Probabilistic seismic risk forecasting of aging bridge networks Mariano Angelo Zanini ⇑ , Flora Faleschini, Carlo Pellegrino University of Padova, Department of Civil, Environmental and Architectural Engineering, Via Marzolo 9, 35131 Padova, Italy article info Article history: Received 8 February 2016 Revised 16 November 2016 Accepted 12 January 2017 Keywords: Annual loss Bridge networks Brownian Passage Time Deterioration Management policies Seismic risk abstract Bridges are the most vulnerable elements in transport systems, and they may undergo structural prob- lems due to environmental conditions and natural disasters. Governmental agencies and owning compa- nies must therefore plan maintenance and retrofit interventions rationally, to avoid potential severe network disruptions. With reference to seismic risk, several studies on the risk assessment of bridge networks, and on aging as one of the main factors affecting the seismic vulnerability of existing bridges, have recently also been reported. In these contributions, the seismic fragility of bridges is considered as a time-dependent parameter, whereas seismic hazard and financial exposure are described according to classic stationary assumptions. The present study proposes an innovative, comprehensive and fully time-dependent probabilistic seismic risk framework, to evaluate the expected average annual loss for stocks of deteriorating bridge structures. This framework is illustrated in a case study of 500 bridges and the results are critically discussed. Ó 2017 Elsevier Ltd. All rights reserved. 1. Introduction Transport systems play a key role in performing economic and strategic activities and, immediately after a catastrophic event, they allow rescue operations to be initiated. However, such systems, which serve large geographic areas, may be vulnerable to a variety of hazardous natural events, such as earthquakes, hurricanes, floods and tsunamis. Network vulnerability is generally a function of individual network component vulnerabilities: in transport systems, bridges are the most vulnerable components and may also have structural problems, due to environmental conditions and aging. Bridges are usually subject to fluctuations in humidity and temperature, and are also significantly exposed to chloride ions in coastal areas and CO 2 in highly anthropic environments and, over time, these aggressive agents may cause extensive deterioration of structural bridge members. Aging causes a reduction in structural capacity and thus to vulnerability which, in some cases, may lead to structural failure if a hazardous event – such as an earthquake – occurs [1,2]. The estimation of structural and seismic capacity reduction induced by deterioration for exist- ing structures is therefore a matter of recent interest, due to the increasing number of aging bridges and the need to define rational strategies for allocating limited financial resources for retrofit interventions. Recent studies investigating the seismic behavior of deteriorating bridges have been published by several authors [3–10], showing the close link between seismic vulnerability and the time dimension. However, for proper characterization of the seismic risk of a structural system, vulnerability must be associated with the particular seismic hazard of the site and a consequence function expressing structural damage in terms of a chosen variable must be chosen. In this regard, structural engineers play a key role in understanding and communicating the risk of seismic hazards and their uncertainty to owners, bankers and insurers (i.e., the eco- nomic and financial aspects). In 2003, the Pacific Earthquake Engi- neering Research (PEER) Center formulated a Performance-Based Earthquake Engineering (PBEE) probability framework [11], based on the calculation of a triple integral equation, in which random- ness and uncertainty are combined according to the total probabil- ity theorem. Seismic hazard assessment, structural response analysis, quantification of damage, and estimate of damage conse- quences in terms of a chosen decision variable are the main sub- tasks required in the framework. The decision variable may represent a direct consequence of seismic damage, such as recon- struction costs (usually expressed in terms of loss ratio, i.e., the cost to repair a structure hit by a quake divided by the total replacement cost) or as an indirect consequence, commonly expressed by specific traffic indicators [12] (e.g., drivers’ total delay) in the case of analysis of transport networks. An improve- ment to the PEER formula was subsequently developed [13,14] to http://dx.doi.org/10.1016/j.engstruct.2017.01.029 0141-0296/Ó 2017 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: marianoangelo.zanini@dicea.unipd.it (M.A. Zanini). Engineering Structures 136 (2017) 219–232 Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct