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 equations of motion of the system considered are derived for large displacements thus allowing for the eventual overturning of the system. The transition conditions between successive phases of motion, derived in terms of the specic Lagrangian co-ordinates used in the formulation of the equations of motion, present innovative aspects which resolve some previously inexplicable behaviour in the structural response reported in the literature. The dynamical behaviour of the model is considered under impulsive and long-duration ground motions. The minimum horizontal acceleration impulses for the uplift and the overturning of the system are evaluated in analytical form. The sensitivity of the model to uplifting and to overturning under impulsive excitations is established as a function of few signicant structural parameters. Numerical applications have been performed changing either the structural parameters or the loading parameter, in order to analyse several dynamical behaviours and also to validate the analytical results. For earthquake ground motions the results, reported in the form of response spectra, show that linearized models generally underestimate, sometimes signicantly, the structural response.