Kinematic bending of piles in inhomogeneous soil is explored in static and dynamic regime. The system under consideration consists of a fixed-head pile embedded in a continuously inhomogeneous viscoelastic soil layer resting on a rigid base. A generalized parabolic function is employed to describe the variable shear modulus in the inhomogeneous stratum. The problem is treated numerically by means of rigorous elastodynamic finite-element analyses and Beam-on-Dynamic-Winkler-Foundation (BDWF) formulations. A design formula for kinematic pile-head moments is derived both for static and dynamic loading by employing a characteristic pile wavenumber. A new normalization scheme for dynamic pile bending is proposed by means of a single dimensionless frequency parameter governing kinematic pile-head moments. A numerical example is also provided.

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 formulae or constants.Dimensionless closed-form solutions are derived for: (1) the distributed (Winkler) springs and dashpots along the pile; (2) the dynamic stiffness and damping coefficients at the pile head; (3) the "active" length beyond which the pile can be treated as infinitely long; (4) the 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 multi-layered inhomogeneous soil. The predictions of the model compare favorably with established solutions, while new results are presented. An illustrative example is provided.

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Abstract. The focus of the present study is upon the influence of liquefaction on the dynamic