Probabilistic Models to Assess the Seismic Safety of Rigid Block-Like Elements 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. To reduce the likelihood of the failure of these kinds of elements, they can be paired with safety devices that are designed to avert the overturning of the blocks. Although safety devices have proven to be effective, their effectiveness changes substantially as a function of the seismic input (which is generally uncertain) and the parameters that characterize the system. Furthermore, there is a need to quantify probabilistically the effectiveness of safety devices. This paper proposes probabilistic models to evaluate the failure probability of block-like elements coupled with a safety device. The paper considers two candidate safety devices: an isolating base and a pendulum mass damper. The proposed models are then used to compare the seismic responses of coupled block-device systems with one of stand-alone rigid block-like elements. To account for the relevant uncertainties, expressions for the probability of failure are developed using a logistic regression model calibrated with a Bayesian approach. The expressions of the probability of failure are then used to construct fragility curves that give estimates of the conditional probability of overturning occurrence as a function of some characteristics of the blocks (i.e., the slenderness of the rigid body) and the safety devices (i.e., the characteristic period) for a given seismic excitation (i.e., 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. The proposed models and fragility estimates can be used to quantify the likelihood of failure of rigid block-like elements due to seismic excitations as well as the effectiveness of two common safety devices. It is found that, for the adopted ratio between the mass of the block-like element and the mass of the safety devices, base isolation works better than a pendulum mass damper.