This keynote lecture describes recent analytical and numerical advances in the modeling of the axial nonlinear dynamic interaction between a single pile and its embedding soil. On one hand, analytical solutions are developed for assessing the nonlinear axial dynamic response of the shaft of a pile subjected to dynamic loads, and in particular to vibratory loads. Radial inhomogeneity arising from shear modulus degradation is evaluated over a range of parameters and compared with those obtained

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... other authors and by a numerical radial discrete model simulating the pile and soil movements from integration of the laws of motion. New approximate non linear solutions for axial pile shaft behaviour developed from general elastodynamic equations are presented and compared to existing linear solutions. The soil non linear behaviour and its ability to dissipate mechanical energy upon cyclic loading are shown to have a significant influence on the mechanical impedance provided by the surrounding soil against pile shaft movement. The limitations of over-simplified modelling of pile response are highlighted.