PSI - Issue 62

Alberto Contardi et al. / Procedia Structural Integrity 62 (2024) 81–88 Contardi A., La Fortezza F./ Structural Integrity Procedia 00 (2019) 000–000

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purpose of achieving the maximum level of safety in a best cost benefit approach. More than a simple order of priority, infrastructure managers need a complete risk analysis that permits to define not only which bridges are to be restored first but also the type of the needed restoration works and the relevant timeframe. A calculation method has been proposed in a previous article † . In the following chapter the main concepts are reminded. The aim of this article is to deepen a part of the method, giving some indications to estimate the failure costs of a generic bridge. In fact, every Bridge Management System must compare the costs of the restoration works with the costs caused by all the possible collapse of the structure and it is impossible to assess correctly which type of interventions should be scheduled if economic and social risks are not evaluated. It’s also important to remember that there is no need to calculate the right figure of the total damage, but it is fundamental to understand at least the magnitude of risk scenarios. The purpose of this paper is not to give a procedure good for every situation and for every bridge (it would require too much space), but to demonstrate that it is possible to use this type of analysis, that it is quite simple to carry on and that it can lead to useful and reliable results. 2. Risk analysis Consider a reference time period   during which it is necessary to ensure the safety of the bridges of an infrastructure. Throughout the time span considered, maintenance is carried out on each bridge by performing a certain number of activities. Each of these activities can be categorized as follows: • ordinary maintenance interventions aimed at increasing the durability of the bridge, without any increase in its resistant capacity • repair interventions through which the individual structural elements can be modified in order to increase the resistant capacity of the bridge • reconstruction of the deck or of the entire bridge. The basic idea of the proposed method, based on what is indicated in Bulletin FIB n. 80 "Partial factor methods for existing concrete structures", chapter 3.2.2., is that the preferable maintenance strategy is the one which involves the lowest possible total cost for the community, where for each bridge the total cost is expressed by the following formula:   =∑  +∑    (1) where: •   means total cost of the i-th intervention on the bridge in question. •   means total damage caused by exceeding the j-th limit state. •   means probability of exceeding the j-th limit state, calculated with respect to the time interval considered, as a function of the pre-selected maintenance actions. The typical limit states for a medium-sized viaduct could be the following: • collapse of a beam (and therefore of an entire part of the deck) due to vertical traffic loads • collapse of a slab mirror due to a concentrated vertical load • collapse of a pile or a group of bearing devices (and therefore of an entire part of the deck) due to a seismic event, wind or braking on the deck • collapse of the entire structure or part of it due to a hydrogeological event. A maintenance strategy that contemplates a series of demanding interventions will involve very high costs and therefore will maximize the first addendum of the formula, but at the same time it will allow to reduce the probability of collapse and therefore to minimize the second term. Conversely, a strategy with much less invasive interventions (at least even one that envisages doing nothing for the entire reference period) will make it possible to eliminate costs but will also lead to the maximum probability of collapse.

† Contardi, A., Pasqualato, G., 2023. Assessment as to the best strategies for the maintenance of existing bridges