Probability models to assess the seismic safety of rigid block-like structures and the effectiveness of two safety devices

When subject to earthquakes, some objects and structures, such as statues, obelisks, storage systems, and transformers, show a dynamic behavior that can be modeled considering the object/structure as a rigid block. Several papers have studied the dynamic behavior of both stand-alone rigid blocks and systems where rigid blocks have been paired with safety devices to prevent or delay the overturning of the blocks. Although the safety devices have generally been proven to be effective, their effectiveness changes substantially varying the parameters that characterize the system and the seismic input. This paper compares the seismic responses of stand along rigid blocks with those of blocks coupled with two candidate safety devices: an isolating base and a pendulum mass damper. To account for the relevant uncertainties, probabilistic seismic demand models are developed using a Bayesian approach. The probabilistic models are then used along with the overturning capacities of the blocks to construct fragility curves that give a prediction of the probability of overturning occurrence as a function of some characteristics of the blocks, of the safety devices, as well as of the seismic excitation, i.e. the slenderness of the body and the peak ground acceleration. The data needed to develop the probabilistic model are obtained integrating the nonlinear equations of motion of the two systems subject to selected ground motions. In the end, some numerical examples are proposed.