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.