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) in the context of earthquake-induced ground motions. Several statistical properties, which are desirable in IMs when they are used to predict EDPs, have been analysed. Specifically, 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, which is related to the ability of IMs to forecast EDPs 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 IMs have been considered herein. Then, from clouds of IM-EDP points, efficiency, sufficiency and steadfastness 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 IM with an adequate level of steadfastness. For MFA, spectral acceleration-based-IMs 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 IMs 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.

Analysis of Ground Motion Intensity Measures and Selection Techniques for Estimating Building Response

“…lists the steadfastness index for different functional forms and IMs. For our dataset, we observe lower steadfastness for Yeudy et al's[6] functional form (Equation (…”

“…Perrault et al [51] considered a multiple IM approach by including PGA, CAV, Sa(T) and Sv(T) within a frequency range close to the fundamental period of the structure. Yeudy et al [6] included seismological parameters (M w and R epi ) directly in the functional forms (Equation ( 24)), noticing an increased efficiency and sufficiency with respect to M w and R epi . By extending Equation ( 24), we show that IMs can be made even more efficient and sufficient by including soil stiffness parameter (Vs30) and structural period (T f ) in the functional forms (Equations ( 25) and ( 26)).…”

“…Luco and Cornell [5] introduced the term "sufficiency" for IM-EDP relationships that are invariant over magnitude, fault mechanism, epicentral distance, and site class. More recently, Yeudy et al [6] proposed a "steadfastness" measure to determine the robustness of IMs with respect to variations in building properties. It is computed as the ratio of mean of proficiencies when buildings are sorted with respect to the number of stories and total proficiency.…”

Minimum magnitude boundaries in probabilistic seismic hazard analysis: an insight from structural engineering

“…The most popular IMs are Sa(T1,5%), Spectral Acceleration at the natural period of a certain structure, Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), and so on (see also Baker (2005); Mehanny (2009); Tothong and Luco (2007); Ebrahimian et al (2015); O'Reilly (2021)). The relationship between the annual rate of exceedance (seismic hazard) and the structural response is significantly influenced by IM (see Cornell et al, 2002;Vargas-Alzate et al, 2022;Ghafory-Ashtiany et al, 2011 and2012;Mousavi et al, 2011). The literature contains a number of IMs, each with potential drawbacks and some form of gain (Luco and Cornell 2007).…”

Enabling efficient regional seismic fragility assessment of multi‐component bridge portfolios through Gaussian process regression and active learning

“…However, these assumptions are often not satisfied by the NRHA data. For instance, the log‐linear EDP‐IM relationship remains doubtful under certain conditions, such as after the formation of the plastic hinges and a collapse mechanism, 31–33 and the homoskedasticity assumption fails to capture the variation of demand uncertainties at different IM levels (e.g., more divergent responses are expected at high IM levels with more significant nonlinearity) 26 . This study considers the nonparametric GPR to develop multivariate PSDMs that outperform the conventional cloud analysis approach.…”