Large displacement behaviour of a structural model with foundation uplift under impulsive and earthquake excitations Earthquake Engineering and Structural Dynamics

This paper considers the dynamical behaviour of a structural model with foundation uplift. The equationsof motion of the system considered are derived for large displacements thus allowing for the eventualoverturning of the system. The transition conditions between successive phases of motion, derived interms of the specic Lagrangian co-ordinates used in the formulation of the equations of motion, presentinnovative aspects which resolve some previously inexplicable behaviour in the structural responsereported in the literature. The dynamical behaviour of the model is considered under impulsive andlong-duration ground motions. The minimum horizontal acceleration impulses for the uplift and theoverturning of the system are evaluated in analytical form. The sensitivity of the model to upliftingand to overturning under impulsive excitations is established as a function of few signicant structuralparameters. Numerical applications have been performed changing either the structural parameters or theloading parameter, in order to analyse several dynamical behaviours and also to validate the analyticalresults. For earthquake ground motions the results, reported in the form of response spectra, show thatlinearized models generally underestimate, sometimes signicantly, the structural response.