Asphalt Mix Master Curve Construction Using Sigmoidal Fitting Function with Non-Linear Least Squares Optimization

TLDR

The study introduces a simplified method for constructing asphalt mix master curves using test data spanning –18 °C to 55 °C. The method employs a sigmoidal fitting function on compressive cyclic modulus data across frequencies and temperatures, models time‑temperature superposition both via established equations and an experimental shifting approach, and is implemented in Excel using a solver for non‑linear least‑squares regression. Analysis of over sixty mixtures shows the experimental shifting approach best matches the Arrhenius equation (R² = 0.922) and provides the most flexible, highest‑fitting master curve among the tested shifting equations.

Abstract

This paper presents a new simplified method of constructing a master curve of asphalt mix using test data covering a large range of temperatures from –18°C to 55°C. It utilizes sigmoidal fitting function and compressive cyclic (complex) modulus test data obtained at matrix combination of different frequencies and test temperatures. In the master curve construction, the time temperature superposition was modeled two different ways. First, using known time-temperature superposition equations, and second, shilling test data experimentally, i.e., not assuming any functional form for the time-temperature relationship. The master curve construction was done using an Excel spreadsheet with the solver function, which is a tool for performing optimization with non-linear least squares regression technique. The analysis of over sixty mixtures indicated that the experimental approach agreed the best with the Arrhenius shifting equation, correlation coefficient R2 being 0.922. Also, the experimental shifting was most flexible, producing the best fit among the studied shifting equations due to the fact that it has the most degree of freedom.