Toppling of Rigid Block under Evolutionary Random Base Excitations

The rigid block considered here represents an idealized model for a piece of equipment, a monument, a storage tank, or even a tall building, which may topple by rocking under intense ground shaking at its base during an earthquake. The base excitations consist of both horizontal and vertical ground accelerations, and they are assumed to be nonstationary processes with evolutionary broad-band spectra. The total energy of the rocking block is approximated as a Markov process, and a modified version of quasiconservative averaging is applied to obtain the governing Itô equation for the process. The reliability of the system (namely, the probability that toppling has not occurred up to a given time t ) is calculated by using the numerical procedure of path integration, on the basis that the transition probability density of the Markov process in a sufficiently short time interval is approximately Gaussian.