Spectral element solution for transversely isotropic elastic multi-layered structures subjected to axisymmetric loading

Spectral element method is proposed to analyze the mechanical response of transversely isotropic elastic multi-layered pavement structure subjected to axisymmetric loading. Based on the basic constitutive equations and modified Love’s function for transversely isotropic elastic media, the governing state equation of a multi-layered transversely isotropic medium was deduced. From the equation, s spectral layer element for a single layer (i.e., a stiffness matrix) was acquired. The global stiffness matrix was obtained by assembling the interrelated layer elements based on the principle of the finite element method and the boundary conditions, and the solution for the corresponding problem was obtained by solving the algebraic equations of the global stiffness matrix. The solutions in the physical domain were acquired by means of the Fourier–Bessel superposition. The validity of the proposed solution was examined by comparing with an existing exact solution and finite element method respectively. Subsequent to solution validation, a parametric study by varying n-values of unbound layer was carried to investigate the influence of the transversal isotropy on pavement response. The proposed analytical solution demonstrated the ability of solving the mechanical response of transversely isotropic elastic multi-layered pavement structures subjected to axisymmetric loading.