Analysis of block random rocking on nonlinear flexible foundation

Antonina Pirrotta, Alberto Di Matteo, Gebel, Pol D. Spanos

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.
Original languageEnglish
Number of pages10
JournalProbabilistic Engineering Mechanics
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Civil and Structural Engineering
  • Nuclear Energy and Engineering
  • Condensed Matter Physics
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering

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