# Modelling the Deterioration of Bridge Decks Based on Semi-Markov Decision Process

Eslam Mohammed Abdelkader (Department of Building, Civil and Environmental Engineering, Concordia University, Quebec, Canada), Tarek Zayed (The Hong Kong Polytechnic University, Hung Hom, Hong Kong) and Mohamed Marzouk (Structural Engineering Department, Faculty of Engineering, Cairo University, Giza, Egypt)
Copyright: © 2019 |Pages: 23
DOI: 10.4018/IJSDS.2019010103
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## Abstract

Deterioration models represent a very important pillar for the effective use of bridge management systems (BMS's). This article presents a probabilistic time-based model that predicts the condition ratings of the concrete bridge decks along their service life. The deterioration process of the concrete bridge decks is modeled using a semi-Markov decision process. The sojourn time of each condition state is fitted to a certain probability distribution based on some goodness of fit tests. The parameters of the probability density functions are obtained using maximum likelihood estimation. The cumulative density functions are defined based on Latin hypercube sampling. Finally, a comparison is conducted between the Markov Chain, semi-Markov chain, Weibull and gamma distributions to select the most accurate prediction model. Results indicate that the semi-Markov model outperformed the other models in terms of three performance indicators are: root-mean square error (RMSE), mean absolute error (MAE), chi-squared statistic (x2).
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## 1. Introduction

Bridges are vital links in transportation networks that should be safe, functional and serviceable during their service life to facilitate the mobility of people and transportation of goods which results in sustainable economic development. Concrete bridges are prone to high level of deterioration because of the variable traffic loading, deferred maintenance, extreme weather conditions, cycles of freeze and thaw, etc. The bridges in Canada are subjected to harsh conditions whereas 22% of the bridges are in a “Fair” condition, 3% of the bridges are in a “Poor” condition, and 1% of the bridges are in a “Very Poor” condition based on Canada’s infrastructure report card (Felio, 2016). One-third of Canada’s bridges have structural or functional deficiencies with short remaining service life where 20 million light vehicles, 750,000 trucks, and 15,000 public transits use Canadian bridges annually (National Research Council Canada, 2013). The average age of the bridges is 24.5 years in 2007 compared to a mean service life of 43.3 years. This means that the bridges in Canada have passed 57% of their useful lifetime (Statistics Canada, 2009a). Bridges in Quebec province have the highest average age of 31 years followed by Nova Scotia with an average age of 28.6 years which means that they require extensive maintenance and repair (Statistics Canada, 2009b).

The degradation in the condition rating of Canada’s infrastructure systems occurs because of two main reasons: 1) the decline in the public investment, and 2) the increase in the average age of the infrastructure systems. The public investment peak was 3% of the gross domestic product (GDP) in the late 1950s and it declined steadily until the mid of 2000s. The decline in the investment is over 40 years from the late of the 1950s to the mid of 2000s. Most of the decline was in the first 20 years where the investment dropped from 1.6% of GDP in 1959 to 0.4% of GDP in 1979) (Mackenzie, 2013). In addition to that, most of Canada’s infrastructure systems were constructed between the 1960s and 1970s. Therefore, they are subjected to high levels of deterioration (Statistics Canada, 2014).

Transportation authorities have developed Bridge Management Systems (BMSs) more than two decades ago in order to maximize the safety, functionality, and serviceability of bridge networks by establishing cost-effective maintenance, repair and rehabilitation activities (MR&R). The management of bridges is nearly impossible without efficient BMSs, especially for large transportation networks. American Association of State Highway and Transportation Officials (AASHTO) and Intermodal Surface Transportation Efficiency Act (ISTEA) defined five main components for BMS which are (Czepiel, 1995): 1) database for data storage, 2) condition rating model, 3) deterioration model, 4) cost model, and 5) optimization model for running system. Deterioration model is one of the main pillars of the BMS because it enables the transportation authorities to predict the future bridge condition ratings. Planning of maintenance, repair and rehabilitation activities of bridges is based on calculating accurate future bridge condition ratings. A high-quality deterioration model enables infrastructure managers to optimize MR&R activities and minimize un-planned maintenance activities. The deterioration model constructs a relationship between the facility condition rating and a group of explanatory variables such as age, traffic volume, weather conditions, percentage of commercial vehicles, etc.

Therefore, the main objectives of the present study are as follows:

• 1.

Review and analyze the research gaps in existing deterioration models of concrete bridge decks;

• 2.

Build a deterioration model based on the semi-Markov decision process;

• 3.

Compare between the developed deterioration model with three other models which are: Markov process, Weibull distribution, and gamma distribution based on some performance metrics.

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## 2. Literature Review

The literature review is divided into two main sections which are: 1) defining the different types of deterioration models, and 2) highlighting the previously developed deterioration model based on their type.

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