Antiplane response of a dike on flexible embedded foundation to incident SH-waves

M. I. Todorovska*, A. Hayir, M. D. Trifunac

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


The response of an elastic circular wedge on a flexible foundation embedded into a half-space is investigated in the frequency domain for incident pane SH-waves. The problem is solved by expansion of the motion in all three media (wedge, foundation and half-space) in cylindrical wave functions (Fourier-Bessel series). The structural model is simple, but accounts for both differential motions of the base and for the effects of soil-structure interaction. Usually, structural models in earthquake engineering consider either differential ground motion, but ignore soil-structure interaction, or consider soil-structure interaction, but for a rigid foundation, thus ignoring differential ground motion. The purpose of the study is to find how stiff the foundation should be relative to the soil so that the rigid foundation assumption in soil-structure interaction models is valid. The shortest wavelength of the incident waves considered in this study is one equal to the width of the base of the wedge. It is concluded that, for this model, a foundation with same mass density as the soil but 50 times larger shear modulus behaves as 'rigid'. For ratio of shear moduli less than 16, the rigid foundation assumption is not valid. Considering differential motions is important because of additional stresses in structures that are not predicted by fixed-base and rigid foundation models.

Original languageEnglish
Pages (from-to)593-601
Number of pages9
JournalSoil Dynamics and Earthquake Engineering
Issue number7
Publication statusPublished - 5 Sept 2001


This work was done while the second author was on leave from the Technical University of Istanbul and was a Postdoctoral Fellow at the University of Southern California. The financial support for his stay from TUBITAK-NATO is gratefully acknowledged. The authors are grateful to T.Y. Hao for her help in preparing the illustrations presented in this paper.

FundersFunder number


    • Differential motion
    • Dynamic interaction
    • Flexible imbedded foundation
    • Soil-structure interaction
    • Wave passage effects


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