Time-Dependent Resilience of Repairable Structures Subjected to Nonstationary Load and Deterioration for Analysis and Design

Civil structures and infrastructures are often subjected by design to the impacts of natural and human-caused hazardous events, and accordingly may suffer from damages, functionality loss, and failure. In order to quantitatively measure the associated likelihood and consequences for quantifying risks, an appropriate measure of structural reliability and resilience is essentially required. This paper presents an explicit measure for the time-dependent resilience of repairable structures as a natural extension of time-invariant and time-dependent structural reliability concepts, taking into account the effects of structural performance deterioration and nonstationary external loads. First, the resilience measure associated with a single load event is discussed, and an integral-free expression is developed for a special case of structural robustness and recovery. Subsequently, the resilience measure for a planning horizon, which is a function of the duration of considered service period, is proposed in a closed form. Remarkably, the time-dependent resilience can be treated as a generalized form of the time-dependent reliability. Motivated by this, the resilience-based design and cost optimization of structures are also discussed. A numerical example is presented to demonstrate the accuracy and applicability of the proposed resilience measure.