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 generalized Winkler model which additionally 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 static regime. While for interface bending 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.