Estimating Markov Transition Probabilities for Reinforced Concrete Structures Using Mechanistic-Empirical Models

Current state-of-the-art bridge management systems (BMSs) use Markov models for both the prediction of deterioration and the determination of optimal intervention strategies for reinforced concrete bridges. In using these systems, the results of inspections on bridge elements to determine the condition states of each element are used to estimate the transition probabilities to be used in the Markov models, when they are available over time. In order to use BMSs when they are not available over time, it is necessary to develop a way to estimate transition probabilities to represent the deterioration of bridge elements. One useful way to do this is to use mechanistic-empirical (ME) models. ME models are widely used to model the deterioration of reinforced concrete bridges based on chemical and physical processes, such as chloride induced corrosion and cracking. When a ME model is used, continuous values of deterioration indicators, such as chloride induced corrosion and cracking, can be predicted over time. These values can be then converted into ranges of discrete values and the distribution of discrete values can be estimated at any time step. In this paper, a novel method to estimate the transition probabilities used in Markov models when there is little to no available inspection data is proposed. The proposed method uses two statistical estimation approaches. The first approach (the analytical approach) is used in situations where it is possible to find an analytical solution so that the transition probabilities can be derived directly from the ME models. The second approach (the Bayesian approach) is used in situations where it is not possible to use the analytical approach. It makes use of Bayesian statistics, which requires the formulation of a likelihood function of the transition probabilities and the use of Markov Chain Monte Carlo (MCMC) methods. The proposed method was demonstrated by estimating the transition probabilities for a reinforced concrete bridge element. In the example, the transition probabilities determined resulted in predicted deterioration from the Markov model that was a good fit with the data generated using the ME model, with high level of confidence. The predicted deterioration was also compared to that estimated when a restricted least squared (RLS) optimization method (a RLS approach) was used to estimate the transition probabilities. It was shown that the sum of the residuals over 30 years when the Bayesian approach was used was approximately 40% smaller than that when the RLS approach was used. In particular, in the example, deterioration was over estimated using the RLS approach.

• Supplemental Notes:
  • This paper was sponsored by TRB committee AFF30 Standing Committee on Concrete Bridges.
• Corporate Authors:

  Transportation Research Board

  500 Fifth Street, NW
  Washington, DC  United States  20001
• Authors:
  • Mizutani, Daijiro
  • Lethanh, Nam
  • Adey, Bryan T
  • Kaito, Kiyoyuki
• Conference:
  • Transportation Research Board 96th Annual Meeting
  • Location: Washington DC, United States
  • Date: 2017-1-8 to 2017-1-12
• Date: 2017

Language

• English

Media Info

• Media Type: Digital/other
• Features: Figures; References; Tables;
• Pagination: 25p
• Monograph Title: TRB 96th Annual Meeting Compendium of Papers

Subject/Index Terms

• TRT Terms: Bayes' theorem; Bridge management systems; Corrosion; Cracking; Deterioration; Empirical methods; Markov processes; Optimization; Probability; Reinforced concrete bridges
• Subject Areas: Bridges and other structures; Highways; Maintenance and Preservation;

Filing Info

• Accession Number: 01626541
• Record Type: Publication
• Report/Paper Numbers: 17-01837
• Files: TRIS, TRB, ATRI
• Created Date: Feb 27 2017 9:25AM