# Reliability Assessment of RC Bridges Subjected to Seismic Loadings
## 1 Introduction  
Many Mexican cities with a high population density, such as Mexico City and Acapulco City, are located in earthquake-prone regions, making them vulnerable to both infrastructure damage and devastation in terms of human lives and economic losses. Communities take years to recover from the economic and social destruction caused by earthquakes. Therefore, earthquake mitigation is of prime importance in the reduction of both the loss of lives and structural damage. In order to ease the recovery period that comes after a seismic event, it is important to estimate the damage condition from a probabilistic point of view, with the objective of calculating an expected structural damage of local infrastructure, such as bridges, which are vital for rescue operations, transport of materials, and emergency equipment. Given the different environmental loads that RC bridges are subjected to during their lifespan, their elements present structural deterioration, causing both a decrease in their structural capacity and a modification of their structural reliability. Therefore, it is indispensable to develop approaches that allow estimating the reliability levels of RC bridges. Several researchers have proposed different approaches to evaluate structural reliability. Based on the above, several researchers have proposed different approaches to evaluating structural reliability. For example, [1,2] estimate the probability failure of structures by means of the Monte Carlo simulation technique using FORM and SORM methods; [3] provide a framework to estimate the time-dependent risk in a multihazard environment in bridges; [4] present a reliability analysis to predict the probability of failure in bridges using the Markov model; [5] estimate the probability of failure of railway bridges for high-speedtrains; [6] propose a reliability assessment in steel bridges considering deterioration due to fatigue. The solution to an engineering problem is not such if it has a short lifespan, or if it generates a structure with overdesigned geometric and physical properties. The high number of uncertainties that engineers face during the design process call for the use of concepts and methodologies of structural reliability. For example, [7] propose a reliability approach to evaluate the structural condition using distribution functions; [8] present an approach to estimate the structural reliability in a rock tunnel obtaining the failure probability from the first-order reliability method (FORM); [9] present a life-cycle management for bridges considering the risk attitude of decision-making; the effect of climate change on performance is also considered. References [10; 11; 12; 13; 14] present approaches with closed-form mathematical expressions. One of the main concerns of structural engineers is how to design a structure capable of resisting extraordinary actions. Such structural demands appear unexpectedly, and can affect the structures, causing undesirable behavior of their components. Thus, it is important to know when the structure could present an undesired behavior. Researchers have proposed different approaches as the basis for obtaining exceedance demand rates (demand hazard curves): [15] perform seismic demand analyses in bridges located in California; [16] analyze the influence of viscous dampers on the probabilistic seismic performance of buildings; [17] calculate exceedance demand rates in concrete buildings; [18] propose demand hazard curves in steel buildings considering the effects of seismic isolation; [19] present a methodology to calculate demand hazard curves in a nuclear power plant; [20] present an approach to estimate seismic exceedance demand rates in gravity dams; [21; 22] compute demand hazard curves in buildings structured with buckling-restrained frames; [23; 24] propose a methodology to perform demand hazard analyses in steel buildings.