A Distributed Impact Model for Seismic Analysis of Planar Rocking Body

The problem of a planar rigid rocking block subject to dynamic loading is of significant interest to the earthquake engineering community due to its wide application. Despite its simple configuration, rocking itself is a highly nonlinear phenomenon which exhibits non-smooth dynamic behavior. The non-smoothness in dynamics comes from the sudden impact of the rocking body with ground when the sign of rotation angle reverses. Therefore the impact model used in the simulation for rocking problem has a profound influence on the dynamic behavior. Most of existing impact models assume that the impulse during impact is concentrated at the pivot point of the block, ignoring the potential distribution of impulses. This study proposes a distributed impact model for dynamic analysis of planar rigid rocking body. The distributed impulses are achieved through the integration of normal forces induced by penetration over a dummy time period during impact. The distributed impact model is subsequently used to evaluate the post-impact quantities of interest. Numerical simulations suggest Housner's impact model is a special case of the proposed model. The developed impact model is also compared with published experimental result, showing good accuracy. Finally, evaluation of overturning spectra under analytical pulse excitations suggests that using the distributed impact model can give substantially different results compared to the classic concentrated impact model for relatively stocky blocks. Similar observations can also be made when evaluating rocking responses under seismic excitations.