Analytical solutions of asphalt pavement responses under moving loads with arbitrary non-uniform tire contact pressure and irregular tire imprint

Circular uniform static load was generally utilised for asphalt pavement design. Software packages for pavement mechanics analysis, such as BISAR, were developed based on the cylindrical coordinate system because of the symmetry of the exerted load. However, three important factors were ignored by previous computational algorithms, namely non-uniform tire contact pressure, irregular tire imprint and moving load. In this paper, analytical solutions of elastic and viscoelastic multilayered system under uniform moving load acting over a rectangular area were deduced using Galilean transform and Fourier transform in the Cartesian coordinate system. Two numerical inversion algorithms (i.e. Gaussian integral and inverse fast Fourier transform) were used to realise the numerical programme of analytical solutions. Then, arbitrary non-uniform tire contact pressure and irregular tire imprint can be easily composed with a series of uniform rectangular loads by considering the principle of superposition. The worked examples of elastic and viscoelastic three-layered system under moving loads with non-uniform contact pressure and irregular tire imprint were calculated by the numerical programme of analytical solutions, and the results were compared with those of the finite-element simulation to verify the validity of the solutions. Similar results were obtained by the two compared methods; however, the computational efficiency and accuracy of the analytical method were better than those of the finite-element simulation. The numerical programme of analytical solutions developed in this study could serve as an effective tool for pavement analysis and design.