Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results (2021)

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.

77   Research Approach Overview To facilitate the integration of the PAM results into pavement performance prediction frame- works, the predicted changes in the binder AIPs (log |G*| at 64°C, 10 rad/s in this case) with aging must be related to the corresponding changes in the asphalt mixture properties. Hence, a systematic aging study was conducted whereby mixtures were prepared at multiple labora- tory long-term aging levels and subjected to dynamic modulus and cyclic fatigue tests using an Asphalt Mixture Performance Tester (AMPT). At each aging level, the binder was extracted and recovered from the mixture and subjected to DSR testing to determine the log |G*| at various temperatures and frequencies. The difference between log |G*| at a given long-term aging con- dition and log |G*| at the reference short-term-aging condition was related to the change(s) in the asphalt mixture modulus with aging. The Asphalt Mixture Aging-Cracking (AMAC) model was established to integrate the effects of oxidative aging into pavement performance predic- tion software. Implementation of AMAC requires testing the mixture at the short-term aged condition only and the evolution of log |G*| from PAM. AMAC would then be able to predict the changes in the asphalt mixture’s linear viscoelastic properties and fatigue properties as a function of depth with time. To study the implications of oxidative aging on pavement perfor- mance, simulations of pavement performance that integrate the effects of long-term aging were conducted using FlexPAVE version 1.1 that has been modified with AMAC. Figure 50 outlines the experimental plan. Test Materials Table 16 details the 11 laboratory-mixed, laboratory-compacted mixtures evaluated in this study. The table provides the mixture IDs, sources, and other information regarding binder, gra- dation, and RAP content. All the mixture designs were used in field projects except for RS9.5B with 0% RAP, RS9.5B with 50% RAP, and the ARC mixtures. The remaining eight mixtures used in the field projects were verified against their respective job mix formulas by validating the aggregate gradation, mixture volumetrics, and binder content of the RAP in the RAP-containing mixtures. The other three mixtures were designed in the laboratory in accordance with NCDOT specifications (NCDOT 2018). The RS9.5B 0% and RS9.5B 50% mixtures were designed using the same component aggregate and RAP as the RS9.5B 30% mixture but with a softer virgin binder. The ARC mixture was designed in the lab using siliceous aggregate from North Carolina with ARC BI-0001 binder, which was expected to be highly susceptible to aging given its C H A P T E R 6 Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging

78 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results Binder Testing (Extraction & Recovery, DSR Testing) Material-Specific Kinetics Parameters Prediction of Age- and Depth-Dependent Cracking Properties Loose Mix Oven Aging at 95°C Mixture Performance Testing Dynamic Modulus Test (AASHTO TP 132) AMPT Cyclic Fatigue Test (AASHTO TP 133) Pavement Performance Figure 50. Proposed experimental plan to investigate the effects of binder properties on asphalt mixture performance. Mixture ID Location/Source %RAP NMAS % AC Binder Grade RS9.5B 0% North Carolina 0% 9.5 mm 6.6% PG 64-22 RS9.5B 30% North Carolina 30% 9.5 mm 5.8% PG 58-28 RS9.5B 50% North Carolina 50% 9.5 mm 5.2% PG 58-28 FC12.5D Florida 20% 12.5 mm 5.0% PG 76-22 ARC ARC BI-0001 Binder and North Carolina Aggregate 0% 9.5 mm 6.4% PG 67-22 LTX TexasLTPP section ID: 48-0802 0% 9.5 mm 5.4% AC-20 LSD South DakotaLTPP section ID: 46-0804 0% 12.5 mm 5.9% Pen. 120-150 LWA Washington StateLTPP section ID: 53-0801 0% 9.5 mm 6.1% AR-4000 (AR_40 by AASHTO designation) NCAT N10 Alabama NCAT (4th cycle) section N10 50% 9.5 mm 6.0% PG 67-22 MnRd C.21 Minnesota MnROAD (2016 experiment) cell 21 20% 12.5 mm 5.4% PG 58-34 ACTRL VirginiaALF (2002) – Lane 8 0% 12.5 mm 5.3% PG 70-22 Note: ARC is Asphalt Research Consortium; LTPP is Long-Term Pavement Performance; AASHTO is American Association of State Highway and Transportation Officials; NCAT is National Center for Asphalt Technology; MnROAD is a pavement test track operated by the Minnesota DOT; ALF is Accelerated Loading Facility. Table 16. Properties of selected mixtures for the development of an AMAC model.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 79   chemistry. This ARC mix was included in the experimental study to ensure that AMAC could be applied to binders with high-aging susceptibility. Sample Preparation Methods The sample preparation methods used to refine the PAM largely coincide with those described in Chapter 3 and Chapter 4 but are repeated here for the convenience of the reader. Asphalt Mixture Aging The mixtures were subjected to short-term aging at 135°C for 4 hours in accordance with AASHTO R 30 prior to long-term aging. The long-term oven aging of the loose mixtures was accomplished by separating the mix into several pans such that each pan had a relatively thin layer of loose mix that was approximately equal to the NMAS of the aged mix, as shown in Fig- ure 51. The pans of loose mixture were conditioned in an oven at 95°C and systematically rotated to minimize any effects of an oven temperature gradient and/or draft on the degree of aging. After long-term aging, the materials were taken out of the oven and mixed to obtain a uniform mixture. To prepare performance test specimens, the loose mixture was reheated to the compac- tion temperature for around 90 minutes or until the mixture temperature achieved equilibrium. A portion of the mix was then used to produce compacted performance test specimens, and the remainder was used for binder extraction and recovery and subsequent DSR testing. Each mixture was evaluated at a maximum of four aging levels: one short-term-aging level and three long-term-aging levels that corresponded to various field-aging levels. Table 17 summarizes the laboratory aging durations used for each mixture. Each laboratory-aging level was translated to corresponding field-aging levels as a function of pavement depth using the recalibrated CAI (discussed in Chapter 3). Hourly pavement temperatures for the CAI calcula- tions were obtained from the EICM using the MERRA-2 weather stations listed in Table 17. Fabrication of Performance Test Specimens Small cylindrical performance test specimens (Ø 38 mm × 110 mm) were prepared for the AMPT dynamic modulus and cyclic fatigue tests in accordance with AASHTO PP 99. The compaction effort was based on the target air void contents for gyratory-compacted specimens (Ø 150 mm × 180 mm); however, the actual target air void content was 4.0% ± 0.5% for the cored and sawn small specimens (Ø 38 mm × 110 mm). Trial batches of short-term aged Figure 51. Loose mix in thin layers for long-term aging in an oven.

80 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results mixtures were used to estimate the mass required for the compaction mold. Compaction trials were carried out, and the small specimens were extracted to measure their air void contents. The target mass values for the short-term aged mixtures were determined and adjusted for the long-term aged mixtures based on their measured/estimated maximum specific gravity (Gmm). Each gyratory-compacted specimen was left to cool for 24 hours at ambient temperature and then cored and sawn to obtain four small specimens for performance testing in accordance with AASHTO PP 99. The air void contents were measured for each small specimen using a CoreLok machine to ensure that the air void contents were within the acceptable range. At each aging level, the mixtures were tested to obtain linear viscoelastic and fatigue properties. Because this aging procedure is resource-expensive, the properties were measured at only a few aging levels. Microextraction and Recovery Microextraction and recovery of the asphalt binder from the asphalt mixtures and field cores were undertaken following the procedure proposed by Farrar et al. (2015). This procedure uses a solvent mixture of toluene and ethanol (85:15). The mixture sample size is limited to 200 g to produce approximately 10 g of asphalt binder per extraction, which is adequate for both ATR- FTIR spectrometry testing and DSR testing. To prevent further aging of the binder, the distilla- tion flask was subjected to vacuum pressure of 80.0 ± 0.7 kPa (600 ± 5 mm Hg) under nitrogen gas during the recovery procedure. The recovered samples were then placed in a degassing oven and heated to 130°C for 60 minutes under nitrogen to remove any remaining traces of the sol- vent. In this study, ATR-FTIR spectrometry testing was conducted following extraction and recovery to ensure that no detectable solvent was present prior to DSR testing. Test Methods Asphalt Binder DSR Testing Frequency sweep tests of all the extracted and recovered asphalt binders were conducted at frequencies ranging from 0.1 Hz to 30 Hz and at 5°C, 20°C, 35°C, 50°C, and 64°C in an Anton Paar MCR 302 rheometer using parallel plate geometry. A 1% strain amplitude was applied at all test frequencies and temperatures after ensuring that the results did not deviate from the linear viscoelastic range. The rheological properties analyzed included |G*| at 64°C and 10 rad/s and |G*| master curves. At least two replicates were tested for each binder, and the aging condition was evaluated. Mixture ID Climate Weather Station Used in EICM Long-Term- Aging Durations (Days) Corresponding Field- Aging Durations at 6 mm Depth (Years) Corresponding Field- Aging Durations at 20 mm Depth (Years) RS9.5B 0% Raleigh, NC 0, 4, 7, 17 0, 4, 7, 17 0, 7, 13, 31 RS9.5B 30% Raleigh, NC 0, 2, 4, 7, 17 0, 2, 4, 7, 17 0, 4, 7, 13, 31 RS9.5B 50% Raleigh, NC 0, 4, 7, 17 0, 4, 7, 17 0, 7, 13, 31 FC12.5D Gainesville, FL 0, 4, 7, 17 0, 2.5, 4, 11 0, 4, 7, 18 ARC Raleigh, NC 0, 4, 8, 16 0, 4, 8, 16 0, 7, 14, 29 LTX College Station, TX 0, 4, 8, 17 0, 3, 5, 11 0, 4, 9, 18 LSD Mobridge, SD 0, 4, 8 0, 6, 11 0, 10, 19 LWA Moses Lake, WA 0, 4, 16 0, 5, 19 0, 8, 33 NCAT N10 Anniston, AL 0, 5, 11, 21 0, 4, 9, 17 0, 7, 15, 29 MnRd C.21 Minneapolis, MN 0, 4, 8, 16 0, 6, 12, 24 0, 10, 20,40 ACTRL Richmond, VA 0, 4, 8, 16 0, 4, 8, 16 0, 7, 14, 27 Table 17. Aging durations for 11 mixtures.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 81   Asphalt Mixture Testing Dynamic Modulus Testing. Frequency sweep tests were conducted using an AMPT and small specimen geometry in accordance with AASHTO PP 99. The test frequencies used were 0.1 Hz, 0.5 Hz, 1 Hz, 5 Hz, 10 Hz, and 25 Hz. The test temperatures needed to build the master curves were initially selected in accordance with AASHTO TP 132 and were 4°C, 20°C, and 40°C. However, the dynamic modulus test results from the first set of specimens revealed an insufficient range of data for the highly aged materials. Therefore, most of the long-term aging dynamic modulus tests were conducted at 4°C, 20°C, 40°C, and 54°C and for very stiff mixtures, additional high temperatures up to 75°C were included in the tests. The load ampli- tude was varied by temperature and frequency to maintain an average on-specimen strain level of 63 microstrain (µε). At least two replicates were tested for each mixture and aging condition. Time-temperature shifting was conducted in the storage modulus (E′) domain rather than in the dynamic modulus (|E*|) domain to construct the master curves. The time-temperature shift (tTS) factors theoretically do not differ among a material’s linear viscoelastic properties. However, Chehab (2002) found that the application of time-temperature superposition in the dynamic modulus domain leads to poor isotherm alignment in the phase angle domain. In contrast, when the tTS factors were determined in the storage modulus domain, both dynamic modulus and phase angle isotherms aligned to form smooth master curves. The storage modulus can be calculated from the measured dynamic modulus and phase angle values using Equa- tion (34). The functional forms used to characterize the storage modulus and tTS factor func- tions used in this study are shown in Equation (35) and Equation (37), respectively. Both functions were optimized simultaneously using a nonlinear optimization scheme. The obtained tTS factors were used to shift the dynamic modulus and phase angle data to construct the master curves. The reduced frequency can be calculated using Equation (36). * cos 180 (34)′ = × θ × π    E E ( )( ) ( )′ = δ + ′ − δ + ( )β+γ log log maxE 1 (35) log E f eR fR = × (36)f f aR T = ( ) ( )α − +α −aT T T T Tref ref10 (37)1 2 2 where E′ = storage modulus (kPa), |E*| = dynamic modulus determined via testing (kPa), θ = phase angle determined via testing (°), E′( fR) = storage modulus at a particular reduced frequency (kPa), max E′ = defined using the Hirsch model, δ, β, γ = fitting coefficients, fR = reduced frequency (Hz), f = physical frequency (Hz), aT = time-temperature shift factor at a given temperature, T = temperature (°C), Tref = reference temperature (°C), and α1, α2 = fitting parameters.

