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

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140 Materials Table 4 presents the materials selected for the systematic aging study. The selected compo- nent materials encompass different aggregate sources and binder types. Based on the interim findings from the development of laboratory aging procedure, a forced draft oven with lateral air convection was used for aging loose asphalt mixtures. Loose mixtures were spread in aluminum pans in a single layer to ensure uniform aging of the material. An aging temperature of 95°C was used as suggested based on the studies documented in the main report. Dynamic Modulus Test Results Figure 9 through Figure 15 present the dynamic modulus master curves for the different asphalt mixtures. The master curves represent the averaged values of two replicates. A significant difference is evident between the dynamic modulus values when the aging duration is increased from short-term aged to longer aging durations. It should be noted that the maximum tempera- ture used to test the dynamic modulus was 40°C. Due to this limitation, the master curves do not show a transition from the linear descending region to the asymptotic region, even for the short-term aged materials. Significant differences are evident between dynamic modulus values at different aging levels. The short-term aged material dynamic modulus master curve has a steeper slope than long-term aged materials. The curvature of the STA master curves is smaller compared to the long-term aged materials. At high reduced frequencies, the dynamic modulus master curves for different aging levels tend to converge to similar values. At high temperatures, much greater variation between dynamic modulus master curves is observed for different aging levels. However, measurements at much lower frequencies or temperatures higher than 40°C are needed to observe the asymptotic behavior at the low-frequency end of the master curve. At very high reduced frequencies, the results show that dynamic modulus master curves tend to converge to similar asymptotes. This behavior is expected as the binder modulus tends to zero and aggregate structure dominates the response. Therefore, with the same aggregate structure, master curves for different aging levels of the same mixture should converge to the same asymptote at very low frequencies. The effect of aging on dynamic modulus time-temperature shift factors (αT) was investigated for different mixtures. Figure 16 shows Log αT versus temperature (4°C, 20°C, 21.1°C, and 40°C) for seven mixtures. The trends suggest an ascending trend for absolute values of αT as the aging level increases, which means shift factors increase at low temperatures and decrease at high temperatures with aging. A polynomial form as presented in Equation (5) was used to represent the shift factors for dynamic modulus master curves. ( ) ( )α = α − + α −log (5)1 2 2T T T TT ref ref A P P E N D I X C Prediction of Mixture Properties Through the Rate of Change of Model Coefficients

Section Asphalt Binder Grade/Modification Aggregate Type Climatic Region Project Mix ID LTPP- SPS 8 South Dakota LSD 120-150 Pen Granite and Limestone Dry/Freeze Washington LWA AR-4000 N/A Wet/Non-Freeze Texas LTX AC-20 Granite and Limestone Wet/Non-Freeze FHWA ALF ALF-Control ACTRL 70-28/SBS Granite Wet/Non-FreezeALF-SBS ASBS 70-22 Granite SHRP AAD SAAD PG 58-28 Granite -AAG SAAG PG 58-10 Granite - Note: LTPP-SPS is Long-Term Performance Program Specific Pavement Study; FHWA ALF is Federal Highway Administration Accelerated Load Facility; SHRP is Strategic Highway Research Program; LSD is LTPP South Dakota mix; LWA is LTPP Washington State mix; LTX is LTPP Texas mix; ACTRL is FHWA ALF Control mix; ASBS is FHWA ALF styrene-butadiene-styrene mix; SAAD is SHRP AAD mix; and SAAG is SHRP AAG. Table 4. Selected sections/material for systematic aging study. 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) ACTRL-STA ACTRL-4D ACTRL-8D ACTRL-16D 0.0E+0 5.0E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) ACTRL-STA ACTRL-4D ACTRL-8D ACTRL-16D Figure 9. Dynamic modulus master curves in log-log and semi-log scales for FHWA ALF Control (ACTRL). 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) LTX-STA LTX-4D LTX-8D LTX-17D 0.0E+0 5.0E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) LTX-STA LTX-4D LTX-8D LTX-17D Figure 10. Dynamic modulus master curves in log-log and semi-log scales for LTPP Texas (LTX). 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) LSD-STA LSD-4D LSD-8D LSD-16D 0.0E+0 5.0E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) LSD-STA LSD-4D LSD-8D LSD-16D Figure 11. Dynamic modulus master curves in log-log and semi-log scales for LTPP South Dakota (LSD).

1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) LWA-STA LWA-4D LWA-16D 0.0E+0 5.0E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) LWA-STA LWA-4D LWA-16D Figure 12. Dynamic modulus master curves in log-log and semi-log scales for LTPP Washington (LWA). |E *| (M Pa ) 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-5 1.0E-2 1.0E+1 1.0E+4 Reduced Frequency (Hz) ASBS-STA ASBS-21D 0.0E+0 5.0E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) ASBS-STA ASBS-21D Figure 13. Dynamic modulus master curves in log-log and semi-log scales for FHWA ALF SBS (ASBS). 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) SAAD-STA SAAD-9D 0.0E+0 5.0E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) SAAD-STA SAAD-9D Figure 14. Dynamic modulus master curves in log-log and semi-log scales for SHRP AAD (SAAD). 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) SAAG-STA SAAG-19D 0.0E+0 5.0E+3 1.0E+4 1.5E+4 2.0E+4 2.5E+4 1.0E-5 1.0E-2 1.0E+1 1.0E+4 |E *| (M Pa ) Reduced Frequency (Hz) SAAG-STA SAAG-19D Figure 15. Dynamic modulus master curves in log-log and semi-log scales for SHRP AAG (SAAG).

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 143   -3 -2 -1 0 1 2 3 0 15 30 45 LTX-STA LTX-4D LTX-8D LTX-17D -3 -2 -1 0 1 2 3 0 15 30 45 LSD-STA LSD-4D LSD-8D LSD-16D Temperature (°C)Temperature (°C) Temperature (°C)Temperature (°C) Lo g α T Lo g α T -3 -2 -1 0 1 2 3 0 15 30 45 ACTRL-STA ACTRL-4D ACTRL-8D ACTRL-16D Lo g α T ACTRL LTX LSD -3 -2 -1 0 1 2 3 0 15 30 45 LWA-STA LWA-4D LWA-16D Lo g α T LWA -3 -2 -1 0 1 2 3 0 15 30 45 ASBS-STA ASBS-21D -3 -2 -1 0 1 2 3 0 15 30 45 SAAD-STA SAAD-9D -3 -2 -1 0 1 2 3 0 15 30 45 SAAG-STA SAAG-19D ASBS SAAD SAAG Lo g α T Lo g α T Lo g α T Temperature (°C)Temperature (°C) Temperature (°C) Figure 16. Log time-temperature shift factor versus temperature for seven mixtures at different aging levels.

