Evaluation of kinematic bending moment for seismically loaded piles at the interface in layered ground

The importance of the kinematic effects, especially at the interface in the layered ground, on the behavior of seismically loaded piles, has been recognized well by academia and industry. In this paper, several widely utilized simplified models for estimating the maximum kinematic pile bending at the interfaces in the layered ground are reviewed, and a series of three-dimensional (3D) numerical models for piles with various spacings, pile numbers, ground conditions, and pile dimensions are employed to examine the kinematic interactions between soil and pile foundations. Based on the extensive numerical parametric study, the group reduction effects for kinematic bending moment are discussed, and the feasibility and reliability of the reviewed simplified models under different ground conditions are evaluated sufficiently. Finally, several empirical formulas for estimating the maximum kinematic pile bending moment under different ground conditions are proposed in this study. Notably, this study presents the first attempt to validate and modify these simplified models specifically for triple-layered ground through comprehensive 3D numerical parametric analysis. Compared with existing models that are mainly applicable to uniform or double-layered ground, the empirical formulas proposed in this study demonstrate applicability for both double-layered and triple-layered ground conditions, significantly enhancing the prediction accuracy of kinematic bending moments of piles under seismic loading in complex ground systems.