82 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results The Hirsch model, as detailed in AASHTO TP 133-19, was used to find the maximum storage modulus value used in Equation (35). The Hirsch model can predict mixture stiffness based on volumetrics and basic material information, such as the voids in mineral aggregate and voids filled with asphalt. A direct implication of the Hirsch model that was found in this study is a fit that underestimates the mixture modulus value at high, reduced frequencies, as will be shown later in this report in the Evolution of Mixture Properties with Long-Term Aging, subsection Linear Viscoelastic Properties. The fitting of the sigmoidal function and shift factor function to construct the master curves for the aged materials is analogous to that used to fit short-term aging data, except for the esti- mation of the minimum and maximum modulus values. The maximum modulus value was calculated using the Hirsch model. At very low temperatures, the mixture volumetrics define the maximum modulus value because the binder component of the mixture is assumed to have a maximum glassy modulus value of 1 gigapascal (GPa) (Christensen, Pellinen, and Bonaquist. 2003). Because the mixture volumetrics are assumed to remain constant as aging progresses, the maximum modulus value calculated using the Hirsch model also remains constant with aging. The master curve trends observed in this research also suggest that the maximum modulus values do not vary with aging level. Similarly, at very high temperatures or very low, reduced frequencies, the effect of the asphalt binder is presumed to be minimal, and the mechanical properties of the asphalt mixture are dominated by the aggregate structure properties. Thus, the minimum value of the modulus was obtained for short-term aging conditions by fitting the sigmoidal function and was applied to all the other aging levels when fitting the sigmoidal model to other aging levels. Cyclic Fatigue Testing Using the Asphalt Mixture Performance Tester. Cyclic fatigue testing was conducted using an AMPT in accordance with AASHTO TP 133-19. The test fre- quency used was 10 Hz. AASHTO TP 133-19 was implemented at the following temperatures: • 9°C for LSD, • 15°C for MnRd C.21 and LWA, • 18°C for RS9.5B0%, RS9.5B30%, RS9.5B50%, ARC, and ACTRL, • 19°C for NCAT N10, • 21°C for FC12.5D, and • 23°C for LTX. Multiple tests were conducted using actuator-controlled strain to achieve different on-specimen strain levels. Many end-failures, i.e., failure outside the linear variable differential transformer (LVDT) measurement range, were encountered during testing, especially for the long-term aged mixtures. Also, for the mixtures that contained limestone, i.e., LTX and LSD, broken aggregate was observed at the failed surfaces in many of the test trials. Both end-failure and broken aggre- gate can complicate cyclic fatigue test analysis for several reasons. End-failure prohibits appro- priate on-specimen displacement measurements by the LVDTs, which leads to erroneous strain measurements and difficulty in determining the number of cycles to failure. Broken aggregate on the failed surface usually is associated with unrealistic brittle failure, which does not comply with the results of fatigue cracking in the mastic phase only. Only results from successful tests (middle failure or failure within the LVDT measurement range, failure in the mastic phase, and failure as defined in AASHTO TP 133-19) were included in the analyses presented in this study. Note that the shimming procedure that was found effective in reducing the end-failure occurrences was not used in this study because all the mixture tests in this study were completed before the shimming procedure was developed.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 83   The cyclic fatigue test data were analyzed using simplified viscoelastic continuum damage (S-VECD) theory, as outlined in AASHTO TP 133-19. S-VECD theory is based on three impor- tant theoretical foundations: the pseudo strain-based elastic-viscoelastic correspondence principle, the work potential theory of continuum damage mechanics, and time-temperature superposition with growing damage. The fatigue behavior of asphalt mixtures characterized using S-VECD theory and determined from merely a few tests can be predicted under dif- ferent loading histories (monotonic versus cyclic), varying rates of loading, different modes of loading (controlled stress versus controlled strain), and various stress/strain amplitudes. This mechanistic-based predictive capability, rather than individual index properties derived from empirically based approaches, is important in interpreting the effects of aging on a variety of asphalt mixtures. The S-VECD model also provides the inputs necessary for the pavement response and performance analyses by FlexPAVE. The calculations involved in calibrating the S-VECD model can be found elsewhere (Underwood, Baek, and Kim 2012). The uniaxial cyclic fatigue tests of the small specimens followed AASHTO TP 133-19, but with three deviations from the specifications for the analysis of test results for highly aged or very stiff mixtures. The first deviation from AASHTO TP 133-19 is in the calculation of the damage evolution rate parameter, α. The α parameter is calculated as shown in Equation (38), where m is the maximum value of the tangential slope of the relaxation modulus versus time in log-log scale. For highly aged materials, the log-log slope of the relaxation modulus versus time plot sometimes contains two peaks, as shown in Figure 52. The relaxation modulus was fitted using the Prony series shown in Equation (39) with 17 elements. The second sharp peak is an artifact of the extrapolation of the data using the Prony series for long reduced times. If more elements are used to fit the Prony series, the second peak disappears. This approach was validated by fit- ting the Prony series with 41 elements. The calculation of α is thus based on m obtained from the first peak and not the second, which coincides with the maximum slope. α = +1 1 (38) m ∑( ) = +∞ − ρ = (39) 1 E t E E eg t g N g 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1.E-06 1.E-03 1.E+00 1.E+03 1.E+06 1.E+09 d lo g E( t) / d lo g (t) Time (s) Figure 52. Log-log slope of relaxation modulus for the damage evolution rate parameter (`) calculation.

84 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results where α = damage evolution parameter, t = time, m = maximum value of the tangential slope of the relaxation modulus versus time plot, E∞ = long-time equilibrium modulus (kPa), Eg = modulus of Prony term number g (kPa), ρg = relaxation time of Prony term g (s), and N = number of Prony terms used. The second deviation from AASHTO TP 133-19 is the definition of the failure point that determines the number of cycles to failure (Nf). The Nf value is defined in AASHTO TP 133-19 as the “cycle in which the measured phase angle drops sharply after a stable increase during cyclic loading.” The drop in phase angle was unclear in many test results of the long-term aged materials. Thus, Nf in this analysis is defined as the cycle in which the product of the modulus and the total number of cycles, |E*| × N, reaches a maximum value after a stable increase during cyclic loading. The difference in the Nf obtained from these two criteria is small for tests that are shorter than around 30,000 cycles, but it is greater for longer tests. The phase angle drop criterion tends to give higher Nf values than those obtained by the drop in |E*| × N. Furthermore, the maximum phase angle often was found to occur after microcracks coalesced into a macrocrack on the surface of the test specimen. Failure is defined as the onset of macrocracking. Therefore, the results sug- gest that the phase angle drop often occurs post-failure. For consistency, the maximum |E*| × N criterion was used to define Nf for both short-term aging and long-term aging data in this study. The third deviation from AASHTO TP 133-19 involves the strain selection guidelines that provide target on-specimen strain levels to achieve fatigue test durations between 5,000 and 40,000 cycles. Although the guidelines provide a systematic method to achieve acceptable test lengths (i.e., between 2,000 and 80,000 cycles), tests conducted at the beginning of the experi- mental program demonstrated that achieving acceptable test lengths for highly aged materials requires target on-specimen strain levels that are much lower than those prescribed for the first test in the guidelines. As such, many tests would be deemed too short to be useful if the guide- lines are followed. Thus, lower strain levels than those suggested in AASHTO TP 133-19 were selected to salvage tests that otherwise would have been deemed too short. The two main engineering properties that result from the S-VECD modeling approach and are to be predicted using AMAC developed in this study are (1) the damage characteristic curve, which is the functional relationship between the integrity (pseudo stiffness), C, of the specimen and the amount of damage, S, in the specimen and (2) the DR failure criterion, which is the average reduction in pseudo stiffness up to failure, as shown in Equation (40). The two resultant sets of curves were found to be independent of the input strain level for a given aging level and mixture. The damage characteristic curves for a given mixture aging-level combination were cumula- tively fitted to the power function shown in Equation (41). ∫ ( ) = −1 (40)0D C dN N R N f f = −1 (41)11 12C C SC where DR = failure criterion, C = pseudo secant modulus or pseudo stiffness, S = amount of damage,

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 85   C11, C12 = fitting parameters, and Nf = number of cycles to failure. In addition to the two engineering properties (C and S), an index parameter, Sapp, was devel- oped by Wang, Underwood, and Kim (2020) to account for both stiffness and fatigue resistance or toughness that affect the cracking potential of a mixture and is based on VECD theory. Sapp was found to be able to distinguish the fatigue performance of various mixtures with differ- ent binder contents, binder grades, RAP contents, binder modification, air void contents, and aggregate gradations (Wang, Underwood, and Kim 2020). The Sapp value is calculated using Equation (42). =    α − α+ α1000 * (42)2 1 1 1 11 1 4 12 S a D C E app T R C Aging Effect in FlexPAVE In Pavement ME, the effect of aging is included in the pavement performance simulations based on the change in the asphalt mixture modulus with time (Applied Research Associates 2004). Although this approach represents significant strides toward accounting for the effects of aging on pavement service life, it neglects the effects of aging on the fatigue resistance of asphalt mixtures. Some studies have attempted to simulate the combined effects of the changes in asphalt mixture modulus and cracking resistance with aging using pavement structural-level analyses. However, these studies assume a single state of aging throughout each performance simulation (e.g., 20-year performance simulations using short-term aged mixture properties versus 20-year performance simulations using long-term aged mixture properties) (Babadopulos et al. 2018, Zhang et al. 2019), that is, in the long-term aging simulations, aged mixture properties were used for the entire simulation of the pavement life without considering the time-dependent evolution of the material properties. Thus, these simulation results may not accurately reflect the effects of oxidative aging on pavement performance. The interaction between the distress mechanisms and the changing material properties with time can be understood only by running realistic simulations of a pavement structure. To investigate the effect of aging on pavement performance, the FlexPAVE version 1.1 com- putational engine was updated to incorporate the evolution of asphalt mixture properties due to aging with respect to both time and pavement depth. The updated FlexPAVE divides the pave- ment life into small segments with fixed aging levels. FlexPAVE analysis assumes that the material properties do not change due to aging during each segment. The depth dependence of aging was incorporated in the updated FlexPAVE by creating sublayers throughout the pavement thickness. Each sublayer is assigned different mixture properties to reflect the aging gradient throughout the pavement depth. In this way, the modified FlexPAVE considers the mixture modulus evolu- tion, tTS factors, damage characteristic curve, and DR failure criterion for each sublayer over time. Accordingly, the effect of aging can be captured in a simplified, yet realistic way. Note that this methodology is a preliminary means to incorporate aging into FlexPAVE. In the future, the evolu- tion of mixture properties with time will be continuous rather than discrete in FlexPAVE. Mixture properties were measured at a maximum of four aging levels in this study. The FlexPAVE modification, which discretizes the service life and depth of the pavement into segments, requires properties that correspond to a minimum of 17 different levels of aging over a 15-year service life. The field aging levels of these 17 segments were converted to corresponding laboratory aging durations at 95°C using the CAI given in Equation (15). Figure 53 presents an illustration of the service life and depth discretization of a pavement and the calculated laboratory aging duration

