Multi-dimensional fragility analysis considering structural cumulative plastic dissipation energy and its application to a NEES frame structure

Abstract

By integrating the force analogy method in the energy balance equation, the study put forward the concept of cumulative plastic strain (CPS) for seismic fragility analysis, which can be defined as the ratio of the demand of plastic dissipation energy to its capacity. The cumulative plastic strain can reflect the structural damage cumulative effect under earthquakes, which makes it especially suitable as the damage index for the structural component. Firstly, fragility curves are developed according to the maximum inter-story drift. Fragility curves of local components can be also developed assuming that a series of cumulative plastic strain thresholds are given. Further, the real threshold values of cumulative plastic strain are obtained through the degree of coincidence of these two kinds of fragility curves. The cumulative plastic strain and the floor acceleration will be determined as the quantification indices for performance limit state of the structural component and non-structural component, respectively. An innovative probabilistic seismic demand model (PSDM) following multivariate logarithmic normal distribution is constructed. Considering the uncertainty and correlation of performance limit states (PLSs), multi-dimensional PLS formula is developed to identify the structural failure domain. A full-scale 2-bay 2-story frame structure for the Network for Earthquake Engineering Simulation (NEES) project is studied to show the proposed theory. To obtain the maximum structural responses, nonlinear dynamic analysis is carried out. Consequently, the structural multi-dimensional fragility curves are derived based on CPS. In addition, the influence of PLS threshold and PLS correlation on the probability of failure is evaluated. Results show that (1) CPS damage index can fully consider the cumulative effect of damage under earthquakes, and make up for the deficiency of the inter-story drift in this aspect. (2) The multi-dimensional fragility framework can deal with the PLSs correlation and engineering demand parameters correlation simultaneously, which will generate a more precise seismic damage assessment result.