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G-1 APPENDIX G. CATALOG OF AGING PROPERTIES OF ASPHALT MIXTURES The kinetics-based aging prediction models for modulus gradient of asphalt mixtures proposed in this project are as follows: ï· Base-line modulus aging submodel: ï¨ ï©ï¨ ï©* * * *0 1 fbk t cbb bi b biE E E E e k tïï½ ï« ï ï ï« (G-1) in which afb field E RT fb fbk A e ï ï½ (G-2) acb field E RT cb cbk A e ï ï½ (G-3) ï· Surface modulus aging submodel: ï¨ ï©ï¨ ï©* * * *0 1 fsk t css si s siE E E E e k tïï½ ï« ï ï ï« (G-4) in which: afs field E RT fs fsk A e ï ï½ (G-5) acs field E RT cs csk A e ï ï½ (G-6) ï· Aging exponent submodel: ï¨ ï© ï¨ ï©0 1 fnk ti i cnn n n n e k tïï½ ï ï ï ï (G-7) in which: afn field E RT fn fnk A e ï ï½ (G-8) acn field E RT cn cnk A e ï ï½ (G-9) where * b E and * s E are the base-line modulus and surface modulus, respectively; * b i E and * s i E are the initial base-line modulus and initial surface modulus, respectively; * 0b E and * 0s E are the intercept of the constant-rate line of base-line modulus and that of surface modulus, respectively; in is the initial aging exponent; 0n is the intercept of the constant-rate line of the aging exponent; fbk , fsk , fnk are the fast-rate reaction constant for base-line modulus, surface modulus, and aging exponent, respectively; cbk , csk , cnk are the constant-rate reaction constant for base-line modulus, surface modulus, and aging exponent, respectively; t = the aging time in days; fbA , fsA , fnA arethe fast-rate pre-exponential factor for base-line modulus, surface modulus, and aging exponent, respectively; afbE , afsE , afnE are the fast-rate aging activation energy for base-line modulus, surface modulus, and aging exponent, respectively; cbA , csA , cnA are the constant-rate pre-exponential factor for base-line modulus, surface modulus, and aging exponent, respectively; acbE , acsE , acnE are the constant-rate aging activation energy for base- line modulus, surface modulus, and aging exponent, respectively; and fieldT are the field aging absolute temperature.
G-2 The aging activation energy and pre-exponential factor are called aging properties herein. They may be input in any of the three Pavement ME Design levels: ï· Level 1: the inputs for this level will be the measured values from the direct tension test on asphalt field cores. The test methods and analysis approaches are documented in Appendix B. ï· Level 2: the inputs for this level will be the falling weight deflectometer (FWD) data. The backcalculated field moduli from the FWD are substituted to the aging prediction models above. Note that since the FWD modulus is usually a single value for a pavement layer, only one set of equations, for example Equations G-4 to G-6, is enough. More details are documented in Chapter 4 of the report, under the title âPrediction of Field Aging Using Deflection Dataâ. ï· Level 3: the inputs will be default values for the aging activation energy and pre- exponential factor. These default values are listed in Tables G-1 and G-2. The values in Table G-1 are from asphalt field cores with modulus gradient data, which are categorized according to the type, pavement location, and air void content of an asphalt mixture. The values in Table G-2 are from the FWD with backcalculated field modulus data, which are categorized according to the climate zone. Table G-1. Default Values of Aging Properties of Asphalt Field Cores Mixture Type Pavement Location Air Void Content afbE (kJ/mol) fbA acb E (kJ/mol) cb A Hot mix asphalt (HMA) Base-line (1.5- ih below surface) <7% 29.01 1.00E04 48.74 3.24E08 Warm Mix Asphalt treated by a foaming process (FWMA) 28.41 7.76E03 48.53 3.01E08 Warm Mix Asphalt with Evotherm (EWMA) 31.00 2.22E04 49.19 3.77E08 HMA >7% 25.55 2.26E03 43.87 7.93E07 FWMA 26.60 3.46E03 45.45 1.52E08 EWMA 26.95 4.07E03 46.35 1.93E08 HMA Surface <7% 23.67 9.73E02 40.44 6.05E07 FWMA 23.76 9.78E02 40.55 5.98E07 EWMA 24.70 1.49E03 41.98 9.49E07 HMA >7% 22.56 5.81E02 38.44 3.33E07 FWMA 21.66 3.93E02 38.69 3.34E07 EWMA 22.99 6.85E02 39.81 4.76E07
G-3 Table G-2. Default Values of Aging Properties of Field Asphalt Pavements Climate Zone af E (kJ/mol) fA ac E (kJ/mol) c A Wet-freeze (WF) 15.21 1.04E+01 40.33 6.87E+07 Wet no-freeze (WNF) 28.80 1.31E+03 46.90 2.69E+07 Dry-freeze (DF) 20.19 9.81E+01 37.07 2.51E+05 Dry no-freeze (DNF) 15.85 9.85E+00 30.79 4.60E+04