86 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results for each discrete unit using the climatic conditions of Raleigh, North Carolina, as an example. Linear interpolation of the measured mixture properties was conducted to populate the informa- tion needed for the 17 calculated laboratory aging durations. The pavement performance simulations conducted in this study included both traffic and thermal loading. Simulations using the modified FlexPAVE were compared against simulations before the modification (i.e., using constant short-term aging properties throughout the simula- tion). The significance of thermal loading with aging was investigated by running and compar- ing further simulations with only traffic loading and with both traffic and thermal loading. The simulated pavement structure consisted of a 7-inch (18-cm) asphalt concrete layer, a 10-inch (25.4-cm) aggregate base, and 15-inch (38-cm) subgrade. The traffic input was 1,000 daily equiva- lent single-axle loads (ESALs) or around 7.3 million ESALs over 20 years. The analysis was performed for a 15-year pavement service life. Only surface mixtures were aged and tested in this study, prompted by the fact that the surface layer is the most susceptible to aging. Since no mixture or aging data were gathered for intermediate layers for each section, only one asphalt layer was considered for the FlexPAVE simulations. For each section, the climatic conditions considered were based on the climate weather stations used in the EICM, as shown in Table 17, and thus, in these simulations, FlexPAVE considers the temperature and seasonal variation on an hourly basis. FlexPAVE predicts the distribution of damage within the pavement’s cross sec- tion throughout the service life. The percentage of damage (percent damage) is defined as the ratio of the sum of the damage factors within the reference cross section area to the reference cross section area itself, as shown in Equation (43). ∑ ∑ =     × = = (43)1 1 Percent Damage N N A A f i i M i i M where i = nodal point number in the finite element mesh, M = total number of nodal points in the finite element mesh, N/Nf = damage factor where N = number of load applications and Nf = number of load appli- cations to failure, and Ai = area represented by nodal point i in the finite element mesh. Figure 53. Illustration of ad hoc evolution of material properties in FlexPAVE 1.1.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 87   FlexPAVE 1.1 uses two overlapping triangles to form a reference area within which the damage evolution can be considered. The top of the inverted triangle has a 170-cm-wide base that is located at the top of the surface layer and a vertex that is located at the bottom of the bottom asphalt layer. The 120-cm-wide base of the second triangle is located at the bottom of the bottom asphalt layer, and its vertex is positioned at the surface layer. Figure 54 presents the final shape of these two overlapping triangles. Figure 55 presents an example of a damage contour in a pavement cross section under the wheel path as output by FlexPAVE 1.1. The highest damage value of 1 signifies total failure and is shown in red. The lowest damage value of 0 signifies an intact pavement layer that 170 cm 120 cm Top Bottom Total Combined Asphalt Layers Figure 54. Reference areas for percent damage definitions. Figure 55. Example damage contour of a pavement cross section obtained from FlexPAVE 1.1.

88 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results is shown in blue. The transition in color from blue to red shows the areas where damage is accumulated. In the example shown in Figure 55, the surface of the pavement is completely damaged. The damage decreases with depth until a non-damaged state is reached. However, at the bottom of the pavement and right underneath the wheel path, the pavement seems to incur some damage. Findings and Applications Evolution of Mixture Properties with Long-Term Aging Linear Viscoelastic Properties Figure 56, Figure 57, Figure 58, and Figure 59 show the dynamic modulus master curves in log-log and semi-log scales, the phase angle master curves, and the tTS factors for each mixture at each aging duration, respectively. The long-term aging levels are indicated by the number of days (D) of oven aging at 95°C. The results demonstrate an increase in modulus value and decrease in phase angle with aging, as expected. The changes in both the modulus values and phase angles at low, reduced frequencies (and thus high temperatures) are more pronounced than at high, reduced frequencies (and thus low temperatures). This trend is also expected because the mixture behavior at low, reduced frequencies or high temperatures is associated with the binder behavior, which is the mixture component that undergoes aging. The relative increase in modulus value varies from mixture to mixture; for example, the ARC mix shown in sub figure (e) of each of the four figures exhibits greater changes in modulus value and phase angle at a given reduced frequency due to long-term aging than the FC12.5D mix shown in subfigure (d) of each of the four figures. The tTS factors that are required to generate the master curves change as the aging level increases. A greater shift between isotherms is generally required as the aging level increases because the rate of change of the material properties decreases as the temperature changes. As described, the sigmoidal function and shift factor function outlined in Equation (35) and Equation (37) were used to fit the storage modulus (E′) that was calculated from the measured dynamic modulus and phase angle. Equation (34) uses the Hirsch model (detailed in AASHTO TP 133-19) to find the maximum storage modulus value. A direct implication of the Hirsch model is a fit that underestimates the modulus of the mixture at high, reduced frequencies, as shown in Figure 60 for six mixtures at the short-term aging condition. Thus, care should be taken when predicting the modulus at low temperatures; this underestimation introduced by the Hirsch model was found to be significant in later parts of the analysis when the predicted modulus values with aging were compared against the measured values. Fatigue Damage Properties Table 18 presents the damage evolution (α) values of all the mixtures at different aging levels (in days, D). The α value increases with the number of days because the maximum log-log slope of the relaxation modulus decreases, which signifies that aging decreases the relaxation rate of the material. The two sets of S-VECD analysis results are presented as (1) damage characteristic curves that represent the functional relationship between the integrity (pseudo stiffness, C) of the specimen and the amount of damage, S, in the specimen; and (2) the DR failure criterion, which is the average reduction in pseudo stiffness up to failure, as shown in Equation (39). Figure 61 and Figure 62, respectively, show the damage characteristic curves and the relationship between the summation of (1 − C) and the number of cycles to failure, whose slope is DR, for each mixture at different aging levels.

1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 7D 17D (a)RS9.5B 0% 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 2D 4D 7D 17D RS9.5B 30% (b) 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 7D 17D RS9.5B 50% (c) 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 7D 17D FC12.5D (d) 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 8D 16D ARC (e) 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 8D 17D LTX (f) 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 8D LSD (g) 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 16D LWA (h) 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 5D 11D 21D NCAT N10 (i) 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 5D 8D 16D MnRd C.21 (j) 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 8D 16D ACTRL (k) Figure 56. Dynamic modulus evolution measured with aging in log-log space for (a) RS9.5B 0%, (b) RS9.5B 30%, (c) RS9.5B 50%, (d) FC12.5D, (e) ARC, (f) LTX, (g) LSD, (h) LWA, (i) NCAT N10, (j) MnRd C.21, and (k) ACTRL.

1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 7D 17D RS9.5B 0% (a) 1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 2D 4D 7D 17D RS9.5B 30% (b) 1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 7D 17D RS9.5B 50%(c) 1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 7D 17D FC12.5D(d) 1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 8D 16D ARC (e) 1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 8D 17D LTX(f) 1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 8D LSD (g) 1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 16D LWA (h) 1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 5D 11D 21D NCAT N10(i) 1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 5D 8D 16D MnRd C.21 (j) 1.0E+2 5.1E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 3.0E+4 1.0E-9 1.0E-5 1.0E-1 1.0E+3 1.0E+7 |E *| (M Pa ) Reduced Frequency (Hz) STA 4D 8D 16D ACTRL(k) Figure 57. Dynamic modulus evolution measured with aging in semi-log space for (a) RS9.5B 0%, (b) RS9.5B 30%, (c) RS9.5B 50%, (d) FC12.5D, (e) ARC, (f) LTX, (g) LSD, (h) LWA, (i) NCAT N10, (j) MnRd C.21, and (k) ACTRL.

0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 4D 7D 17D RS9.5B 0%(a) 0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 2D 4D 7D 17D RS9.5B 30%(b) 0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 4D 7D 17D FC12.5D(d) 0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 4D 8D 16D ARC(e) 0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 4D 8D 17D LTX(f) 0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 4D 7D 17D RS9.5B 50%(c) 0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 4D 8D LSD(g) 0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 4D 16D LWA(h) 0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 5D 11D 21D NCAT N10(i) 0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 5D 8D 16D MnRd C.21(j) 0 5 10 15 20 25 30 35 40 45 50 1.0E-9 1.0E-6 1.0E-3 1.0E+0 1.0E+3 1.0E+6 Ph as e An gl e (° ) Reduced Frequency (Hz) STA 4D 8D 16D ACTRL(k) Figure 58. Phase angle evolution measured with aging for (a) RS9.5B 0%, (b) RS9.5B 30%, (c) RS9.5B 50%, (d) FC12.5D, (e) ARC, (f) LTX, (g) LSD, (h) LWA, (i) NCAT N10, (j) MnRd C.21, and (k) ACTRL.

-4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 4D 7D 17D RS9.5B 0% (a) -4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 2D 4D 7D 17D RS9.5B 30% (b) -4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 4D 7D 17D RS9.5B 50% (c) -4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 4D 7D 17D FC12.5D (d) -4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 4D 8D 16D ARC (e) -4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 4D 8D 17D LTX (f) -4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 4D 8D LSD (g) -4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 4D 16D LWA (h) -4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 5D 11D 21D NCAT N10 (i) -4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 5D 8D 16D MnRd C.21 (j) -4 -2 0 2 4 6 8 -20 0 20 40 60 Lo g( a T ) Temperature (°C) STA 4D 8D 16D ACTRL (k) Figure 59. tTS factor evolution measured with aging for (a) RS9.5B 0%, (b) RS9.5B 30%, (c) RS9.5B 50%, (d) FC12.5D, (e) ARC, (f) LTX, (g) LSD, (h) LWA, (i) NCAT N10, (j) MnRd C.21, and (k) ACTRL.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 93   0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 1.0E-10 1.0E-06 1.0E-02 1.0E+02 1.0E+06 E' (k Pa ) Reduced Frequency (Hz) Measurement Sigmoidal Fit ACTRL (a) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 1.0E-10 1.0E-06 1.0E-02 1.0E+02 1.0E+06 E' (k Pa ) Reduced Frequency (Hz) Measurement Sigmoidal Fit LTX (b) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 1.0E-10 1.0E-06 1.0E-02 1.0E+02 1.0E+06 E' (k Pa ) Reduced Frequency (Hz) Measurement Sigmoidal Fit RS9.5B 0% (c) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 1.0E-10 1.0E-06 1.0E-02 1.0E+02 1.0E+06 E' (k Pa ) Reduced Frequency (Hz) Measurement Sigmoidal Fit RS9.5B 50% (d) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 1.0E-10 1.0E-06 1.0E-02 1.0E+02 1.0E+06 E' (k Pa ) Reduced Frequency (Hz) Measurement Sigmoidal Fit FC12.5D (e) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 1.0E-10 1.0E-06 1.0E-02 1.0E+02 1.0E+06 E' (k Pa ) Reduced Frequency (Hz) Measurement Sigmoidal Fit NCAT (f) Figure 60. Effect of Hirsch model estimation of maximum modulus on sigmoidal fitting of short-term aged mixtures: (a) ACTRL, (b) LTX, (c) RS9.5B 0% RAP, (d) RS9.5B 50% RAP, (e) FC12.5D, and (f) NCAT.

