Time-dependent reliability of corrosion-affected RC beams. Part 2: Estimation of time-dependent failure probability

This paper forms the second part of a study which addresses time-dependent reliability analyses of reinforced concrete (RC) beams affected by reinforcement corrosion. Part 1 of the reliability study is presented in the preceding companion paper, wherein for a typical simply supported RC beam, the estimation of time-dependent mean strengths and time-dependent coefficient of variations (c.o.v.) associated with the strengths is presented. These probabilistic descriptions, i.e., mean and c.o.v. for the time-dependent strengths are presented for two limit states: (a) flexural failure, and (b) shear failure. This paper presents the estimation of time-dependent failure probability for a corrosion-affected RC beam; probabilistic descriptions for time-dependent strengths for the beam are taken from the preceding companion paper. Estimation of time-dependent failure probability is also presented by using Monte Carlo Simulation (MCS) that provides an insight about dependence of failure probability on the variability associated with the time-dependent strengths. Analytical formulations are then presented for estimating time-dependent failure probability considering the variability in degradation functions, wherein degradation function is defined as the ratio of strength at time, t, to the initial strength for an un-corroded state of the RC beam. Reasonably good agreement has been observed between the failure probabilities evaluated from analytical formulations and MCS. Parametric analyses show that the failure probability is sensitive to the variability associated with the degradation functions; if it is larger than about 4%.