144 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results Sigmoidal Function Fit The logistic sigmoidal model presented by Witczak and his colleagues (Pellinen, Witczak, and Bonaquist 2004; Fonseca and Witczak 1996; Mirza and Witczak 1995) is applied in the Pavement ME Design program to model the behavior of asphalt mixtures. The Hirsch model also is used to predict mixture stiffness based on volumetric and basic material information, e.g., the voids in mineral aggregate (VMA) and voids filled with asphalt (VFA), in conjunction with the sigmoidal function. The logistic sigmoidal function, which takes a symmetric form, is represented as Equation (6). ( ) = δ + α + ( )β−γ ξ log * 1 (6) log E e where |E*| = dynamic modulus, δ = minimum modulus value, α = |E*| − δ, is the span of modulus value, β, γ = shape parameters, and ζ = reduced frequency. Parameters γ and β affect the slope and the horizontal position of the turning point or inflection point, respectively. In this equation, β/γ is the location parameter for the reduced frequency at which Log |E*| = δ + α/2 or the inflection point for the sigmoidal function (Rowe, Baumgardner, and Sharrock 2009). The parameter α is the span between the low and high asymptotes and is calculated by subtracting the maximum Log |E*| value from the minimum Log |E*| value, or δ. Figure 17 shows the sigmoidal function and the representation of its parameters. In the Pavement ME Design guide, the maximum dynamic modulus value, |E*|max, which is the maximum dynamic modulus value that the mixture can have, is estimated based on the Hirsch predictive model, as represented in Equations (7) and (8). ( ) ( ) ( ) = −     + ∗       + − − + * 4,200,000 1 100 3 * 10,000 1 1 100 4,200,000 3 * (7) maxE P VMA G VFA VMA P VMA VMA G VFA c b c b Figure 17. Representation of sigmoidal function parameters (after Pellinen, Witczak, and Bonaquist 2004).

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 145   ( ) ( ) ( ) ( ) ( ) ( ) = + + 20 3 * 650 3 * (8) 0.58 0.58P G VFA VMA G VFA VMAc b b where Pc = aggregate contact volume, VMA = voids in mineral aggregates, percent, VFA = void filled with mineral aggregates, percent, and |G*|b = glassy modulus of asphalt binder, usually considered as 1.0 GPa. The sigmoidal model presented as Equations (7) and (8) was applied to all the dynamic modulus test results in this study. The curve-fitting involved non-linear error minimization by altering six parameters, including the two time-temperature shift factors (α1 and α2), and the sigmoidal low asymptotic parameter in addition to the shape factors (δ, γ, and β). The model was first fitted for the short-term aging of each mixture. Then, by fixing δ and |E*|max to the short-term aging values, least squares optimization to solve for parameters was carried out for the other aging durations. As discussed above, it is speculated that at very high temperatures or very low reduced frequencies, the effect of the asphalt binder is minimal, and the mechanical properties of the asphalt mixture are dominated by the properties of the aggregate structure. Therefore, it was assumed that δ does not change with aging level. Further more, based on the predictive Hirsch model used in the Pavement ME Design guide, at very low temperatures, the volumetrics of the mixture define the maximum dynamic modulus value. The master curve trends observed in this research also indicate that, regardless of significant differences between the aging durations of the same mixture at intermediate and relatively high temperatures, the differences tend to be minor at low temperatures. However, this assumption may be examined further by testing the asphalt mixture specimens with different aging durations at lower temperatures in future works. Figure 18 and Figure 19 show the fitted sigmoidal function for the ALF Control and SHRP AAG dynamic modulus master curves at different aging durations, respectively. Prediction of Mixture Master Curve at Different Aging Levels Using M Predicting the effects of the asphalt binder aging properties on an asphalt mixture’s mechan- ical behavior is challenging due to two factors. First, the parameters that can link the aging behavior of the asphalt binder to the mechanical properties of the asphalt mixture must be 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E-05 1.0E-03 1.0E-01 1.0E+01 1.0E+03 1.0E+05 |E *| (k Pa ) Reduced Frequency (Hz) ACTRL-STA Sigmoidal Fit-ACTRL-STA ACTRL-4D Sigmoidal Fit-ACTRL-4D ACTRL-8D Sigmoidal Fit-ACTRL-8D ACTRL-16D Sigmoidal Fit-ACTRL-16D Figure 18. Measured dynamic modulus master curves and fitted sigmoidal functions for ALF Control at different aging levels.

146 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results determined, and second, these parameters must be able to provide the means to estimate the material’s behavior for a wide range of temperatures or loading histories. A study of binder aging behavior suggests that the parameter M may be a suitable property that can indicate and define a binder’s susceptibility to oxidative aging. A higher binder M value indicates that more oxidation reactive components are available, and, therefore, the binder is more susceptible to oxidative aging. On the other hand, fitting models, such as the logistic sigmoidal function that can be defined using only a few parameters, can represent the asphalt mixture dynamic modulus over a wide range of loading times and temperatures. Therefore, an effort was made in this study to eval uate any relationship between the binder M and the parameters of the sigmoidal functions that were fitted to the dynamic modulus master curves of the asphalt mixtures at different aging durations. Figure 20 and Figure 21 show the changes in the two sigmoidal parameters in terms of aging durations. Parameter β increases in the negative direction, which indicates that the inflection point of the fit moves to the left side (lower reduced frequency). Parameter γ, however, decreases, indicating that the slope of the linear region of the sigmoidal fit or master curve decreases with aging. This observation was consistent for all the asphalt mixtures. Furthermore, although linear correlations with high R-squared values were fitted to parameters β and γ with aging durations, 1.0E+04 1.0E+05 1.0E+06 1.0E+07 1.0E+08 1.0E-05 1.0E-03 1.0E-01 1.0E+01 1.0E+03 1.0E+05 |E *| (k Pa ) Reduced Frequency (Hz) SAAG-STA Sigmoidal Fit-SAAG-STA SAAG-19D Sigmoidal Fit-SAAG-19D Figure 19. Measured dynamic modulus master curves and fitted sigmoidal functions for SHRP AAG at different aging levels. y = -0.045x - 1.609 R² = 0.955 y = -0.048x - 2.057 R² = 0.949 y = -0.045x - 0.944 R² = 0.916 y = -0.048x - 1.140 R² = 0.979 y = -0.059x - 0.180y = -0.099x - 0.638 y = -0.058x - 1.389 -3 -2.5 -2 -1.5 -1 -0.5 0 0 5 10 15 20 25 β Aging Duration (Days) ACTRL LTX LSD LWA ASBS SAAD SAAG Figure 20. Parameter a versus aging durations.