94 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results Figure  61 shows an upward shift of the damage characteristic curves as the aging level increases for all mixtures. Generally, the damage characteristic curves of the stiff mixtures tend to be higher than those of the other mixtures; however, this outcome does not imply better or worse performance. Although aging increases the material’s stiffness such that, for a given S value, the aged material exhibits greater stiffness or higher C values, the aged material becomes more prone to damage (i.e., the damage evolution is faster). This phenomenon can be reflected by higher C values at failure, indicating that the material becomes less tolerant to damage com- pared to under short-term aging conditions. The only mixture that shows the opposite trend with respect to C at failure is ACTRL where the damage characteristic curves of the more aged mixtures fall above those of the less aged mixtures, but the C value at failure does not change significantly with aging. An indicator of the material’s diminishing toughness with age is the DR value (Wang and Kim 2017), which exhibits a decreasing trend with aging for a given mixture, as shown in Figure 62. DR is shown as the slope of the relationship passing through zero between the average reduction in pseudo stiffness and the number of cycles to failure. A higher DR value generally indicates better fatigue resistance compared to a lower DR value. Again, ACTRL does not follow the expected trend. The ACTRL mixture’s DR values are similar at all aging levels evaluated. However, the performance of the mixture cannot be evaluated based solely on the position of the damage characteristic curves or DR values because both the modulus and inher- ent fatigue resistance play a role in determining the mixture’s fatigue performance within a pavement. If two mixtures exhibit the same fatigue resistance, but one is stiffer than the other, the stiffer mixture will have a longer fatigue life. Similarly, a more fatigue-resistant mixture will have a longer fatigue life than another mixture of similar stiffness but less fatigue resistance. Sapp is an index parameter that was developed to account for these two factors (stiffness and fatigue resistance or toughness) that affect the cracking potential of a mixture and is based on VECD theory. The Sapp value is calculated using Equation (42). Table 19 shows the Sapp values of the 11 study mix- tures. As shown, the Sapp values decrease dramatically with aging. The only exception is ACTRL where Sapp increases slightly with aging. The LTX mixture shows a relatively non-changing Sapp for the first two aging levels but decreases as aging becomes more severe. Development of Asphalt Mixture Aging-Cracking (AMAC) Model Measuring the asphalt mixture properties at multiple aging levels that span the entire range of in-service conditions on a routine basis is impractical due to time and resource constraints. Therefore, alternative methods are needed to predict the evolution of the asphalt mixture prop- erties with the changes in asphalt binder AIPs that are due to oxidative aging. An AMAC model RS9.5B 0% RS9.5B 30% RS9.5B 50% FC12.5D ARC LTX LSD LWA NCAT N10 MnRd C.21 ACTRL STA 3.66 3.80 3.97 3.66 3.74 2.37 3.54 3.17 3.88 3.72 2.80 2D 3.90 4D 4.01 4.01 4.04 4.05 4.01 2.57 3.84 3.32 3.04 5D 4.10 4.21 7D 4.09 4.10 4.12 4.35 8D 4.24 2.60 3.76 4.25 3.21 11D 4.10 16D 5.05 3.92 4.37 3.43 17D 4.58 4.29 4.17 4.20 2.71 21D 4.47 Table 18. The damage evolution parameter, `, as a function of laboratory aging duration (Days, D).

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 95   0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 2D 4D 7D 17D RS9.5B 30% (b) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 4D 7D 17D RS9.5B 50% (c) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 4D 8D 16D ARC (e) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 4D 16D LWA (h) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 5D 11D 21D NCAT N10 (i) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 5D 8D 16D MnRd C.21 (j) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 4D 8D 16D ACTRL (k) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 4D 8D LSD (g) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 4D 8D 17D LTX (f) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 4D 7D 17D FC12.5D (d) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 C S STA 4D 7D 17D RS9.5B 0% (a) Figure 61. Damage characteristic curve evolution measured with aging for (a) RS9.5B 0%, (b) RS9.5B 30%, (c) RS9.5B 50%, (d) FC12.5D, (e) ARC, (f) LTX, (g) LSD, (h) LWA, (i) NCAT N10, (j) MnRd C.21, and (k) ACTRL.

y = 0.5656x y = 0.5117x y = 0.5209x y = 0.3573x 0E+0 1E+4 2E+4 3E+4 0.0E+0 1.0E+4 2.0E+4 3.0E+4 4.0E+4 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 4D 7D 17D RS9.5B 0% (a) y = 0.5531x y = 0.501x y = 0.4921x y = 0.4038x y = 0.3377x 0E+0 1E+4 2E+4 0.0E+0 1.0E+4 2.0E+4 3.0E+4 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 2D 4D 7D 17D RS9.5B 30% (b) y = 0.4318x y = 0.3727x y = 0.2599x y = 0.1972x 0E+0 2E+3 4E+3 6E+3 8E+3 1E+4 0.0E+0 1.0E+4 2.0E+4 3.0E+4 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 4D 7D 17D RS9.5B 50% (c) y = 0.4766x y = 0.4057x y = 0.3006x y = 0.1815x 0E+0 2E+3 4E+3 6E+3 8E+3 1E+4 0.0E+0 1.0E+4 2.0E+4 3.0E+4 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 4D 7D 17D FC12.5D (d) y = 0.527x y = 0.4719x y = 0.3467x y = 0.192x 0E+0 1E+4 2E+4 3E+4 4E+4 0.E+00 2.E+04 4.E+04 6.E+04 8.E+04 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 4D 8D 16D ARC (e) y = 0.455x y = 0.3564x y = 0.3221x 0E+0 1E+4 2E+4 0.0E+0 2.0E+4 4.0E+4 6.0E+4 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 4D 16D LWA (h) y = 0.4122x y = 0.309x y = 0.269x y = 0.3015x 0E+0 3E+3 6E+3 9E+3 1E+4 0.0E+0 1.0E+4 2.0E+4 3.0E+4 4.0E+4 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 5D 11D NCAT N10 (i) y = 0.6503x y = 0.4127x y = 0.416x y = 0.2465x 0E+0 1E+4 2E+4 0.0E+0 1.0E+4 2.0E+4 3.0E+4 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 5D 8D 16D MnRd C.21 (j) y = 0.3599x y = 0.3682x y = 0.3514x y = 0.3611x 0E+0 1E+4 2E+4 3E+4 4E+4 5E+4 6E+4 0.0E+0 5.0E+4 1.0E+5 1.5E+5 2.0E+5 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 4D 8D 16D ACTRL (k) y = 0.4944x y = 0.5366x y = 0.4249x y = 0.3149x 0E+0 1E+4 2E+4 3E+4 4E+4 5E+4 6E+4 7E+4 0.0E+0 5.0E+4 1.0E+5 1.5E+5 2.0E+5 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 4D 8D 17D LTX (f) y = 0.484x y = 0.4027x y = 0.3776x 0E+0 1E+4 2E+4 3E+4 4E+4 5E+4 6E+4 0.0E+0 5.0E+4 1.0E+5 1.5E+5 Cu m ul at iv e (1 -C ) Nf (Cycle) STA 4D 8D LSD (g) Figure 62. Failure criterion (DR) evolution measured with aging for (a) RS9.5B 0%, (b) RS9.5B 30%, (c) RS9.5B 50%, (d) FC12.5D, (e) ARC, (f) LTX, (g) LSD, (h) LWA, (i) NCAT N10, (j) MnRd C.21, and (k) ACTRL.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 97   is presented herein that can be used to predict the mixture long-term aging properties, assuming that the mixture short-term aging properties are known, whether measured or assumed. For this work, the mixture short-term aging properties were measured. Initially, the mixture properties, as a function of laboratory aging duration, were related to the rate of change in the coefficients of the model parameters for the dynamic modulus master curve, S-VECD damage characteristic curve, and the DR failure criterion [i.e., sigmoidal function given in Equation (35), tTS factor second-order polynomial function given in Equation (37), and the damage characteristic curve power function given in Equation (41)]. Although this method offered a means to predict the various model coefficients in terms of the laboratory aging duration, it was not useful in predicting the mixture long-term aging properties for in-service conditions. The mixture properties need to be characterized in terms of laboratory aging duration that can be converted to field aging durations, but this method would pro- vide only snapshots of the material properties with time instead of a continuous evolution. More information about the development and results obtained from this method are found in Appendix C. An alternative method, therefore, was established to predict the long-term aging properties of asphalt mixtures given the short-term aging mixture properties combined with aging model predictions of log |G*| evolution. This alternative method is based on the time-aging super- position concept. In terms of linear viscoelastic properties, time-aging superposition implies that asphalt mixture master curves that correspond to different aging levels coincide when they are shifted horizontally on the log frequency axis. Here, the time-aging superposition principle is also applied to S-VECD damage characteristic curves and the DR failure criterion. The time- aging superposition concept originated in the polymers field (Bradshaw and Brinson 1997), and its applicability to asphalt mixtures has been verified by several researchers (Masad et al. 2008, Ling et al. 2017). Development of a Framework to Predict Changes in Mixture Modulus with Aging Evaluation of the Time-Aging Superposition Concept for Shifting Modulus Master Curves. If time-aging superposition is applicable, the end result is one master curve (henceforth called an aging master curve) that represents the horizontally shifted individual master curves of dif- ferent aging levels, or, alternatively, the horizontally shifted raw data of all tested age levels, fre- quencies, and temperatures of a single mixture. The horizontal shift is achieved by calculating a reduced frequency using Equation (46) that relies on a total shift factor. This factor is called the “total shift factor” because it is shifting the isotherms not only due to temperature but also the effect of age level. A tTS factor, singly, would shift the isotherms to a reference temperature. Table 19. Evolution of fatigue resistance, represented by Sapp with short-term aging (Days, D). RS9.5B 0% RS9.5B 30% RS9.5B 50% FC12.5D ARC LTX LSD LWA NCAT N10 MnRd C.21 ACTRL STA 21.6 21.4 11.9 13.8 21.7 15.3 14.6 13.2 11.3 21.8 7.8 2D 17.9 4D 19.5 16.0 10.6 8.4 15.4 15.9 9.8 11.3 9.8 5D 6.5 10.4 7D 17.6 13.0 5.5 4.8 8D 9.1 13.2 8.5 9.0 10.1 11D 4.9 16D 2.9 8.2 5.0 11.7 17D 8.3 6.8 3.3 2.7 8.6 21D 5.8

98 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results A common form of the tTS factor function is shown in Equation (44). A time-aging shift (tAS) factor, on the other hand, would shift the isotherms to a reference age level. As will be shown later, Equation (45) is a form of the tAS factor function where log |G*| acts as an aging state variable. The total shift factor would thus shift the isotherms to a reference temperature and age level. ( ) ( )( )= α − + α −log (44)1 2 2a T T T TT ref ref ( )( )= × −log log * log * (45)a c G GA ref = ×f f a for Age Level Tr ij i j& (46) where aT = tTS factor at a given temperature, T = temperature (°C), Tref = reference temperature (°C), α1, α2 = fitting parameters, aA = tAS factor at a given age level, |G*| = dynamic shear modulus at a specific aging level, |G*|ref = dynamic shear modulus measured at the reference age level, c = fitting parameter, aij = total shift factor with respect to temperature i and/or age j, fr = reduced frequency (Hz), and f = frequency (Hz). Figure 63 shows shifting the raw data of the NCAT mixture based on age level (number of days) and temperature. The total shift factor was used to calculate the reduced frequency for each temperature-aging level combination. All aij values were optimized alongside the sigmoidal function parameters used in Equation (35). The gray data points include all the data after the application of both time-temperature and time-aging superposition. The results demonstrate that shifting the raw data on the log frequency axis allows the creation of a single master curve to describe the change in modulus as a function of changing frequency, temperature, and age level. The following sections present a methodology to determine the shift factors. First, whether a single functional form for a total shift factor is feasible is investigated; after this, it is determined 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 3.0E+07 1E-10 0.000001 0.01 100 1000000 1E+10 E' (k Pa ) Reduced Frequency (Hz) STA 5 Days 11 Days 21 Days Sigmoidal Fit Shifted Data (a) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 3.0E+07 1E-10 0.000001 0.01 100 1000000 1E+10 E' (k Pa ) Reduced Frequency (Hz) 4°C 20°C 40°C Sigmoidal Fit Shifted Data (b) Figure 63. Master curve construction derived from STA and LTA raw data for NCAT mixture in terms of (a) age level (days) and (b) test temperature.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 99   that separate functional forms must be used to characterize the tTS and tAS factors. The func- tional forms for both shift factors and a method to calibrate both shift factors are presented. This analysis represents this project’s final recommendation as to how these shift factors should be obtained in practice. Alternative methods have been investigated during this project, but the calibration of those methods was deemed too experimentally demanding, so they are presented in the Appendix C instead. Evaluation of a Single Functional Form for Both tTS and tAS Factors. In Pavement ME, the predicted changes in binder viscosity that are derived from the GAS model are translated to corresponding changes in the asphalt mixture’s dynamic modulus using the time-aging super- position concept. Table 8 provides the GAS model predictive equations for viscosity, whereas Table 20 provides the calculations by which viscosity is used to predict the mixture modulus in Pavement ME. In Pavement ME, the predicted changes in binder viscosity, with aging obtained from the GAS model, are used to calculate the required shift along the log-time axis for modu- lus determination using the difference between the viscosity at the desired aging level and the reference short-term aging condition multiplied by a constant, c, as shown in Table 20, Step 1. The resultant reduced times are used in the asphalt mixture dynamic modulus sigmoidal model to calculate the corresponding asphalt mixture dynamic modulus values as a function of age. The parameter c is calibrated using the relationship between the binder viscosity temperature dependence and the mixture tTS factors determined at the short-term aging condition. Thus, the equation shown in Step 1 in Table 20 is applied for both time-temperature superposition and time-aging superposition. Also, the change in binder viscosity from the reference condition viscosity is a state variable that can be translated to changes in the mixture modulus, regardless of whether the source of the change is temperature or aging. Pellinen and Witczak (2002) demonstrated that the shifting of asphalt mixture isotherms to form a master curve yields good results. Therefore, asphalt mixture modulus prediction accu- racy could be improved if the application of time-temperature superposition is decoupled from time-aging superposition to form the mixture master curve at short-term aging conditions. To this end, the Pavement ME framework was first evaluated with one deviation: the dynamic shear modulus (|G*|) was used instead of viscosity. As discussed previously, Pavement ME assumes that the tAS and tTS factors for a given mixture can be determined using a single function of the difference in log-viscosity values between the desired condition and the reference condition. The shift factor defined by the Pavement ME framework that is recast in terms of |G*| instead of C al cu la tio n of m ix tu re m od ul us a t a ny te m pe ra tu re , a gi ng le ve l, an d/ or d ep th k no w in g th e ch an ge in v is co si ty 1. Calculation of the Reduced Time at Short-Term Aging where a change of viscosity can be due to temperature or age ,log( ) log( ) (log( ) log( ))rr t z Tt t c = time of loading at STA and a reference temperature , = time of loading at any temperature or aging level, = aged viscosity at time t and depth z, MPoise, = viscosity at STA and a reference temperature , and c = parameter determined by nonlinear optimization with sigmoidal parameters at STA. 2. Calculation of Mixture Modulus at the Effective Time * log( )1 rt log E e = dynamic modulus, pounds per square inch (psi), and = parameters describing the shape of the master curve determined by nonlinear optimization at STA. Table 20. Modulus evolution in Pavement ME using the time-aging superposition concept.

