixtures. Frequency sweeps at var- ious temperatures are run to measure the complex dynamic modulus of each mix. The dynamic modulus and phase angle master curves are then constructed from these data and the relaxation master curve is obtained through linear viscoelas- tic conversion. The damage characteristic curve of each mix is obtained by running uniaxial monotonic tests to failure or by running constant amplitude fatigue tests to failure. The characteristic damage curve is used to predict the number of cycles to failure at different strain amplitudes to determine the fatigue endurance limit of the mixture. Fatigue tests with increasing strain amplitude are run in uni- axial tension to directly identify the fatigue endurance of the mixtures. The testing and analysis procedures are described in the following sections, starting with the dynamic modulus tests, followed by monotonic tests, fatigue tests, and finally the prediction of endurance limit. Test Specimens A summary of the air void content and testing performed on each specimen at UNH is shown in Table 5.1. All test spec- imens were fabricated at NCAT using an SGC and shipped to UNH, where they were cut and cored to 75-mm diameter, 150-mm tall specimens. Steel plates were glued to the ends of the uniaxial specimens using plastic epoxy glue in a gluing jig designed to align the specimen vertically. Four LVDTs spaced 90 apart around the circumference of the specimen were attached to the surface of the specimen using a 100-mm gage length. Dynamic Modulus and Phase Angle Master Curves Uniaxial complex modulus tests were performed on at least three specimens from each mixture. The testing was done at the following five temperatures: −10C, 0C, 10C, 20C, and 30C and at eight frequencies: 0.1, 0.2, 0.5, 1, 2, 5, 10, and 20 Hz. The dynamic modulus and phase angle values at each frequency and temperature were calculated from stresses and LVDT measured strains. The individual dynamic mod- ulus curves were shifted along the frequency axis to construct the dynamic modulus master curve using the time-temperature superposition principle. The reference temperature was selected as 20C. The resulting master curve for dynamic modulus (|E∗|) is expressed by the following sigmoidal equation: where, a, b, c, and d are positive regression coefficients. The term fr represents the reduced frequency, given by where, aT is the shift factor which is a function of temperature and f is the actual frequency at which the individual curves are obtained. The solver function in Microsoft Excel is used to simul- taneously determine the sigmoidal fit coefficients and the shift factors for the individual specimens using error min- imization. An overall mixture master curve is determined by fitting the sigmoidal function in Equation 19 to all of the individual specimen master curves. Figures 5.1 through 5.4 show the individual and overall dynamic modulus master log log log ( )f f ar T= + 20 log exp log ( )E a b c d fr = + + − −( )1 19 C H A P T E R 5 Uniaxial Tension Results and Analyses

45 Table 5.1. Summary of specimens and tests conducted. Mix SpecimenNo. Air Voids % |E*| Test Monotonic Test Fatigue Test Comments (After Core and Cut) Constant Amplitude Increasing Amplitude 1 8.6 Broke during |E*| testing 2 7.0 X 3 7.3 Broke during |E*| testing 4 7.3 X 5 7.5 X 6 6.8 X 7 7.7 X 8 7.2 X 9 7.7 X 10 7.5 X 11 7.7 X X 12 7.0 Broke during |E*| testing 13 7.7 X X 14 6.9 X 15 6.9 X 16 6.7 X 17 6.7 X PG 67-22, Optimum 18 6.6 X 1 6.5 Broke during |E*| testing 2 6.9 X X 3 6.1 X X 4 7.0 X X PG 76-22, Optimum 5 6.2 X X 1 2.2 X X 2 1.5 X X PG 67-22, Optimum+ 3 2.2 X X Monotonic test data not usable 4 1.3 X X 5 2.1 X X 6 3.6 X X 7 3.6 Broke during |E*| testing 8 2.7 X X 9 3.0 Broke during |E*| testing 10 3.0 X X 1 1.5 X X 2 1.3 X 3 1.9 X X 4 1.2 X X 5 1.0 Broke during |E*| testing 6 3.1 X X 7 3.2 X X 8 2.7 X X 9 3.7 X X PG 76-22, Optimum+ 10 2.8 X X

