Physics-based fragility functions: Their mathematical formulation and use in the reliability and resilience analysis of transportation infrastructure

Transportation infrastructure provide vital services that support and enable societal functions. Therefore, ensuring their reliability and resilience is of critical importance. The performance of transportation infrastructure relies largely on the performance of bridges. As a result, the performance analysis of bridges subject to natural and/or anthropogenic hazards in relation to the initial damage and the subsequent recovery provides essential information for risk mitigation and management. Fragility functions are commonly used to estimate the vulnerability of bridges subject to hazards. A fragility is defined as the conditional probability of attaining or exceeding a specified performance level given a (set of) hazard intensity measure(s). The development of the fragility functions for bridges has been the subject of much research. This chapter presents a review of the general formulation of physics-based fragility functions as well as the development of time-varying fragility functions that considers the effects of deterioration mechanisms and improvement strategies. The formulation is general and applicable to different structures including, but not limited to, bridges. The chapter also discusses how to update the estimates of the fragility functions using the information from the structural health monitoring (SHM) and non-destructive testing (NDT). The chapter then presents the integration of fragility and recovery functions into time-varying network reliability analysis. Focusing on transportation infrastructure, the chapter reviews the state-of-the-art physics-based fragility functions for bridges subject to multiple hazards and illustrates the use of fragility and recovery functions for the reliability and resilience analysis of an example transportation infrastructure.