Experimentally Driven 3D Viscoelastic Modelling and Validation of Flexible Pavement with Waste Cooking Oil and Nano-Silica Modified Asphalt Under Stationary and Quasi-Static Loads

Abstract This study develops a three-dimensional finite element model of a flexible pavement containing C320 asphalt modified with waste cooking oil (WCO) and nano-silica (NS). A formulation with 4.0% treated WCO and 2.0% NS was selected through binder screening. Across 24 temperature-frequency conditions, dynamic modulus decreased from 8.60 to 0.56 GPa and phase angle increased from 10.8° to 38.5°. MATLAB R2025a was used to fit the master curve, shift factors and five-term Prony-series parameters. The fit gave R², RMSE, and MAPE values of 0.998, 0.100 GPa, and 3.42%, respectively, for dynamic modulus and 0.994, 0.610°, and 2.58%, respectively, for phase angle. Abaqus/Standard was used to develop the pavement model. Effective asphalt and support-layer stiffnesses were calibrated against Austroads stationary single-axle single-tyre (SAST) pavement-box measurements at 20 °C, giving a calibration MAPE of about 1.40%. Independent validation used a separate stationary single-axle dual-tyre (SADT) pavement-box dataset at 20 °C that was not included during calibration, with no further parameter adjustment. Model predictions of 0.341 mm, 101 µε and 151 µε were compared with measured values of 0.372 ± 0.020 mm, 92 ± 6 µε and 166 ± 10 µε, giving individual errors of 8.33%, 9.78% and 9.04% and a validation MAPE of 9.05%. The validated model was then used to compare stationary and quasi-static stepped SAST and SADT loading. When peak finite element outputs were used for this comparison, SADT gave lower normalised peak responses than SAST.