Use of Recurrent Markov Chains for Modeling the Crack Performance of Flexible Pavements

Abstract

Accurate prediction of the pavement crack condition is vital for pavement rehabilitation budget allocation. Due to largely nonlinear surface layer properties, randomness in the cracking mechanism, and the complexities involved with deterministic modeling, deterioration of the pavement crack condition has been more efficiently characterized as a stochastic process with Markov chains being an appropriate and popular modeling technique. However, routine Markov modeling techniques suffer from the shortcomings that the transient probabilities have to be computed only implicitly from extensive historical statistics of crack performance and they are also insensitive to timely variations in pavement condition transition trends. This paper presents a new methodology that involves the use of a recurrent or dynamic Markov chain for modeling the pavement crack performance with time in which the transition probabilities are determined based on a logistic model. This model is compatible with basic Markovian concepts since it only uses the current crack condition data along with other relevant data. It is also capable of continuously updating the transition probabilities in an explicit manner. A case study is performed to compare the newly developed recurrent Markov chain with the currently popular static Markov chain. For this comparison, transition probabilities corresponding to both methods are derived from the State of Florida's pavement condition survey database. It is illustrated how the recurrent Markov chain clearly outperforms the static Markov chain in terms of the forecasting accuracy. Therefore it is concluded that by incorporating the dynamics of crack state transition and randomness experienced with the pavement cracking process, the recurrent Markov chain provides a more appropriate, applicable, and above all, a computationally efficient methodology for modeling the pavement deterioration process with respect to cracks.