E0-190-2008_(6)Chapter_4

# E0-190-2008_(6)Chapter_4 - Dynamic Soil Structure...

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Kenji MIURA, Dr. Eng. Professor Graduate School of Engineering Hiroshima University Dynamic Soil Structure Interaction

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Dynamic Soil Structure Interaction Chapter 4: Dynamic Impedance Function and Foundation Input Motion Kenji MIURA, Dr. Eng. Professor Graduate School of Engineering Hiroshima University
4. Dynamic Impedance Function and Foundation Input Motion A Sway-Rocking Model is one of dynamic analysis methods for Soil-Structure Interaction (SSI) System. Δ Θ K HH K RR Foundation Building Sway-Rocking Model In this model, a basement or a foundation footing is assumed to be rigid and the interaction effect is incorporated through the dynamic soil springs called Dynamic Impedance Function ”. Foundation Input Motion ” due to earthquake disturbance is applied at the dynamic impedance functions .

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Here, we consider the physical meaning and the evaluation method of the Dynamic Impedance Function and the Foundation Input Motion using a rigid buried structure, which models the foundation as shown below.
(1) The foundation is rigid and vibrating in the lateral direction without rotation . For the simplicity, we assume the foundation is vibrating under the following assumptions: (2) An earthquake disturbance is due to SH type incident earthquake wave propagating upward.

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(3) Soil springs attaching the foundation to the free field soil are K S and K b at the representative points.
An equation of the motion for the foundation model is formulated by: (1) where, Eq.(1) can be rewritten into: (2) m : mass of foundation K s , K b : soil springs U f : lateral displacement of foundation u s , u b : lateral displacement of free field soil

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Putting: b S K K K + = (3) Eq.(2) : (4) Also, putting: (5) Eq.(4) can be rewritten as: (6) can be rearranged as: (2)