Modelling of rocking structures: Are our models good enough?

Numerical models developed to predict the seismic response of structures deforming into the inelastic range often fail the conventional validation test: They fail to reproduce the experimentally obtained response to a particular ground motion with acceptable accuracy. This paper claims that this is too strict of a test for seismic response modelling. 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. This is a weaker model validation test that requires that the structural model to only to be unbiased and to introduce less uncertainty than the uncertainty of the excitation itself. In this paper, we propose a weak form of seismic response analysis model validation. As an example, we use the 1963 Housner dynamic response model of a rocking structure. We performed 600 shaking table seismic response tests using a welldefined and repeatable rocking structure as well as 600 numerical simulations of these tests, and compared both the individual test response and the statistical aggregates of these response focused on predicting limit states such as overturning or maximum tilt angle. We show that the 1963 Housner model passes the weak validation test even though it fails the strong validation test. Therefore, the model is good enough for the scope of Earthquake Engineering. In conclusion, we propose broader application of weak validation models and outline possible acceptance criteria consistent with probabilistic seismic performance objectives for design and evaluation of structures.