For the simplicity we assume the foundation is

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Unformatted text preview: elow. For the simplicity, we assume the foundation is vibrating under the following assumptions: (1) The foundation is rigid and vibrating in the lateral direction without rotation. (2) An earthquake disturbance is due to SH type incident earthquake wave propagating upward. (3) Soil springs attaching the foundation to the free field soil are KS and Kb at the representative points. An equation of the motion for the foundation model is formulated by: (1) where, m : mass of foundation Ks, Kb : soil springs Uf : lateral displacement of foundation us, ub : lateral displacement of free field soil Eq.(1) can be rewritten into: (2) Putting: K = K S + Kb Eq.(2) : (3) (2) can be rearranged as: (4) Also, putting: (5) Eq.(4) can be rewritten as: (6) Expressing uf by: u f = x + ue (7) and substituting Eq.(7) into Eq.(6): (6) then, Eq.(8) can be obtained. (8) (8) Eq.(8) equals a...
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