Dissertations, Theses, and Capstone Projects

Date of Degree


Document Type


Degree Name





Michel Ghosn

Subject Categories

Civil Engineering | Engineering | Statistics and Probability


Bridge System, Markov Chain, Progressive Collapse, Structural Redundancy, Subset Simulation, System Reliability


Highway bridges like most structural systems are usually designed on a member by member basis and little consideration is provided to the effect of a local failure on system safety. There are concerns that some systems optimized to meet code-specified member design criteria may not provide sufficient levels of structural redundancy to withstand a possible local failure. In fact, a local failure of one structural element may result in the failure of another element creating a chain reaction that might progress throughout the whole structure or a major portion of it leading to a catastrophic collapse. Several recent catastrophic structural collapses have alerted the structural engineering community to the importance of designing structures with sufficient levels of structural redundancy and robustness to make them capable of withstanding local failures and retaining some level of limited functionality. This has led several agencies to develop criteria for evaluating the robustness of structural systems. However, in a departure from LRFD-based code developments, these recently proposed criteria, which are based on deterministic concepts, do not properly account for the random material properties, the variations in the strengths of the members, or the uncertainties associated with modeling the response of structural systems. Furthermore, it is not clear if the existing criteria which were developed for office buildings are applicable to highway bridges subjected to highly stochastic live loads or whether these criteria will lead to similar safety levels for different types of structures.

The object of this Dissertation is to propose a methodology to evaluate the redundancy of highway bridge systems and verify their ability to withstand progressive collapse should a local failure take place. In keeping with current code development approaches, the proposed methodology must be calibrated to provide an acceptable and consistent level of reliability for different types of structures accounting for the uncertainties in estimating the bridge behavior and material properties.

A first step for achieving the objectives of this study is to define non-subjective reliability-based criteria for evaluating the performance of originally intact bridge systems, those that have been subjected to local damage, and assessing the ability of the system to survive the sudden occurrence of local damage. The development of such reliability-based criteria requires the availability of probabilistic analysis algorithms capable of handling complex structural systems with low probability of failure. The review of existing structural system reliability methods shows that a Markov-Chain simulation known as the Subset Simulation method offers many advantages over other available methods for evaluating the reliability of complex structural systems with high numbers of failure modes and low probabilities of failure. To further improve the existing subset simulation algorithm, a hybrid Markov chain Monte Carlo method referred to as "RASS" is proposed. The proposed improvements include: a) a more efficient advanced Markov Chain sample generation algorithm; b) a Delayed Rejection process that allows partial local adaptation of the generated candidate samples at each time step of the Markov chain; c) an Adaptive Algorithm that uses the history of the chain to update the variances of the intermediate proposal probability distribution function; d) a Regeneration process to help in reducing the correlation between the generated samples; and e) a componentwise generation of samples is used to reduce the computational effort associated with multivariate input.

This study demonstrates that the proposed simulation approach is robust to dimension size and is efficient in computing small probabilities of failure for complex structural systems. In addition, this approach can be used to obtain approximate expressions for the limit state equations for the pertinent failure modes.

The applicability of the proposed reliability algorithm in analyzing the system performance of bridge structures and evaluating their levels of redundancy as well as their ability to resist dynamic progressive collapse is demonstrated through several examples for typical I-girder bridges, steel box-girder bridges, and truss systems.

Since involved reliability analyses are beyond the day-to-day practice of bridge engineers, this study proposes an approach to develop a deterministic progressive collapse analysis method for bridges. Following current practice in the development of structural design codes, the deterministic analysis and associated criteria are calibrated to provide adequate and consistent levels of structural reliability for different bridge topologies. The validity of the proposed approach for calibrating progressive collapse analysis criteria is illustrated using two different bridge configurations subjected to different local damage scenarios.