100 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results viscosity yields Equation (47). The corresponding reduced frequency is calculated using Equa- tion (48) and input to the sigmoidal function shown in Equation (49) that is calibrated at the short-term aging condition to determine the mixture dynamic modulus at the desired tempera- ture and aging level. ( )( ) = × −log log * log * (47)a c G G ref = × (48)f f ar ( ) = δ + α + ( )β+γ log * 1 (49) log E e fr where a = total shift factor with respect to temperature and/or age, c = fitting parameter, |G*| = dynamic shear modulus at 10 rad/s at a specific temperature and/or aging level, |G*|ref = dynamic shear modulus measured at short-term aging at 21.1°C and 10 rad/s, fr = reduced frequency (Hz), f = frequency (Hz), |E*| = dynamic modulus (kPa), and δ, α, β, γ = fitting parameters. In Pavement ME, the δ, α, β, γ, and c values are determined via nonlinear optimization to minimize the error between the dynamic modulus sigmoidal predictions and measured data that correspond to the short-term aging condition only. The dynamic shear modulus values for this optimization were obtained from the test results of the binders extracted and recovered from mixtures prepared under short-term aging conditions. Temperature-frequency sweep test results were used to construct the dynamic shear modulus master curves using the Christensen- Anderson-Marasteanu (CAM) model. To apply Equation (47), the log |G*| values at each mix- ture test temperature were back-calculated from the fitted CAM model. The difference between the log |G*| at a given mixture test temperature and the log |G*| at the reference temperature in Equation (47) yields the shift factors. Note that because viscosity is a function of only tempera- ture and age, the original form of Equation (47) used in Pavement ME was simple to implement. However, the dynamic shear modulus is also a function of frequency, and so here, the |G*| and |G*|ref values in Equation (47) are at a fixed temperature and age and at 10 rad/s. Binders extracted and recovered from the long-term aged mixtures were tested and used to construct dynamic shear modulus master curves in a process analogous to that used for the binders extracted and recovered from the short-term aged mixtures. The results were used to calculate the dynamic shear modulus values that corresponded to a 10 rad/s frequency at each mixture test temperature and aging level. These dynamic shear modulus values were used to calculate the joint tTS and tAS factors that corresponded to each mixture test temperature and aging level using Equation (47). The reduced frequency values were then calculated using Equa- tion (48) and input to Equation (49) to predict the dynamic modulus values as a function of age and temperature. The predicted dynamic modulus values were compared against the measured dynamic modu- lus data; Figure 64 presents the results. Figure 64 (a) and Figure 64 (b) show the discrepancy between the measured and predicted dynamic modulus data in the reduced frequency domain in semi-log and log-log scales, respectively, for one mixture (NCAT) for illustration. The lines in these graphs represent that the sigmoidal model predictions, and the data points correspond to the measured dynamic modulus data as a function of the reduced frequencies calculated using

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 101   Equations (47) and (48). Figure 64 (a) and Figure 64 (b) show that the Pavement ME scheme introduces errors in the isotherm shifting at the short-term aging condition because the data do not form a smooth curve at the high, reduced frequencies/low temperatures. However, qualita- tively speaking, the shift is reasonable overall in the case of short-term aging. For the long-term aging data, the tTS and tAS are ill-defined due to the poor collapse after shifting. These trends also were observed for all the other mixtures and aging levels considered. The implications of using Equation (47) to define the tTS and tAS are further demonstrated in Figure 64 (c) and Figure 64 (d), where the predicted and measured dynamic modulus values are compared for all of the mixtures evaluated in semi-log scale and log-log scale, respectively. The widespread and slight underprediction bias highlights the need for an improved approach to predict the increase in asphalt mixture modulus as a function of the increase in asphalt binder dynamic shear modulus that is due to aging. Use of Separate Functional Forms for tTS and tAS Factors. Before considering other functional forms, the implications of using Equation (47) to model the temperature dependence of the tTS factors and the age dependence of the tAS factors separately were studied. In this approach, it is theorized that the time and temperature equivalence is captured entirely through the tTS factor, which is independent of aging, and that all the aging effects are manifest in the tAS factor. If this approach, i.e., using Equation (47) for the tAS factor or a similar equation, can be proven to be applicable, then the tTS factor and the modulus master curve can be characterized using short-term aging mixture data. Then, the tAS factor can be known by simply measuring/ predicting the changes in the dynamic shear modulus that are due to oxidative aging. 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 3.0E+07 1.00E-10 1.00E-05 1.00E+00 1.00E+05 |E *| (k Pa ) Reduced Frequency (Hz) STA 21 Days STA Sigmoidal Fit 21 Days Sigmoidal Prediction (a) 5.0E+05 5.0E+06 5.0E+07 1.0E-07 1.0E-02 1.0E+03 1.0E+08 |E *| (k Pa ) Reduced Frequency (Hz) STA 21 Days STA Sigmoidal Fit 21 Days Sigmoidal Prediction (b) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 3.0E+07 0.0E+00 1.0E+07 2.0E+07 3.0E+07 |E *| Pr ed ic te d (k Pa ) |E*| Measured (kPa) (c) R2 = 0.8840 RMSE = 2.17E+06 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E+05 1.0E+06 1.0E+07 1.0E+08 |E *| Pr ed ic te d (k Pa ) |E*| Measured (kPa) (d) Figure 64. Comparison between predictions and measurements of dynamic modulus values for (a) NCAT mixture in frequency domain and semi-log scale, (b) NCAT mixture in frequency domain and log-log scale, (c) all considered mixtures in semi-log scale, and (d) all considered mixtures in log-log scale.

102 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results Equation (47) can be modified to include only the tTS factor, as shown in Equation (50). The properties of the 11 mixtures evaluated were coupled with the extracted and recovered binder properties at the short-term aging level. A 64°C reference temperature was used to be consistent with the PAM, which yields log |G*| at 64°C and 10 rad/s for a specific field-aged condition and pavement depth. ( )( )= × −log log * log * (50), ,10 , ,10a c G GT T STA T rad s STA Tref rad s where aT = mixture tTS factor at temperature, T, cT = fitting parameter, |G*|STA,T,10rad/s = dynamic shear modulus at a short-term aging condition and at T and 10 rad/s, and |G*|STA,Tref,10rad/s = dynamic shear modulus at a short-term aging condition and at a reference temperature and 10 rad/s. For this investigation, shifting was again conducted in the storage modulus (E′) domain rather than in the dynamic modulus (|E*|) domain. The functional form used to characterize the storage modulus master curve is a sigmoidal function analogous to that used in Pavement ME to describe the dynamic modulus master curve, as shown in Equation (35). A second-order polynomial is known to be able to describe the temperature dependence of tTS factors precisely (Witczak 2005). Therefore, optimized tTS factors were obtained by simultaneously fitting the sigmoidal coefficients and tTS factor function parameters in Equation (37) using a nonlinear optimization scheme. To check the validity of Equation (50) to describe the temperature dependence of the tTS factors, the optimized tTS factors obtained as described earlier, along with the difference in log |G*| values, were used to calibrate the fitting parameter, c. The tTS factors were then calculated based on the calibrated c and the difference in log |G*| values to check whether Equation (50) is able to predict the tTS factors that were used to calibrate it. The extracted and recovered binder log |G*| values were calculated at each mixture test temperature and at 10 rad/s as obtained using the fitted master curves and the difference between the log |G*| values at 64°C and each mixture test temperature. Figure 65 (a) shows the relationship between the tTS factors and the difference in log |G*| values for two representative mixtures (NCAT and LTX). Although a strong relationship is evident between the optimized tTS factors and the difference in log |G*| values, the discrepancy observed between the measured points (optimized shift factors) and the fitted lines is significant enough to disturb the isotherm shift needed to form a smooth storage modulus master curve; this phenomenon is evident in Figure 65 (b) through Figure 65 (e). Thus, Equation (50) cannot produce as reliable a tTS factor as the phenomenological-based, second-order polynomial func- tion. Parametric optimization of the variables in Equation (35) can be carried out simultane- ously with those in Equation (37) using short-term aging data through a nonlinear optimization scheme, as previously described. Next, the applicability of Equation (47) to the tAS factor in isolation of the tTS factor was investigated. As opposed to the tTS factors, the tAS factors need to be linked to the changes in binder properties with aging. Equation (47) becomes Equation (51) when written in terms of tAS alone. ( )( ) = × −log log * log * (51), ,10 , ,10a c G GA modulus LTA Tref rad s STA Tref rad s

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 103   where aA = tAS factor, c = fitting parameter, |G*|LTA, Tref, 10rad/s = dynamic shear modulus at a certain long-term aging condition and at the reference temperature and 10 rad/s, and |G*|STA,Tref,10rad/s = dynamic shear modulus at the reference short-term aging condition and at the reference temperature and 10 rad/s. A similar approach was adopted to evaluate the tAS factor as was used to examine the tTS factor. First, the short-term aging master curve and associated tTS function were determined. Then, the tTS factors from the short-term aging analysis were assumed to be equal to those y = 2.4362x y = 1.401x 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 0.0 1.0 2.0 3.0 4.0 5.0 lo g( a T ) log |G* |STA,T,10rad/s -log|G* |STA,Tref,10rad/s NCAT LTX (a) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 0.001 1 1000 1000000 1E+09 E' (k Pa ) Reduced Frequency (Hz) 4°C 20°C 40°C Sigmoidal Fit NCAT Optimized log(aT) (b) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 0.001 1 1000 1000000 1E+09 E' (k Pa ) Reduced Frequency (Hz) 4°C 20°C 40°C Sigmoidal Fit NCAT Predicted log(aT) (c) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 0.001 1 1000 1000000 1E+09 E' (k Pa ) Reduced Frequency (Hz) 4°C 20°C 40°C Sigmoidal Fit LTX Optimized log(aT) (d) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 0.001 1 1000 1000000 1E+09 E' (k Pa ) Reduced Frequency (Hz) 4°C 20°C 40°C Sigmoidal Fit LTX Predicted log(aT) (e) Figure 65. (a) Relationship between tTS factors and difference in log |G*| values, (b) NCAT shift using optimized log (aT), (c) NCAT shift using predicted log (aT), (d) LTX shift using optimized log (aT), and (e) LTX shift using predicted log (aT).