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 147   the behavior was not linear. It seems that the changes in values occurred rapidly at the begin- ning and became slower at longer aging durations. This trend also was observed for some binder aging properties, such as the |G*| and carbonyl + sulfoxide area. Table 5 presents the binder M values and slopes of the sigmoidal parameters versus aging. A comparison of the rates of change for β and γ to binder M indicates that no correlation is evident. The slopes of the two parameters versus aging are fairly close among the different mixtures, which may be advantageous for prediction purposes; however, aging susceptibility could not be distinguished among the different mixtures. Although consistent trends were observed for the changes in the sigmoidal parameters in terms of aging, linking these parameters to the aging susceptibility of asphalt binders was unsuccessful. Next, the interaction of the two parameters with binder M was investigated. As discussed earlier, β/γ indicates the inflection point for the sigmoidal parameter or dynamic modulus master curve. Figure 22 presents the β/γ versus aging durations for the different mix- tures. A comparison of the trends for the different mixtures shows that the slopes of β/γ versus aging duration are more mixture source-sensitive compared to the slopes of β and γ alone. Table 6 presents the binder M values and β/γ slopes for the seven mixtures. When these slopes were plotted versus binder M (Figure 23), a relationship between the two variables became evident. A power-form correlation was fitted to the data series using the sum of square error minimization. The power form and the constants are expressed as Equation (9). β γ = + (9)slope aM c b where a = −0.0123, b = −3.9005, and c = 0.1990. Figure 21. Parameter f versus aging durations. y = 0.0084x - 0.5459 R² = 0.895 y = 0.0064x - 0.5067 R² = 0.786 y = 0.0058x - 0.4425 R² = 0.9797 y = 0.0086x - 0.5213 R² = 0.9976 y = 0.0077x - 0.6836 y = 0.0069x - 0.6152 y = 0.006x - 0.85 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 0 5 10 15 20 25 γ Aging Duration (Days) ACTRL LTX LSD LWA ASBS SAAD SAAG ACTRL LTX LSD LWA ASBS SAAD SAAG Binder M 0.743 0.880 0.747 0.865 0.623 1.104 0.572 Slope of β −0.045 −0.048 −0.045 −0.048 −0.059 −0.099 −0.058 Slope of γ 0.0084 0.0064 0.0058 0.0086 0.0077 0.0069 0.0060 Table 5. Binder M and sigmoidal parameters slopes with aging.

148 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results ACTRL LTX LSD LWA ASBS SAAD SAAG Binder M 0.743 0.880 0.747 0.865 0.623 1.104 0.572 Slope of β/γ 0.1638 0.1780 0.1624 0.1741 0.1168 0.1914 0.0918 Table 6. Binder M and sigmoidal parameters slopes with aging. y = 0.1638x + 2.9142 R² = 0.9722 y = 0.178x + 4.052 R² = 0.9424 y = 0.1624x + 2.0812 R² = 0.9781 y = 0.1741x + 2.1296 R² = 0.9986 y = 0.1168x + 0.2636 y = 0.1914x + 1.0369 y = 0.0918x + 1.6347 0.0 2.0 4.0 6.0 8.0 0 5 10 15 20 25 β/ γ Aging Duration (Days) ACTRL LTX LSD LWA ASBS SAAD SAAG Figure 22. Representation of a/f versus aging durations. Using this correlation, the β/γ slope for the corresponding binder M could be obtained. The intercept of β/γ versus aging duration was obtained from the sigmoidal function fitted to the short-term aged material dynamic modulus master curves. Thus, β/γ can be estimated for any mixture at any duration by obtaining the binder M and β/γ of short-term aged materials. The next step was to backcalculate β and γ for each aging duration. The backcalculation of the two parameters required estimating one parameter based on the trends observed for the different mixtures and different aging durations and then calculating the other parameter using the estimated β/γ for each aging duration. Looking at the trends for the two sigmoidal parameters versus aging duration, γ is relatively insensitive to the aging duration compared to parameter β. Therefore, with an averaged slope of 0.0071 for all seven mixtures and γ of the short-term aging of each mixture as the intercept, the γ values at the other aging durations can be estimated. Having the estimated β/γ and γ, parameter β was backcalculated for the different aging durations. The same α and δ of the short-term aged material of each mixture were applied to create the sigmoidal curves for the different aging durations. Figure 24 is a flowchart that explains the steps taken to backcalculate the sigmoidal param- eters from the correlation between binder M and the slope of β/γ versus aging duration. Using the procedure introduced above, sigmoidal parameters can be generated for different aging durations of asphalt mixtures using the corresponding binder M and dynamic modulus master curves of short-term aged materials. The accuracy of the predicted sigmoidal parameters depends mainly on how well the assumed trends represent the actual behavior of the param- eters in terms of aging duration. As discussed previously, a linear trend was assumed for each parameter versus aging duration; however; this assumption is not very accurate. This inaccuracy adds to the error, especially when estimations of γ and β are carried out at short aging durations. In an effort to fit the power functions to γ versus aging, the fit was found to be more accurate

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 149   0 0.05 0.1 0.15 0.2 0.25 0.5 0.7 0.9 1.1 1.3 β/ γ Sl op e M Slope of β/γ Fit β/γ =-0.0123M-3.9005+0.1990 R2=0.9934 Figure 23. Slope of aging durations versus binder M. The fitted power-form curve is also shown as a dashed line. Figure 24. Flowchart for backcalculating sigmoidal parameters from binder M and slope of a/f versus aging duration. Note: STA refers to short-term aged material.

150 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results than the linear correlation; however, the power function’s constants differed significantly among the mixtures. Using the average of those constants created more problems in the shape of the predicted master curves compared to the linear correlations. Based on this finding, linear cor- relations for γ and β and β/γ versus aging duration were considered. The simplicity of using a linear form for the different parameters also was deemed to be a desirable outcome. Figure 25 to Figure 31 present the actual and predicted sigmoidal curves for the different mixtures. Table 7 presents the error encountered for each prediction case. The error for ACTRL and LTX mixtures at 4 days and 8 days of aging is relatively high. However, the high error is mostly observed for low reduced frequencies (or high temperatures), which predicted curves fall lower than the actual curves. This error is mostly due to approximate linear correlations of γ and β with aging. An attempt to use non-linear correlation between parameters and aging duration caused more significant problems. 1.0E+4 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E-5 1.0E-3 1.0E-1 1.0E+1 1.0E+3 |E *| (k Pa ) Reduced Frequency STA Actual - 4 Days Predicted - 4 Days Actual - 8 Days Predicted - 8 Days Actual - 16 Days Predicted - 16 Days ACTRL Figure 25. Sigmoidal fits actual versus predicted for ALF Control. 1.0E+4 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E-5 1.0E-3 1.0E-1 1.0E+1 1.0E+3 |E *| (k Pa ) Reduced Frequency STA Actual - 4 Days Predicted - 4 Days Actual - 8 Days Predicted - 8 Days Actual - 17 Days Predicted - 17 Days LTX Figure 26. Sigmoidal fits actual versus predicted for LTPP Texas.

1.0E+4 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E-5 1.0E-3 1.0E-1 1.0E+1 1.0E+3 |E *| (k Pa ) Reduced Frequency STA Actual - 4 Days Predicted - 4 Days Actual - 8 Dyas Predicted - 8 Days Actual - 16 Days Predicted - 16 Days LSD 1.0E+4 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E-5 1.0E-3 1.0E-1 1.0E+1 1.0E+3 Reduced Frequency STA Actual - 4 Days Predicted - 4 Actual - 8 Dyas Predicted ay Actual - 16 Days Predicted LSD Figure 27. Sigmoidal fits actual versus predicted for LTPP South Dakota. 1.0E+4 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E-5 1.0E-3 1.0E-1 1.0E+1 1.0E+3 |E *| (k Pa ) Reduced Frequency STA Actual - 4 Days Predicted - 4 Days Predicted - 8 Days Actual - 16 Days Predicted - 16 Days LWA Figure 28. Sigmoidal fits actual versus predicted for LTPP Washington. 1.0E+4 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E-5 1.0E-3 1.0E-1 1.0E+1 1.0E+3 |E *| (k Pa ) Reduced Frequency STA Actual - 21 Days Predicted - 21 Days Predicted - 4 Days Predicted - 8 Days ASBS Figure 29. Sigmoidal fits actual versus predicted for ALF SBS.

