Probabilistic Modeling of Dynamic Modulus Master Curves for Hot-Mix Asphalt Mixtures

Since the introduction of the dynamic modulus E^* concept in the recent Mechanistic–Empirical Pavement Design Guide, there has been considerable interest in establishing reliable prediction models for E^*. An investigation of the effectiveness of commonly used predictive models shows that E^* predictions exhibit significant scatter around the measured values, with percentage of errors reaching about 6200%. A need exists for characterizing the uncertainties that are inherent in E^* to serve as input to any future robust reliability analysis that aims at properly determining the probability of unsatisfactory performance of asphalt pavement systems. The primary objective of this study was to present a probabilistic model that would allow the user to determine a priori probability distribution for E^* given knowledge about temperature and frequency. The seven-parameter model was based on the sigmoidal function and the shift factor that related reduced frequency to real frequency and temperature. The model was calibrated on the basis of a well-known published database that included 7,400 laboratory measurements of E^* for 346 asphalt mixes. Monte Carlo simulations were used to propagate the uncertainties in the seven model parameters and determine realistic estimates of the mean, coefficient of variation, and probability distribution of E^* at different frequencies and temperatures. Results showed that E^* could be modeled by using a lognormal distribution with a mean that was estimated from the mean values of the parameters and a coefficient of variation that varied from a minimum of 0.55 for high values of reduced frequency to a maximum of 1.55 for lower values of reduced frequency.