Prediction of Crack Propagation in U-Rib Components Based on the Markov Chain

Abstract

A Markov chain model was introduced to study the crack propagation law of butt welds in the U-ribs of the orthotropic steel decks of a long-span steel box girder suspension bridge, such as the Xihoumen Bridge. First, the time–frequency characteristics of the long-term strain monitoring data of the steel box girder of the Xihoumen Bridge were analyzed. A wavelet wave analysis was used to separate the stress–time history of the bridge deck structure caused by environmental temperature. Moreover, to eliminate the low-amplitude stress variation caused by random environmental excitation and measurement noise, the appropriate threshold was selected for the wavelet transform coefficient at different scales. The rain flow counting method was used to statistically analyze the strain monitoring data under vehicle loads. The fatigue stress range was obtained, and the daily effective stress range was calculated. Then, the state transition probability matrix of the vulnerable point crack propagation at the joint was constructed by the equation of linear elastic fracture mechanics. Based on the Markov chain, the fatigue crack depth value along the service time and the crack depth propagation curve of the joint was obtained using the probability distribution vector of the initial state and the state transition probability matrix. The results reveal that the established fatigue state analysis model can consider the correlation of each state in the crack propagation process of the components and can predict the variation in the U-rib fatigue state of the orthotropic steel decks along the service time of the bridge according to the changes in vehicle flow. The analysis model helps assess the service performance of orthotropic steel decks of steel box girders.