An approach to estimate both the reliability index β and its complement, the probability of failure, through closed-form expressions that consider aleatory and epistemic uncertainties, is proposed. Alternatively, exceedance demand rates are obtained based on simplified expressions and numerical integration. Reliability indicators are calculated, considering the uncertainties in the compressive strength of concrete, steel yield, and section geometry, together with the aleatory uncertainties related to seismic loadings. Such indicators are estimated in a continuous RC bridge located in Acapulco, Guerrero, Mexico. The bridge was designed to comply with a drift of 0.004. Exceedance demand rates for drift thresholds from 0.001 to 0.012 are estimated, and maximum differences of 5.5% are found between the closed-form expression and numerical integration. The exceedance demand rate expressed by means of its inverse, the return period, indicates that the serviceability limit state is exceeded after 58 years of the bridge construction. The reliability index decreases by about 1.66%, and the probability of failure increases by about 16.1% when the epistemic uncertainties are considered. The approach shows the importance of epistemic uncertainties in the estimation of reliability indicators.

A methodology to estimate the structural fragility of RC bridges, considering the effects of seismic loadings and corrosion over time, is presented. Two scenarios are considered: (a) The structure is exposed only to seismic loads, (b) Both the effect of corrosion and seismic loads are present in the system. The uncertainties related to material properties, structural geometry, seismic occurrences, corrosion initiation time, cracking and corrosion evolution are considered. Different time stages, such as 0, 50, 75, 100, and 125 years are selected to evaluate the effect of both seismic loads and seismic loads plus corrosion. The calculation of fragility curves implies a structural design, nonlinear modeling of structures with simulated properties, estimation of both corrosion times and seismic occurrences, and evaluation of structural demand over time considering the effect of seismic loads and corrosion. An illustrative example is provided on an RC continuous bridge with AASHTO beams, cap beams and circular columns located in Acapulco, Guerrero, Mexico. A performance level equal to 0.002 is chosen for the design of the structure. Results show that the probability of exceeding the design performance levels for both cases (seismic and seismic plus corrosion) are similar at the stage of time equal to zero (a newly built bridge). However, such probabilities, after 150 years, are equal to 0.61 and 0.85 due to the cumulative damage caused by seismic and seismic plus corrosion, respectively. The estimation of the probability of exceeding a certain performance level, considering the effect of corrosion together with seismic loads, highlights the importance of considering more than one type of solicitation for these kinds of structural systems. Lastly, recommendations about design are given.

This paper proposes an approach to calculate demand hazard curves considering the effect of both corrosion and seismic loadings over time. The corrosion is defined as the reduction of the cross-sectional area in the reinforced bars of concrete, induced by chloride ions. Three corrosion phases are considered: starting time of corrosion, cracking, and evolution time. Seismic loads are characterized as a stochastic Poisson process. Uncertainties related to the randomness of geometric properties, mechanical properties, and seismic loadings are considered. The approach is illustrated in a continuous bridge designed to comply with a drift of 0.002. The structure is located in Acapulco, Guerrero, Mexico. Fragility curves and demand hazard curves are obtained at 0, 45, 57, 75, 100, and 125 years, based on the global drift. The effect of both corrosion and seismic loadings over time increase the annual rate of demand up to 308% between 0 years (without damage) and 125 years after the bridge construction.