A Novel Master Curve Formulation with Explicitly Incorporated Temperature Dependence for Asphalt Mixtures: A Model Proposal with a Case Study

Abstract

Accurately modelling and simulating the stiffness modulus of asphalt mixtures is essential for reliable pavement design and performance prediction under varying environmental and loading conditions. The preceding is commonly achieved through master curves, which relate stiffness to loading frequency at a reference temperature. However, conventional master curves face two primary limitations. Firstly, temperature is not treated as a state variable; instead, its effect is indirectly considered through shift factors, which can introduce inaccuracies due to their lack of thermodynamic consistency across the entire range of possible temperatures. Secondly, conventional master curves often encounter convergence difficulties when calibrated with experimental data constrained to a narrow frequency spectrum. In order to address these shortcomings, this investigation proposes a novel formulation known as the Thermo-Stiffness Integration (TSI) model, which explicitly incorporates both temperature and frequency as state variables to predict the stiffness modulus directly, without relying on supplementary expressions such as shift factors. The TSI model is built on thermodynamics-based principles (such as Eyring’s rate theory and activation free energy) and leverages the time–temperature superposition principle to create a physically consistent representation of the mechanical behaviour of asphalt mixtures. This manuscript presents the development of the TSI model along with its application in a case study involving eight asphalt mixtures, including four hot-mix asphalts and four warmmix asphalts. Each type of mixture contains recycled concrete aggregates at replacement levels of 0%, 15%, 30%, and 45% as partial substitutes for coarse natural aggregates. This diverse set of materials enables a robust evaluation of the model’s performance, even under non-traditional mixture designs. For this case study, the TSI model enhances computational stability by approximately 4 to 45 times compared to conventional master curves. Thus, the main contribution of this research lies in establishing a valuable mathematical tool for both scientists and practitioners aiming to improve the design and performance assessment of asphalt mixtures in a more physically realistic and computationally stable approach.