152 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results 1.0E+4 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E-5 1.0E-3 1.0E-1 1.0E+1 1.0E+3 |E *| (k Pa ) Reduced Frequency STA Actual - 19 Days Predicted - 19 Days Predicted - 4 Days Predicted - 8 Days SAAG Figure 31. Sigmoidal fits actual versus predicted for SHRP AAG. 1.0E+4 1.0E+5 1.0E+6 1.0E+7 1.0E+8 1.0E-5 1.0E-3 1.0E-1 1.0E+1 1.0E+3 |E *| (k Pa ) Reduced Frequency STA Actual - 9 Days Predicted - 9 Days SAAD Figure 30. Sigmoidal fits actual versus predicted for SHRP AAD. Prediction of Time-Temperature Shift Factors As discussed previously in this chapter, a polynomial form with two parameters, α1 and α2, was applied to obtain the time-temperature shift factors for the dynamic modulus master curves. To find a general trend that could explain the behavior of the two parameters as a function of aging duration, all data were plotted together. Figure 32 and Figure 33 show the data for the two parameters versus aging duration. The parameter α1 is a small number, ranging from 0.0002 to 0.0013 for the mixtures studied here. Therefore, it was expected that this parameter would have a small effect on the time-temperature shift factor. The parameter α2 is considerably larger in magnitude than α1, ranging from −0.12 to −0.15, and is, as a matter of fact, more important. Furthermore, α2 shows more consistent trends with age level compared to α1. The general trend that was observed for parameter α1 suggests that the values of α1 converge to approximately the same value of 0.0005 at long aging durations. Therefore, the slope between the α1 of short-term aged mixes and α1 = 0.0005 at 20 days of aging was used to obtain the

Prediction of Mixture Properties Through the Rate of Change of Model Coefcients 153   ASBS SAAD SAAG Reduced Freq. (Hz) 4 8 16 4 8 17 4 8 16 4 16 21 9 19 0.00001 44 33 14 53 39 11 24 19 6 11 -1 -2 0 -1 0.00002 45 32 12 51 38 10 25 20 7 11 -3 -2 0 -1 0.0001 43 27 8 46 33 9 26 22 9 11 -7 -3 0 1 0.0005 39 21 3 38 28 7 27 23 11 10 -10 -5 0 3 0.001 37 18 1 35 26 7 26 24 11 9 -11 -6 0 4 0.005 30 11 -2 26 20 5 26 24 13 7 -13 -7 1 6 0.01 27 8 -3 23 18 5 25 24 13 7 -13 -7 1 6 0.05 19 2 -5 15 13 4 23 23 13 5 -14 -7 1 6 0.1 16 0 -5 12 11 3 22 22 13 4 -14 -7 1 5 0.5 10 -3 -6 6 8 2 19 21 13 2 -13 -7 1 5 1 7 -4 -6 4 6 2 17 20 13 1 -13 -7 1 4 5 3 -6 -6 1 4 2 14 18 12 0 -11 -6 1 3 10 2 -6 -6 0 3 1 13 17 12 0 -11 -5 1 3 50 0 -6 -5 -1 2 1 10 14 11 -1 -10 -4 1 2 100 -1 -6 -5 -2 2 1 9 13 10 -1 -9 -4 1 2 500 -2 -5 -4 -2 1 1 7 11 9 -1 -8 -3 0 1 1000 -2 -5 -4 -2 1 1 6 10 9 -1 -7 -3 0 1 5000 -2 -4 -3 -2 0 0 5 8 7 -1 -6 -2 0 1 10000 -2 -4 -3 -2 0 0 4 8 7 -1 -5 -2 0 1 50000 -2 -3 -2 -2 0 0 3 6 6 -1 -4 -1 0 0 ACTRL LTX LSD LWA Percent Error Table 7. Error associated with dynamic modulus predictions at different number of days of aging in the oven. 0.0E+0 3.0E-4 6.0E-4 9.0E-4 1.2E-3 1.5E-3 0 5 10 15 20 25 α 1 Aging Duration (Days) ACTRL LTX LSD LWA ASBS SAAD SAAG Figure 32. The rst time-temperature shift parameter `1 versus aging duration. -0.18 -0.16 -0.14 -0.12 -0.10 0 5 10 15 20 25 α 2 Aging Duration (Days) ACTRL LTX LSD LWA ASBS SAAD SAAG Average Slope of α2 = -0.0012 Figure 33. Trends for the second time-temperature shift parameter `2 versus aging duration.

154 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results α1 values at different aging durations. When compared with actual α1 values, this approximation resulted in adequate predictions for the different mixtures. To develop an empirical method to predict the parameter α2 using the short-term aged data, an average of the slopes of the α2 versus aging duration was applied for all the mixtures. Except for the SAAG mixture, all the mixtures showed a relatively consistent change in the parameter α2 versus aging duration. The average of the slope of α2 for all the mixtures was −0.0012, which is relatively small. Figure 34 shows the obtained and predicted time-temperature shift factors for the ALF Control mix at different temperatures. Table 8 presents the actual and predicted αT values for all the mixtures. Except for the SAAG mixture, which shows inconsistency with the general α2 trends of the other mixtures, the predictions seem to be good. However, the empirical methods should be examined for their effect on asphalt pavement performance predictions. Cyclic Fatigue Test Results Cyclic direct tension tests on small specimens were conducted in the AMPT. Significant challenges were encountered for some LTPP materials at high aging levels. Multiple tests resulted in broken aggregates in the failure interface. The presence of broken aggregates, either during or post-testing, leads to erroneous fatigue analysis. The two mixtures containing lime- stone, LTPP Texas and LTPP South Dakota, were the mixtures with major broken aggregate issues. For these two mixtures, even testing on short-term aged materials showed some broken aggregates in the cracked surfaces. Figure 35 and Figure 36 show examples of broken aggre- gates in cracked surfaces for LTPP Texas and LTPP South Dakota, respectively. The light colors in the cracked surface are broken aggregates that are mostly limestone. The number of end-failures and specimens showing problems, such as broken aggregates, increased with the aging level for all studied mixtures. However, more test replicates were carried out for the problematic cases. Damage characteristic curves and failure criteria are shown in Figure 37 through Figure 43. The damage characteristic curves presented here are the averaged results of two or more cyclic fatigue test replicates at different strain levels. As expected, the curves shift up with aging. Each curve is represented by a power form of Equation (10). = −1 (10)11 12C C SC -3 -2 -1 0 1 2 3 0 15 30 45 Lo g α T Temperature (°C) ACTRL-STA ACTRL-4D ACTRL-8D ACTRL-16D 4D-Predicted 8D-Predicted 16D-Predicted Figure 34. Actual and predicted shift factors for different temperatures.