46 0 10000 20000 30000 40000 50000 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz D yn am ic M od ul us , M Pa Master Curve at 20°C Individual Specimens Figure 5.1. Dynamic modulus master curves for PG 67-22 optimum. Master Curve at 20°C Individual Specimens 0 10000 20000 30000 40000 50000 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz D yn am ic M od ul us , M Pa Figure 5.3. Dynamic modulus master curves for PG 67-22 optimum plus. Individual Specimens Master Curve at 20°C 0 10000 20000 30000 40000 50000 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz D yn am ic M od ul us , M Pa Figure 5.2. Dynamic modulus master curves for PG 76-22 optimum.

curves obtained for the four mixtures. Figure 5.5 shows the overall dynamic modulus curves (obtained from fit) for all four mixtures together. The shift factors determined from the dynamic modulus master curves were then used to shift the individual phase angle curves at each temperature to obtain the phase angle master curve for each specimen. The phase angle master curves are fit with a sigmoidal function of the form in Equation 19. Fig- ures 5.6 through 5.9 show the individual and overall phase angle master curves for individual mixtures. Figure 5.10 shows the overall phase angle master curves for all four mixtures together. 47 Mix Master Curve at 20°C Individual Specimens 0 10000 20000 30000 40000 50000 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz D yn am ic M od ul us , M Pa Figure 5.4. Dynamic modulus master curves for PG 76-22 optimum plus. 67-22, Opt 76-22, Opt 67-22, Opt+ 76-22, Opt+ 0 10000 20000 30000 40000 50000 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz D yn am ic M od ul us , M Pa Figure 5.5. Dynamic modulus master curves for all mixes tested. Combined Mix Individual Specimens 0 20 40 60 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz Ph as e A ng le , D eg re e Figure 5.6. Phase angle master curves for PG 67-22 optimum.

48 Individual Specimens Master Curve 0 20 40 60 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz Ph as e A ng le , D eg re e Figure 5.9. Phase angle master curves for PG 76-22 optimum plus. Master Curve at 20°C Individual Specimens 0 20 40 60 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz Ph as e A ng le , D eg re e Figure 5.7. Phase angle master curves for PG 76-22 optimum. Master Curve at 20°C Individual Specimens 0 20 40 60 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz Ph as e A ng le , D eg re e Figure 5.8. Phase angle master curves for PG 67-22 optimum plus.

Damage Characteristic Curve The characteristic curve for a mixture describes the rela- tionship between C, which is normalized pseudo stiffness calculated through viscoelastic theory, and S, which is the dam- age parameter calculated from continuum damage mechanics theory. Practically, C can be thought of as the material’s integrity at any point in time and S as the level of damage over time. As the amount of damage in the material increases, the material integrity decreases. A mixture’s characteristic curve can be constructed from monotonic or cyclic tests. The steps involved in the construction of the characteristic curves are described in Appendix E. Monotonic Testing Figures 5.11 through 5.14 show the characteristic curves obtained from on-specimen LVDTs for each individual mix- ture tested under monotonic loading. The individual speci- 49 67-22, Opt 76-22, Opt 67-22, Opt+ 76-22, Opt+ 0 20 40 60 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz Ph as e A ng le , D eg re e Figure 5.10. Phase angle master curves for all mixes tested. 0 0.25 0.5 0.75 1 0 0.5 1 1.5 S 2 2.5 3 C Individual Specimens Generalized power model Exponential model Figure 5.11. Characteristic curves using on-specimen LVDTs for different strain rates for PG 67-22 optimum. men data are fit using both a generalized power model and an exponential model (60, 61), given in Equations 21 and 22, respectively. where, C11, C12, and k are regression coefficients (hereafter referred to as damage curve coefficients) obtained by ordinary least squares technique. The generalized power law does a better job fitting the actual data obtained from the tests. Figures 5.15(a) and (b) show the characteristic curve fits for all mixtures obtained using the gen- eralized power model and exponential model, respectively. The behavior of the PG 76-22 optimum plus mixture appears to be significantly different from the other mixtures; the curve for this mixture only represents one specimen, so more testing C e kS= − ( )22 C C S C = − ( )1 2111 12 ( )

