Lateral Impedance of Single Piles in Inhomogeneous Soil

The flexural stiffness and damping (dynamic impedance) of a single vertical pile in an inhomogeneous soil deposit with continuously increasing stiffness with depth, is studied. An analytical formulation based on the Beam-on-Dynamic-Winkler-Foundation (BDWF) model is implemented. The model is used in conjunction with a virtual work approximation and pertinent shape functions for the deflected shape of a long flexible pile, which are analogous to those used in finite-element formulations. Explicit closed-form solutions are derived for: (1) the dynamic pile stiffness; and (2) the damping coefficient at the pile head. Both swaying and rocking vibrations are considered and all associated impedance coefficients (swaying, rocking, and cross swaying-rocking) are determined. Results from the method are found to be in good agreement with earlier solutions, while new results are developed. The errors resulting from the use of an “equivalent” homogeneous profile with average properties are discussed