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 155   ACTRL Actual LTX Actual STA 4D 8D 16D STA 4D 8D 17D Temp. (°C) Log αT Log αT Log αT Log αT Log αT Log αT Log αT Log αT 4 2.34 2.70 2.66 2.73 2.55 2.71 2.65 2.78 20 0.13 0.15 0.15 0.16 0.15 0.16 0.16 0.17 21.1 0 0 0 0 0 0 0 0 40 -1.95 -2.13 -2.25 -2.47 -2.32 -2.42 -2.57 -2.71 ACTRL Predicted LTX Predicted 4 - 2.39 2.45 2.56 - 2.62 2.68 2.83 20 - 0.14 0.14 0.15 - 0.16 0.16 0.17 21.1 - 0 0 0 - 0 0 0 40 - -2.07 -2.19 -2.43 - -2.43 -2.53 -2.77 LSD Actual LWA Actual STA 4D 8D 16D STA 4D 8D 16D Temp. (°C) Log αT Log αT Log αT Log αT Log αT Log αT Log αT 4 2.15 2.26 2.46 2.58 2.24 2.27 2.54 20 0.13 0.14 0.14 0.16 0.13 0.14 0.15 21.1 0 0 0 0 0 0 0 40 -2.24 -2.24 -2.17 -2.50 -2.07 -2.13 -2.47 LSD Predicted LWA Predicted 4 - 2.25 2.34 2.54 - 2.31 2.53 20 - 0.14 0.15 0.16 - 0.14 0.15 21.1 - 0 0 0 - 0 0 40 - -2.30 -2.37 -2.50 - -2.17 -2.45 ASBS Actual SAAD Actual SAAG Actual STA 4D 21D STA 9D STA 8D 19D Temp. (°C) Log αT - Log αT Log αT Log αT Log αT - Log αT 4 2.57 - 2.76 2.28 2.50 2.46 - 2.55 20 0.14 - 0.17 0.13 0.15 0.14 - 0.15 21.1 0 - 0 0 0 0 - 0 40 -1.99 - -2.65 -2.01 -2.28 -2.16 - -2.46 ASBS Predicted SAAD Predicted SAAG Predicted 4 - - 2.76 - 2.43 - - 2.75 20 - - 0.17 - 0.14 - - 0.17 21.1 - - 0 - 0 - - 0 40 - - -2.73 - -2.25 - - -2.68 Table 8. Actual and predicted time-temperature shift factors for all mixtures.

156 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results Figure 35. Examples of broken aggregates in the crack surface for LTPP Texas. Figure 36. Examples of broken aggregates in the crack surface for LTPP South Dakota. Where parameters C11 and C12 define the intercept and the slope of the power function, respectively. Two failure criteria, DR and GR, were used to interpret the performance of the mixtures under cyclic direct tension testing. No firm conclusion could be drawn by com- paring the sensitivity of the two failure criteria. However, in general, the DR-based crite- rion ranked the fatigue performance of different aging durations more consistently than the GR criterion. A comparison of these two failure criteria for each mixture at different aging durations indicates that the cracking susceptibility of the mixtures increases with aging. However, for some mixtures, the difference between short-term aged and long-term aged materials was not considerable. Nevertheless, the effect of aging on each asphalt mixture’s performance should be considered as the combined effect of change in stiffness (i.e., dynamic modulus value) and fatigue performance.

Prediction of Mixture Properties Through the Rate of Change of Model Coefcients 157   FHWA ALF Control y = 0.4516x y = 0.4555x y = 0.4356x y = 0.4053x 0.0E+0 2.0E+4 4.0E+4 6.0E+4 8.0E+4 0.E+00 5.E+04 1.E+05 2.E+05 2.E+05 Cu m ul at iv e (1 -C ) Nf (Cycle) ACTRL-STA ACTRL-4D ACTRL-8D ACTRL-16D R² = 0.9943 R² = 0.9954 R² = 0.9778 1.0E+0 1.0E+1 1.0E+2 1.0E+3 1.E+03 1.E+04 1.E+05 1.E+06 G R Nf (Cycle) ACTRL-STA ACTRL-4D ACTRL-8D ACTRL-16D 0.0 0.2 0.4 0.6 0.8 1.0 0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 C S ACTRL-STA ACTRL-4D ACTRL-8D ACTRL-16D (a) (b) (c) y = 3E+07x-1.331 y = 4E+07x-1.353 y = 1E+08x-1.422 y = 3E+08x-1.494 Figure 37. Cyclic fatigue test results for FHWA ALF Control, (a) damage characteristic curves, (b) DR failure criteria, (c) GR failure criteria. LTPP Texas G R 0.0 0.2 0.4 0.6 0.8 1.0 0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 C S LTX-STA LTX-4D LTX-8D LTX-17D (a) y = 0.5466x y = 0.5392x y = 0.4251x y = 0.3758x 0.0E+0 1.0E+5 2.0E+5 3.0E+5 4.0E+5 0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 Cu m ul at iv e (1 -C ) Nf (Cycle) LTX-STA LTX-4D LTX-8D LTX-17D (b) R² = 0.9939 R² = 0.979 R² = 0.9995 R² = 0.9756 1.0E-1 1.0E+0 1.0E+1 1.0E+2 1.0E+3 1.0E+4 1.0E+5 1.E+03 1.E+04 1.E+05 1.E+06 Nf (Cycle) LTX-STA LTX-4D LTX-8D LTX-17D (c) y = 4E+07x-1.305 y = 2E+08x-1.474 y = 9E+07x-1.408 y = 1E+08x-1.431 Figure 38. Cyclic fatigue test results for LTPP Texas, (a) damage characteristic curves, (b) DR failure criteria, (c) GR failure criteria.

158 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results LTPP South Dakota 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 5.0E+04 1.0E+05 1.5E+05 2.0E+05 C S LSD-STA LSD-4D LSD-8D LSD-16D (a) y = 0.5152x y = 0.4361x y = 0.3769x y = 0.3632x 0.0E+0 3.0E+4 6.0E+4 9.0E+4 1.2E+5 0.E+00 1.E+05 2.E+05 3.E+05 Cu m ul at iv e (1 -C ) Nf (Cycle) LSD-STA LSD-4D LSD-8D LSD-16D (b) 1.0E+0 1.0E+1 1.0E+2 1.0E+3 1.E+03 1.E+04 1.E+05 1.E+06 Nf (Cycle) LSD-STA LSD-4D LSD-8D LSD-16D (c) G R y = 2E+07x-1.299 y = 4E+07x-1.33 y = 4E+08x-1.526 y = 1E+09x-1.696 Figure 39. Cyclic fatigue test results for LTPP South Dakota, (a) damage characteristic curves, (b) DR failure criteria, (c) GR failure criteria. LTPP Washington 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+00 1.0E+05 2.0E+05 3.0E+05 4.0E+05 C S LWA-STA LWA-4D LWA-16D (a) y = 0.5129x y = 0.4553x y = 0.4424x 0.0E+0 1.0E+4 2.0E+4 3.0E+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) LWA-STA LWA-4D LWA-16D (b) y = 1E+06x-1.023 y = 7E+07x-1.395 y = 2E+07x-1.251 1.0E+0 1.0E+1 1.0E+2 1.0E+3 1.E+03 1.E+04 1.E+05 G R Nf (Cycle) LWA-STA LWA-4D LWA-16D (c) Figure 40. Cyclic fatigue test results for LTPP Washington, (a) damage characteristic curves, (b) DR failure criteria, (c) GR failure criteria.

