1. Presentation 3 Reliability Analysis
R. Nielsen

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

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

4. Reliability Analysis Approach (cont.)
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.
Permanent Deformation will be determined using the 2002 AASHTO Design Guide (MEPDG) prediction models.
Statement 4 needs to be clarified. I think “actual” refers to the deformation from the AASHTO design guide, while the “predicted” E* comes from AAA’s model. Both quantities are random variables.

5. probability distributions

6. HMA Dynamic Modulus, E*
Ultimately, we’ll want to plot both the probability distribution and the experimental histograms for this data.

7. Binder Dynamic Shear Modulus, G*

8. Gyratory Stability

9. Maximum Specific Gravity

10. Air Voids, AV%

11. Normal Distributed Variables
Mean, μ
Std. Dev., σ
Gyratory Stability, GS (kN.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%

12. Lognormal Distributed Variables
Temperature, °C
Mean, μ
Std. Dev., σ
Dynamic Modulus, E* (MPa)
4.4
21.1
37.8
802.90
54.4
Dynamic Shear Modulus, G* (MPa)
3.1683
3.6721
0.2340
0.2973