The finite element method was designed to solve soil-pile-structure interaction under seismic excitation by introducing solid beam elements to reproduce beam flexure and soil-pile interaction. Dynamic lateral load-deflection relationships were characterized by ratio of soil reaction per unit pile length to product of pile displacement relative to free-field motion and dynamic stress-strain properties of soil. Three hetergeneous soil profiles with equivalent linear approximation of nonlinear stress-strain behavior were used with this new finite element method to study the characteristics of dynamic lateral load-deflection relationships. Results were compared with those by other investigators and showed that the proposed method provided improved means of evaluating load-deflection relationships of piles. Results of this study were used to compute discrete soil-pile springs and dashpots for use in a beam-on-Winkler foundation model. (ASCE)
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Kagawa et al. (1980) studied this question.