New insights into the relationship between seismic intensity measures and nonlinear structural response

Abstract This paper focuses on the probabilistic analysis of Intensity Measures ( IM s) and Engineering Demand Parameters ( EDP s) in the context of earthquake-induced ground motions. Several statistical properties, which are desirable in IM s when they are used to predict EDP s, have been analysed. Specifically, efficiency, sufficiency and steadfastness have been quantified for a set of IM s with respect to two EDP s: the maximum inter-storey drift ratio, MIDR , and the maximum floor acceleration, MFA . Steadfastness is a new statistical property proposed in this article, which is related to the ability of IM s to forecast EDP s for large building suites. In other words, this means that efficiency does not significantly vary when different types of buildings are simultanously considered 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, representing specific building typologies, can be grouped together within a more generic one. The main sources of uncertainty involved in the calculation of the seismic risk have been considered in the analysis. To do so, the nonlinear dynamic responses of probabilistic multi-degree-of-freedom building models, subjected to a large data set of ground motion records, have been calculated. These models have been generated to simulate the dynamic behavior of reinforced concrete buildings whose number of stories vary from 3 to 13. 18 spectrum-, energy- and direct-accelerogram-based IM s have been considered herein. Then, from clouds of IM - EDP points, efficiency, sufficiency and steadfastness have been quantified. For MIDR , results show that IM s 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 IM with an adequate level of steadfastness. For MFA , spectral acceleration-based- IM s are more efficient than velocity-based ones. A comparison is also presented on the use of linear vs quadratic regression models, and their implications on the derivation of fragility functions. Concerning sufficiency, most of the 18 IM s analysed do not have this property. Nonetheless, multi-regression models have been employed to address this lack of sufficiency allowing to obtain a so-called ‘ideal’ IM .