A competing Markov model for cracking prediction on civil structures

• We model cracking processes on pavement surface using a novel Markov model.
• We discuss a competing process in selecting the representative cracking types and crack damage levels in practice.
• We develop an algorithm for estimating values of model’s parameters using Bayesian estimation approach and Markov Chain Monte Carlo simulation.
• Development of cracking types are interdependent deterioration processes.

Cracks on the surface of civil structures (e.g. pavement sections, concrete structures) progress in several formations and under different deterioration mechanisms. In monitoring practice, it is often that cracking type with its worst damage level is selected as a representative condition state, while other cracking types and their damage levels are neglected in records, remaining as hidden information. Therefore, the practice in monitoring has a potential to conceal with a bias selection process, which possibly result in not optimal intervention strategies. In overcoming these problems, our paper presents a non-homogeneous Markov hazard model, with competing hazard rates. Cracking condition states are classified in three types (longitudinal crack, horizontal crack, and alligator crack), with three respective damage levels. The dynamic selection of cracking condition states are undergone a competing process of cracking types and damage levels. We apply a numerical solution using Bayesian estimation and Markov Chain Monte Carlo method to solve the problem of high-order integration of complete likelihood function. An empirical study on a data-set of Japanese pavement system is presented to demonstrate the applicability and contribution of the model.