50 Individual Specimens Generalized power model Exponential model 0 0.25 0.5 0.75 1 0 0.5 1 1.5 S 2 2.5 3 C Figure 5.12. Characteristic curves using on-specimen LVDTs for PG 76-22 optimum. Individual Specimens Generalized power model Exponential model 0 0.25 0.5 0.75 1 0 0.5 1 1.5 S 2 2.5 3 C Figure 5.13. Characteristic curves using on-specimen LVDTs for PG 67-22 optimum plus. Individual Specimens Generalized power model Exponential model 0 0.25 0.5 0.75 1 0 0.5 1 1.5 S 2 2.5 3 C Figure 5.14. Characteristic curves using on-specimen LVDTs for PG 76-22 optimum plus.

must be done to determine if this is representative behavior or a problem with the one test specimen. Initially, specimens failed near the end plates during mono- tonic tests, which is likely due to the presence of high air void content at the ends of the specimens. The specimens were shortened by cutting more material from the top and bottom. This was successful in producing failure in the middle of the specimens. In addition to making shorter specimens, LVDTs were located plate to plate along with the on-specimen LVDTs during the monotonic tests (two on-specimen and two plate- to-plate LVDTs). The advantage of using the plate-to-plate LVDTs is that the material response can be captured even if the specimens fail outside the on-specimen LVDT gage length. Monotonic tests performed at various strain rates can be used to investigate whether there is any significant effect of plasticity in the mixture behavior. If there is a significant portion of viscoplastic strain in the material response, the C versus S curves will be different for the various strain rates. Figures 5.16(a) and (b) show the C versus S curves at differ- ent strain rates measured using the on-specimen and plate- to-plate LVDTs, respectively. It can be seen from these figures that the curves for the various strain rates fall on top of each other except for the plate-to-plate curve for Specimen 10. There are some issues related to the strain data obtained from plate-to-plate LVDTs for this specimen. Thus, the data for the remaining specimens indicates that the effect of viscoplastic- ity in the monotonic test results is not significant. Fatigue Testing A total of five specimens of PG 67-22 optimum were tested under cyclic fatigue loading using four on-specimen LVDTs. The testing was performed at 20°C by controlling the cross- head displacements. Haversine waveforms were applied to the 51 67-22, opt 76-22, opt 67-22, opt+ 76-22, opt+ 67-22, opt 76-22, opt 67-22, opt+ 76-22, opt+ 0 0.25 0.5 0.75 1 0 0.5 1 1.5 S1 2 2.5 3 C1 0 0.25 0.5 0.75 1 0 0.5 1 1.5 S (a) Generalized power model (b) Exponential model 2 2.5 3 C Figure 5.15. Overall characteristic curves using on-specimen LVDTs for all mixtures tested under monotonic loading.

