Contents lists available at ScienceDirect Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn Simplified probabilistic seismic assessment of RC frames with added viscous dampers Luca Landi ⁎ , Cristina Vorabbi, Omar Fabbri, Pier Paolo Diotallevi Department DICAM, University of Bologna, Bologna, Italy ARTICLE INFO Keywords: Nonlinear fluid viscous dampers Nonlinear dynamic analysis Probabilistic method Median Dispersion SAC-FEMA ABSTRACT The object of this paper is the study of simplified probabilistic procedures for the seismic assessment of nonlinear structures equipped with nonlinear fluid viscous dampers. The considered reference probabilistic approach is the SAC-FEMA method, which allows to obtain the probability of exceeding a given performance level. The specific purpose is to study the correlation between the results obtained through the probabilistic seismic assessment method for structures with and without dampers, with emphasis on these results in terms of dispersion. A wide set of recorded ground motions was therefore selected and applied to the considered RC frames. The study was performed without applying scaling factors to the earthquake records, but by selecting different sets of records for increasing values of seismic intensity. All the obtained results were examined considering different criteria, in order to determine the set of time-history analyses to be used for the probabilistic evaluation. Different methods were then applied to obtain the dispersion of the seismic demand. With reference to the application of the SAC-FEMA method, a sensitivity analysis was also performed, considering different procedures to interpolate the hazard curve. From the analyses, it was possible to derive the expressions that allow the results for structures with and without dampers to be correlated, as well as to offer suggestions for applying the SAC-FEMA method. A second purpose of the paper is to propose and apply, in the probabilistic assessment, a direct procedure. This procedure was recently presented by some of the authors as a method to be used for obtaining the response of nonlinear structures with nonlinear viscous dampers as an alternative to expensive nonlinear dynamic analyses. 1. Introduction Over the past fifty years, a large part of research has been dedicated to earthquake-resistant systems developed to raise seismic perfor- mance levels while keeping construction costs within reasonable levels. This aspect is particularly evident in the case of existing buildings that are unable to satisfy the seismic requirements provided by current codes. The retrofit objective of satisfying the seismic requirements of new structures is often economically prohibitive and very difficult to achieve. In these cases an innovative technique as the dissipation of energy by added damping devices may be very promising in improving the seismic performance [1–12]. In rehabilitation interventions, fluid- viscous dampers offer some advantages [3,4], as their behaviour is independent of frequency and their dissipative capacity is very high. Performance-Based Earthquake Engineering (PBEE) is a frame- work used to identify and define desired structural performances for specified seismic intensity levels. Currently, the most advanced PBEE methodologies, such as the PEER PBEE procedure [13,14], have been developed to evaluate seismic performance in terms of expected economic losses, a parameter of particular interest to decision makers. The PEER PBEE procedure consists of four steps of analysis: hazard analysis for the specific site of the building, structural analysis, damage analysis and loss analysis. In all the steps, the related uncertainties are explicitly considered in a probabilistic manner. The second step, in particular, involves a series of nonlinear time-history analyses executed to obtain a probabilistic description of the seismic demand for the building at increasing seismic intensity levels. In this framework, the widespread probabilistic SAC-FEMA ap- proach [15] can be useful for developing simplified procedures [16,17]. This method provides a closed form expression for evaluating the annual probability of exceeding a given limit state, while accounting for record-to-record variability and modelling uncertainties. The method is based on the first two steps in the PBEE process, hazard analysis and structural analysis, and, in general, it requires a series of nonlinear time-history analyses to be performed. This probabilistic approach has been followed in the present study. The purpose of this paper is to http://dx.doi.org/10.1016/j.soildyn.2017.03.003 Received 5 August 2016; Received in revised form 31 January 2017; Accepted 3 March 2017 ⁎ Corresponding author. E-mail address: l.landi@unibo.it (L. Landi). Soil Dynamics and Earthquake Engineering 97 (2017) 277–288 0267-7261/ © 2017 Elsevier Ltd. All rights reserved. MARK