Presentation 3 Reliability Analysis R Nielsen 1 Variables

Presentation 3 Reliability Analysis R. Nielsen 1

Variables l l l HMA Dynamic Modulus, E* Binder Dynamic Shear Modulus, G* Gyratory Stability, GS Maximum Specific Gravity, Gmm Binder Content, Pb% Air Voids, AV% 2

Reliability Analysis Approach 1. Determine the probability distributions of tested variables. where, fx(x): Probability Density. x: Random Variable. μ: Sample Mean. σ: Sample Standard Deviation. 3

Reliability Analysis Approach (cont. ) 2. 3. 4. Generate Random Variables Using Simulation (e. g Latin Hypercube Sampling, 100, 000 random variables). Use Generated variables to predict E*. Compare permanent deformation determined using actual versus predicted E* values. l Permanent Deformation will be determined using the 2002 AASHTO Design Guide (MEPDG) prediction models. 4

PROBABILITY DISTRIBUTIONS 5

HMA Dynamic Modulus, E* 0, 0001 9 E-05 8 E-05 7 E-05 fx(x) 6 E-05 5 E-05 4 E-05 3 E-05 2 E-05 1 E-05 0 0 5000 10000 15000 E*, MPa 20000 25000 6

Binder Dynamic Shear Modulus, G* 0, 03 0, 025 fx(x) 0, 02 0, 015 0, 01 0, 005 0 0 20 40 60 G*, MPa 80 100 120 7

Gyratory Stability 0, 3 0, 25 fx(x) 0, 2 0, 15 0, 1 0, 05 0 10 12 14 GS, k. N. m 16 18 8

Maximum Specific Gravity 25 fx(x) 20 15 10 5 0 2, 383 2, 403 2, 423 2, 443 2, 463 2, 483 Gmm 9

Air Voids, AV% 120 100 fx(x) 80 60 40 20 0 3, 5% 4, 0% 4, 5% 5, 0% 5, 5% 6, 0% Pb 10

Normal Distributed Variables Variable Mean, μ Std. Dev. , σ Gyratory Stability, GS (k. N. m) 14. 83 1. 443 Maximum Specific Gravity, Gmm 2. 434 0. 0202 Binder Content, Pb% 4. 69% 0. 364% Air Voids, AV% 7. 1% 0. 279% 11

Lognormal Distributed Variables Variable Dynamic Modulus, E* (MPa) Dynamic Shear Modulus, G* (MPa) Temperature, °C Mean, μ Std. Dev. , σ 4. 4 9783. 63 3983. 922 21. 1 3275. 49 2134. 864 37. 8 802. 90 704. 634 54. 4 228. 998 207. 523 4. 4 20. 5114 22. 5838 21. 1 3. 1683 3. 6721 37. 8 0. 2340 0. 2973 54. 4 0. 02834 0. 03488 12