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 journalArticle

11 Citations (Scopus)

Abstract

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
Volume12
Issue number3
DOIs
Publication statusPublished - Jun 2014

Fingerprint

damping
stiffness
strip
Damping
Stiffness
footing
Bearing capacity
hysteresis
bearing capacity
Hysteresis
Energy dissipation
oscillation
safety
Soils
Radiation
history
vertical motion
energy
strata
approximation

Keywords

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

Cite this

Adamidis, O. ; Gazetas, G. ; Anastasopoulos, I. ; Argyrou, Ch. / Equivalent-linear stiffness and damping in rocking of circular and strip foundations. In: Bulletin of Earthquake Engineering. 2014 ; Vol. 12, No. 3. pp. 1177-1200.
@article{75906a00bdd84ed5b7a32c811ac8d2ec,
title = "Equivalent-linear stiffness and damping in rocking of circular and strip foundations",
abstract = "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.",
keywords = "Equivalent linear, Seismic response, Shallow foundations, Soil failure, Soil-structure interaction, Uplifting",
author = "O. Adamidis and G. Gazetas and I. Anastasopoulos and Ch Argyrou",
year = "2014",
month = "6",
doi = "10.1007/s10518-013-9554-0",
language = "English",
volume = "12",
pages = "1177--1200",
journal = "Bulletin of Earthquake Engineering",
issn = "1570-761X",
publisher = "Springer Verlag",
number = "3",

}

Equivalent-linear stiffness and damping in rocking of circular and strip foundations. / Adamidis, O.; Gazetas, G. (Lead / Corresponding author); Anastasopoulos, I.; Argyrou, Ch.

In: Bulletin of Earthquake Engineering, Vol. 12, No. 3, 06.2014, p. 1177-1200.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Equivalent-linear stiffness and damping in rocking of circular and strip foundations

AU - Adamidis, O.

AU - Gazetas, G.

AU - Anastasopoulos, I.

AU - Argyrou, Ch

PY - 2014/6

Y1 - 2014/6

N2 - 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.

AB - 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.

KW - Equivalent linear

KW - Seismic response

KW - Shallow foundations

KW - Soil failure

KW - Soil-structure interaction

KW - Uplifting

UR - http://www.scopus.com/inward/record.url?scp=84900999522&partnerID=8YFLogxK

U2 - 10.1007/s10518-013-9554-0

DO - 10.1007/s10518-013-9554-0

M3 - Article

VL - 12

SP - 1177

EP - 1200

JO - Bulletin of Earthquake Engineering

JF - Bulletin of Earthquake Engineering

SN - 1570-761X

IS - 3

ER -