Probabilistic analysis and simulation of crack propagation in concrete pavements and surfaces

The surface of concrete pavement is susceptible to cracking. The propagation of a crack in a concrete structure may take the form of a one-dimensional line crack, a two-dimensional surface crack, or a three-dimensional volume crack. Predicting crack propagation in a concrete pavement surface is a complicated task. The whole process of formation, propagation, and orientation of cracks can be considered a stochastic process that necessitates a probabilistic investigation approach. In the present study, crack propagation in concrete pavements is studied from a probabilistic point of view using the concepts of multinomial Markov Chains using Random Walks. The study is based on actual probabilities of propagation and orientation of cracks obtained by tracing crack paths from a large dataset of images using custom-built software. Two random walker models are developed using the trinomial and multinomial Markov Chains. The master equation is developed assuming the trinomial Markov Chain, which has been brought for further theoretical and numerical developments. Examples of inferences and numerical simulations are presented to showcase the potential uses and applications of the proposed probabilistic approach for the design and scheduling of inspection visits and maintenance/rehabilitation strategies of concrete pavements and surfaces.