Markov Chain-Based Stochastic Modeling of Chloride Ion Transport in Concrete Bridges

Abstract

Over the last decade, there has been a lot of interest in models for evaluating and predicting the condition of existing bridges in North America due to the large number of them in an advanced state of deterioration. The models have been used to develop optimal strategies to prolong the service life of bridges, allocate limited financial and technical resources and maintain the required level of reliability of the bridges. The main process of deterioration of concrete bridges is corrosion of the reinforcing steel due to chloride ions and models for this type of deterioration can be classified as physical or statistical. The physical models describe the diffusion of chloride ions in concrete and chemical reactions while the statistical models, such as Markov chains, are used to model the progression of states of deterioration of the concrete structures. The physical models are appropriate to analyze deterioration processes for various structures and conditions of exposure but are computationally too demanding for the portfolio analysis of a large number of structures. Markov chain models have been extensively used for the latter purpose but require an extensive historical database to correctly estimate transition probabilities between deterioration states. The objective of this paper is to propose a novel procedure for estimating transition probabilities for Markov chain models by utilizing targeted simulations from physical models. The transition probabilities can be derived from specific climatological regions and concrete properties. The proposed framework provides the required input for portfolio analyses for a large number of different types of structures exposed to different climatological conditions. The procedure is demonstrated with the TransChlor® software and for a group of structures located in Montreal, Canada.