Probabilistic Validation of the Housner Rocking Model

Abstract

Abstract.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 sti↵ness [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.

Physics-informed artificial intelligence models for the seismic response prediction of rocking structures

“…On the other hand, rocking structures are capable of uplifting and sustaining a strong nonlinear motion, while limiting the development of base moments since they are not fixed to the foundation or the ground (Thiers-Moggia and Málaga-Chuquitaype, 2021). It has been proposed that this uplift can act as a sort of rocking isolation for both bridges and buildings (Bachmann et al, 2019; Thiers-Moggia and Málaga-Chuquitaype, 2020; Vassiliou et al, 2021). However, until recently it was been believed that analytical or numerical models can not accurately predict the rocking motion, as many efforts faced frequent failure in the recreation of experimental data (ElGawady et al, 2011; Kalliontzis and Sritharan, 2018).…”

Material Testing of Micro-Concrete and 3d-Printed Reinforcement for Use in Small-Scale Seismic Testing of Rc Structures

“…In parallel, conventional validation test of numerically reproducing the experimentally obtained response to a particular ground motion with acceptable accuracy is too strict of a validation test for structural models [13,14]. The Earthquake Engineering design problem involves predicting the statistics of the response to an ensemble of ground motions characterizing a given seismic hazard; not to a single ground motion.…”