104 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results at each long-term aging condition and were used to construct individual master curves for each aging level. An algorithm was then developed to determine the optimized tAS factors by systematically shiing the long-term aging storage modulus (E′) master curves to coincide with the reference short-term aging master curve. e algorithm nds the dierence in reduced fre- quency between a point on the long-term aging master curve and a corresponding point on the short-term aging master curve with an equal modulus value. A similar procedure was conducted for each measured point, resulting in a vector of tAS factors that were then averaged to obtain the representative tAS shi factor for that aging level. Figure 66 (a) and (b) show the storage modulus master curve shi at each aging level (using only one mixture, NCAT, for illustration) in semi-log scale and log-log scale, respectively. Note that here, the sigmoidal t is that of the short-term aging condition. e tAS factors obtained using this procedure were plotted against the dierence in log |G*| values, similar to the plot given in Figure 65 (a) for the tTS factors. e data needed to create this relationship include the mixture storage modulus master curves at short-term aging and other aging levels and the binder shear modulus at short-term aging and other aging levels at 64°C and 10 rad/s. e binders here were extracted and recovered from laboratory-aged mixtures and tested using the DSR. Figure 67 illustrates the strong relationship between the tAS factors and the dierence in log |G*| values for two mixtures (NCAT and LTX). A similar exercise was conducted for the tTS factors, whereby the signicance of the dierence observed between the measured points 5.0E+05 5.0E+06 5.0E+07 E' (k Pa ) Reduced Frequency (Hz) (b) 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 3.0E+07 100000010000.001 10.000001 100000010000.001 10.000001 E' (k Pa ) Reduced Frequency (Hz) (a) STA 5 Days 11 Days 21 Days Sigmoidal Fit 5 Days - Pre Shift 21 Days - Pre Shift 11 Days - Pre Shift STA 5 Days 11 Days 21 Days Sigmoidal Fit 5 Days - Pre Shift 21 Days - Pre Shift 11 Days - Pre Shift Figure 66. Storage modulus (E’) master curve shift to obtain tAS factors in (a) semi-log scale and (b) log-log scale. y = 2.4362x y = 2.434x y = 1.401x y = 1.0018x 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 0.0 1.0 2.0 3.0 4.0 5.0 lo g( a) log |G*|-log|G*|ref NCAT tTS NCAT tAS LTX tTS LTX tAS Figure 67. Relationship between tAS factors and tTS factors versus the difference in log |G*|.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 105   (optimized shift factors obtained using the algorithm) and the fitted line on the smooth master curve shift was studied. Figure 68 (a), (b), (d), and (e) present the results for the two mixtures. These results suggest that the tAS factors are not sensitive to the differences observed in Fig- ure 67 between the optimized and predicted log(aA) values. This finding also entails that Equa- tion (51) is valid for characterizing the age dependence of tAS factors based on the changing binder properties with aging. Note that the sigmoidal fit shown is that of the short-term aging condition. The results also demonstrate that Equation (37) and Equation (51) should be used for the tTS factors and tAS factors, respectively. Because the short-term aging storage modulus data can be used to fit the sigmoidal function and tTS factor function, the tAS function is the only other component that is needed to predict the storage modulus at any other aging level given an aging model to predict the dynamic shear modulus evolution with aging. With the dynamic shear modulus known, either measured in the laboratory as demonstrated in the previous analysis or predicted using the PAM, the fitting parameter c is effectively the only parameter needed to predict the long-term aging storage modulus value. Note that, because the short-term aging data are used to fit the sigmoidal function and the tTS factor function, only one set of tTS factors needs to be applied across all age levels. In other words, the tTS factors are assumed to remain constant with aging. This assumption is contra- dictory to the results in Figure 59 that show the change in tTS factor function with aging; nonetheless, it is a necessary assumption for this analysis approach. During this investigation, an interesting correlation was observed. Figure 67 shows the tAS and tTS factor values with respect to differences in the logarithm of the dynamic shear modulus; a close correlation between these two functions is evident. Recall that Pavement ME supposes that both functions are the same, and Figure 67 provides some data to support that supposition, at least as an approximation. Of course, the error in the approximation is somewhat large when 0E+0 1E+7 2E+7 3E+7 1E-01 1E+03 1E+07 1E+11 1E+15 E' (k Pa ) Reduced Frequency (Hz) Sigmoidal Fit STA 5 Days 11 Days NCAT Optimized log(aA) (a) 0E+0 1E+7 2E+7 3E+7 1E-01 1E+03 1E+07 1E+11 1E+15 E' (k Pa ) Reduced Frequency (Hz) Sigmoidal Fit STA 5 Days 11 Days 21 Days NCAT Fitted log(aA) (b) 0E+0 1E+7 2E+7 3E+7 1E-01 1E+03 1E+07 1E+11 1E+15 E' (k Pa ) Reduced Frequency (Hz) Sigmoidal Fit STA 4 Days 8 Days 17 Days LTX Optimized log(aA) (d) 0E+0 1E+7 2E+7 3E+7 1E-01 1E+03 1E+07 1E+11 1E+15 E' (k Pa ) Reduced Frequency (Hz) Sigmoidal Fit STA 4 Days 8 Days LTX Fitted log(aA) (e) 0E+0 1E+7 2E+7 3E+7 1E-01 1E+03 1E+07 1E+11 1E+15 E' (k Pa ) Reduced Frequency (Hz) Sigmoidal Fit STA 5 Days 11 Days 21 Days NCAT Predicted log(aA) (c) 0E+0 1E+7 2E+7 3E+7 1E-01 1E+03 1E+07 1E+11 1E+15 E' (k Pa ) Reduced Frequency (Hz) Sigmoidal Fit STA 4 Days 8 Days 17 Days LTX Predicted log(aA) (f) Figure 68. (a) NCAT shifting using optimized log(aA), (b) NCAT shifting from fitting of log(aA) versus difference in log |G*|, (c) NCAT shifting from fitting of log(aT) versus difference in log |G*|, (d) LTX shifting using optimized log(aA), (e) LTX shifting from fitting of log(aA) versus difference in log |G*|, and (f) LTX shifting from fitting of log(aT) versus difference in log |G*|.

106 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results both tAS and tTS are included because, as the previous analysis shows, slight deviations can translate into large discrepancies in the continuity of the individual isotherms. Nevertheless, this correlation may be accurate enough to calculate the c variable for the tAS factor and thus eliminate the need for dynamic modulus testing of long-term aged mixtures. Figure 68 (c) and (f) show the potential errors associated with using this approximation. Table 21 shows the differ- ences between c values when c is calibrated using measured dynamic shear modulus values and when using tTS data. Using the estimated c values from log(aT) versus the difference in log |G*| values, the storage modulus was predicted for each mixture at multiple aging levels and various temperatures (4°C, 20°C, and 40°C) and frequencies (0.1 Hz, 0.5 Hz, 1 Hz, 5 Hz, 10 Hz, and 25 Hz). Fig- ure 69 (a) and Figure 69 (b) show LOE plots with 576 points that were generated to compare the predicted and measured storage modulus values. Both figures show good agreement between the predicted and measured values with minimal spread around the LOE for all 11 mixtures at different aging levels. However, a discrepancy is evident at high storage modulus values that correspond to the low temperature (4°C). Recall that short-term aging data are used to fit the sigmoidal function. That function is then shifted along the x-axis (reduced frequency) by a certain factor to match the desired aging level. The observed discrepancy exists because the predicted storage modulus values are generated based on the shifted sigmoidal function, which, in this study, was found to underestimate the modulus value at low temperatures when coupled with the Hirsch model. Therefore, to investigate the difference between the measured and predicted storage modulus values without the misleading sigmoidal extrapolation effect (i.e., to investigate only the tAS pre- dictive accuracy), the measured short-term aging storage modulus data themselves were shifted and compared against the measured long-term aging storage modulus data. Linear interpola- tion between the shifted short-term aging data points was conducted to determine the storage modulus values at reduced frequencies that correspond to the measured long-term aging data points. Figure 69 (c) and Figure 69 (d) present comparisons between the measured long-term aging storage modulus values and interpolated (or predicted) storage modulus values with 440 data points. Both figures demonstrate that the discrepancy is indeed due to the sigmoidal extrapolation. The good agreement and small spread around the LOE indicate that using Equa- tion (51), with c values estimated from the log(aT) versus difference in log |G*| relationship, to calculate the tAS factors and using Equation (37) that is calibrated based on mixture short-term Optimized fitting parameter (from measured tAS factor relationship with difference in log |G*| values) Estimated fitting parameter (from tTS factor relationship with difference in log |G*| values) RS9.5B 0% 1.27 1.55 RS9.5B 30% 1.77 1.71 RS9.5B 50% 1.80 1.93 FC12.5D 1.76 1.92 ARC 1.28 1.69 LTX 1.00 1.40 LSD 1.22 1.52 LWA 1.31 1.56 NCAT N10 2.43 2.44 MnRd C.21 1.36 1.66 ACTRL 1.03 1.42 Table 21. Fitting parameter estimates for tAS factor function for master curve predictions.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 107   aging data to calculate the tTS factors, provide good storage modulus predictions with aging. Another functional form for fitting short-term aging storage modulus data can be considered in future work to mitigate the issue observed in the storage modulus extrapolation at high, reduced frequencies. The tTS and tAS factors obtained from shifting in the storage modulus domain were applied within the dynamic modulus domain to evaluate the established AMAC’s accuracy, as these fac- tors represent the primary inputs for ME pavement analysis frameworks. The measured dynamic modulus values at short-term aging were shifted and compared against the measured long-term aging dynamic modulus data. A similar interpolation method to that described above was fol- lowed to formulate the comparisons between the measured and predicted dynamic modulus 0.0E+0 5.0E+6 1.0E+7 1.5E+7 2.0E+7 2.5E+7 3.0E+7 0.0E+0 1.0E+7 2.0E+7 3.0E+7 E' P re di ct ed (k Pa ) E' measured (kPa) Universal Shift Effective Time Shift LOE (a) 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E+5 1.0E+6 1.0E+7 1.0E+8 E' P re di ct ed (k Pa ) E' measured (kPa) Universal Shift Effective Time Shift LOE (b) 0.0E+0 5.0E+6 1.0E+7 1.5E+7 2.0E+7 2.5E+7 3.0E+7 0.0E+0 1.0E+7 2.0E+7 3.0E+7 E' P re di ct ed (k Pa ) E' measured (kPa) (c) 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E+5 1.0E+6 1.0E+7 1.0E+8 E' P re di ct ed (k Pa ) E' measured (kPa) (d) 0.0E+0 5.0E+6 1.0E+7 1.5E+7 2.0E+7 2.5E+7 3.0E+7 0.0E+0 1.0E+7 2.0E+7 3.0E+7 |E *| Pr ed ic te d (k Pa ) |E*| measured (kPa) (e) R2 = 0.9574 RMSE = 1.15E+06 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E+5 1.0E+6 1.0E+7 1.0E+8 |E *| Pr ed ic te d (k Pa ) |E*| measured (kPa) (f) Figure 69. Comparison of measured and predicted storage modulus (E) values in (a) arithmetic scale and (b) log-log scale; comparison of measured and predicted E values independent of sigmoidal extrapolation in (c) arithmetic scale and (d) log-log scale; and comparison of measured and predicted dynamic modulus (|E*|) values independent of sigmoidal extrapolation in (e) arithmetic scale and (f) log-log scale.

