Analytical layer-element solution for three-dimensional problem of multilayered foundation

Starting from the basic equations of elasticity for three-dimensional problem, the analytical solution in the integral transform domain is obtained by use of the decoupled transform technique and the Fourier transform method. Based on the analytical solution, the exact stiffness matrix which is called analytical layer-element for the three-dimensional problem of multilayered elastic foundation is derived. The global stiffness matrix is assembled by means of the principle of finite layer method, and the solutions for the three-dimensional problem of multilayered foundation in the transform domain are obtained by solving the algebraic equations of the global stiffness matrix. Finaly, the solutions in the physical domain are acquired by inverting the Fourier transform. The validity of the proposed theory and numerical method is examined by comparing the results in this study with those of Boussinesq solution and the finite element soft ABAQUS, and numerical calculation shows that the influence of stratification on the displacement of foundation is remarkable.