This thesis presents a probability model to predict the maximum rotation of rocking bodies exposed to seismic excitations given specific earthquake intensity measures. After obtaining the nonlinear equations of motion and clarification of the boundaries applied to a rocking body to avoid sliding, a complete discussion is provided on the estimation of approximate period and equivalent damping ratio for the rocking motion. Thereafter, instead of using an iterative solution, which was previously proven defective, a new approximate technique is developed by finding the best representative ground motion intensities. Suitable transformation and normalization 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 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. At the end, a comprehensive and practical form of fragility curves and numerical examples are provided for design purposes.
