Dynamic Mechanical Characterization of Warm-Mixed Steel Slag-Crumb Rubber Modified Asphalt Mixture in Wide- and Narrow-Frequency Domains

To investigate the dynamic mechanical properties of warm-mix steel slag-crumb rubber modified asphalt mixtures across wide- and narrow-frequency domains and evaluate the applicability of warm-mix technology, four distinct mixtures were prepared. The dynamic modulus characteristics under measured temperatures and frequencies were initially analyzed through complex modulus testing to elucidate narrow-frequency-domain mechanical behavior. Subsequently, leveraging the linear viscoelastic (LVE) theory and time-temperature superposition principle (TTSP), both the 2 Springs, 2 Parabolic Elements and 1 Dashpot (2S2P1D) mechanical element model and Modified Havriliak-Negami (MHN) mathematical model were established based on experimental data to characterize wide-frequency-domain dynamic responses. The results demonstrate substantial consistency in mechanical interpretation between narrow- and wide-frequency domain datasets, with enhanced information resolution achieved in wide-frequency analysis. Both models demonstrate comparable accuracy in characterizing the thermomechanical behavior of warm-mix steel slag-crumb rubber modified asphalt mixture across extended frequency and temperature ranges, while showing negligible performance discrepancies between the 2S2P1D and MHN formulations. Furthermore, both Cole-Cole and Black diagrams convincingly demonstrate the reliability of model predictions. This systematic investigation confirms the technical viability of warm-mix steel slag-crumb rubber modified asphalt mixture while establishing a dual-validated modeling framework for comprehensive performance prediction.