Analytical evaluation of impedances and kinematic response of inclined piles

Abstract

This paper presents an analytical model, based on the beam-on-dynamic Winkler foundation approach, for the evaluation of impedances and kinematic response of single inclined piles. The pile is modelled as a Euler–Bernoulli beam having a generic inclination and the soil–pile interaction is captured by defining soil impedances according to expressions available in the literature for viscoelastic layers undergoing harmonic vibrations of a rigid disk. The coupled flexural and axial behaviour of the pile is governed by a system of partial differential equations, with the relevant boundary conditions, that is solved analytically in terms of exponential matrices. The solution for piles embedded in layered soils is achieved according to the direct stiffness approach by using the analytical solutions derived for generic pile sections embedded in homogeneous soils. Expressions of both the soil-foundation impedance functions and the foundation input motion are derived. Some applications, including comparisons of results with those obtained from rigorous boundary element formulations, are performed to evaluate the model capabilities. Classical stiffness and damping coefficients, based on the propagation of shear and pressure waves in plane-strain condition, are used in the applications to account for the soil–pile interaction; anyway, different formulations can be easily implemented.Results of applications, concerning piles with different inclination in both stiff and soft soils, demonstrate that the model, characterised by a very low computational effort, is able to capture the response of inclined piles subjected to seismic loading. Furthermore, with reference to linear problems, the model allows the derivation of the pile stiffness matrix that can be implemented in commercial computer software based on the finite element approach.