Horizontal Stiffness and Damping of Piles in Inhomogeneous Soil

A practically oriented analytical procedure for determining the dynamic stiffness and damping (impedance coefficients) of a laterally loaded pile in soil exhibiting different types of inhomogeneity with depth, is presented. To this end, an energy method based on the Winkler model of soil reaction in conjunction with pertinent shape functions for the deflected shape of the pile are employed. A new elastodynamic model for the wave field around a pile is also introduced. The method is self-standing and free of empirical formulas or constants. Dimensionless closed-form solutions are derived for (1) the distributed (Winkler) springs and dashpots along the pile; (2) dynamic stiffness and damping coefficients at the pile head; (3) active length, beyond which the pile can be treated as infinitely long; and (4) relative contributions to the overall head stiffness and damping of the soil and the pile media. Swaying, rocking, and cross swaying-rocking impedances are considered for parabolic, exponential, and multilayered inhomogeneous soil. The predictions of the model compare favorably with established solutions, while new results are presented. An illustrative example is provided.