Dynamic response to plane strain problem of multilayered orthotropic foundation under moving loads

Based on the dynamic equation for plane strain problem of single-layer orthotropic foundation under moving harmonic loads, the transfer matrix of single-layer orthotropic foundation in the Cartesian coordinates is deduced through the Fourier transform and the introduction of state vector. Then the computational model for the layered orthotropic foundation is established. Considering the contact condition and the continuous condition between layers, the analytic expressions for the displacements and stresses at arbitrary depth in the plane strain problem of multilayered orthotropic foundation are derived by means of the transfer matrix method. Based on the theoretical solutions, the corresponding calculation programs are compiled to verify the calculated results of the single-layer orthotropic foundation and to study the influences of layered characteristics and orthotropic properties of soils on the amplitudes of vertical displacement of soil surface. The results indicate that neglecting the layered characteristics of soils and orthogonal anisotropy of the upper soils cannot accurately describe the dynamic characteristics of foundation.