### Abstract

An approximation is developed for obtaining the nonlinear stiffness K_{R} and damping C_{R} 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 K_{R} and C_{R} are expressed in readily usable dimensionless forms. K_{R}, normalized by its linear elastic value, is shown to be a unique function of: (1) the vertical factor of safety F_{s} 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 ξ_{R} (derived from C_{R}): 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 F_{s}; 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 K_{R} and ξ_{R}, but they also highlight its limitations.

Original language | English |
---|---|

Pages (from-to) | 1177-1200 |

Number of pages | 24 |

Journal | Bulletin of Earthquake Engineering |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jun 2014 |

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### Keywords

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

### Cite this

*Bulletin of Earthquake Engineering*,

*12*(3), 1177-1200. https://doi.org/10.1007/s10518-013-9554-0

}

*Bulletin of Earthquake Engineering*, vol. 12, no. 3, pp. 1177-1200. https://doi.org/10.1007/s10518-013-9554-0

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

Research output: Contribution to journal › Article

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 -