The vibration behavior of piled foundations is an important consideration in fields such as earthquake engineering, construction, machine-foundation design, offshore structures, nuclear energy, and road and rail development. This paper presents a review of the past 40 years' literature on modeling the frequency-dependent behavior of pile foundations. Beginning with the earliest model of a single pile, adapted from those for embedded footings, it charts the development of the four pile-modeling techniques: the “dynamic Winkler-foundation” approach that uses springs to represent the effect of the soil; elastic-continuum-type formulations involving the analytical solutions for displacements due to a subsurface disk, cylinder, or other element; boundary element methods; and dynamic finite-element formulations with special nonreflecting boundaries. The modeling of pile groups involves accounting for pile-soil-pile interactions, and four such methods exist: interaction factors; complete pile models; the equivalent pier method; and periodic structure theory. Approaches for validating pile models are also explored.

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