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 159   FHWA ALF SBS 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+0 2.0E+5 4.0E+5 6.0E+5 C S ASBS-STA ASBS-21D (a) y = 0.7354x y = 0.4704x 0E+00 1E+04 2E+04 3E+04 4E+04 5E+04 0E+00 2E+04 4E+04 6E+04 8E+04 Cu m ul at iv e (1 -C ) Nf (Cycle) ASBS-STA ASBS-21D (b) 1E+00 1E+01 1E+02 1E+03 1E+04 1E+03 1E+04 1E+05 Nf (Cycle) ASBS-STA ASBS-21D (c) G R y = 1E+08x-1.313 y = 5E+07x-1.403 Figure 41. Cyclic fatigue test results for FHWA ALF SBS, (a) damage characteristic curves, (b) DR failure criteria, (c) GR failure criteria. SHRP AAD 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+0 2.0E+5 4.0E+5 6.0E+5 C S SAAD-STA SAAD-9D (a) y = 0.5949x y = 0.5303x 0E+00 1E+04 2E+04 3E+04 4E+04 0E+00 2E+04 4E+04 6E+04 Nf (Cycle) SAAD-STA SAAD-9D (b) R² = 0.9992 R² = 0.9968 1E+00 1E+01 1E+02 1E+03 1E+04 1E+05 1E+02 1E+03 1E+04 1E+05 1E+06 G R Nf (Cycle) SAAD-STA SAAD-9D (c) Cu m ul at iv e (1 -C ) y = 1E+07x-1.149 y = 3E+07x-1.284 Figure 42. Cyclic fatigue test results for SHRP AAD, (a) damage characteristic curves, (b) DR failure criteria, (c) GR failure criteria.

160 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results Prediction of Damage Characteristic Curves at Different Aging Levels The prediction of damage characteristic curves for different aging durations helps simulate performance predictions over a pavement’s lifespan. Likewise, for the prediction of dynamic modulus master curves, the best approach to predict the pseudo stiffness (C) versus damage (S) curves is to determine how the fitting parameters change with aging. Both C and S are calculated using pseudo strain (εR), which means that the shape and position of the C versus S curves also depend on the stiffness of the mixture. The effect of binder aging on mixture stiffness was considered to correlate the C11 and C12 parameters to parameter M, which utilized the same methodology that was used to predict the dynamic modulus master curves. Figure 44 and Figure 45 show the variation of C11 in semi-log scale and C12 arithmetic scale. The slopes of the exponential function for C11 with aging and the linear function for C12 with aging were compared against binder yh, as shown in Figure 46 (a) and (b). A linear correlation is evident between the slope of the exponential function for C11 and the aging duration versus binder M. However, the correlation for the slope of C12 with aging duration versus binder M is non-linear. The correlations were applied to determine the C11 and C12 slopes with aging for each mixture. After determining the slope of C11 with aging in exponential form and that of C12 with aging in linear form, the initial inputs from the short-term aged mixtures were used to estimate the fitting parameters for the other aging durations. This procedure is summarized in the flowchart presented in Figure 47. SHRP AAG 0.0 0.2 0.4 0.6 0.8 1.0 0.0E+0 2.0E+5 4.0E+5 6.0E+5 C S SAAG-STA SAAG-19D (a) y = 0.4283x y = 0.376x 0E+00 1E+04 2E+04 3E+04 4E+04 0E+00 5E+04 1E+05 C um ul at iv e (1 -C ) Nf (Cycle) SAAG-STA SAAG-19D (b) 1E+00 1E+01 1E+02 1E+03 1E+02 1E+03 1E+04 1E+05 1E+06 G R Nf (Cycle) SAAG-STA SAAG-19D (c) y = 1E+07x-1.162 y = 3E+08x-1.53 Figure 43. Cyclic fatigue test results for SHRP AAG, (a) damage characteristic curves, (b) DR failure criteria, (c) GR failure criteria.

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 161   y = 0.0013e-0.063x R² = 0.7884 y = 0.0022e-0.086x R² = 0.999 y = 0.0030e-0.0612x R² = 0.8872 y = 0.002e-0.081x R² = 0.9884 y = 0.0008e-0.0404x y = 0.003e-0.036x y = 0.0072e-0.127x 0.0001 0.001 0.01 0 5 10 15 20 25 C 11 Aging Duration (Days) ACTRL LTX LSD LWA SAAG ASBS SAAD Figure 44. Change of C11 with aging level. C 12 y = 0.0029x + 0.5368 R² = 0.5833 y = 0.0054x + 0.4743 R² = 0.9931 y = 0.0035x + 0.4765 R² = 0.8378 y = 0.0056x + 0.4927 R² = 0.9948 y = 0.0024x + 0.5153 y = 0.0026x + 0.4428 y = 0.0101x + 0.3527 0.3 0.4 0.5 0.6 0 5 10 15 20 25 Aging Duration (Days) ACTRL LTX LSD LWA SAAG ASBS SAAD Figure 45. Change of C12 with aging level. Table 9 presents the C11 and C12 parameters for both actual fit and predictions. In general, the C12 predictions from the binder M and short-term aged mixture properties seem to be more accurate than the C11 predictions. The predicted C11 and C12 parameters were used to develop damage characteristic curves. Figure 48 shows the predicted and measured damage characteristic curves for the different mixtures. The predictions seem to undershoot in most of the cases. Also, the shape of the curves is very sensitive to the C11 values, and this inability to predict C11 makes all the predictions more challenging. Thus, the effect of error when predicting damage characteristic curves on perfor- mance predictions needs to be evaluated.

y = -0.1722x + 0.0655 R² = 0.9821 -0.14 -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 0.00 0 0.5 1 1.5 Sl op e of C 11 M (a) y = 0.000474e2.780691x R² = 0.990617 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.3 0.6 0.9 1.2 Sl op e of C 12 M (b) Figure 46. Slope of (a) C11 and (b) C12 with aging versus binder M. Figure 47. Steps for prediction of C11 and C12 using binder M. Aging at 95°C (Days) Actual C11 Predicted C11 Actual C12 Predicted C12 ACTRL 4 7.73E-04 1.29E-03 0.572 0.536 8 7.50E-04 1.00E-03 0.557 0.551 16 5.31E-04 6.06E-04 0.579 0.581 LTX 4 1.60E-03 1.58E-03 0.492 0.500 8 1.08E-03 1.11E-03 0.515 0.523 17 5.20E-04 5.07E-04 0.568 0.573 LSD 4 1.80E-03 2.67E-03 0.509 0.482 8 1.43E-03 2.07E-03 0.524 0.497 16 8.85E-04 1.24E-03 0.556 0.527 LWA 4 1.16E-03 1.50E-03 0.530 0.511 16 5.07E-04 5.46E-04 0.587 0.575 ASBS 21 2.10E-03 1.92E-03 0.430 0.446 SAAD 9 2.29E-03 2.66E-03 0.443 0.447 SAAG 19 3.75E-04 4.29E-04 0.561 0.560 Table 9. Power function coefficients fitted to actual C versus S curves and predicted based on binder M.

