# Seismic Risk Analysis of Existing Link Slab Bridges Using Novel Fragility Functions
## 5 Conclusions  
A comprehensive probabilistic framework is proposed and adopted in this study to perform seismic reliability and risk analysis of existing link slab (LS) bridges, which  
Figure 16: Annual failure rates comparison among bridges with different geometries: (**a**) single-element failure rates; (**b**) failure mechanism combinations; (**c**) failure rates on bearings; (**d**) failure rates on links; (**e**) failure rates on piers; (**f**) legend of case studies. represent a widely diffused structural typology within the infrastructural networks of many countries. The methodology is extensively presented in the former part of the paper in order to highlight the novelty and the strengths with respect to classic seismic vulnerability analysis. The main difference with respect to the common approaches relies on the types of fragility functions adopted: the ones adopted in this study are capable of retrieving more specific and detailed information on the possible failure modes, without limiting the analysis to the global failure conditions while also considering several intermediate damage scenarios (including one or more damage mechanisms) and providing insights on the numerosity of elements involved within a given damage scenario. A set of case studies is presented, consisting of Link-Slab reinforced concrete bridges with different geometries, which were preliminarily designed according to the codes enforced during the 1970s, modelled in OpenSees and then subjected to reliability analyses exploiting the proposed probabilistic framework. According to outcomes stemming from the study, it is observed that the main failure mechanisms characterizing this bridge typology involve the link bars and the bearings. The former represents the peculiarity of these systems, introduced to exploit several advantages in terms of driving comfort (reduced number of expansion joints) and functionality (hyperstaticity under horizontal actions and simply supported beam scheme under gravity loads). At the same time, these elements might represent a primary source of vulnerability; indeed, annual failure rates much higher than expected are observed. However, thanks to a refined fragility analysis, it was possible to further investigate the entity of the problem in terms of damage extent. It was observed how the higher failure rates are actually related to the disruption of a very limited number of links (less than 25%), while the collapse probabilities associated with more widespread damages are lower and comparable to the reference-expected hazard level at the collapse limit state. Regarding the failure rates of bearings, it is realistic to have MAF values higher than the code limit considering that neoprene pads commonly adopted in existing bridges were not designed to withstand earthquakes and the rubber property is not comparable to that of modern devices and isolators. This vulnerability could be removed by replacing the old supports with newer and more suitable ones. Piers, despite being designed with simplified seismic rules, were revealed to have proper safety margins against the collapse. Such main results hold (with minor variations) for all the bridge geometries investigated. Besides these results being specifically related to the examined case studies, the following general comments on the methods can be made. The proposed strategy was revealed to be suitable to provide a higher level of information on the reliability of the systems because it allows the association of different levels of risk (hence safety margins) to failure scenarios which differ in terms of elements/mechanisms involved and damage extension. Such a higher level of detail in the risk analysis may be useful to better quantify post-earthquake consequences (e.g., costs and losses) and define more tailored retrofit interventions, which are outside the scope of the present work but are considered worth mentioning.