Robust Modeling Framework for Transportation Infrastructure System Protection Under Uncertainty

This dissertation presents a modelling framework that will be useful for decision makers at federal and state levels to establish efficient resource allocation schemes to transportation infrastructures on both strategic and tactical levels. In particular, at the upper level, the highway road network carries traffic flows that rely on the performance of individual bridge infrastructure which is optimized through robust design at lower level. A system optimization model is developed to allocate resources to infrastructure systems considering traffic impact, which aims to reduce infrastructure rehabilitation cost, long term economic cost including travel delays due to realization of future natural disasters such as earthquakes. At the lower level, robust design for each individual bridge is confined by the resources allocated from upper level network optimization model, where optimal rehabilitation strategies are selected to improve its resiliency to hedge against potential disasters. The above two decision making processes are interdependent, thus should not be treated separately. Thus, the resultant modeling framework will be a step forward in the disaster management for transportation infrastructure network. This dissertation first presents a novel formulation and a solution algorithm of network level resource allocation problem. A mean-risk two-stage stochastic programming model is developed with the first-stage considering resources allocation and second-stages shows the response from system travel delays, where the conditional value-at-risk (CVaR) is specified as the risk measure. A decomposition method based on generalized Benders decomposition is developed to solve the model, with a concerted effort on overcoming the algorithmic challenges imbedded in non-convexity, nonlinearity and non-separability of first- and second- stage variables. The network level model focusing on traffic optimization is further integrated into a bi-level modeling framework. For lower level, a method using finite element analysis to generate a nonlinear relationship between structural performances of bridges and retrofit levels. This relationship was converted to traffic capacity-cost relationship and used as an input for the upper-level model. Results from the Sioux Falls transportation network demonstrated that the integration of both network and FE modeling for individual structure enhanced the effectiveness of retrofit strategies, compared to linear traffic capacity-cost estimation and conventional engineering practice which prioritizes bridges according to the severity of expected damages of bridges. This dissertation also presents a minimax regret formulation of network protection problem that is integrated with earthquake simulations. The lower level model incorporates a seismic analysis component into the framework such that bridge columns are subject to a set of ground motions. Results of seismic response of bridge structures are used to develop a Pareto front of cost-safety-robustness relationship from which bridge damage scenarios are generated as an input of the network level model