Impedances of inclined piles: an analytical solution

The paper presents an analytical solution, based on the beam-on-dynamic Winkler foundation approach, for the evaluation of the dynamic impedances of inclined single piles. The Euler-Bernoulli beam model is adopted for the pile whereas analytical expressions available in literature for viscoelastic layers undergoing harmonic vibrations of a rigid disk are used for the soil. The system of partial differential equations, governing the coupled flexural and axial behaviour of the pile embedded in a homogenous soil layer, is solved analytically in terms of exponential matrices. By assuming non-homogeneous kinematic boundary conditions, the dynamic stiffness matrix of the soil-pile system is derived analytically. In the case of layered soils, the pile is discretized into segments within which soil properties are constant and the dynamic stiffness matrix of the system is obtained according to the direct stiffness approach assembling contributions of all segments. Expressions of the soil-foundation impedance functions are derived by the problem condensation. Comparisons of results with those obtained from rigorous boundary element formulations demonstrate that the model, characterised by a very low computational effort, is able to reproduce the dynamic compliance of the soil-pile system with a good level of accuracy.