52 rate=0.135/min (Spec #5) rate=0.135/min (Spec #6) 0.135/min (Spec #7) rate=0.02/min (Spec #9) rate=0.1/min (Spec #8) rate=0.0675/min (Spec #10) rate=0.135/min (Spec #6) rate=0.135/min (Spec #7) rate=0.02/min (Spec #9) rate=0.1/min (Spec #8) rate=0.0675/min (Spec #10) 0 0.25 0.5 0.75 1 0 0.5 1 1.5 S 2 2.5 3 C 0 0.25 0.5 0.75 1 0 0.5 1 1.5 S (b) Plate to Plate LVDTs (a) On-specimen LVDTs 2 2.5 C Figure 5.16. C versus S curves at different strain rates for PG 67-22 optimum specimens. Specimen ID Average On- Specimen LVDT Strain, ms Crosshead Strain, ms Nf Comments Specimen 14 242 1050 17,480 Failed in the middle Specimen 15 254 1017 10,728 Failed in the middle Specimen 16 n/a n/a n/a Failed at first cycle Specimen 17 134 1300 >26,687 Did not fail Specimen 18 223 1017 1731 Failed near top end plate Table 5.2. Summary of fatigue tests performed on PG 67-22 optimum specimens. specimen until failure occurred. Table 5.2 summarizes the fa- tigue testing. Specimen 17 was the first specimen tested. The research team anticipated that the specimen would fail within 10,000 cycles, so the test was halted after about 26,000 cycles to determine what was happening. Due to machine compli- ance, the actual strains measured by the LVDTs were roughly one-quarter of the applied crosshead strain, so the strain am- plitude was increased for subsequent tests. The fatigue tests are neither controlled strain nor con- trolled stress tests, rather a mixed mode of loading occurs be- cause the crosshead rate is controlled, but the on-specimen strains are used for analysis. Figures 5.17(a) and (b) show typ- ical stress and strain history, respectively, recorded during a constant amplitude fatigue test. The load continuously de- creases due to the development of damage, and decreases dra- matically at failure. The mean strain increases continuously

where, ε0 is the strain level required to sustain N number of load repetitions, S is the damage parameter value at failure (measured from the damage characteristic curve for the mixture at the point where C = 0.3, identified in previous research [32]), I is the initial pseudo stiffness, |E∗| is the dynamic modulus at testing frequency (f ), and α is the material constant, p = 1 + (1 − C12)α. Plots of strain level (ε0) versus design load repetitions (N) obtained for individual asphalt mixtures are presented in ε α α α α α α α 0 2 1 2 2 1 24= −[ ] −( ) ( ) − + f e I k N E kS  ( ) ε α α α0 2 11 12 2 0 125 23= ( ) ( ) f S p IC C N E p . ( )  53 (a) Stress history (b) Strain history Figure 5.17. Typical stress/strain history for constant amplitude uniaxial fatigue test. Specimen #15 Specimen #14 Monotonic 0 0.5 1 1.5 2 0.0 0.5 1.0 1.5 S 2.0 2.5 3.0 C Figure 5.18. Comparison monotonic and cyclic curves for PG 67-22 optimum. during the tests until failure, at which point the mean strain drops. Figure 5.18 shows the characteristic curves constructed from both the fatigue and monotonic tests for the PG 67-22 optimum mixture. Previous research has shown better agree- ment between samples and between monotonic and cyclic tests (32). Evaluation of Endurance Limit Prediction from Characteristic Damage Curves Once dynamic modulus, initial stiffness, testing frequency, and damage curve coefficients are known, the strain level required to sustain any number of design load repetitions can be predicted. Equations 23 and 24 can be used to find required strain level with generalized power law and exponential mod- els, respectively (60, 61).

Figures 5.19 through 5.22. A comparison of the relations of all mixtures together is presented Figures 5.23(a) and (b) for the generalized power law and exponential models, respectively. The strain levels required to sustain 50 million cycles of repetitions for all mixtures are shown in Table 5.3 and pre- sented graphically in Figure 5.24. The values obtained using the exponential model are much lower than those obtained from the generalized power law model. There is more confi- dence in the values from the generalized power law because this function fits the C-versus-S data for these mixtures bet- ter than the exponential function. 54 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E+00 1.0E+081.0E+061.0E+041.0E+02 St ra in Number of repetitions Exponential model Generalized power model Figure 5.19. Plot of strain level versus load repetitions for PG 67-22 optimum. Exponential model Generalized power model 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E+00 1.0E+081.0E+061.0E+041.0E+02 St ra in Number of repetitions Figure 5.20. Plot of strain level versus load repetitions for PG 76-22 optimum. Exponential model Generalized power model 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E+00 1.0E+081.0E+061.0E+041.0E+02 St ra in Number of repetitions Figure 5.21. Plot of strain level versus load repetitions for PG 67-22 at optimum plus.

55 Exponential model Generalized power model 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E+00 1.0E+081.0E+061.0E+041.0E+02 St ra in Number of repetitions Figure 5.22. Plot of strain level versus load repetitions for PG 76-22 at optimum plus. 67-22 @ Opt. 76-22 @ Opt. 67-22 @ Opt. + 76-22 @ Opt. + 67-22 @ Opt. 76-22 @ Opt 67-22 @ Opt. + 76-22 @ Opt+ 1.0E-05 1.0E-04 1.0E-03 1.0E+00 1.0E+081.0E+06 1.0E+04 1.0E+02 St ra in Number of repetitions 1.0E-04 1.0E-03 1.0E-02 1.0E+00 1.0E+081.0E+06 1.0E+04 1.0E+02 St ra in Number of repetitions (a) Generalized power models (b) Negative exponential models Figure 5.23. Plot of strain level versus load repetitions LVDTs for all mixtures.

Increasing Strain Amplitude Test This test consists of applying blocks of haversine loading to a uniaxial test specimen. Initially, a relatively low strain am- plitude that is thought to be below the fatigue endurance limit is applied. Typically, this is close to the same amplitude at which dynamic modulus tests are performed. Approximately 10,000 cycles are applied at this amplitude to allow the speci- men to reach steady-state response. The applied strain ampli- tude is then increased and 10,000 more cycles are applied. This procedure is continued until the specimen fails. Figures 5.25(a) and (b) show a typical load and strain history, respectively, recorded during an increasing amplitude fatigue test. It should be noted that, for this project, the crosshead displacement was controlled while the on-specimen LVDT measurements were used for strain analysis. Machine compliance made it difficult to precisely control the strain amplitude in the spec- imen at the different levels. Concept of Pseudo Strain The use of pseudo strain instead of engineering strain in constitutive analysis removes the hysteretic effect of vis- coelasticity. For example, a plot of stress versus strain data obtained from a dynamic modulus test produces a hysteresis loop, as shown in Figure 5.26. The load levels applied during a dynamic modulus test are low enough not to induce damage, so the hysteresis loop is purely due to the viscoelastic response of the material. The hysteresis loop collapses when the pseudo strain is plotted versus the stress, as seen in Figure 5.27. If dam- age occurs in the material, a hysteresis loop will appear in the stress-pseudo strain plot. The analysis of the increasing strain amplitude fatigue tests involves calculating the pseudo strain and then plotting pseudo strain versus stress at each strain amplitude to deter- mine the strain level at which loops begin to appear. The pres- ence of a loop in the stress-pseudo strain plot indicates that damage is occurring in the specimen. Figures 5.28 and 5.29 show the stress versus pseudo strain plots for PG 67-22 op- timum plus and PG 76-22 optimum plus specimens, respec- tively. For the PG 67-22 optimum plus specimen, it is clear that there is no loop at the lowest strain amplitude, a loop appears to just be forming at the middle strain amplitude and a loop is definitely apparent at the highest strain amplitude. These two figures indicate that the fatigue endurance limit (strain level below which no damage is occurring) for this specimen is around 150 ms. For the PG 76-22 optimum plus specimen shown in Figure 5.29, the loop appears in the sec- ond load level, which is 245 ms. Hence, the fatigue endurance limit is somewhere between 93 and 245 ms. Table 5.4 sum- marizes the results of the increasing amplitude fatigue tests for all specimens tested. It should be noted that only three mixtures were subject to this test method. The third column in Table 5.4 shows the bounds of the strain level at which loop formation was observed. For sev- eral specimens, the first level tested resulted in loop forma- tion, so only an upper bound is reported. The specimen stiffness at 50 cycles and air void content are also shown in Table 5.4. From this information, it is evident that there are two groups of specimens for the 67-22 optimum plus and 76-22 optimum plus mixtures. The 67-22 optimum plus Spec- imens 1 and 2, and the 76-22 optimum plus Specimens 1 and 3, have lower air void contents and correspondingly higher stiffnesses and strain range at which loop formation occurs than the other specimens. Using engineering judgment, the 56 Table 5.3. Computed critical micro-strain to sustain 50 million cycles. Asphalt Mixture Grade Damage Characteristic Curve Form 67-22 Optimum 76-22 Optimum 67-22 Optimum+ 76-22 Optimum+ Exponential model 96 70 64 47 Generalized power model 261 197 194 164 0.0000 0.0001 0.0002 0.0003 67-22 @ Optimum 76-22 @ Optimum 67-22 @ Optimum+ 76-22 Optimum+ St ra in Asphalt concrete mix Exponential Model Generalized Power Model Figure 5.24. Comparison of critical strain to sustain 50 million cycles for all mixtures.

