Development of Probabilistic Framework for Performance-Based Seismic Assessment of Structures Considering Residual Deformations

Recently, the importance of considering residual (permanent) deformations in the performance assessment of structures has been recognized. Advanced structural systems with re-centering properties as those based on unbonded post-tensioning tendons are capable of controlling or completely eliminating residual deformations. However, for more traditional systems, which count for the vast majority of buildings, residual deformations are currently considered an unavoidable result of structural inelastic response under severe seismic shaking.

In this article, a probabilistic framework for a performance-based seismic assessment of structures considering residual deformations is proposed. The development of a probabilistic formulation of a combined three-dimensional performance matrix, where maximum and residual deformations are combined to define the performance level corresponding to various damage states for a given seismic intensity levels, is first presented. Combined fragility curves expressing the probability of exceedence of performance levels defined by pairs of maximum-residual deformations are then derived using bivariate probability distributions. The significance of evaluating and accounting for residual deformations within a Performance-based Earthquake Engineering (PBEE) approach is further confirmed via numerical examples on the response of Single Degree of Freedom (SDOF) systems, with different hysteretic behavior, under a selected suite of earthquake records. Joined fragility curves corresponding to various performance levels, defined as a combination of maximum and residual response parameters, are derived while investigating the effects of hysteretic systems and strength ratios. It is observed that stiffness degrading Takeda systems result in lower residual deformations than elasto-plastic systems and show lower probability of exceeding a jointed maximum-residual performance level. For a chosen performance level, Takeda systems with higher strength ratios show better performance, particularly with lower intensity of excitations.