Seismic reliability of multi-storey buildings equipped with viscous dampers

Viscous dampers are energy dissipation devices widely employed for the seismic control of new and existing building frames. To date, the performance of systems equipped with viscous dampers has been extensively analyzed by employing deterministic approaches, i.e. by using a one-to-one relationship between the seismic intensity and a response parameters (usually coinciding with the mean response of a set of ground motions with a specific intensity level). However, these approaches neglects the response dispersion due to input uncertainties (the site seismic hazard condition and the record-torecord variability effects) as well as uncertainties of dampers properties. A more comprehensive performance assessment can be carried out by using probabilistic methodologies cable of fully accounting for different sources of uncertainty and the relevant effects on the structural reliability. This paper analyzes the probabilistic seismic performance of building frames equipped with viscous dampers by adopting a probabilistic methodology based on response hazard curves, providing the mean annual frequency (MAF) of exceedance of the response parameters of interest for the performance assessment of building structural and non-structural components and dampers. Finally, in order to quantify the difference between the demands evaluated by the probabilistic and deterministic approaches, ratios (REDP) between the probabilistic demand (characterized by different values of the MAF of exceedance) and the deterministic demand are evaluated. An application example is developed by considering a multi-storey steel frame selected from the SAC Phase II project and widely used in studies on seismic response control problems. A set of cases involving dampers with different exponents α designed for the same deterministic performance objective at a reference seismic intensity is considered. The probability distribution and the demand hazard of the response parameters of interest are evaluated and discussed in a range of variation of annual frequency of exceedance spanning from service to ultimate limit states, considering a range of the nonlinear exponent spanning from 0.15 to 1.00. Particular attention is focused on response parameters relevant to dampers (stroke and force). The ratios R are calculated from these parameters and the obtained values may be interpreted as amplification factors to be applied to the deterministic demand in order to obtain a desired safety level for the damper design. It is shown that the damper nonlinearity strongly affects the building and dampers performance and different trends are observed for different demand parameters. A comparison with code provisions shows that amplification factors currently used for the structural design provide non-homogeneous safety levels and should be improved by considering response variations due to the linear/nonlinear behaviour of the viscous dampers.