Impedance matrices for circular foundation embedded in layered medium

Gin-Show Liou, I.L. Chung

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


A numerical scheme is developed in the paper for Calculating torsional, vertical, horizontal, coupling and rocking impedances in frequency domain for axial-symmetric foundations embedded in layered media. In the scheme, the whole soil domain is divided into interior and exterior domains. For the exterior domain, the analytic solutions with unknown coefficients are obtained by solving three-dimensional (31)) wave equations in cylindrical coordinates satisfying homogeneous boundary conditions. For the interior domain, the analytical solutions are also obtained by solving the same 3D wave equations satisfying the homogeneous boundary conditions and the prescribed boundary conditions. The prescribed conditions are the interaction tractions at the interfaces between embedded foundation and surrounding soil. The interaction tractions are assumed to be piecewise linear. The piecewise linear tractions at the bottom surface of foundation will be decomposed into a series of Bessel functions which can be easily fitted into the general solutions of wave equations in cylindrical coordinates. After all the analytic solutions with unknown coefficients for both interior and exterior domains are found, the variational principle is employed using the continuity conditions (both displacements and stresses) at the interfaces between interior and exterior domains, interior domain and foundation, and exterior domain and foundation to find impedance functions.

Some numerical results of torsional. vertical, horizontal, coupling and rocking impedances with different embedded depths will be presented and comments on the numerical scheme will be given. (c) 2008 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)677-692
Number of pages16
JournalSoil Dynamics and Earthquake Engineering
Issue number4
StatePublished - Apr 2009


  • Wave propagation; Impedance matrix; Dynamic stiffness; Soil-structure interaction

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