Probabilistic seismic demand model and fragility estimates for rocking symmetric blocks

Abstract

This paper presents a probability model to predict the maximum rotation of rocking bodies exposed to seismic excitations given particular earthquake intensity measures. After obtaining the nonlinear equations of motion and a clarification of the boundaries applied to a rocking body needed to avoid sliding, a complete discussion is provided for the estimation of the approximate period and equivalent damping ratio for the rocking motion. After that, instead of using an iterative solution, which has been proven defective, a new approximate technique is developed by finding the best representative ground motion intensities. Suitable transformations and normalizations are applied to these intensities, and the Bayesian updating approach is employed to construct a probability model. The proposed probability model is capable of accurately predicting the maximum rotation of a symmetric rocking block given the displacement design spectra, peak ground acceleration, peak ground velocity, and arias intensity of an earthquake. This probabilistic model along with the approximate capacity of rocking blocks are used to estimate the fragility curves for rocking blocks with specific geometrical parameters. In the end, a comprehensive and practical form of fragility curves are provided for design purposes along with numerical examples.