Modeling Bridge Deterioration with Markov Chains

Abstract

This paper describes methods for determining and utilizing Markov chains in the evaluation of highway bridge deterioration. Using a data base of 850 bridges in New York State, Markovian transition matrices (MTM) are first found for the overall bridge condition. Then, transition matrices are developed for the condition rating of individual bridge components (e.g., superstructures, decks, and piers). In each case, chains are determined for various types of construction. Also discussed is the modeling of correlated elements such as the primary structure and joint condition and the ability to determine the correlation for a set of data. The consequence of small data bases is discussed, and an explanation is offered for unexpected values of the transition probabilities. Finally examined is the use of Markovian analysis for predicting the evolution of the average condition rating of a set of bridges, and expected value of condition rating for a single bridge. Markov transition matrices are introduced to model the effects of repairs and to determine repair policies that will lead to constant average condition rating.