Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Document Type


Publication Date



Survival time, reliability, bridge superstructures, Hypertabastic distribution


Bridge reliability analyses form the basis of modern bridge design provisions. Such analyses are also used to evaluate bridge condition and assess future maintenance needs. The majority of these reliability assessments are based on evaluating risks associated with the various load effects exceeding their corresponding resistance. However, bridge components such as decks and superstructures typically do not reach the end of their service lives by exceeding the strength limit states (structural failure). Survival analyses, which are commonly used in biomedical research, consider different factors affecting survival time (or service life) by analyzing large-scale data on survival time and corresponding factors. The survival (reliability) and hazard (failure rate) functions of the bridge (elements) are then determined by fitting the data to an appropriate statistical distribution. Only a few bridge reliability evaluations have been based on survival analyses.

In this research, reliability of bridge superstructures in Wisconsin was investigated through the hypertabastic accelerated failure time survival model. The 2012 National Bridge Inventory (NBI) data were used in the survival analysis. The parameters of the model were determined using the maximum likelihood method.

The type of bridge superstructure, bridge age, maximum span length (MSL) and average daily traffic (ADT) were taken into account to evaluate superstructure survival time. A recorded NBI superstructure condition rating of 5 was considered to be the end of service life for the superstructure.

The results show that the type of superstructures, (ADT), and (MSL) are important factors in survival time of bridge superstructures. The mean age of steel superstructures at the end of service life was larger than that for concrete superstructures. At a given age, as the maximum span length increases, the reliability of the superstructure decreases and the failure rate increases. Similarly, increasing ADT has a significant effect on reducing the superstructure reliability and increasing the failure rate. Although the code-specified bridge design life is 75 years, results showed a very small level of superstructure reliability at that age.