Probabilistic Modeling of the Inherent Variability in the Dynamic Modulus Master Curve of Asphalt Concrete

Pavement engineers and practitioners have come to recognize the urgent need to quantify the variability in dynamic modulus, |E*|, because of its influence on the predicted performance of asphalt pavements and to adopt realistic quality assurance or quality control measures associated with pavement construction. The objective of this study was to characterize the inherent variability in |E*| across the full spectrum of the |E*| master curve (fitted with a sigmoidal function for various reduced frequencies). The study analyzed |E*| data from six mixes that included at least eight replicates within a robust probabilistic framework that allowed for a preliminary quantification of uncertainty caused by the inherent variability in |E*|. Monte Carlo simulations were used to propagate the uncertainties of the sigmoidal model coefficients to determine the mean, coefficient of variation, and probability distribution of |E*| as a function of reduced frequency. In addition, the inherent uncertainty in |E*| was propagated through forward modeling to characterize the resulting uncertainty in the predicted rut depth in the asphalt layer for a set of pavement structures. The findings show that the values of the inherent uncertainty of |E*| are relatively small for cases with reduced frequencies that are high but increase dramatically for reduced frequencies that are in the medium to low range. This uncertainty increases as the nominal maximum aggregate size (NMAS) of the mix under investigation increases. It was found that the uncertainty significantly affects the probability distribution of rut depth and implies higher variability for cases of hot weather, slow traffic, or large NMAS.