Equivalent-linear stiffness and damping in rocking of circular and strip foundations

O. Adamidis, G. Gazetas (Lead / Corresponding author), I. Anastasopoulos, Ch Argyrou

    Research output: Contribution to journalArticlepeer-review

    32 Citations (Scopus)


    An approximation is developed for obtaining the nonlinear stiffness KR and damping CR of a shallow circular or strip footing undergoing rocking oscillation on a homogeneous but inelastic undrained clayey stratum. Based on the parametric results of 3-D and 2-D finite-element analyses, equivalent-linear KR and CR are expressed in readily usable dimensionless forms. KR, normalized by its linear elastic value, is shown to be a unique function of: (1) the vertical factor of safety Fs against static bearing capacity failure, and (2) the angle of rotation θ{symbol} normalized by a characteristic angle θ{symbol}s. The latter is approximately the angle for which uplifting usually initiates at one edge of the foundation. Three sources contribute to the value of the dimensionless damping ratio ξR (derived from CR): wave radiation, which is a function of frequency but is shown to amount to <3 %; soil inelasticity (hysteresis), for which graphs are developed in terms of θ{symbol}/θ{symbol}s and Fs; and energy loss due to impact and the collateral vertical motion when severe uplifting takes place, which is tentatively determined from dynamic M: θ{symbol} loops. Comparative parametric seismic time-history analyses provide an adequate validation of the iterative equivalent-linear approximation which implements the developed equivalent KR and ξR, but they also highlight its limitations.

    Original languageEnglish
    Pages (from-to)1177-1200
    Number of pages24
    JournalBulletin of Earthquake Engineering
    Issue number3
    Publication statusPublished - Jun 2014


    • Equivalent linear
    • Seismic response
    • Shallow foundations
    • Soil failure
    • Soil-structure interaction
    • Uplifting

    ASJC Scopus subject areas

    • Geotechnical Engineering and Engineering Geology
    • Geophysics
    • Civil and Structural Engineering
    • Building and Construction


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