Kinematic pile-head bending under large earthquake-induced shear strains

The problem of kinematic bending moments imposed at the head of a single pile during the passage of seismic waves is explored under large shear strains in the surrounding soil. To this end, non-linear soil response at free-field conditions is derived numerically by a freely-available 1D code and then utilized to calibrate the constitutive law of soil introduced in a rigorous 3D Finite-Difference (FD) model of the soil-pile system employed to obtain pile's head bending moments. The pile is considered embedded to a normally-consolidated clay and seven earthquake records with different amplitude and frequency content are imposed as input motions at the base of the soil layer, thus allowing the investigation of pile kinematic bending with increasing levels of shear strains in the soil, exceeding the limit of equivalent-linear soil behavior. The performance of a simple analytical expression for predicting the kinematic bending moment at the pile-head is compared to the rigorous FD solution. It is concluded that this simple solution is still applicable, with slight modifications, for high shear strains related to non-linear soil behavior close to shear failure, provided that the proper mobilized soil properties from 1D soil response analysis are introduced.