Risk Assessment Methods and Applications to Cultural Heritage.

Seismic risk assessment is one of the engineering’s most complex challenges. From this perspective, understanding earthquakes and the risks they pose, is a matter that has stretched scientists and engineers for centuries. The seismic events in the last years represent one of the most devastating natural disasters. The destructive feature of the last earthquakes is highlighted by seismic events over the years in Italy such as Irpinia 1980, Marche-Umbria 1997, Molise 2002, L’Aquila 2009, Emilia 2012, Central Italy 2016 and worldwide such as Tohoku Earthquake 2011, Off west coast of northern Sumatera, Indonesia, 2012, Nepal 2015 and many others. The seismic events influence across scales from economic to social and psychological aspects, from individual to regional communities in a short and long-term development. Reasons of their destructive feature certainly include the increase in world population, but also the development of cities located in high seismic hazard with high vulnerabilities structures, such as cultural heritage assets or buildings with project deficiencies or the ones located in prone areas. It became increasingly important as urban populations and communities, to estimate the potential impact of future earthquakes using the previous knowledge in the engineering, science, social sciences and economics so that effective decisions could be made to reduce the disastrous effects of the seismic events. It is evident the importance of this topic from all the point of view, and scientists and engineers have the tools to deal with it, in order to mitigate the risk. In this light, the importance of having a strategy and a comprehensive understanding that minimize and reduce the risk of losses became crucial. The risk evaluation must include a proper assessment of the hazard, as well as the assessment of the vulnerability of the structures and infrastructures and the exposure of the site considered. The seismic hazard is the probability that an earthquake will occur in a given area, within a given time period, and with ground motion intensity exceeding a given threshold. The seismic vulnerability generally refers to the probability of a damage given the occurrence of a hazard and, the presence of people, livelihoods, environmental functions and infrastructure are indicated as exposure, a sort of “scale factor” of the vulnerability problem. Of course, these specific evaluations cannot be based only on a qualitative approach and on the observation of the building behaviour from the past. The analysis of the hazard, based on the probabilistic seismic hazard analysis (PSHA), is an analytical methodology that estimates the likelihood that will be exceeded at a given location in a given time period by a seismic event (Baker, 2013). The results of such analysis are expressed as estimated probabilities per unit time or estimated frequencies (such as expected number of events per year). Buldninz et al. in 1997 publisheda guidance and recommendations for PSHA, taking into account the importance of the uncertainties in the analysis. This confirms the complexity of the hazard evaluation, that for this reason is not deeply analysed and not being the main topic of this work. On the contrary, the level of accuracy of the seismic vulnerability evaluation is one of the main topics of this Thesis and it depends on the size of the study performed. In particular, the estimation of buildings vulnerability is performed mainly relying on complex models, which have to consider large amounts of in-situ data and they are generally capable of covering only a limited geographical area. On the other hand, the evaluation of seismic vulnerability at territorial level allows using both empirical and analytical methods, which could cover larger regions. Moreover, the vulnerability assessment can be achieved by classes’ vulnerability, and the size of these classes is a direct consequence of the final variability of the response. Prediction of potential economic losses and, more generally, consequences due to hazardous events, is a key point for prevention planning and emergency organization. To this aim, it is necessary to define reliable models for event predictions, both empirical or analytical, building response and consequences evaluation. Indeed historically, the impact of an earthquake on the economy of a country may be remarkable. Evaluations and management on architectural resources from an economic point of view should be deeply analysed and considered. The Performance Based Earthquake Engineering framework (PBEE) presented by the Pacific Earthquake Engineering Research (PEER) Center (Deierlein et al., 2003) is a robust methodology that allows to evaluate the structural performance in a rigorous probabilistic manner without relying on expert opinion, considering the uncertainty in the seismic hazard, structural response, potential damage and economic losses. The PBEE involves four different stages: hazard analysis, structural analysis, damage analysis and loss analysis (Cornell and Krawinkler 2000, Deierlein et al., 2003) in order to quantify the decision variables. Cornell and Krawinkler presented a scheme that can be considered an effective foundation for the development of performance-based guidelines. In particular, they suggested a generic structure for coordinating, combining, and evaluating the