Analytical stiffness matrix of viscoelastic layered foundation under loading in Cartesian coordinate system

Based on the basic viscoelastic equations of Cartesian coordinate system, the analytical solutions of three-dimensional and plane strain in the integral transform domain were obtained by using the Fourier-Laplace transform and the matrix theory, and then the corresponding element stiffness matrix was derived. The global stiffness matrixes were assembled by matrix matching method, and the solutions for the corresponding problem of multilayered foundation in the transform domain were obtained by solving the algebraic equations of the global stiffness matrix. The solutions in the physical domain were acquired by inverting the Fourier-Laplace transform. The validity of the proposed method was examined by comparing the results of viscoelastic problem reducing to elastic problem with existing solutions, and the influences of viscosity parameter of viscoelastic foundation on the settlement were analyzed. The result shows that the soil creep increases with the increase of the viscosity parameter, and the duration of the final foundation settlement is longer.