108 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results data shown in Figure 69 (e) and Figure 69 (f ). Again, the agreement and small spread around the LOEs demonstrate that the tAS factor using Equation (51) and assuming that tTS factors do not vary with aging [i.e., use of tTS factors for all age levels obtained from short-term aging data using Equation (37)] provide good dynamic modulus predictions with aging. Because the tAS factors are not sensitive to the c values used in Equation (51), an average c value of 1.71 was used in this study to calculate the tAS factors and make the predictions. As shown in Figure 69 (a) and Figure 69 (b), the spread increases along the LOE, but the agreement remains good. The advantage of using a universal c value is testing ease. No binder dynamic shear modulus measurement is needed to make storage modulus and dynamic shear predic- tions with aging. The decrease in the predictive accuracy is considered acceptable nonetheless, given the benefits of testing simplicity. Note that the universal shift datasets presented in Fig- ure 69 (a) and (b) constitute a circular prediction, i.e., the same mixtures are used to calibrate the universal shift factor as those shown graphically in Figure 69 (a). Although the data look good overall, additional independent validation would strengthen confidence in the universality of the constant. Summary. In summary, two methods can be employed to predict the storage modulus or dynamic modulus at any laboratory or field aging level using the PAM combined with the asphalt mixture master curve at the short-term aging condition. These two methods are defined as Level 1 and Level 2 herein. Level 1 provides greater storage modulus or dynamic modulus predictive accuracy, whereas Level 2 leads to less accurate storage modulus or dynamic modulus predictions but provides ease of use. For Level 1 analysis, either short-term aging dynamic shear modulus values at 10 rad/s at mixture test temperatures or temperature-frequency sweep data for dynamic shear modulus master curve construction at the short-term aging condition are needed to calibrate the fitting parameter (c) in Equation (51). For Level 2 analysis, no additional testing is needed, and a universal c value of 1.71 is used. Development of a Framework to Predict Changes in Mixture Fatigue Properties with Aging The prediction of fatigue properties involves the prediction of the damage characteristic curve and the failure criterion DR. A similar concept to the master curve shifting process presented earlier is used here to predict the damage characteristic curve, where a shift factor is defined in terms of the change in log |G*|, as shown in Equation (52). ( )( ) = × −log log * log * (52), ,10 , ,10a n G GA fatigue LTA Tref rad s STA Tref rad s where aA = shift factor for the damage characteristic curve, n = fitting parameter, |G*|LTA,Tref,10rad/s = dynamic shear modulus at a certain long-term aging condition and at refer- ence temperature and 10 rad/s, and |G*|STA,Tref,10rad/s = dynamic shear modulus at reference short-term aging condition and at reference temperature and 10 rad/s. The shift factors for the modulus master curves presented earlier are obtained by shifting the long-term aging master curve to the reference aging condition for short-term aging. Here, the long-term aging damage characteristic curves are shifted to a reference aging condition of short- term aging by rescaling the damage S, as shown in Equation (53). An algorithm was developed to shift the damage characteristic curves systematically in the C versus log (S) space so that they

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 109   align at C values between 0.4 and 0.6. The obtained optimized shift factors along with the differ- ence in log |G*| values were used to calibrate n in Equation (52). = (53)S S ar A where Sr = rescaled/reduced S, S = amount of damage in the specimen, and aA = shift factor for the damage characteristic curve. Figure 61 shows the damage characteristic curves before shifting. Figure 70 shows the damage characteristic curves shifted to a reference aging condition of short-term aging for two repre- sentative mixtures, NCAT and LTX. The last point in each damage characteristic curve shown in Figure 70 corresponds to the average number of failure cycles obtained from multiple tests conducted at a specific aging condition. To achieve the shift using the developed algorithm, extrapolation was undertaken using Equation (41) to elongate the damage characteristic curves to include C values at around 0.4. The shift factors obtained from this procedure were plotted against the difference in log |G*| values (i.e., log |G*|LTA,Tref,10rad/s – log |G*|STA,Tref,10rad/s). The data needed to create this relationship include the mixture damage characteristic curves at short-term aging and long-term aging conditions as well as the binder dynamic shear modulus at short-term aging and other aging levels at 64°C and 10 rad/s. The binders used herein were extracted and recovered from the conditioned mixtures and tested using the DSR. Figure 71 illustrates the relationship between the shift factor and the difference in log |G*| values for all mixtures. The slopes of the lines in Figure 71 represent the parameter n in Equation (52). 0.0 0.2 0.4 0.6 0.8 1.0 1 3 5 7 C log(S) STA 5 Days 11 Days NCAT (a) 0.0 0.2 0.4 0.6 0.8 1.0 1.0E+0 5.0E+4 1.0E+5 1.5E+5 2.0E+5 C S STA 5 Days 11 Days 21 Days NCAT (b) 0.0 0.2 0.4 0.6 0.8 1.0 1 3 5 7 C log(S) STA 4 Days 8 Days 17 Days LTX (c) 0.0 0.2 0.4 0.6 0.8 1.0 1.0E+0 5.0E+4 1.0E+5 1.5E+5 2.0E+5 C S STA 4 Days 8 Days 17 Days LTX (d) Figure 70. Shifting damage characteristic curves to reference aging condition of short-term aging in (a) C versus log(S) space for NCAT, (b) C versus S space for NCAT, (c) C versus log(S) space for LTX, and (d) C versus S space for LTX.

110 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results Obtaining n directly for a given mixture requires cyclic fatigue testing at multiple age levels, which is not practical. Thus, several attempts were made to estimate the parameter n for the shift factor equation. The best predictions were obtained by assuming a universal n value of 0.2025 based on the averaged n value measured from the study mixtures. The universal n value, mixture cyclic fatigue test results at the short-term aging condition, and PAM predictions of log |G*| allow the shift factor aA in Equation (52) to be calculated, which then allows the damage characteristic curve to be predicted as a function of age level using Equation (54). ( ) ( )= − = − 1 1 (54) 11 11 12 12 12 C C S a C C a S A C A C C where C = pseudo secant modulus, S = amount of fatigue damage in the specimen, C11, C12 = fitting parameters of short-term aging damage characteristic curve, and aA = shift factor for damage characteristic curve for certain long-term aging conditions with universal n = 0.2025. Table 22 presents the n values calculated for each mixture. These values range from 0.13 for FC12.5D to 0.27 for RS9.5B30% with a mean of 0.2025, median of 0.203, and standard deviation of 0.04. Based on Figure 71, some variability is evident in the n values among the mixtures and for the data points within a mixture. Figure 72 presents a comparison of the predicted (dashed lines and labeled with ‘P’ in the legend) and measured (solid lines and labeled with ‘M’ in the legend) damage characteristic curves for all 11 mixtures evaluated in this study. Note that the data shown in Figure 72 con- stitute a circular prediction, i.e., the same mixtures are used to calibrate the universal shift factor as are shown graphically in Figure 72. Although the data look good overall, additional independent validation would strengthen confidence in the universality of the constant. 0.0 0.5 1.0 1.5 2.0 lo g (a A ) f at ig ue y = 0.266x y = 0.2427x y = 0.1582x y = 0.1992x y = 0.203x y = 0.228x y = 0.1558x y = 0.2323x y = 0.1291x y = 0.2162x y = 0.197x 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 log |G*|LTA,Tref,10rad/s – log |G*|STA,Tref,10rad/s Linear (RS9.5B 30%) Linear (MnRd) Linear (ARC) Linear (RS9.5B 0%) Linear (RS9.5B 50%) Linear (LSD) Linear (LWA) Linear (ACTRL) Linear (FC12.5D) Linear (NCAT) Linear (LTX) Figure 71. Relationship between damage characteristic curve shift factors and difference in log |G*| values.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 111   The change in the failure criterion DR can also be predicted as a function of aging level, which in this analysis is based on changes in log |G*| due to aging. At time zero, the predicted DR must be equal to the measured short-term aging value. As the aging level increases—and accordingly, the log |G*| also increases—the predicted DR is expected to decrease. The decrease in DR as a func- tion of age is supported by the measured data shown in Figure 62. The predictive equation for DR must also reach a constant minimum value at the maximum attainable log |G*| value, which according to PAM is a value of 4.5 kPa specifically for field aging conditions (Chapter 4). Recall from Chapter 4 that, based on a small pilot study, the highest log |G*| value at 64°C, 10 rad/s that could be obtained through direct testing was less than 4.5 kPa. In that experiment, the binder that was aged for longer durations crumbled into pieces upon handling and could not be formed into a sample for testing. Therefore, although the modulus of such material might theoretically continue increasing upon aging, the material loses integrity and ceases to have any meaningful performance. In order to meet the above condition for DR prediction (equal to DRSTA at time zero, decreases with increasing aging level, and reaches a minimum value at the maximum attainable log |G*|), Equation (55) is established. ( )= − − ( ) ( )( ) − ∆ ∆0.1 (55) 1.44 log * 4.5 max log * log * , ,10 D D D eLTAR STAR STAR G G G LTA Tref rad s where max Δ log |G*| = 4.5 – log |G*|STA,Tref,10rad/s Δ log |G*| = log |G*|LTA,Tref,10rad/s – log |G*|STA,Tref,10rad/s The above equation yields a minimum value of 0.1 for the maximum log |G*| of 4.5 kPa. Note that the minimum measured DR value was found to be 0.18 for mixture FC12.5D aged for 17 days in the oven at 95°C. A separate sensitivity analysis involving a pavement performance analysis software is needed to optimize the minimum DR value. Such a study is outside the scope of this report. To optimize Equation (55), the ACTRL data at all aging levels and LTX data at 4 days of aging were excluded because DR did not follow the expected decreasing trend with increasing aging level, as shown in Figure 62 (k) and (f) for ACTRL and LTX, respectively. The parameter Mixture ID Optimized n (from measured damage characteristic curve shift factor relationship with difference in log |G*|) values RS9.5B 0% 0.199 RS9.5B 30% 0.266 RS9.5B 50% 0.203 FC12.5D 0.129 ARC 0.158 LTX 0.197 LSD 0.228 LWA 0.156 NCAT N10 0.216 MnRd C.21 0.243 ACTRL 0.232 Table 22. Fitting parameter estimates for shift factor function for damage characteristic curve predictions.

0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 4D-P 4D-M 7D-P 7D-M 17D-P RS9.5B 0% (a) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 4D-P 4D-M 7D-P 7D-M 17D-P 17D-M RS9.5B 30% (b) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 4D-P 4D-M 7D-P 7D-M 17D-P 17D-M RS9.5B 50% (c) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 4D-P 4D-M 7D-P 7D-M 17D-P 17D-M FC12.5D (d) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 4D-P 4D-M 8D-P 8D-M 16D-P ARC (e) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 4D-P 4D-M 8D-P 8D-M 16D-P 16D-M LSD (f) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 4D-P 4D-M 8D-P 8D-M 17D-P 17D-M LTX (g) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 4D-P 4D-M 8D-P 16D-M 16D-P LWA (h) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 5D-P 5D-M 11D-P 11D-M 21D-P 21D-M NCAT (i) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 5D-P 5D-M 8D-P 8D-M 16D-P 16D-M MnRd (j) 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 2.0E+05 4.0E+05 6.0E+05 C S STA-M 4D-P 4D-M 8D-P 8D-M 16D-P 16D-M ACTRL (k) Figure 72. Comparisons of measured (solid lines) and predicted (dashed lines) damage characteristic curves for (a) RS9.5B 0%, (b) RS9.5B 30%, (c) RS9.5B 50%, (d) FC12.5D, (e) ARC, (f) LSD, (g) LTX, (h) LWA, (i) NCAT N10, (j) MnRd C.21, and (k) ACTRL.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 113   obtained from this optimization is considered universal and can be applied to all the other mix- tures (i.e., excluding ACTRL and LTX). To predict DR at any aging level using Equation (55), the data needed to include the DR values at short-term aging and the difference in log |G*| values. Figure 73 shows the predicted DR values plotted against the measured DR values. The excluded ACTRL and LTX values are shown in gray. As demonstrated, the predictions are at times significantly off from the measurements (difference > 0.1), considering the DR variation threshold of ±0.04 reported by Wang and Kim (2017). Although this discrepancy might have implications for performance predictions, the decreasing trend of the predicted DR values with age will at least still allow the integration of the effect of aging on the fatigue resistance in FlexPAVE. Figure 74 shows the decreasing trend of DR with increasing aging level (increasing change in log |G*|), with the measured values shown in blue diamonds and the predicted values shown by the solid line. Note that the data shown in Figure 73 constitute a circular prediction, i.e., the same mixtures are used to calibrate Equation (55) as are shown graphically in Figure 73. Summary of the AMAC Model A framework was developed that can be used to predict the changes in asphalt mixture properties due to long-term aging when knowing (1) the mixture short-term aging properties, whether measured or alternatively obtained and (2) the log |G*| of the binder at LTA level of interest at 64°C, 10 rad/s. The PAM (described in Chapter 4) can be used to predict the required log |G*| at any long-term aging condition. The changes in asphalt mixture properties that can be predicted using this framework include the dynamic modulus, the damage characteristic curve, and the DR failure criterion. For the mixture modulus, the sigmoidal fit at short-term aging can be used to predict the modulus at other aging levels using the time-aging superposition concept. The tAS factor func- tion is shown in Equation (51). Two levels are available to estimate the fitting parameter c in Equation (51). First, and most accurately, c can be estimated to be the slope of the line that passes through zero when plotting log (aT) versus the difference in log |G*| values at the short-term aging condition (an example is given in Figure 67). This approach requires knowing the short- term aging log |G*| value at 10 rad/s at mixture test temperatures. The second approach assumes a constant c that is equal to 1.71 for any mixture. The tTS factors are assumed to be constant with aging and equal to the tTS factors obtained from short-term aging. Both the tTS and tAS factors are used to calculate a reduced frequency following Equation (48) that then is used within the sigmoidal function to predict the mixture modulus at a given long-term aging condition. 0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 D R LT A M ea su re d DR LTA Predicted R2 = 0.5308 RMSE = 0.0643 LTX ACTRL Figure 73. Predicted DR values compared to measured DR values.

