Soil–pile interaction in vertical vibration in inhomogeneous soils

Abstract This paper develops a novel reference analytical solution for axially loaded piles in inhomogeneous soils, extending the pioneering elastodynamic model of Nogami and Novak (1976) to piles embedded in vertically inhomogeneous soils. Following the classical earlier model, the pile is modelled as a rod, using the strength‐of‐materials solution, and the soil layer as an approximate continuum, which rest on rigid rock. The approximation lies in reducing the number of dependent variables by eliminating certain stresses and displacements in the governing elastodynamic equations: the vertical normal and vertical shear stresses in the soil are controlled exclusively by the vertical component of the soil displacement. Soil inhomogeneity is introduced via a power law variation of shear modulus with depth, and perfect bonding is assumed at the soil–pile interface. The proposed generalized formulation treats two types of inhomogeneity by employing pertinent eigen expansions of the dependent variables over the vertical coordinate. The response is expressed in terms of generalized Fourier series and includes: (i) displacements and stresses along the pile and the pile–soil interface; and (ii) displacement and stress in the soil. Contrary to available models for homogeneous soils, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered.