Analytical layer element method for solving plane strain problem of multi-layered soils

An analytical layer element method is proposed to solve the plane strain problem of multi-layered soils. Starting from the governing equations of the plane strain problem the analytical solution is obtained by introducing the Fourier transform and solving differential equations. And then, according to the analytical solution, an exact stiffness matrix for the multi-layered plane strain problem is established, which is called analytical layer element. The global stiffness matrix is established by using the principle of the finite layer method, and the solutions for the plane strain problem of multi-layered soils in the transform domain are obtained by solving the algebraic equations about the global stiffness matrix. The actual solutions in the physical domain are acquired by inverting the Fourier transform. Numerical analysis is carried out to discuss the influence of the layered characteristics on the vertical displacements of the soil.