Impedance matrices for axial symmetric foundations on layered media

A procedure to generate the impedance matrix of foundation resting on an elastic layered half-space medium is proposed. The prescribed harmonic loadings due to the foundation are decomposed into an infinite Fourier series with respect to the azimuth. For each Fourier component, the analytic solution is obtained by solving the differential equations of wave propagation satisfying the prescribed boundary conditions, and the stress and the displacement continuity conditions at the horizontal interfaces in the layered system. Using this analytic solution, the impedance matrix is obtained by applying the variational principle and the reciprocal theorem with the assumption that the interaction stresses between the foundation and the soil is piecewise linear in the radial direction of cylindrical coordinates. An example of a two-layer system is often presented.