PROBABILISTIC VALIDATION OF THE HOUSNER ROCKING MODEL

Abstract eng:
The rocking oscillator has drawn the attention of many researchers since the publication of Housner’s [1] seminal paper. As the response of the rocking oscillator is highly non-linear and exhibits negative stiffness [2] many researchers have suggested treating the rocking oscillator as a chaotic system, in the sense that small perturbations of its governing parameters result to widely diverging outcomes. Researchers that have tried to experimentally validate Housner’s model have shown that, given the modelling uncertainty, it is hard to confidently predict the time history response of a rocking block to a specific ground motion. This makes practicing engineers hesitant to adopt rocking as an earthquake response modification strategy. However, accurately predicting the response to a single ground motion would be ideal but it is not a necessary condition to trust a model: there is so much uncertainty in the expected ground motion that could overshadow the modelling uncertainty. To take the former uncertainty into account, in common practice, engineers use an ensemble of ground motions when they perform a time history analysis. Therefore, it is reasonable to try to compare numerical experimental testing results in terms of their statistics. If the numerical model is capable of capturing the statistics of the experimental testing, then, in terms of civil engineering design, the model is trustworthy. The first ones to adopt a probabilistic approach were Yim, Chopra and Penzien [3] who as early as in 1980 observed some order in rocking motion when they studied it from a probabilistic point of view. They observed specific trends in their numerical results when, instead of using only one, they used 10 synthetic ground motions. This paper compares the numerical and experimental response of a rigid rocking block when excited by an ensemble of 100 ground motions that share the statistical properties of original ground motion.

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