AN EFFICIENT PROBABILISTIC FRAMEWORK FOR SEISMIC RISK ANALYSIS OF STRUCTURAL SYSTEMS EQUIPPED WITH LINEAR AND NONLINEAR VISCOUS DAMPERS

Seismic passive protection with supplemental damping devices represents an efficient strategy to produce resilient structural systems with improved seismic performances and notably reduced post-earthquake consequences. Such strategy offers indeed several advantages with respect to the ordinary seismic design philosophy: structural damages are prevented; the safety of the occupants is ensured and the system remains operational both during and right after the earthquake; no major retrofit interventions are needed but only a post-earthquake inspection (and if necessary, replacement) of dissipation devices is required; a noticeable reduction of both direct and indirect outlays is achieved. However, structural systems equipped with seismic control devices (dampers) may show potentially limited robustness, since an unexpected early disruption on the dampers may lead to a progressive collapse of the actually non-ductile system. Although the most advanced international seismic codes acknowledge this issue and require dampers to have higher safety margins against the failure, they only provide simplified approaches to cope with the problem, often consisting of general demand amplification rules which are not tailored on the actual needs of different device typologies and which lead to reliability levels not explicitly declared. The research activity carried out within this Thesis stems from the need to fill the gaps still present in the international regulatory framework, and respond to the scarcity of specific probabilistic studies geared to characterize and understand the probabilistic seismic response of such systems up to very low failure probabilities. In particular, as a first step towards this goal, the present work aims at addressing the issue of the seismic risk of structures with fluid viscous dampers, a simple and widely used class of dissipation devices. A robust probabilistic framework has been defined for the purposes of the present work, made up of the combination of an advanced probabilistic tool for solving reliability problems, consisting of Subset Simulation (with Markov chain Monte Carlo and Metropolis-like algorithms), and a stochastic ground motion model for statistical seismic hazard characterization. The seismic performance of the system is described by means of demand hazard curves, providing the mean annual frequency of exceeding any specified threshold demand value for all the relevant global and local Engineering Demand Parameters (EDPs). A wide range of performance levels is monitored, encompassing the serviceability conditions, the ultimate limit states, up to very rare performance demand levels (with mean annual frequency of exceedance around 10-6) at which the seismic reliability shall be checked in order to confer the system an adequate level of safety margins against seismic events rarer than the design one. Some original contributions regarding the methodological approaches have been obtained by an efficient combination of the common conditional probabilistic methods (i.e., multiple-stripe and cloud analysis) with a stochastic earthquake model, in which subset simulation is exploited for efficiently generate both the seismic hazard curve and the ground motion samples for structural analysis purposes. The accuracy of the proposed strategy is assessed by comparing the achieved seismic risk estimates with those provided via Subset Simulation, the latter being assumed as reference reliability method. Furthermore, a reliability-based optimization method is proposed as powerful tool for investigating upon the seismic risk sensitivity to variable model parameters. Such method proves to be particularly useful when a proper statistical characterization of the model parameters is not available. The proposed probabilistic framework is applied to a set of single-degree-of-freedom damped models to carry out an extensive parametric analysis, and to a multi-story steel building with linear and nonlinear viscous dampers for the aims of a deeper investigation. The influence of viscous dampers nonlinearity level on the seismic risk of such systems is investigated. The variability of viscous constitutive parameters due to the tolerance allowed in devices’ quality control and production tests is also accounted for, and the consequential effects on the seismic performances are evaluated. The reliability of simplified approaches proposed by the main international seismic codes for dampers design is assessed, the main regulatory gaps are highlighted and proposals for improvement are given as well. Results from this whole probabilistic investigation contribute to the development of more reliable design procedures for seismic passive protection strategies.