The P2.5D finite element method for periodic structures in half-space soil with application to periodic pile rows

In this study, by using periodic pile rows (PPRs) as an example, a new finite element method, namely, the periodic 2.5D finite element method (P2.5D FEM) is developed for the periodic structure embedded in soil. Similar to the 2.5D FEM, the major advantage of the proposed P2.5D FEM is its ability to reduce the 3-D dynamic problem associated with the periodic soil-structure system to a series of 2-D problems. The considered PPR-soil system, referred to as the periodic pile-soil system (PPSS) subsequently is supposed to be subjected to a harmonic point load. To develop the P2.5D FEM for the PPSS, the harmonic point load is decomposed into its wavenumber domain components first. The response of the PPSS to each wavenumber domain load component is then resolved into a series of pseudo plane waves propagating along the z-direction. The quantities for the pseudo plane wave are discretized by the FEM along the cross-section of the PPSS, and the FEM equations for the pseudo plane waves are then established. The eigenequation for the pseudo plane waves can be developed with the aforementioned FEM equations. Summation of the eigenvectors of the eigenequation for the PPSS yields the displacement for the PPSS due to the wavenumber domain load component. Synthesizing the displacements due to all the wavenumber domain load components via the inverse Fourier transform with respect to the wave number yields the overall displacement of the PPSS produced by the point load. To show the capability of the proposed P2.5D FEM for the PPSS, some numerical results about the wave barrier effect of PPRs are presented. The developed P2.5D FEM in this study is applicable to the dynamic analysis of various periodic structures embedded in the half-space soil under different types of dynamic loads.