Seismic risk analysis for reinforced concrete structures with both random and parallelepiped convex variables

Abstract

This article develops an improved seismic risk assessment formulation exhibiting both random and bounded uncertainties using a probability and parallelepiped convex set mixed model. Limit thresholds for different types of components are described via a probabilistic model. The distribution parameters of limit thresholds are originally treated by employing a multidimensional parallelepiped convex model, in which marginal intervals are utilised to represent scattering levels for the distribution parameters, while relevant angle are employed to express the correlation between uncertain distribution parameters. The structural responses, i.e., engineering demand parameters (EDPs), are considered as correlated random variables and are assumed to follow a multidimensional lognormal distribution. A performance limit state function, which allows considering the relationship between the EDPs and the corresponding limit thresholds, is employed to reflect the coexistence of both random and parallelepiped convex variables. The limit state function is mapped into the standard parameter space via a transformation technique. Then, the improved seismic risk formulation, characterised through a probability and parallelepiped convex mixed variables, can be derived with the combination of the seismic fragility function and the ground motion hazard curve. The main purpose is to illustrate that the performance limit states should be properly modeled as random and parallelepiped convex mixed variables rather than only random or deterministic quantities. A six-story reinforced concrete building designed according to Chinese codes are used to illustrate the proposed approach for constructing hazard curves. The interstory drift and the peak floor acceleration are the selected EDPs, calculated through incremental dynamic analysis. The results demonstrate that the calculated failure probabilities for different limit states in 50 years are found capable of meeting the requirements of Chinese seismic norms after the proposed seismic risk formulation is adopted.