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 163   0.0 0.2 0.4 0.6 0.8 1.0 0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 C S ACTRL-STA ACTRL-4D ACTRL-8D ACTRL-16D Predicted-ALF CTRL-4D Predicted-ALF CTRL-8D Predicted-ALF CTRL-16D ACTRL 0.0 0.2 0.4 0.6 0.8 1.0 0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 C S LTX-STA LTX-4D LTX-8D LTX-17D Predicted-LTX-4D Predicted-LTX-8D Predicted-LTX-17D LTX 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 LSD-STA LSD-4D LSD-8D LSD-16D Predicted-LSD-4D Predicted-LSD-8D Predicted-LSD-16D LSD 0.0 0.2 0.4 0.6 0.8 1.0 0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 C S LWA-STA LWA-4D LWA-16D Predicted-LWA-4D Predicted-LWA-8D Predicted-LWA-16D LWA 0.0 0.2 0.4 0.6 0.8 1.0 0.E+00 2.E+05 4.E+05 6.E+05 C S ASBS-STA ASBS-21D Predicted-ASBS-21D ASBS 0.0 0.2 0.4 0.6 0.8 1.0 0.E+00 2.E+05 4.E+05 6.E+05 C S SAAD-STA SAAD-9D Predicted-SAAD-9D SAAD 0.0 0.2 0.4 0.6 0.8 1.0 0.E+00 2.E+05 4.E+05 6.E+05 C S SAAG-STA SAAG-19D Predicted-SAAG-19D SAAG Figure 48. Measured and predicted damage characteristic curves.

164 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results Prediction of Failure Criteria Using Binder Aging Properties Predicting fatigue resistance is more challenging than predicting stiffness-related properties such as dynamic modulus master curves. Figure 49 shows the evolution of the DR criterion with regard to aging for the different mixtures. The slope of change for DR with aging duration was compared with that of binder M (Figure 50). The correlation does not suggest a strong relation- ship between the slopes of DR and binder M. Regardless of the weak correlation between the slopes of DR and binder M, the relationship was used to predict the DR values at different aging durations of the mixtures. Table 10 shows the measured versus predicted DR values. Considering the DR variation threshold of ±0.04 reported by Wang, Norouzi, and Kim (2016), the prediction for most mixtures seems to be appropriate. This threshold represents the variation that is expected between the results of cyclic fatigue rep- licates for the same asphalt mixtures. However, the error in predicting the DR values should be evaluated in terms of their effect on fatigue performance. Prediction of Changes in Mixture Modulus Using Time-Aging Superposition For this investigation, shifting was conducted in the storage modulus (E’) domain rather than in the |E*| domain. As mentioned previously, Chehab (2002) found that the time-temperature superposition application in the |E*| domain leads to poor isotherm alignment in the phase angle domain. In contrast, when the time-temperature shift (tTS) factors were determined in the E′ domain, they found that both |E*| and phase angle isotherms align to form smooth master curves. If the time-aging superposition is applicable, the end result is one master curve, henceforth called an aging master curve, representing the horizontally shifted individual master curves of different aging levels, or alternatively, the horizontally shifted raw data of all tested age levels, frequencies, and temperatures of a single mixture. The difference between these two shifts (i.e., of the master curves or the raw data) is the tTS factor functions for each age level. If the raw data is shifted, one tTS factor function is assumed for all age levels of that mixture, which could be y = -0.0052x + 0.484 R² = 0.9823 y = -0.0129x + 0.5832 R² = 0.9102 y = -0.0091x + 0.4832 R² = 0.7983 y = -0.0058x + 0.5085 R² = 0.9231 y = -0.0091x + 0.6851 y = -0.0102x + 0.5844 y = -0.0021x + 0.437 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0 5 10 15 20 25 DR Aging Duration (Days) ACTRL LTX LSD LWA ASBS SAAD SAAG Figure 49. Change of DR with aging.

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 165   inaccurate. If the master curves are shifted, different tTS factor functions are obtained for each age level when constructing these master curves ahead of shifting. Figure 51 shows shifting the raw data of the NCAT mixture as delineated based on age level on one hand, and on tem- peratures on the other hand, while setting STA condition as the reference age level and 21.1°C as the reference temperature. It is obvious that a mere horizontal shift of the raw data was able to create a single master curve to describe the modulus change as a function of changing frequencies, temperatures, and age levels. y = -0.0112x + 0.0011 R² = 0.3084 -0.016 -0.012 -0.008 -0.004 0 0 0.2 0.4 0.6 0.8 1 1.2 Sl op e of D R M Slope of DR-Actual Slope of DR-Predicted Figure 50. Slope of DR versus binder M. Aging at 95°C (Days) Actual DR Predicted DR Difference ACTRL 4 0.47 0.45 -0.02 8 0.44 0.42 -0.02 16 0.40 0.37 -0.03 LTX 4 0.57 0.54 -0.03 8 0.45 0.50 0.05 17 0.37 0.43 0.06 LSD 4 0.44 0.53 0.09 8 0.37 0.49 0.12 16 0.36 0.44 0.08 LWA 4 0.47 0.49 0.02 16 0.42 0.39 -0.03 ASBS 21 0.50 0.57 0.07 SAAD 9 0.50 0.49 -0.01 SAAG 19 0.40 0.34 -0.06 Table 10. Measured and predicted DR values for different mixtures at different aging durations.

166 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results The horizontal shift factors needed to create the smooth aging master curve represent total shift factors constituting both tTS factors and time-aging shift (tAS) factors. These total shift factors (a Total) are plotted in Figure 52 in two domains: versus temperature and versus aging duration. Since STA is the reference age level, and hence the tAS factors are null, the shift factors shown in Figure 52 (a) for STA are exclusively the tTS factors. The upward shift shown in Figure 52 (a) for the different aging levels is due to the tAS factors. The tTS factors follow the commonly known form of a second-order polynomial. As mentioned before, the tTS factors for all age levels are assumed constant in this method; this can be shown through the parallelism of the functions shown in Figure 52 (a). Figure 52 (b) shows the total shift factors plotted against the aging duration for each testing temperature. At the reference temperature of 21.1°C where the tTS are null, the shift factors would exclusively be the tAS factors. The shift factors for 20°C shown in Figure 52 (b) are fairly close to those at 21.1°C, which is demonstrated by the total shift factor equaling almost zero at 0 days (STA). The vertical shift shown for the total shift factors of the other temperatures is due to the contribution of the tTS factors. The most note worthy observation from this exercise is perhaps the observed trend that the tAS factors assume. The trend can possibly be considered bilinear, but to describe it in terms that were used before to describe the evolution of log |G*| with aging duration, the behavior of tAS factors exhibits an initial fast period, or a spurt, followed by a slower period with a constant rate. 1.0E+04 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) 1.0E+04 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 51. Master curve construction from STA and LTA raw data: (a) delineated with respect to age level, and (b) and delineated with respect to test temperature. y = 0.0009x2 - 0.1955x + 3.7094 y = 0.0009x2 - 0.1936x + 4.7771 y = 0.0009x2 - 0.1957x + 5.3409 y = 0.0009x2 - 0.1955x + 6.1596 -3 -2 -1 0 1 2 3 4 5 6 0 10 20 30 40 50 Temperature (°C) STA 5D 11D 21D (a) -4 -3 -2 -1 0 1 2 3 4 5 6 0 5 10 15 20 25 lo g (a To ta l) lo g (a To ta l) Aging Duration (Days) 4°C 20°C 40°C (b) Figure 52. The total horizontal shift factors as plotted: (a) versus temperature and delineated with respect to age levels, and (b) versus aging duration and delineated with respect to test temperatures.

