Earthquakes and Structures

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Finite element formulations for free field one-dimensional shear wave propagation

  • Received : 2023.08.28
  • Accepted : 2024.01.10
  • Published : 2024.02.25
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Abstract

Dynamic equilibrium equations for finite element analysis were derived for the free field one-dimensional shear wave propagation through the horizontally layered soil deposits with the elastic half-space. We expressed Rayleigh's viscous damping consisting of mass and stiffness proportional terms. We considered two cases where damping matrices are defined in the total and relative displacement fields. Two forms of equilibrium equations are presented; one in terms of total motions and the other in terms of relative motions. To evaluate the performance of new equilibrium equations, we conducted two sets of site response analyses and directly compared them with the exact closed-form frequency domain solution. Results show that the base shear force as earthquake load represents the simpler form of equilibrium equation to be used for the finite element method. Conventional finite element procedure using base acceleration as earthquake load predicts exact solution reasonably well even in soil deposits with unrealistically high damping.

Keywords

Acknowledgement

This work was partially supported by the "Radioactive Waste Management Program" of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) granted financial resources from the Ministry of Trade, Industry and Energy, Republic of Korea (Project No. 20193210100040).

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