Proposing a novel double sigmoidal model to fit the master curve for various polymer-modified asphalt

Master curve technique is frequently used to characterize the linear viscoelasticity of polymer modified asphalt (PMA), however, there is no widely accepted master curve for PMA. This study aims to propose a novel double sigmoidal model that can be used universally for all asphalts, especially highly modified PMAs. To do so, one plain asphalt and six representative PMAs are examined. Extended temperature sweep tests (-40 degrees C to 140 degrees C) are conducted to grasp the whole picture of the master curve. Three representative mathematical models (CAM, sigmoidal, double sigmoidal) are selected and compared in terms of fitting in both modulus and phase angle. The results suggest that double sigmoidal model suits all types of asphalts for all testing temperature ranges, and it features the ability to model the rubbery state and rubbery-viscous transition of highly modified PMA (RMSE < 0.02). A phase angle expression of the double sigmoidal model is also developed, which shows great potential in characterizing the strength of polymer network within the PMA. Also, it avoids the impact from the partial break of the time-temperature superposition principle (TTSP) and reveals the true shape of the phase angle master curve. Finally, master curve models are recommended based on different testing temperature ranges.