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Earthquakes and Structures Volume 26, Number 2, February 2024 , pages 163-174 DOI: https://doi.org/10.12989/eas.2024.26.2.163 |
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 open accessFinite element formulations for free field one-dimensional shear wave propagation |
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Sun-Hoon Kim and Kwang-Jin Kim
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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. | ||
| Key Words | ||
| base acceleration; base shear force; dynamic equilibrium equation; elastic half-space; free field analysis; shear wave propagation | ||
| Address | ||
| Sun-Hoon Kim: Department of Civil and Environmental Engineering, U1 University, Yeoungdong-kun, Chungbuk 29131, Republic of Korea Kwang-Jin Kim: Comtec Research, Seocho-ku, Seoul 06650, Republic of Korea | ||