Mechanical response of pavement considering the fractional derivative characteristics of asphalt mixtures

• Fractional Derivative Constitutive Model for Rubber-Modified Asphalt Mixtures • Establishment of Dynamic Modulus Master Curves • Finite Element Analysis of Asphalt Pavement Structure Rubber-modified asphalt mixtures are increasingly valued for their enhanced fatigue resistance and environmental benefits; however, accurately modeling their dynamic viscoelastic behavior remains challenging. In this study, a fractional-derivative constitutive model is evaluated to address this issue. Dynamic modulus tests were conducted on mixtures with 30%, 40%, and 50% rubber content over temperatures ranging from 15°C to 60°C and loading frequencies from 0.1 Hz to 25 Hz. The experimental data were used to construct master curves that capture the temperature- and frequency-dependent characteristics of the mixtures and provide a basis for model validation. Three fractional-derivative models—Kelvin (FDK), Maxwell (FDM), and Zener (FDZ)—were compared, and the FDZ model demonstrated superior fitting accuracy and broader applicability across the investigated frequency range. For numerical implementation, the FDZ constitutive equation was discretized using the Grünwald–Letnikov definition, and a finite-difference scheme was employed to derive the stress–strain incremental relations and the Jacobian matrix. The FDZ model was further validated via finite element analysis of a two-dimensional asphalt pavement structure, successfully predicting key structural responses, including surface deflection, tensile stress and strain in the surface layer, and compressive strain in the subgrade. Overall, integrating the fractional viscoelastic model into a structural analysis framework bridges material-level characterization with engineering application, supporting improved pavement design and durability assessment.