Strain effects on kinematic pile bending in layered soil

The kinematic bending of single piles in two-layer soil is explored to account for soil stiffness degradation and associated damping increase with increasing levels of shear strain, a fundamental aspect of soil behaviour which is not incorporated in current simplified seismic design methodologies for pile foundations.A parametric study of a vertical cylindrical pile embedded in a two-layer soil profile to vertically-propagating S waves, carried out in the time domain by a pertinent beam-on-dynamic-Winkler-foundation (BDWF) model, is reported. Strain effects are treated by means of the equivalent-linear procedure which provides soil stiffness and damping ratio as function of shear strain level. Whereas the approach still represents a crude representation of the actual soil behaviour to dynamic loading, it is more realistic than elementary solutions based on linear visco-elasticity adopted in earlier studies.The paper highlights that soil nonlinearity may have either a detrimental or a beneficial effect on kinematic pile bending depending on the circumstances. The predictive equations for kinematic pile bending in visco-elastic soil recently developed by the Authors are extended to encompass strain effects. Numerical examples and comparisons against experimental data from case histories and shaking table tests are presented.