57 (a) Load History (b) Strain History Time LV D T re ad in g 4 Time Lo ad Figure 5.25. Typical stress/strain history for increasing amplitude uniaxial fatigue test. Strain, m/m St re ss , M Pa Figure 5.26. Stress versus strain plot for several cycles of loading. Pseudo Strain, m/m St re ss , M Pa Figure 5.27. Stress versus pseudo strain plot for several cycles of loading. Pseudo strain St re ss (M Pa ) Figure 5.29. Stress versus pseudo strain plots for PG 76-22 optimum plus. Pseudo Strain St re ss , M Pa Figure 5.28. Stress versus pseudo strain plots for PG 67-22 optimum plus.

The increasing amplitude fatigue test is promising and requires some continued research to refine the method. One of the main challenges in this test is controlling the strain amplitude measured on the specimen. It is difficult to do this by controlling the crosshead during the test because of machine compliance. The amount of compliance changes with different loading levels and is difficult to predict. There are several ways to mitigate this problem. The ideal solution is to control the test using the on-specimen LVDTs, however, great care must be taken in running tests on closed-loop sys- tems in this way. Another alternative is to run load-controlled tests and determine the appropriate load levels by using the measured dynamic modulus and target strain amplitude. A draft Proposed Standard Practice for Predicting the Endurance Limit of Hot Mix Asphalt (HMA) by Pseudo Strain Approach is presented in Appendix B. 58 Table 5.4. Summary of increasing amplitude fatigue test data. Mixture SpecimenNumber Loop Formation Strain Range Stiffness @ 50th Cycle (MPa) Air Voids, % Estimated Endurance Limit 15 <1811 8955 6.9 17 107<LF<121 11594 6.7 67-22 Opt 18 <2291 7927 6.6 ~120 1 150<LF<262 14756 2.2 2 247<LF<345 17698 1.5 ~250 6 67<LF<82 7747 3.6 8 94<LF<147 9752 2.7 67-22 Opt+ 10 73<LF<155 10653 3.0 ~150 1 <2361 8997 1.5 3 <2371 8896 1.9 ~230 6 59<LF<125 11250 3.1 7 102<LF<225 7905 3.2 8 110<LF<123 9859 2.7 9 96<LF<240 6636 3.7 76-22 Opt+ 10 <1311 8868 2.8 ~115 Note: 1Indicates loop formed at lowest strain level tested. Table 5.5. Overall fatigue endurance limit summary. Estimated Fatigue Endurance Limit (ms) Test Method PG 67-22 Optimum PG 67-22 Optimum+ PG 76-22 Optimum PG 76-22 Optimum+ Generalized power law 261 194 197 164 C versus S Prediction Exponential 96 64 70 47 Low air void 250 230 Increasing Amplitude Fatigue Test High air void 120 150 Not tested 115 estimated endurance limit values for the different mixtures are shown in the last column. Summary of Endurance Limit Values A summary of the fatigue endurance limit values deter- mined from the different test methods is shown in Table 5.5. The estimated endurance limits for the different groups of specimens based on air void content are shown in the table. The C versus S prediction method does not follow ex- pected trends with respect to increasing asphalt content. The increasing amplitude fatigue test shows an increase in endurance limit with an increase in asphalt content for the PG 67-22 mixtures. However, there is not much difference between the estimated endurance limits for the different as- phalt grades.