Risk assessment of block random rocking on nonlinear foundation subject to evolutionary seismic ground motion

This study develops an approximate semi-analytical framework for assessing the toppling survival probability of a rigid block subject to stochastic seismic excitation defined in accordance with modern aseismic codes provisions. The rocking system incorporates a nonlinear flexible foundation model that allows for uplifting and nonlinear damping, reflecting realistic soil–structure interaction effects. A nonlinear contact force of the Hunt and Crossley’s kind is employed. Using a stochastic averaging approach, the proposed method accounts for the unbounded response behavior associated with toppling, paralleling challenges observed in systems with negative stiffness. The nonstationary probability density function (PDF) of the rocking amplitude is formulated to quantify the survival probability over time efficiently. This technique offers significant computational advantages over traditional numerical simulations while capturing the effects of time-dependent excitation intensity and frequency content. Numerical examples, including rigid blocks rocking on various nonlinear flexible foundations under evolutionary seismic excitations, validate the proposed framework. Comparisons with Monte Carlo simulations confirm the accuracy and reliability of the method, emphasizing its utility for probabilistic assessment in seismic engineering contexts.