ارزیابی لرزه ای احتمالی ساده از قاب های RC با میراگرهای ویسکوز اضافه شده Simplified probabilistic seismic assessment of RC frames with added viscous dampers

1. Introduction Over the past fifty years, a large part of research has been dedicated to earthquake-resistant systems developed to raise seismic performance 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, fluidviscous 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 framework 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 approach [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 study the correlation between the results of the probabilistic assessment method for structures with and without dampers, with particular emphasis on the results in terms of dispersion caused by ground motion variability. This paper has studied, in particular, the variability and influence of the parameters in the closed form expression, such as the dispersion of seismic demand. This research takes into account the near collapse limit state, a wide set of ground motions and different methods to approximate the hazard curves. The analyses were performed without applying scaling factors to the earthquake records, and different records for increasing values of seismic intensity were instead used. Considering the current trend of developing simplified procedures to assess performance while avoiding expensive nonlinear time-history analyses, a second purpose of the paper is to apply a direct procedure for assessing the response of nonlinear structures with nonlinear viscous dampers. This procedure was recently proposed by some of the authors and was applied within the considered probabilistic approach.