Dynamic modulus master curve construction of asphalt mixtures: Error analysis in different models and field scenarios

Asphalt mixture stiffness is a key property in any pavement long-life performance analysis; it is used to predict a material's strain response for any given applied stress. To accurately describe experimental data, different mathematical models have been reported in literature, which allow for extrapolation to ranges not evaluated in laboratory tests. However, a precision analysis comparing each of them is necessary. This study evaluated 50 data points from five temperatures, ten loading frequencies, and 48 different asphalt mixtures to construct dynamic modulus master curves. Sigmoidal, Christensen-Anderson-Marasteanu (CAM), and Havriliak-Negami (HN) models were calibrated with three different target error functions, in addition to 2 Springs, 2 Parabolic creep elements, and 1 Dashpot (2S2P1D) to analyze their relative and absolute errors. In the first part, the mechanical analogs (2S2P1D and HN) achieved the best results. In the second part, the error added by the Williams-LandelFerry (WLF) and polynomial function, which describe the time-temperature shift factors used to construct the dynamic modulus master curves, was calculated; this suggested that the polynomial function better fits the master curves' shift factors. In the third part, three Enhanced Integrated Climate Models (EICM) with different pavement depths and temperatures throughout the year together with the influence of vehicle speed and a depth equation were used to meet a reduced frequency interval that represents practical field conditions. Therefore, by filtering the errors found in part one using the field-representative reduced frequency interval, the fitting models (based on regression adjustments) can reach lower error levels closer to those of the mechanical analog models although still greater than those of the 2S2P1D model. In summary, it is possible to obtain a reliable pavement stiffness prediction using a less robust model as long as the dynamic modulus tested database is wide enough to express the desired reduced frequency range. Nevertheless, the use of a mechanical approach model such as 2S2P1D better describes the dynamic modulus experimental results, which leads to a more reliable prediction in addition to enabling characterization of the rheological behavior of asphalt materials.