Basic solution of saturated layered ground by thin layered method and its paraxial boundary

The dynamic response of saturated layered ground subjected to harmonic force is investigated. By using the Fourier series expansion and Hankel transform, the Biot’s dynamic equations in each layer are reduced into a series of ordinary differential equations, which can be solved by the thin layered method (TLM). And the general solutions for displacement and pore pressure in frequency domain are derived by analytical inversion of the Hankel transform. In order to overcome the problem that TLM only can work in finite depth, a solution of paraxial approxination, which can act as the underlayer boundary of TLM, is obtained by using the Taylor’s series expansion with respect to the stiffness matrix of saturated half-space soil in wave-number domain. Finally, two examples are presented to validate the proposed method.