Analysis of block random rocking on nonlinear flexible foundation

• Published in: Probabilistic engineering mechanics Vol. 59; p. 103017
• Main Authors: Di Matteo, A., Pirrotta, A., Gebel, E., Spanos, P.D.
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01.01.2020; Elsevier Science Ltd
• Subjects: Computer simulation; Dampers; Equations of motion; Exact solutions; Excitation; Impact loads; Monte Carlo simulation; Nonlinear differential equations; Nonlinear equations; Nonlinear flexible foundation; Numerical integration; Random base excitation; Rigid blocks; Rocking motion; Stochastic models; White noise; Nonlinear flexible foundation; Rocking motion; Random base excitation
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2020.103017

In this paper the rocking response of a rigid block randomly excited at its foundation is examined. A nonlinear flexible foundation model is considered accounting for the possibility of uplifting in the case of strong excitation. Specifically, based on an appropriate nonlinear impact force model, the foundation is treated as a bed of continuously distributed springs in parallel with nonlinear dampers. The statistics of the rocking response is examined by an analytical procedure which involves a combination of static condensation and stochastic linearization methods. In this manner, repeated numerical integration of the highly nonlinear differential equations of motion is circumvented, and a computationally efficient semi-analytical solution is obtained. Comparisons with pertinent Monte Carlo simulations demonstrate the efficiency and reliability of the proposed approach. Finally, the survival probability related to toppling of the blocks subject to filtered white noise excitation is investigated, for different kinds of block geometries, foundation materials, and filter parameters.