Modeling and validation of three-dimensional sliding-rocking rigid block subjected to earthquake excitation

A freestanding rigid block subjected to earthquake excitation is a problem of significant interest to the earthquake engineering community because it has many direct applications in the seismic performance evaluation of both structural and non-structural components. Previous studies on this classical problem usually assume planar rocking is the only motion that can be activated. However, this is clearly not true when friction coefficient is not sufficiently large or the earthquake excitation is bi-directional. To address this knowledge gap, this paper presents a three-dimensional sliding-rocking rigid body model suitable for dynamic analysis. Important aspects for this model, which include the formulation of nonlinear equations of motion, transitional criteria for different motion modes, as well as the approach to handle the impact, are described. Validation of the proposed model consists of two parts. The first part is the comparison with the numerical prediction from a different model available in the literature. The second part is the comparison with the experimental study from a series of shake table tests using vision-based measurement. These comparisons suggest the proposed model provide relatively good accuracy. Finally, a case study of overturning probability of a non-structural component shows that using a three-dimensional modeling approach can give substantially different result compared to a two-dimensional rocking model, which highlights the necessity of adopting such model.