implicit considerations in performance-based seismic assessment. The main challenge is to provide a direction toward which the various PEER research efforts should converge, identifying two different options. The first one is to develop a general methodology for estimating the annual expected costs associated with the seismic risk (initial, maintenance, insurance, etc., plus annualized earthquake losses). This building loss estimation option is very attractive because it permits an evaluation of retrofit or design alternatives, but should be "compatible" with seismic retrofit projects and new designs. The second option is the development of a methodology that focuses on specific performance levels, from continuous operation to collapse prevention and the annual probability of exceeding these levels. Finally, the authors stated that the final challenge for PEER researchers is not the estimation of losses or performance prediction, but it is based on the effective contribution in the reduction of losses and the improvement of safety.Deierlein et al., described the performance assessment process through four generalized variables that characterize information in a logical manner. The process identified by Deierlein et al. starts with the definition of a parameter describing the ground motion intensity at the site of the structure, the Intensity Measure (e.g., peak ground acceleration, spectral acceleration, etc.), whose probabilistic features are described by means of seismic hazard curve expressing the mean annual rate of exceedance for different intensity values. Next, Engineering Demand Parameters, such as interstory drift, floor accelerations or other engineering response quantities, are calculated (e.g., via simulation approaches and through numerical analyses of structural systems) to characterize the response of the system conditional to the earthquake occurrence. The Engineering Demand Parameters can be then easily linked to Damage Measures, which describe the physical damage to the structure and its components. Moreover, damage states are delineated by their consequences on Decision Variables, consisting of economic losses, downtimes, and casualty rates. To summarize, Deierlein et al. stated that the key aspect of the methodology is a representation and tracking of uncertainties in predicting performance metrics that are relevant to decision making for seismic risk mitigation. In 2003 also Porter summarized the development of a performance-based earthquake engineering methodology by the Pacific Earthquake Engineering Research Center (Porter, 2003). A complete methodology of loss estimation is presented in various works such as Risk-UE (Milutinovic and Trendafiloski, 2003) and Hazus (FEMA, 2003). The Risk-UE project developed vulnerability models describing the relation between potential building damage and their specific seismic hazard, followed by their fragility models and damage probability matrices based on analytical studies and expert judgment. Then a standardized damage survey and building inventory form is proposed. This is useful for rapid collection of relevant data, building damage and post-earthquake building usability classification. Hazus project described the methods for performing earthquake loss estimation. A simple illustration of the scheme used in Hazus is proposed in Figure 1-1.The primary purpose of that project is the development of guidelines and procedures for making earthquake loss estimates at a regional scale. A secondary purpose of the project is to provide a basis for assessing nationwide risk of earthquake losses. In that project, the authors pointed out the importance of studying this method considering the uncertainties that are inherent in any loss estimation methodology. The uncertainties may derive from incomplete scientific knowledge concerning earthquakes and their effects upon buildings and facilities. They can be also the result of the approximations and simplifications that are necessary for comprehensive analyses, especially at territorial level. In this light, understanding and quantifying uncertainty is essential to develop a reliable probabilistic model for structural seismic risk assessment (Ellingwood and Kinali 2009). In order to rigorously assess the seismic risk of a structure, all the uncertainties related to the ground motions affecting a given site, the structural response, the associated damage and the cost to repair a damaged structure should be accounted for. A number of uncertainties are present in the earthquake action, in the choice of the materials and geometrical structural properties, in the modelling and analysis of the structure and in the numerical prediction of structural seismic performance.In particular, the work of Ellingwood and Kinali pointed out the fact that all sources of uncertainty should be included in risk assessment, basing this choice on the preferences of the stakeholders and decision-makers. In detail, they illustrated how such uncertainties are propagated through seismic risk assessment of steel frame building structures, typical of regions of low-to-moderate seismicity in the Central and Eastern United States. For structural risk assessment, the uncertainties analysis is part of the evaluation. In particular, in this Thesis the uncertainties analysis will be focalized on the vulnerability assessment, where the response variability of classes’ vulnerability