PSI - Issue 44

Fabrizio Paolacci et al. / Procedia Structural Integrity 44 (2023) 307–314 Fabrizio Paolacci et al. / Structural Integrity Procedia 00 (2022) 000–000

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1. Introduction

In the last years, the international codes and the scientific community focused on a performance-based design approach of structures. Performances can be quantified in terms of mean annual frequency, or in term of probability conditioned on a given ‘earthquake scenario’, represented by the worst expected event or the event with the high probability of occurrence. The seismic performance should be considered uncertain both in earthquake occurrence and structural behavior. In this respect, it was proposed to decouple the assessment of the seismic performance of a structure in two distinct sub-steps, (Cornell 1996): the probabilistic seismic hazard analysis (PSHA), as proper feature of the site, and the fragility curves, as feature of the structure. If h is a parameter (or a vector of parameters) that represents the seismic hazard, f H (h) represents its probability density in a time interval and F F ( D | h) is the probability of exceeding the limit state D conditioned to h , the risk can be evaluated as: P(D) = ∫ F F ( D | h) × f h (h)dh (1) The main disadvantage of this approach is that the ground motion is a non-stationary random process, whose characteristics are not easily predictable, especially if a multiple seismic source need to be considered. Moreover, if ℎ is a vector, the evaluation of the function F F ( D | h) can be rather challenging. In this respect, nonlinear dynamic analyses are usually needed, for which a large set of hazard-consistent ground motion records is necessary. For these reasons, it is usually preferable to synthetize the seismic hazard properties by using a scalar or vector-valued Intensity Measure (IM), which must be capable to incorporate the main characteristic of the seismic action (sufficiency), showing at the same time a good correlation with the selected response quantities (efficiency), (Vamvatstikos et al 2005, Phan and Paolacci 2016). Typical IMs are scalar and often identified with the Peak Ground Acceleration PGA, (Paolacci et al 2015), or the spectral acceleration * ( ) at a given vibration period T (usually the fundamental one), (Paolacci et al 2014). In this respect, PGA leads to a large dispersion of the response, whereas better results can be attained using * ( ) , (Shome et al 1998). Nevertheless, some works have also demonstrated that the use of S a (T) can be problematic, especially when, high non-linearity is presents or higher vibration modes are also important, (Alavi and Krawinkler 2004). Baker (2007) proposed vector-valued ground motion intensity using a set of IMs, which is composed by S a (T) and the so called e parameter has been proposed. The parameter e considers the randomness related to the record-to-record variability. In addition, it can be considered as an indicator of the spectral shape. The use of this IM appears effective, even though it is more involved. The definition of e allowed the generation of a new generation of response spectra to be used in the record selection: Conditional Mean Spectrum (CMS). This has been proposed as alternative to the Uniform Hazard Spectrum (UHS) that seem to be in general too much conservative. In Lin et al (2013), the authors proposed a conditional spectrum (CS) that also considers the variability of the response at a certain period, different from the fundamental one. Despite the huge diffusion of CMS approach, it has been strongly criticized. The reason of this criticism derives from the fact that CSM is only based on spectral acceleration, whereas the destructive potential of an earthquake depends also on many other parameters (earthquake intensity PGA, Arias Intensity, earthquake duration, etc..). Moreover, approaches like the abovementioned one do not solve completely the problem. Consequently, the aim of this paper is to propose a novel algorithm for records selection to employ in risk analysis, which can control the record-to-record variability without resorting to the artificial scaling of the accelerograms and thus can be easily employed in three-dimensional structural analysis. 2. A new approach for structural risk assessment Despite the use of different methods for ground motions selection, the fundamental criticism related to the use of iso-probable spectra remains intact. Improved approaches to account for the record-to-record variability do not solve completely the problem. In fact, the CS and its improved versions are still characterized by two additional critical aspects, (Phan et al 2020): i) they represent scenario-based approaches, for which the incompleteness of the disaggregation datasets could represent a problem, especially for the determination of the correlation factors between spectra ordinates for different periods; ii) they are strongly dependent on the ground motion prediction equation. In this respect, some authors tried to mitigate this lack of correlation by means of multiple GMPEs, without solid