Kinematic bending of piles in made ground

This work explores earthquake-induced kinematic bending in the so far unresolved case of a pile embedded in a two-layer soil with a thin surface layer. The problem is treated analytically by means of a generalised Winkler model, which in addition considers the effect of boundary conditions at the pile head over earlier contributions on the subject. Novel analytical closed-form expressions of the kinematic bending moment at the pile head and at the interface between the two soil layers are provided for both fixed- and free-head piles. The analytical solutions are validated through a rigorous finite-element model, which proves a remarkable accuracy in the static regime. While for interface bending the past literature indications for the dynamic coefficient make the proposed formula accurate for both shallow and deep interface, a novel dynamic interaction factor, describing dynamic effects for pile-head bending, is introduced. A numerical example provides guidance on application of the formulae in real design scenarios.