The dynamic response analysis, the soil reactions must include damping and are often modeled by uncoupled springs and dashpots. The constants of these springs and dashpots of visco-elastic soil may be derived from continuum equations under plane strain conditions. Such approximate soil model con yield reasonable results under the dynamic condition as comparison to examine the nature of the local spring and damping constants in terms of a more rigorous solution in which the three-dimensionality of the soil medium and its dynamic interaction with the pile are accounted for This is the aim of this paper.
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Nogami et al. (1980) studied this question.