Dynamic Modulus Model of Hot Mix Asphalt: Statistical Analysis Using Joint Estimation and Mixed Effects

This paper presents the specification and estimation of a model for hot-mix asphalt dynamic modulus $|E^{*}|$ using 6,821 observations of 265 specimens from three different data sets containing variables in common such as air voids, binder content, and gradation and variables about mix characteristics and testing conditions not available in some data sets, such as confinement level, number of freeze-thaw cycles, antistripping agents, and fibers. The model parameters were estimated using joint estimation and mixed effects. Joint estimation allowed the identification of parameters from information available only in some data sets and the determination of bias parameters. It also resulted in more efficient parameter estimates derived from all data sets. The mixed-effects approach was used to account for unobserved heterogeneities between samples. Together with proper consideration of heteroskedasticity, these approaches allowed the estimation of a comprehensive model closely satisfying all regression assumptions, providing accurate values of $|E^{*}|$ for any combination of temperature and frequency, and accounting for different testing conditions, component materials, and mixture volumetrics. All the previous factors were found to be statistically significant and to affect dynamic modulus according to a priori expectations. This paper discusses the characteristics of the data sets, the model specification, and general statistical results.