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A simplified 3D model for soil-structure interaction with radiation damping and free field input

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Abstract

This paper addresses the time history finite element analysis of rock-structure interaction. Modeled is not only the lateral energy dissipation, but also the interaction between the far field and the numerical model itself. This is accomplished by a preliminary analysis of the far field as a shear beam (for lateral excitation), and then velocities and displacements are transferred to the model as nodal forces through damping and stiffness matrices respectively. Details of the finite element implementation are given, along with an extensive series of simulations comparing this method, with the one of Lysmer for both 2D and 3D models. The model is derived from the principle of virtual work, and its implementation does not require any modification of existing finite element codes, only clever pre and postprocessing of results are needed.

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Abbreviations

E :

Young modulus

F :

force vector

C :

Damping Matrix

\({{{\bf C}}^L_i}\) :

Lysmer Damping matrix along axis i

F C :

Equivalent nodal forces due to free field velocities

F K :

Equivalent nodal forces due to free field displacements

F R :

Equivalent nodal forces due to free field Rayleigh damping

K :

Stiffness matrix

M :

Mass matrix

N :

Shape functions

t :

Traction vector

t i :

Element size along axis i

\({{\bf u}, \dot{{\bf u}},\ddot{{\bf u}}}\) :

Nodal displacements, velocities and accelerations

U int :

Internal strain energy

V :

Wave velocity

W ext :

External work

ν :

Poisson’s ratio

λ:

Lame parameter

ρ :

Mass density

μ :

Shear modulus

Γ:

Boundary of Ω

Ω:

Element volume

σ :

Stress tensor

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Authors and Affiliations

  1. University of Colorado, Boulder, Colorado, USA

    V. Saouma

  2. Yamaguchi University, Yamaguchi, Japan

    F. Miura

  3. LMT-Cachan, (ENS Cachan/CNRS/UPMC/PRES UniverSud), Paris, France

    G. Lebon

  4. Tokyo Electric Power Service Company, Tokyo, Japan

    Y. Yagome

Authors
  1. V. Saouma
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  2. F. Miura
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  3. G. Lebon
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  4. Y. Yagome
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Correspondence to V. Saouma.

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Saouma, V., Miura, F., Lebon, G. et al. A simplified 3D model for soil-structure interaction with radiation damping and free field input. Bull Earthquake Eng 9, 1387–1402 (2011). https://doi.org/10.1007/s10518-011-9261-7

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  • DOI: https://doi.org/10.1007/s10518-011-9261-7

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