Seismic and wind performance of five-storied pagoda of timber heritage structure affected by Great East Japan Earthquake of 2011 and typhoon Jelawat of 2012

The seismic vulnerability of historical centers at a territorial scale cannot be assessed performing detailed analysis which are usually adopted at the single building scale. In fact, a traditional complete survey would be extremely time-consuming and not sustainable for this purpose. The approach described in this paper is based on the idea that it is possible to infer quantities which cannot be directly detected from buildings outside inspection starting from parameters that can be measured. In order to achieve this purpose, a Bayesian approach is applied, updating initial hypotheses when new data become available. In this context, the procedure herein proposed aims at applying a probabilistic approach instead of a deterministic one to define facades inter-storey height starting from buildings height knowledge. In order to validate the method, for out of plane local mechanisms of collapse (walls overturning), horizontal loads multiplier 0 values are calculated and compared to results obtained by using data collected on-site. lated to the safety of buildings subjected to seismic actions (MIBAC 2010). The Italian Ministry of Cultural Heritage reached the awareness that its involvement in practices of good maintenance is essential to ensure buildings structural safety. In this context, initiatives to increase the efficiency of activities involving the safeguard of historic architectural heritage are implemented with the aim of encouraging the establishment of measures for the seismic risk mitigation of historic centres in its own central and local offices. Among the most significant initiatives, the Circular n. 15 “Provisions on the protection of architectural heritage and seismic risk mitigation” (Circular n.15, 2015) provides a new incremental approach that involves both the implementation of local interventions on buildings improving structural safety without involving sensitive additional costs and the improvement of reliability of seismic risk maps. Prevention is one of the main topics of the abovementioned circular, given the need to increase buildings seismic safety, which can be applied only if a preliminary widespread and deep knowledge of buildings vulnerabilities and possible intervention applicable on architectural heritage can be obtained. Buildings knowledge can only be achieved through the systematic collection of information about them; data can be gathered by adopting a specific form attached to the circular to be completed by technicians and practitioners when presenting practices to perform extraordinary maintenance or seismic improvement intervention on buildings (or part of them) listed as “cultural heritage”. A virtuous process is ongoing, considering that the real improvement of seismic security of historic centers is only achievable by activating processes that continuously involves all the people implicated in the construction process (owners, designers, builders, government offices, etc.). 3 DESCRIPTION OF THE BAYESIAN APPROACH In view of previous considerations, it is clear that over the years there will be a continuous increase of available information about historical buildings located in the Italian territory. The need to understand how to use this large amount of data in the best way, by adopting procedures able to continuously update information and at the same time to fill the gaps related to the lack of information, is extremely important (Modena 2012). It is also fundamental to remember that data updating can take place without periodicity and that information could be obtained for single buildings time after time; moreover, they can not necessarily involve entire widespread areas but just single buildings or part of them. The procedure must guarantee the possibility of a continuous information updating. The methodology herein proposed allows inferring quantities/data that cannot be directly detected on site starting from parameters that can be measured. In this context, a stochastic approach is applied instead of a deterministic one in order to provide probabilistic vulnerability assessments on a territorial scale through the application of a Bayesian approach (Modena, 2014). Considering the needs established above, the approach allows deducing buildings unknown information starting from collected certain data, updating initial probability density functions when new data becomes available. The method can be synthesized by applying this simple scheme: prior distribution data posterior distribution This process, which provides a continuous learning experience acquisition when new data are obtained, is called Bayesian update. If continuous random variables are used, Bayes theorem can be written as follows:                   d y p p y p p y p | | | (1) where: p(θ) is the prior distribution (quantifies all information available before experimental results are observed) p(y|θ) is the likelihood, which, as θ varies, represents the probability of obtaining observed experimental results p(θ|y) is the posterior distribution and is the result of Bayesian inference, and represents final distribution after experimental results have been observed. By collecting new data, the process can be iteratively repeated: the posterior distribution becomes the new prior distribution, and a new posterior probability density function can be obtained. This procedure can be repeated each time new data are available. A prior distribution can be defined as a distribution conjugated to the adopted sample model (or equivalently to likelihood) if prior and posterior distributions are characterized by the same functional form (Liseo 2008). As an example, if a normal-inversegamma distribution is chosen as prior distribution and likelihood is a normal distribution, the resulting posterior distribution, obtained by applying Bayes theorem, is a normal-inverse-gamma. 4 APPLICATION OF THE APPROACH TO THE LOCAL MECHANISMS OF COLLAPSE ANALYSIS The proposed method is carried out by implementing the local mechanisms of collapse analyses. In this context, it is essential to provide a general overview of the current Italian legislation in order to justify this application. Circular. 617 (C8A.3), underlines that "the analysis of a structural unit, according to the methods applied for isolated buildings without adequate modeling or with an approximate modeling of the interaction with the adjacent buildings, assumes a conventional meaning. Therefore, it is assumed that the analysis of the global seismic capacity of the structural unit can be verified by the use of simplified methods [. ] ". And yet (C8.7.1.1): "For the assessment of existing buildings, in addition to the global seismic analysis to be carried out by applying the methods prescribed by the new buildings standards [. ] should be also considered the analysis of local mechanisms of collapse. When constructions do not show a clear global behavior, but react to an earthquake as a set of subsystems (local mechanisms), a global model has no correspondence with the real seismic behavior. " Aggregate buildings, by their definition, are characterized by an articulated and not unitary genesis, which usually leads them to react to an earthquake as "a set of subsystems" (C 8.7.1.1). Given these remarks, a study based on the analysis of the local mechanisms of collapse by the implementation of a probabilistic approach is undoubtedly significant. The out of plane local mechanisms of collapse involve walls orthogonally stricken by a seismic action. As an example, the definition of buildings vulnerability with respect to these types of mechanisms allows to identify facades facing the road that could be submitted to collapse if an earthquake occurs, preventing the transit of emergency vehicles. It is possible to establish, on the basis of such evaluations, suitable access and escape routes. 5 THE CHOICE OF PARAMETERS First of all, the development of the described approach and its application to the local mechanisms of collapse analysis needs to define the parameters to be taken into account for the analyses. Considering the innovativeness of this approach, in this first step the procedure is tested on simple cases. The method refinement is going to involve more parameters allowing the approach to be closer to real historical buildings configuration. The study considers the analysis of freestanding walls. Their considered geometrical and mechanical parameters are: masonry properties; walls thickness; thickness variation between different floors; building height; inter-storey height; number of floors. The procedure allows defining horizontal loads multiplier α0 of freestanding walls, on the basis of their thickness and inter-storey height variation. Masonry properties are defined a priori, considering buildings vertical structures features. Geometrical input data treated as certain (easily identifiable) ones are building total height and number of floors. These data are easily available since they can be obtained through buildings outside inspections, limiting time and costs consuming. Such information may be reached even eliminating the on-site survey phase: data can be easily recovered through the use of online maps and aero photogrammetry (Fabris 2013). Buildings observation by using online maps allows the identification of the number of floors of each building (Figure 1). The photogrammetry can be used as a useful tool for the definition of buildings total heights. It can be obtained calculating the difference between the roofs height and the height of some measured points on the ground level, located in proximity of a considered building. It is necessary to measure multiple points on the ground floor because buildings are not on a perfectly flat soil. Measurements should be repeated using multiple stereo pairs averaging obtained results. Figure 1. Example of aero photogrammetry applied to Verona (Italy) historic center: the availability of a huge number o