Dynamic response of a multi-layered pavement structure with subgrade modulus varying with depth subjected to a moving load

The dynamic response of a three-dimensional multi-layered pavement system subjected to a moving load is calculated by an analytical solution method. In this method, the pavement structure is assumed to be a transverse isotropic viscoelastic multi-layered structure with partially bonded interface, and the subgrade is considered to be a transverse isotropic half-space medium with its modulus varying with depth. The load is considered as a three-dimensional elliptical moving load with a constant speed. This study is divided into three key steps. Firstly, the ordinary differential equations of pavement and subgrade structures are obtained via the double Fourier transform, and the general solutions of dynamic response are obtained according to the theory of ordinary differential equations and the Frobenius method. Secondly, combined with the boundary conditions, the method of wave vector matrix, and the inverse Fourier integral transform, the dynamic responses of pavement structure in time domain are calculated. The accuracy of the analytical solution is verified by comparing against the solution from a finite element method. Lastly, the sensitivity analysis is conducted to assess the influence of four parameters on the dynamic response, namely, the horizontal load, the condition of interlayer contact, the transverse isotropy, and the non-uniform distribution of subgrade moduli. The calculation methods and the corresponding results can further develop a theory of the multi-layered system.