First Advisor

Thomas Schumacher

Term of Graduation

January 2023

Date of Publication


Document Type





Bayesian Network, Bridges, Failure, Probabilistic, Reliability, Uncertainty

Physical Description

1 online resource ( pages)


From the day a new structure is made available for use, to the day that the structure is no longer able to fulfill an intended purpose, structural safety is a vital interest. Managing a portfolio of structures can be a difficult undertaking for an asset manager, particularly if different types of structures are being maintained. The goal is to manage assets in the most efficient manner which can be influenced by, at a minimum, safety and financial concerns.

A potential tool for an asset manager or owner is the use of Bayesian Networks (BNs). When a BN is used to model the structural capacity of individual components and the external loads applied to those components, then an important piece of information becomes available. Through the BN, an asset manager can have an estimate of the component Probability of Failure ($P_{\!f}$). These component values for $P_{\!f}$ can be compared directly, or combined to develop estimates of system probabilities of failure. For a bridge portfolio, the asset manager can compare the $P_{\!f}$ values of individual girders on a given bridge, or the $P_{\!f}$ values of bridges considered as systems of individual components. From these values, the owner can decide how maintenance and replacement activities can be scheduled, where the elements/systems with the higher $P_{\!f}$ would be given priority.

The objective of this research is to develop tools that show the viability of using Bayesian Networks to model bridge structures so that an objective estimate of $P_{\!f}$ is provided for individual components. To do this, models are created that directly calculate the component capacity (R) taking into account statistical uncertainty of primary variables such as steel yield strength ($f_y$) and concrete compressive strength ($f_c^\prime$), in addition to the effects of concrete deterioration. The structural capacity ($R$) is compared directly to modeled load effects ($Q$), resulting in a limit state node ($R-Q$), from which the $P_{\!f}$ and reliability index, $\beta$, are directly determined.

Bridge load ratings are used to indicate how much capacity is present in excess of that needed to support dead loads, or how much live load can still be supported without failure. A load rating can be calculated to reflect a target structural reliability. For example, the AASHTO Load and Resistance Rating (LRFR) load rating process strives for a reliability index of $\beta=3.5$ for an \emph{Inventory} rating, and a reliability index of $\beta=2.5$ for an \emph{Operating} rating. A very handy advantage of using BNs to determine the structural $P_{\!f}$ and reliability is that the live load can be easily scaled to result in a target reliability, resulting in the direct determination of the load rating factor of the component.

Multiple BNs are described in this dissertation, where bridges using three types of materials are modeled: steel, reinforced concrete, and prestressed concrete. A common thread through each of the examples is to illustrate how the capacities are modeled for each bridge type, how the $P_{\!f}$ values are determined, and then how the Rating Factor (RF) values are determined.

An additional strength of using BNs is the ability of the network to be extended. For example, only concrete deterioration is currently considered, but other modes of deterioration could be added to the models to include cross section loss of steel due to corrosion in steel girders or steel reinforcement in concrete members.

This dissertation uses the multi-paper format in accordance with PSU Graduate School guidelines. Therefore, Chapter 1 serves as an introduction, Chapters 2-4 are journal papers that have been published or are under review at the time of dissertation submission, and Chapter 5 is the final chapter with a summary and discussion about future work.


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Available for download on Saturday, February 01, 2025