Bi-level resource allocation framework for retrofitting bridges in a transportation network

Bridges connect roadways over natural barriers to form transportation networks. Retrofitting at-risk bridges is a proactive strategy to reduce the vulnerability of the traffic network in the face of natural and manmade disasters. The challenge lies in the allocation of limited resources to different bridges that must not only capture the structural performance of a bridge, but also the impact of the bridge on a transportation network. This paper present a novel, bi-level resource allocation framework that integrates the network protection problem based on traffic optimization at the network level with the structural enhancement problem at the bridge level to achieve cost-effective retrofit strategies for at-risk bridges. In particular, a stochastic programming model was used at the upper level to allocate resources to the network of bridges considering the improvement in bridge traffic capacity through the allocated budget. At the lower level, finite element models were developed to estimate a relationship between the structural performance of bridges and retrofit levels. This relationship was converted to a traffic capacity-cost relationship and used as an input for the upper-level model. The integrated modeling framework is demonstrated with the Sioux Falls, South Dakota, road network, in which critical factors (such as budget levels) on the retrofit strategy were analyzed.