114 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 50%3RS9.5B 50 (c) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 30%RS9.5B 30 (b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 50%3LSD (g) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 50%3LTX (f) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 50%3ARC (e) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 50%3NCAT (i) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 50%3LWA (h) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 50%3ACTRL (k) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 0% (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 50%3FC12.5D (d) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 D R log |G*|LTA, Tref, 10 rad/s - log |G*|STA, Tref, 10 rad/s Predicted DR RS9.5B 50%3MnRd (j) Figure 74. Comparisons of measured (data points) and predicted (solid lines) DR for (a) RS9.5B 0%, (b) RS9.5B 30%, (c) RS9.5B 50%, (d) FC12.5D, (e) ARC, (f) LTX, (g) LSD, (h) LWA, (i) NCAT N10, (j) MnRd C.21, and (k) ACTRL. For the damage characteristic curves, Equation (52) is used to calculate a tAS factor that is used to shift the damage characteristic curves for short-term aging to any long-term aging condition of interest following Equation (54). Note that the parameter n in Equation (52) is constant for any mixture and is equal to 0.2025. For DR, Equation (55) is used to calculate DR at a given long- term aging condition of interest. Pavement Performance Simulations Using FlexPAVE Figure 75 presents the FlexPAVE simulation results with integration of the effects of aging. In each subfigure, the percent total damage, the percent top damage, and the percent bottom damage are shown for each condition (with/without aging and with/without thermal loading).

Figure 75. Damage evolution with time: (a) RS9.5B 0%, (b) RS9.5B 30%, (c) RS9.5B 50%, (d) FC12.5D, (e) ARC, (f) LTX, (g) LSD, (h) LWA, (i) NCAT N10, (j) MnRd C.21, and (k) ACTRL.

116 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results “Total damage” refers to the damage calculated using the entire reference cross-sectional area of the pavement; “top damage” refers to the damage calculated using the top part of the total refer- ence area; and “bottom damage” refers to the damage calculated using the bottom part of the total reference area, as defined by Kim et al. (2017) and shown in Figure 54. Note that damage here does not correspond to cracking. An empirical transfer function would have to be used to translate percent damage to percent cracking, which is beyond the scope of this study. Table 23 presents the final percentage of damage after 15 years for each condition. The trends presented in Figure 75 indicate that the changes in the mixture properties over time do not have a significant effect on pavement performance if thermal stress is not con- sidered, as shown by comparing the orange lines (with aging) to the blue lines (without aging) in Figure 75. Traffic loading affects the entire pavement section. The magnitude of the induced stress in traffic loading depends on the asphalt mixture’s stiffness and its ability to relieve the traffic stress. The mixture’s modulus value and viscosity are measured using dynamic modulus tests and expressed through stiffness and phase angle master curves. Although aging makes the material stiffer, which in turn reduces the induced traffic stress, aging also embrittles asphalt mixtures. The reduction in traffic stress helps to reduce cracking susceptibility, but the brittleness increases cracking susceptibility. However, when thermal loading is included in the computations, the observed damage increases significantly, as shown by comparing the blue (without thermal) and green (with thermal) lines in Figure 75 for the simulations without aging to the red (with thermal) and orange (without thermal) lines for simulations with aging. The asphalt mixture’s resistance to thermal loading depends on the induced stress, the ability of the material to relieve the stress, and the ability of the material to resist the damage due to the induced stress. Thermal loading, which is like the loading used in a displacement-controlled test, affects the pavement surface. The magnitude of the induced thermal stress in thermal loading depends on the asphalt mixture’s Mixture ID With Thermal Loading No Thermal Loading Total Damage Bottom Damage Top Damage Total Damage Bottom Damage Top Damage RS9.5B 0% Aging 40.05 7.40 60.78 2.20 5.67 0.00No Aging 7.76 6.43 8.61 2.47 6.36 0.01 RS9.5B 30% Aging 40.82 7.08 62.24 2.15 5.53 0.00 No Aging 6.00 5.96 6.02 2.12 5.44 0.00 RS9.5B 50% Aging 72.96 30.38 100 2.82 7.25 0.00 No Aging 49.31 8.90 74.97 2.57 6.62 0.00 FC12.5D Aging 100 100 100 8.82 22.80 0.00No Aging 59.48 18.66 85.40 4.56 11.73 0.01 ARC Aging 46.67 8.49 70.91 2.17 5.57 0.00No Aging 4.72 5.08 4.50 1.95 5.02 0.00 LTX Aging 89.14 72.04 100 19.52 38.86 7.25No Aging 31.73 37.85 27.85 17.44 37.20 4.90 LSD Aging 51.14 18.84 71.65 6.12 15.71 0.04No Aging 16.92 13.31 19.21 5.10 13.05 0.05 LWA Aging 29.12 16.61 37.06 6.45 16.52 0.06No Aging 6.52 14.97 1.16 5.83 14.89 0.08 NCAT N10 Aging 100 100 100 6.08 15.65 0.01No Aging 81.11 51.38 100 4.32 11.11 0.00 MnRd C.21 Aging 65.69 23.10 92.74 3.47 8.93 0.01No Aging 30.93 9.56 44.50 2.99 7.67 0.01 ACTRL Aging 50.56 27.17 65.42 10.16 25.55 0.39No Aging 19.62 29.83 13.15 12.18 29.70 1.05 Table 23. Percentage of damage at end of 15-year simulation.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 117   stiffness. Aging increases the stiffness (i.e., increases the induced stress), decreases the phase angle (i.e., decreases the ability of the mixture to relieve the stress), and makes the material more brittle (i.e., decreases the tolerance of the material to damage). Accordingly, as pavement sections age, the deteriorating effect of thermal stress and the likelihood of top-down cracking both increase. The effect of aging was relatively small in the simulations without thermal stress (orange and blue lines) compared to those with thermal stress (red lines to the green lines). This find- ing highlights the importance of performing pavement simulations under realistic traffic and thermal loading. The last observation to be made from Figure 75 is that damage with aging manifests mainly as top damage (shown as dotted lines), which is expected because aging affects the surface of the pavement the most. In some sections, such as NCAT N10 and FC12.5D, the top and bottom damage are both 100%. The evolution of the top damage is much faster than that of the bottom damage although the percentage of damage at the end of the service life is the same (100%). Recall that for this study, the FlexPAVE computational engine was updated to incorporate the evolution of asphalt mixture properties due to aging with respect to both time and pavement depth. The updated FlexPAVE divides the pavement life into small segments with fixed aging levels. FlexPAVE analysis assumes that the material properties do not change as a function of aging during each segment. The depth dependence of aging was incorporated by creating sublayers throughout the pavement thickness. Each sublayer was assigned different mixture properties to reflect the aging gradient along pavement depth. Note that this methodology is a preliminary means to incorporate aging into FlexPAVE and is the cause for the discontinuities in percent damage shown in Figure 75. In the future, the evolution of mixture properties with time in FlexPAVE will be continuous rather than discrete. Summary A systematic aging study of 11 mixtures was conducted in this project. The study followed the long-term aging protocol proposed by the original NCHRP Project 09-54 whereby each mixture was subjected to different levels of aging. The linear viscoelastic properties and fatigue properties of the study mixtures were measured. The mixtures exhibited an increase in modulus value, a decrease in phase angle, and a change in tTS factors with aging. The fatigue analysis results show a general deterioration in performance for all the mixtures except one, ACTRL. The deteriora- tion is indicated by higher and shorter damage characteristic curves, lower DR values, and lower Sapp values in comparison to the short-term aging results. AMAC, a model to predict the mixture modulus and fatigue properties with long-term aging, was also developed in this study. The coupling of AMAC with the dynamic shear modulus (|G*|) predictions using PAM is promising for use with new pavement analysis software. AMAC was shown to be applicable to modern mixtures, including high RAP-containing mixtures, polymer- modified mixtures, and mixtures with low PG binder. For prediction of linear viscoelastic prop- erties, AMAC can be used at two levels. Both levels require the measurement of the mixture E′ (alternatively |E*| and phase angle) master curve under short-term aging conditions. Level 1 requires having the binder dynamic shear modulus at short-term aging at multiple test tempera- tures and long-term aging level of interest at 64°C and 10 rad/s. The binder dynamic shear mod- ulus at the long-term aging condition can be obtained by either measuring or prediction using the PAM discussed in Chapter 4. Level 2 does not require having binder dynamic shear modulus data at short-term aging and instead uses a universal tAS factor. Level 2 still requires the same dynamic shear modulus values at the long-term aging level of interest at 64°C and 10 rad/s. This universal tAS factor was calibrated based on 11 mixtures with different properties, including

118 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results high RAP-containing mixtures, polymer-modified mixtures, and mixtures with low PG binder. Level 1 provides greater accuracy of the |E*| predictions, whereas Level 2 provides relatively less accuracy in the |E*| predictions but provides ease of use. For the prediction of fatigue properties, the binder dynamic shear modulus at long-term aging level of interest at 64°C and 10 rad/s as well as the fatigue properties of the mixture at short-term aging are needed. The effects of the evolution of the material properties on structural performance were studied using FlexPAVE version 1.1. The FlexPAVE computational engine was modified to change the material properties to a stepwise incremental form. The output damage results from the FlexPAVE simulations suggest that the effect of aging on pavement performance is evident only when simulations with realistic traffic and climatic conditions are considered (both traffic and thermal loading). For traffic loading, which is similar to a stress-controlled test, the increased stiffness due to aging reduces the induced traffic stress, which decreases the cracking susceptibility. For thermal loading, which is similar to a displacement-controlled test, the increased stiffness due to aging increases the induced thermal stress, which increases the cracking susceptibility. Aging also decreases the phase angle (i.e., decreases the ability of the mixture to relieve the stress) and makes the material more brittle (i.e., decreases the tolerance of the material to damage), which increases the cracking susceptibility. The competition between increased stiffness and decreased durability due to aging as well as the applied traffic and thermal loading affect the percent of manifested damage. The above preliminary findings highlight the need to consider both traffic and thermal loading in pavement performance simulations and suggest that aging does con- tribute to the deterioration of pavements. Finally, Figure 76 is a flow chart that summarizes the use and inputs required for AMAC and PAM.

Development of a Framework to Predict Changes in Asphalt Mixture Performance Due to Oxidative Aging 119   Figure 76. Flow chart summarizing inputs required for PAM and AMAC.