A Framework for Stochastic Finite Element Analysis of Reinforced Concrete Beams Affected by Reinforcement Corrosion

Abstract

Corrosion of reinforcing bars is the major cause of deterioration of reinforced concrete (RC) structures in North America, Europe, the Middle East, and many coastal regions around the world. This deterioration leads to a loss of serviceability and functionality and ultimately affects the structural safety. The objective of this research is to formulate and implement a general stochastic finite element analysis (SFEA) framework for the time-dependent reliability analysis of RC beams with corroding flexural reinforcement. The framework is based on the integration of nonlinear finite element and reliability analyses through an iterative response surface methodology (RSM). Corrosion-induced damage is modelled through the combined effects of gradual loss of the cross-sectional area of the steel reinforcement and the reduction bond between steel and concrete for increasing levels of corrosion. Uncertainties in corrosion rate, material properties, and imposed actions are modelled as random variables. Effective implementation of the framework is achieved by the coupling of commercial finite element and reliability software. Application of the software is demonstrated through a case study of a simply-supported RC girder with tension reinforcement subjected to the effects of uniform (general) corrosion, in which two limit states are considered: (i) a deflection serviceability limit state and (ii) flexural strength ultimate limit state. The results of the case study show that general corrosion leads to a very significant decrease in the reliability of the RC beam both in terms of flexural strength and maximum deflections. The loss of strength and serviceability was shown to be predominantly caused by the loss of bond strength, whereas the gradual reduction of the cross-sectional area of tension reinforcement was found to be insignificant. The load-deflection response is also significantly affected by the deterioration of bond strength (flexural strength and stiffness). The probability of failure at the end of service life, due to the effects of uniform corrosion-induced degradation, is observed to be approximately an order of magnitude higher than in the absence of corrosion. Furthermore, the results suggest that flexural resistance of corroded RC beams is controlled by the anchorage (bond) of the bars and not by the yielding of fully bonded tensile reinforcement at failure. This is significant since the end regions can be severely corroded due to chloride, moisture, and oxygen access at connections and expansion joints. The research strongly suggests that bond damage must be considered in the assessment of the time-dependent reliability of RC beams subjected to general corrosion.