This is a classic collective risk problem. If the risk of flood-induced failure is known for individual culverts and bridges along the railway line, what is the risk to the rail link as a whole?
If there are N crossings in all, the annual probability of failure would appear to be N times the annual probability of failure at a typical structure. But this presumes that the crossings are far enough apart, and the regimes of the rivers sufficiently different, for flooding at any one site to be independent of flooding at the other sites.
In practice, this is never the case. There is spatial dependence in river flooding, and the N crossings will behave like Ne independent crossings, where Ne lies somewhere between 1 (fully dependent case) and N (fully independent case).
Dependence is good news for the rail operator: the rail link will tend to fail less frequently than in the independent case. However, it is a mixed blessing for the company maintaining the track. After a long trouble-free period, they may suddenly have many structures to repair.
There is exciting research to be done on modelling inter-site dependence in river flooding. Some recent work showed that inter-site dependence in river flooding is stronger than that in extreme rainfalls. This is thought to reflect the important role of antecedent wetness, and spatial dependence therein. A paper (Why analyse inter-site dependence in river flooding?) discusses applications to more conventional flood risk problems.
If you would like to know more, please do get in touch.