A numerical approach is presented to calculate the dynamic response of a group of rigid surface foundations. The formulation is unconditionally stable and has the computational simplicity with only the algebraic calculations involved. It imposes no limit to the foundation shape, foundation separations, thickness of the layered medium and magnitude of frequency. In the analysis, the foundation–ground interface is discretized into a number of sub square-regions. The Green’s function, which is obtained by the Fourier–Bessel transform and precise integration method, is employed to calculate the dynamic response of each sub-region. Finally, a system of linear algebraic equation in terms of the contact forces within each sub-region is observed, which leads to the desired dynamic impedance functions of the foundations. Comparison is carried out between the proposed method and the solutions available in the literature. Parametric studies on the dynamic interaction between adjacent foundations are also described. Addressed in this study are the effects of the distance and direction of foundation alignment. Several conclusions are drawn the significance of each factor. Illustrative results for a case of several closely-spaced foundations are also presented. Although the dynamic interaction analysis of foundations is concerned here, further applications of this approach can be extended to the interaction analysis of structures.
A numerical approach for a hemivariational inequality concerning the seismic interaction between adjacent buildings
