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This paper aims to incorporate the fractional derivative viscoelastic model into a finite element analysis. Firstly, based on the constitutive equation of the fractional derivative three-parameter solid model (FTS), the constitutive equation is discretized by using the Grünwald–Letnikov definition of the fractional derivative, and the stress increment and strain increment relationship and Jacobian matrix are obtained by using the difference method. Subsequently, we degrade the model to establish stress increment and strain increment relationships and Jacobian matrices for the fractional derivative Kelvin model (FK) and fractional derivative Maxwell model (FM). Finally, we further degrade the fractional derivative viscoelastic model to derive stress increment and strain increment relationships and Jacobian matrices for a three-component solid model and Kelvin and Maxwell models. Based on these developments, a UMAT subroutine is implemented in ABAQUS 6.14 finite element software. Three different loading modes, including static load, dynamic load, and mobile load, are analyzed and calculated. The calculations primarily involve a convergence analysis, verification of numerical solutions, and comparative analysis of responses among different viscoelastic models. [ABSTRACT FROM AUTHOR]

Currently, the research on the mechanical properties of rubber-modified asphalt mixtures primarily focuses on small-scale investigations, with insufficient exploration into the performance of rubber particles and their relationship with the mechanism and properties of modified asphalt mixtures. Limited studies have been conducted on large-scale rubber modification in asphalt mixtures. Due to frequent use and subsequent high damage to existing asphalt pavements, incorporating rubber-modified asphalt mixtures can partially alleviate premature deterioration. Dynamic modulus tests were conducted using MTS equipment under unconfined conditions to investigate the viscoelastic behavior of rubber-modified asphalt mixtures with high rubber content and elucidate the influence of rubber particle content on the elastic deformation and recovery capability. The dynamic mechanical properties of the mixtures were determined at different loading rates, temperatures, and types of rubber-modified asphalt mixtures. Based on the test data, variations in the dynamic modulus, phase angle, storage modulus, loss modulus, loss factor, and rut factor of the rubber-modified asphalt mixtures under different loading frequencies, temperatures, and types were analyzed. The results demonstrate the pronounced viscoelastic behavior of rubber-modified asphalt mixtures. The mixtures exhibit enhanced elasticity at low temperatures and high frequencies, while their viscosity becomes more prominent at high temperatures and low frequencies. Under constant test temperatures, an increase in load loading frequency leads to a higher dynamic modulus; conversely, a decrease in dynamic modulus is observed with increasing test temperatures. The dynamic modulus of ARHM-25 at a frequency of 10 Hz is found to be 12.99 times higher at 15 °C compared to that at 60 °C, while at 30 °C, the dynamic modulus at 25 Hz is observed to be 2.72 times greater than that at 0.1 Hz. Furthermore, the rutting resistance factors of the asphalt mixtures increase with loading frequency but decrease with temperature. The rutting factor for ARHM-13 at a frequency of 10 Hz is found to be 22.98 times higher at 15 °C compared to that at 60 °C, while at a temperature of 30 °C, the rutting factor for this material is observed to be 3.09 times greater at a frequency of 25 Hz than at 0.1 Hz. These findings suggest that rutting is most likely when vehicles drive at low speeds in hot weather conditions. [ABSTRACT FROM AUTHOR]

This study addressed the complex problems of selecting a constitutive model to objectively characterize asphalt mixtures and accurately determine their viscoelastic properties, which are influenced by numerous variables. Inaccuracies in model or parameter determination can result in significant discrepancies between the calculated and measured results of the pavement's structural dynamic response. To address this, the research utilized the physical engineering principles of asphalt pavement structure to perform dynamic modulus tests on three types of high-content rubberized asphalt mixtures (HCRAM) within the surface layer. The research aimed to investigate the influencing factors of the dynamic modulus and establish a comprehensive master curve. This study also critically evaluated the capabilities of three viscoelastic models—the three-parameter solid model, the classical Maxwell model, and the classical Kelvin model—in depicting the dynamic modulus of HCRAM. The findings indicated a negative correlation between the dynamic modulus of the asphalt mixture and temperature, while a positive association exists between the loading frequency and temperature, with the impact of the loading frequency diminishing as the temperature increases. Notably, the three-parameter solid model was identified as the most accurate in describing the viscoelastic properties of the HCRAM. Furthermore, the dynamic response calculations revealed that most indexes in the surface layer's dynamic response are highest when evaluated using the three-parameter viscoelastic model, underscoring its potential to enhance the pavement performance's predictive accuracy. This research provides valuable insights into optimizing the material performance and guiding the pavement design and maintenance strategies. [ABSTRACT FROM AUTHOR]