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 167   The observation that the trend of tAS factors with aging duration is similar to that of log |G*| with aging duration calls for an attempt to fit the tAS factors with a functional form similar to that of Equation (1) in the main text of this report, which is the kinetics model. This functional form is shown below in Equation (11). The advantage of using this form is having only one fitting parameter. (( )( )= − ′ ′       − − ′ + ′log 1 1 exp (11)a N k k k t k NtA c f f c where aA = time-aging shift (tAS) factor, kf′ = fast rate, kc′ = constant rate, t = reaction time (days), and N = fitting parameter. Fitting Equation (11) and obtaining tAS factors for each aging level requires knowing tTS factors beforehand. It was shown that assuming constant tTS factors for all age levels can yield an aging master curve. Thus, the master curves at each aging level were constructed using tTS factors of the STA condition at a reference temperature of 21.1°C and then shifted to coincide with the STA condition master curve as shown in Figure 53 by optimizing Equation (11) using a non-linear optimization scheme to obtain material-specific N parameter. This optimization was first done using kf′ and kc′ equal to kf and kc of the kinetics model. Then, kf′ and kc′ were cali- brated using tAS factors obtained from the first optimization, followed by the optimization of Equation (11) once again. This process was carried out iteratively three times until constant and universal kf′ and kc′ values were obtained. Prediction of Mixture tAS Factors from Binder tAS Factors It was expected that the parameter N would be analogous to the parameter M in the kinetics model in its implication of the aging susceptibility of the binder. A higher N would mean a more aging susceptible binder as would a higher M mean. Table 11 below shows the fitting param- eters N and M for all the mixtures and how the mixtures rank based on these two parameters 0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07 3.0E+07 0.000001 0.01 100 1000000 E' (k Pa ) Reduced Frequency (Hz) STA 5 Days 11 Days 21 Days Sigmoidal Fit (a) 5.0E+05 5.0E+06 5.0E+07 0.000001 0.01 100 1000000 E' (k Pa ) Reduced Frequency (Hz) STA 5 Days 11 Days 21 Days Sigmoidal Fit (b) Figure 53. E’ master curve shift to obtain tAS factors shown in (a) semi-log scale, and (b) log-log scale.

168 Long-Term Aging of Asphalt Mixtures for Performance Testing and Prediction: Phase III Results individually. As can be seen in Table 11, however, the ranking of the mixtures using N and M is evidently very different. This implies that N cannot be easily obtained from M; the lack of any correlation is more evident in plotting N versus M as shown in Figure 54. Obtaining N, with STA properties known, would mean that the mixture modulus can be pre- dicted easily by horizontally shifting the STA master curve. Since M cannot be used to obtain N, another approach that is based on relating shifting of binder |G*| master curve to the mixture E’ master curve will be presented below. The |G*| values for this analysis were obtained from the test results of the binders extracted and recovered from mixtures prepared at the STA and LTA conditions. Temperature-frequency sweep test results were used to construct the |G*| master curves using the Christensen-Anderson- Marasteanu (CAM) model. The |G*| master curves at different aging levels are shifted to coincide with the STA master curve in a process similar to that applied for the E’ master curves discussed earlier. Equation (11) is fitted, and now the fitting parameter Nbinder is obtained. N binder is well- related to N as shown in Figure 55, which implies that if Nbinder is known, N can be determined, and E’ master curves can be predicted at any age level. At this stage, the use of Equation (11) is limited to isothermal conditions at 95°C, because the data that were used to calibrate kf′ and kc′ belong to the 11 mixtures used thus far, which were aged at 95°C in the oven for multiple durations. Note that Equation (11) is capable of predicting the tAS factor for a specific in-service condition if the Arrhenius forms of kf′ and Mixture ID N Mixture ID M ACTRL 0.652 NCAT N10 0.481 LWA 0.665 FC12.5D 0.643 LTX 0.742 RS9.5B-50% 0.682 LSD 0.767 LSD 0.684 RS9.5B-0% 0.951 RS9.5B-30% 0.726 FC12.5D 0.953 ACTRL 0.772 NCAT N10 0.960 LTX 0.852 MnRd C.21 0.980 MnRd C.21 0.856 RS9.5B-50% 1.038 LWA 0.865 RS9.5B-30% 1.085 RS9.5B-0% 0.888 ARC 1.160 ARC 1.075 Table 11. Ranking of different mixtures based on N and M. y = 0.0932x + 0.8325 R² = 0.0072 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 N M Figure 54. Lack of correlation between the fitting parameters N and M.

Prediction of Mixture Properties Through the Rate of Change of Model Coefficients 169   kc′ are used (Equation (2) and Equation (3)—in the main text of the report—which require the pavement temperature history as input), and adequate calibration and verification are done. Adequate calibration means that parameters in Equation (2) and Equation (3) in the main text of the report should be calibrated based on isothermal aging at multiple temperatures for multiple mixtures, while verification entails checking that Equation (11) is capable of predicting the tAS for non-isothermal conditions using the universal parameters obtained from the calibra- tion. In this analysis, data for these 11 mixtures aged at temperatures other than 95°C were not available to conduct the calibration. This, alongside the fact that binder |G*| master curves at multiple aging durations are required to obtain Nbinder which leads to obtaining N, prompts for an investigation of another method that allows predicting tAS at in-service conditions with minimal experimental cost. The kinetics model was properly calibrated using data gathered at multiple temperatures and verified to predict non-isothermal conditions as shown in the original NCHRP Project 09-54. The pavement aging model with its refinement presented in the main text of this report is based on the kinetics model and was shown to adequately predict the evolution of log |G*| as a function of field aging. Therefore, if the evolution of log |G*| can be used to predict tAS, the shortcomings mentioned before can be overcome. Hence, this approach is abandoned in favor of the approach presented in the main text of the report. y = 0.4359x + 0.4664 R² = 0.6835 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.5 1 1.5 2 N Nbinder Figure 55. Correlation between Nbinder and N.