depends on the size of the class itself. This Thesis aims to provide a contribution to the understanding of the uncertainty propagation in the seismic risk assessment. This topic has been investigated using two different approaches; in the former approach vulnerability is described by empirical models, and in the latter one vulnerability is described by analytical models. The first approach has been used to evaluate the seismic risk of historical churches and an original empirical model is proposed, starting from the damage survey carried out after the 2016 Central Italy seismic sequence. The main aspect of originality is provided by the statistical analysis of the dataset, and by the probabilistic model developed for the damage and consequences prediction. A major specificity is that the dataset used to develop the probabilistic models, includes also undamaged and collapsed churches instead of damaged constructions only. The model presented can be of applicable in the risk assessment at territorial level and may be a useful tool to select the most promising mitigation actions, and to support the related decision making process. The strategy used to define the historical church model can be of interest in the development of damage and consequences predictive models of other type of constructions (e.g. masonry buildings, reinforced concrete buildings, etc.). The second approach, based on an analytical description of construction vulnerability, has been investigated in the last part of the Thesis. In particular, existing analytical models have been used and the analysis focuses on the uncertainties propagation by studying the sensitivity of the risk metric to the variance of the response models. This approach has been applied to a set of reinforced concrete structures highly damaged after a seismic sequence, classified based on the height of the buildings and that may be considered part of the Italian cultural heritage, due to a construction technique that it is now obsolete and abandoned (Morabito and Podestà, 2015). In this case, all the steps of the seismic risk framework have been investigated. Finally, a comparison between predictions coming from analytical models and the real damage observed after the Central Italy seismic events is presented, in order to understand the level of reliability of analytical methods. Chapter 2 contains an introduction to the main problem of the vulnerability analysis and a review of the state of the art related to the practical methods for the probabilistic evaluation of the seismic vulnerability, focusing on the empirical and analytical approaches, the main methods used in the applications of the Thesis.Chapter 3 presents the main sources of uncertainties that could affect the variability of the response of the churches in one case, and reinforced concrete buildings in the other case, strictly linked to the vulnerability classes’ size. The sources of uncertainties include seismic input, model parameter uncertainties related to the observed data in the case of the empirical method or geometrical and mechanical structural properties if the analytical method is used. Epistemic uncertainties are also considered, related to the limited data and knowledge in the adopted model. In this chapter, a review of the state of the art of this topic, in particular of the statistical models, is presented. Chapter 4 and 5 will treat the two case studies using the different methods. In particular, Chapter 4 begins with an analysis of observational damage from post earthquake investigations carried out on churches of the Marche Region hit by the 2016 Central Italy seismic sequence. Then, these data are collected and processed to give a better view of the vulnerability of this type of structures. An improvement in a probabilistic way of this study has made, firstly related to the seismic damage and then to the consequences. The damage is expressed by a continuous index and a complete database of damaged, undamaged and collapsed churches is considered. This empirical model is applied to illustrate the potential application of this risk analysis in decision-making process. Then, a probabilistic response consequence model is presented, by considering also a deep analysis on the soil features. This probabilistic response consequence model may be of interest in the development of effective strategies to mitigate and prevent the risk and can be a tool of supporting the reduction of direct economic losses. Chapter 5 presents the analytical method using a sample formed by reinforced concrete buildings classified on the basis of their height. In this case, the seismic response of the structures is described by means of fragility curves proposed in literature according with the typologies of building of the area considered. A loss analysis is also carried out in terms of expected annual losses. Moreover, a comparison with the observed damage experienced by the buildings after the 2016 Central Italy seismic sequence is provided. The propagation of the uncertainties in the framework of the risk has been considered as well, and in particular, the variability in the fragility curves parameters. The sensitivity analysis has been conducted evaluating the First-Order sensitivity index and the Total sensitivity index and considering different hazard references curves. Finally, in Chapter 6, some conclusions are drawn and future developments are discussed.