Mechanical analysis of asphalt pavement structure incorporating the fractional derivative characteristics of asphalt mixture under moving load

In traditional pavement mechanics analysis, it is commonly assumed that the load follows a double circular uniform distribution, and the pavement structure is modeled as a layered elastic continuous system. However, the actual load does not conform to a double circular uniform distribution in the real world. Essential factors such as load shape and size, driving speed, and horizontal load are not considered. Additionally, the influence of rolling and other factors that lead to transverse isotropic properties are not considered. The mechanical calculations assume complete continuity between layers without considering semi-continuous or completely smooth interfaces. Furthermore, the viscoelastic properties of asphalt concrete are not considered. The analytical method is employed in this paper to calculate the mechanical response of a three-dimensional multi-layer asphalt pavement system under a double elliptic moving load. The fractional derivative viscoelastic model is utilized for the surface layers. This research consists of three steps: Firstly, the ordinary differential equation of the pavement structure is derived through double Fourier transformation, and the general solution for the mechanical response of the pavement structure is obtained using ordinary differential equations and the Frobenius method. Secondly, by incorporating boundary conditions, transfer matrix method, and Fourier inverse integral transform, the time-domain mechanical response of the pavement structure is computed. By simplifying the model, we verify the accuracy of our analytical solution by comparing it with existing solutions in the literature. Finally, a sensitivity analysis is conducted to evaluate the impact of seven parameters on the mechanical response of asphalt pavements. These parameters include load moving speed, horizontal load magnitude, temperature variation, transverse isotropy property, interlayer contact condition, load shape, and size distribution. By analyzing the sensitivity of these parameters, we can gain insights into their influence on the overall performance of asphalt pavements. Applying these calculation methods and the resulting findings can significantly enhance our understanding of multi-layer pavement system theory. By utilizing these methods and analyzing our results, we can gain valuable insights into the behavior and performance of multi-layer pavement systems. This enhanced understanding contributes to developing theoretical knowledge and has practical implications for pavement systems' design and construction practices.