ABSTRACT
The physical condition and performance of reinforced concrete bridges that are deteriorating due to chloride induced corrosion of the reinforcement are often predicted using two types of models. The first type is the mechanistic-empirical model that has been extensively used in the field of structural analysis, and can be used to make predictions on a continuous scale. The second type is the Markov model that has been extensively used in the field of bridge management, and can be used to make prediction on a discrete scale. When mechanistic-empirical models are used predictions are made taking into consideration detailed information with respect to how the materials are expected to behave over time (DuraCrete 2000). When Markov models are used, the probability of transitioning from one discrete state to another is estimated using collected information on past condition (Lethanh et al. 2015). In many situations, e.g. when there is an absence of data, it would be beneficial to be able to derive the transition probabilities to be used in Markov models directly from mechanistic-empirical models.
In this paper, a methodology is proposed to estimate the transition probabilities to be used in a Markov model to predict the future condition of a reinforced concrete bridge deck from mechanistic-empirical models. In the methodology, a mechanistic-empirical model is first used to generate condition state data at every time step over a specific time period. The data is then used in the proposed model to estimate the optimal transition probabilities, i.e. the ones that result in the smallest sum of error terms, which are the difference between the predicted state probabilities and observed state probabilities in consecutive years.
The methodology is demonstrated by estimating the optimal transition probabilities for a reinforced concrete bridge in Switzerland.
Figure 1 shows the distribution of state vector obtained from the mechanistic-empirical model. This proportional data was used to generate the optimal Markov transition probability (Table 1). The distribution of state vector over 100 years are shown in Figure 2, which is very similar to the state vector in Figure 1. Distribution of condition state with mechanistic-empirical model. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315207681/cd556cd4-4dcf-4efe-8e29-56fc67b8bfbd/content/fig264_1.tif"/> Markov Transition probability.
CS
1
2
3
4
5
1
0.9396
0.0528
0.0073
0.0001
0.0002
2
0
0.9624
0.0376
0
0
3
0
0
0.9379
0.0545
0.0076
4
0
0
0
0.9141
0.0859
5
0
0
0
0
1
Distribution of condition state with the proposed optimization model. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315207681/cd556cd4-4dcf-4efe-8e29-56fc67b8bfbd/content/fig264_2.tif"/>