Insight on kinematic bending of flexible piles in layered soil

The behaviour of a kinematically stressed pile in layered soil under the passage of vertically-propagating seismic S waves is investigated by means of rigorous three-dimensional Finite-Element (FE) analyses. Both pile and soil are idealized as linearly viscoelastic materials, modelled by solid elements and pertinent interpolation functions in the realm of classical elastodynamic theory. The system is analyzed by a time-Fourier approach in conjunction with a modal expansion in space. Constant viscous damping is considered for each natural mode, and a FFT algorithm is employed to switch from frequency to time domain and vice versa in natural or generalized coordinates. The scope of the paper is to: (a) provide some rigorous elastodynamic results in both frequency and time domains that can be used as reference cases; (b) elucidate the role of a number of key phenomena and salient dimensionless parameters for the amplitude of pile bending at an interface separating two soil layers of different stiffness; (c) propose a simplified semi-analytical formula for evaluating such moments; (d) provide some remarks about the role of kinematic bending in seismic design of pile foundations, with emphasis on the long-standing issue of establishing an optimal pile diameter to resist such bending. The results of the study offer a new interpretation of kinematic pile bending in terms of the interplay between pile and soil, expressed through dimensionless layer thickness, pile-to-soil stiffness ratio and impedance contrast at the layer interface. A case study from Japan is presented. © 2012 Elsevier Ltd.