Viscoelastic properties of warm recycled asphalt mixture based on S-$$\boldsymbol{\varphi }$$ model

To investigate the influence of temperature, frequency, and RAP content on the viscoelastic properties of warm-mix recycled asphalt mixtures, dynamic modulus tests were conducted on mixtures with different RAP contents (0%, 50%, 70%) across four temperatures and six frequencies. The results show that at high temperatures and low frequencies, the dynamic modulus of the warm-mix recycled asphalt mixtures is higher than that of the hot-mix asphalt (HMA) control. At low temperatures and high frequencies, the dynamic modulus of the warm-mix recycled mixtures is not significantly different from the HMA control. This indicates greater high-temperature stiffness in the warm-mix recycled mixtures relative to the hot-mix reference, while no significant difference is observed at low temperatures. Compared to the 70% RAP mixture, the 50% RAP mixture exhibits the largest increase in dynamic modulus at high temperature (50 °C) and the smallest decrease in phase angle at low temperature (5 °C) relative to the control. Therefore, 50% RAP warm mix recycled asphalt mixture has better high and low temperature performance. According to the principle of time–temperature equivalence, the S (generalized sigmoidal) model and the $$\boldsymbol{\varphi }$$ (improved phase-angle) model were fitted synchronously with shared WLF shift factors, ensuring thermorheological consistency. The synchronous S- $$\boldsymbol{\varphi }$$ model accurately fits the variation of both dynamic modulus and phase angle with frequency.