Probabilistic resilience assessment framework of structures considering the combined functionality-recovery-duration uncertainty

Abstract

In the current stage, the risk-guided performance-based earthquake engineering (PBEE) has become the main direction in the earthquake community. As an important part of risk, seismic resilience indicators have been increasingly emphasized and elevated to new levels in recent years. Seismic resilience refers to the capacity of social entities to reduce disaster risks and to facilitate recovery efforts with the least social disruption in possible. Currently, the calculations of resilience indicators are commonly based on the deterministic approach. In fact, resilience indicators are also random variables, and the corresponding recovery time, recovery function or residual function in resilience calculation may vary within a range for different intensity levels and limit states. Therefore, characterizing resilience indicators through probabilistic models or confidence intervals can be a more practically valuable and meaningful strategy for future research. In this paper, a probabilistic resilience assessment framework of structures is proposed, and a sinusoidal-based continuous recovery function characterized by different limit states and recovery modes is given. The combined uncertainties of functionality, recovery and duration are incorporated into the framework, and an application example via the reinforced concrete frame is given to implement the framework. Besides, the sensitive analysis of different variables to the resilience assessment result is performed, and the comparison between the deterministic and probabilistic analysis is further discussed. In general, the framework consists of three parts, i.e., (1) Generating samples, fragility and damage states; (2) Calculating total stochastic recovery functions for resilience analyses; and (3) Performing probabilistic seismic resilience analyses. If deterministic analysis is used, the resilience index is only a value, while if probabilistic analysis is used, the resilience index will be a variable with a corresponding probability and distribution range. Compared with other variables, the amplitude and wavelength have a stronger influence in the result of resilience index. This is because these two parameters are function-dependent and will directly affect the envelope curve in the resilience calculation. Although the changes in coefficient of variation (COV) will affect the curve results, the macro characteristics are consistent when comparing different target resilience index. Moreover, as the intensity rises, there is a statistical decrease in both the average residual functionality and resilience indicators, along with a statistical increase in the average recovery durations. The annual exceeding probability decreases as the target resilience level increases, while the life-cycle exceeding probability increases when the target resilience level decreases for the same year. In a sense, the integrated probabilistic resilience framework realizes the decoupling of resilience indicators for different performance groups and limit states, and provides a reference for the further stochastic resilience assessment from a probabilistic perspective.