Statistical Validation of Rigid Body Rocking Response Models Against Experimental and Numerical Data
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Slender, free-standing structures subjected to ground motions, may substantially decrease the seismic moment and shear at the base by uplifting and rockingmotion. However, the rocking motion response is sensitive to all parameters, and slight differences in the parameters, can lead to significant changes in the time history. The aim of this study is to explore whether the rocking response could be predicted by a statistical approach. Could the maximum response and the probability of overturning of a rigid rocking oscillator subjected to an ensemble of ground motions with same statistical properties be predicted in terms of average quantities? Two recorded ground motions are used as a basis for generation of two ensembles of 100 statistically similar ground motions. The rocking motion of the oscillator subjected to the ensembles, are tested experimentally on a shaking table to three different prototype scales. Thus 600 laboratory tests establish an experimental basis for statistical comparison with numerical predictions. Conclusions: There is observed an apparent correlation between the statistical distribution of maximum rocking response for the numerical and laboratory results.Based on a limited number of 100 predictions, the maximum response of a rigid rocking oscillator could be well estimated by mean and median values for the two smallest prototype scales. The largest scale shows larger relative errors on the predicted means, but the values are numerically small and prone to be dominated by physical and numerical disturbance. The effect of a slight parameter change that is unpredictable on the individual level, is shown to be more predictable on the distribution of maximum response. These findings support the view that maximum rocking response could be predicted in a statistical manner. Contrastingly, the obtained prediction of overturning is shown to be uncertain and highly sensitive to small changes in coefficient of restitution or accelerations. Based on a limited number of 100 predictions, the probability of overturning is not well estimated. The results that are observed, call in to question whether the probability of overturning could be predicted with the limited number of 100 tests. The estimates on overturning could presumably be improved by increasing the number of test or by studying overturning with more than one variable.