New Insights Into the Relationship Between Seismic Intensity Measures and Nonlinear Structural Response

Abstract

This paper focuses on the probabilistic analysis of Intensity Measures (IMs) and Engineering Demand Parameters (EDPs) for earthquake excitations. Several statistical properties, which are desirable in IMs when they are used to predict EDPs, have been analyzed. The main sources of uncertainty involved in the calculation of the seismic risk have been considered in the analysis. Efficiency, sufficiency and steadfastness have been quantified for a set of IMs with respect to two EDPs: the maximum inter-storey drift ratio, MIDR, and the maximum floor acceleration, MFA. Steadfastness is a new statistical property proposed in this article. It is related to the ability of IMs to forecast EDPs for big building suites. This also means that efficiency does not significantly vary when different types of buildings are included in the statistical analyses. This property allows reducing the number of calculations when performing seismic risk estimations at urban level since, for instance, a large variety of fragility curves of specific buildings can be grouped together within an only one, but more generic, fragility function. The nonlinear dynamic response of probabilistic multi-degree-of-freedom buildings’ models, subjected to a large data set of ground motion records, have been considered to perform the statistical analysis. Specifically, reinforced concrete buildings whose number of stories vary from 3 to 13 stories have been analysed. 18 spectrum-, energy- and direct-accelerogram-based IMs have been considered harein. From the statistical properties of the generated clouds of IM-EDP points, efficiency and sufficiency properties have been quantified. For MIDR, results show that IMs based on spectral velocity are more efficient and steadfast than the ones based on spectral acceleration; spectral velocity averaged in a range of periods, AvSv, has shown to be the most efficient and steadfast IM. The opposite happens for MFA, that is, spectral acceleration-based-IMs are more efficient than the velocity-based ones. A comparison on the use of linear vs quadratic regression models, and their implications on the derivation of fragility functions, is presented as well. Concerning sufficiency, most of the 18 basic IMs analyzed herein do not have this property. However, multi-regression models have been employed to address this lack of sufficiency allowing to obtain a so-called ‘ideal’ IM.