The influence of crack widths on the cracks' behavior in concrete bridges

An often-seen defect in bridges, especially concrete ones, are cracks of various sizes. Whereas small cracks mostly require monitoring, bigger cracks can harm the bridge's safety, leading to closures and extensive maintenance works. We aim to investigate how the different crack widths influence the development of the cracks and their sensitivity to environmental influences, such as temperature. Our example data set stems from a concrete bridge from 1961 in Bochum, Germany. The crack widths are modeled based on a random coefficient autoregressive model by Nicholls and Quinn (1982), which gives more flexibility to the effect of the past. Risk measures known from financial mathematics can, subsequently, help to predict whether the development of a crack leads to a problematic width for a given time horizon. Moreover, due to its nonstationary nature, we benefit from local distance correlation as defined by Jentsch et al. (2020) to describe the interrelation between temperature and crack width.