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F-1 APPENDIX F. CATALOG OF FRACTURE PROPERTIES OF ASPHALT MIXTURES The pseudo J-integral based Parisâ law proposed in this project is as follows: ï¨ ï©nR d A J dN ï¦ ï¢ï¢ï½ (F-1) where ï¦ is the damage density; RJ is the pseudo J-integral; and Aï¢ and nï¢ are modified Parisâ law parameters associated with the evolution of the damage density, which are called fracture properties here. They are 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 repeated load test. The test methods and analysis approaches are documented in Appendix D. ï· Level 2: the inputs for this level will be the air void content, asphalt binder content, aggregate gradation, and relaxation modulus. These inputs are substituted into the prediction equations (Equations F-2 and F-3) for Aâ and nâ to estimate their values. More details of the prediction equations are documented in Chapter 4 of the report, under the title âEstimation of Fracture Coefficients by Performance-Related Propertiesâ. ï¨ ï© 1 2 1 116.052 0.135 % 6.500ln % 8.147 5.512 81.515 with 0.943 m n AV AB m E R ï¹ ï¦ ï¶ ï¢ ï½ ï ï« ï« ï« ï« ï ï§ ï· ï¨ ï¸ ï½ (F-2) ï¨ ï©1.246 3.61510 nA ï¢ï ï«ï¢ ï½ (F-3) where %AV is the air void content, in %; %AB is the asphalt binder content by weight of mixture, in %; ï¹ is the aggregate shape parameter; and E1 and m are relaxation modulus parameters, E1 in MPa. ï· Level 3: the inputs will be default values for Aâ and nâ. These default values are listed in Table F-1. They are categorized according to the type, PG grade (if available), modulus (representative elastic modulus), air void content, binder content of an asphalt mixture. The representative elastic modulus is defined in Equation F-4 and elaborated in Chapter 4 of the report. * 1 1 2 2 p p re f t t E E E t ï½ ï© ï¹ï¦ ï¶ ï½ ï« ï½ïª ïºï§ ï· ï¨ ï¸ïª ïºï« ï» (F-4) where reE is the representative elastic modulus; *E is the dynamic modulus; and ï¨ ï©E t is the relaxation modulus; f is the frequency of a load pulse; and pt is the pulse time of a load. It is worth mentioning that the values of the fracture properties obtained at Level 1 are the most accurate. When the test facility is not available or there is a need for a quick estimation of Aâ and nâ, the prediction equations at Level 2 are recommended, which yield more accurate results than the default values at Level 3.
F-2 Table F-1. Default Values of Fracture Properties of Asphalt Mixtures Mixture Type PG Grade Air Void Content (%) Asphalt Binder Content (%) Representative Elastic Modulus Ere (MPa) nâ Aâ Dense- graded hot asphalt mix N/A 2.0 6.0 2100 1.933 2.69E-06 5200 1.7 1.45E-06 3100 2.104 4.79E-07 7.9 6.8 1500 2.16 7.08E-07 3300 2.322 3.02E-07 5900 2.5 4.47E-07 PG 76-22 4.0 4.4 3100 5.023 1.02E-09 3986 7.563 1.82E-14 6765 9.798 4.79E-16 7.0 4.4 2167 6.519 9.12E-11 3002 9.864 1.95E-15 4401 10.308 4.68E-16 PG 64-16 4.0 4.4 3983 2.578 5.13E-09 5852 3.035 2.82E-10 7767 7.412 2.19E-14 7.0 4.4 3150 3.472 1.70E-08 4392 4.987 2.29E-11 5954 7.996 2.51E-15 PG 58-28 4.0 4.4 1370 5.072 1.82E-106006 7.419 2.14E-12 7.0 4.4 1610 6.832 6.92E-103263 9.266 1.29E-14 Stone mastic asphalt N/A 3.0 7.0 2400 2.050 4.79E-07 3660 2.10 1.10E-06 4330 2.117 1.86E-06 Sand asphalt N/A 8.3 10 2100 2.158 2.69E-06 3400 2.458 1.45E-06 4800 2.100 7.08E-07
