Bayes'sche Ansätze zur Zuverlässigkeit bestehender Bauwerke

Due to environmental, economic and socio-political reasons, significance and field of application of existing structures' reliability assessments extend rapidly, also in view of the preservation of cultural heritage. Over recent decades, the Bayesian analysis has been increasingly recognized as an efficient procedure for the definition of the probability models for the random variables governing the reliability of the structure. It is especially applied in case of material mechanical parameters, where a prior is firstly defined according to engineering judgments and then updated with the result of material tests. However, if the choice of the prior distribution is wrong, the result of the analysis might be incorrect. Material tests are usually destructive, leading to a loss of the integrity of the structure and even of its cultural value, in case of heritage buildings. Therefore it is of paramount importance to propose procedures according to which more sound prior distributions are defined and non-destructive approach to the Bayesian analysis are promoted. In this work, a general methodology that increases the robustness of the Bayesian analysis with respect to the prior distribution for the description of material mechanical random parameters is defined. The methodology focuses on the identification of homogeneous material classes considering certain mechanical properties, and the definition of the related statistical parameters, directly analysing the results of material acceptance tests. A practical application of this procedure is developed for the identification of concrete classes in Italy during the 1960s analyzing the results of compressive tests on standard cubes. On the other hand, it is shown by practical application on relevant case studies that a more realistic reliability evaluation can be obtained without touching the structure, refining the probability models of action or action effects. In the first case study (a concrete water tank from the 1960s) the Bayesian updating of the Finite Element model is carried out considering the results of static and dynamic tests. In the second case study (a masonry aqueduct built in the 16th century) the Bayesian updating of the wind speed is performed according to the results of field studies.Aus umwelt-, wirtschafts- und gesellschaftspolitischen Gründen erstrecken sich die Zuverlässigkeitsbewertungen der bestehenden Bauwerken auch im Hinblick auf die Erhaltung des kulturellen Erbes rasch. In den letzten Jahrzehnten wurde die Bayes'sche Analyse zunehmend als effizientes Verfahren zur Definition der Wahrscheinlichkeitsmodelle für die Zufallsvariablen, die die Zuverlässigkeit des Bauwerks bestimmen, angewendet. Die Bayes'sche Analyse wird insbesondere für Materialmechanischen Parametern angewendet, bei denen eine ‘a priori’ Wahrscheinlichkeitsverteilung zunächst nach ingenieurtechnischen Einschätzungen definiert und dann mit dem Ergebnis von Materialprüfungen aktualisiert wird. Wenn jedoch die Wahl der ‘a priori’ Wahrscheinlichkeitsverteilung falsch ist, kann das Ergebnis der Analyse falsch sein. Materialprüfungen sind in der Regel zerstörerisch, was zu einem Verlust der Integrität des Bauwerks und sogar seines kulturellen Bedeutungen führt, wenn es sich um Baudenkmäler handelt. Daher ist es wichtig, Verfahren vorzuschlagen, nach denen fundiertere ‘a priori’ Wahrscheinlichkeitsverteilungen definiert werden und ein zerstörungsfreier Ansatz für die Bayes'sche Analyse gefördert wird. In dieser Arbeit wird einerseits eine allgemeine Methodik definiert, die die Robustheit der Bayes'schen Analyse in Bezug auf die ‘a priori’ Wahrscheinlichkeitsverteilung für die Beschreibung der mechanischen Zufallsparameter des Materials verbessert. Die Methodik konzentriert sich auf die Identifizierung homogener Materialklassen und ihrer statistischen Parameter unter Berücksichtigung bestimmter mechanischen Eigenschaften, wobei die Ergebnisse der Materialprüfungen direkt analysiert werden. Eine praktische Anwendung dieses Verfahrens wird für die Identifizierung von Betonklassen in Italien in den 1960er Jahren entwickelt, indem die Ergebnisse von Druckversuchen an Standardwürfeln analysiert werden. Andererseits wird durch die praktische Anwendung an relevanten Beispielen gezeigt, dass eine realistischere Zuverlässigkeitsbewertung erreicht werden kann, ohne die Bauwerke zu berühren und die Wahrscheinlichkeitsmodelle von Aktionen oder Aktionseffekten zu verfeinern. In der ersten Fallstudie (ein Betonwassertank aus den 1960er Jahren) wird die Bayes'sche Aktualisierung des Finite-Elemente-Modells unter Berücksichtigung der Ergebnisse statischer und dynamischer Tests durchgeführt. In der zweiten Fallstudie (ein im 16. Jahrhundert erbautes Mauerwerk-Aquädukt) wird die Bayes'sche Aktualisierung der ‘a priori’ Wahrscheinlichkeitsverteilung der Windgeschwindigkeit nach den Ergebnissen von Feldstudien durchgeführt

Climate Change: impact on snow loads on structures

A general procedure to evaluate future trends in snow loads on structures is illustrated aiming to study influences of climate change at European scale, to assess its impact on the design of new structures as well as on the reliability levels of existing ones, also in view of the next revision of the Eurocodes. Analysing high quality registered meteorological data of daily temperatures, rain and snow precipitations in nine Italian weather stations, conditional probability functions of occurrence of snow precipitation, accumulation and melting have been preliminarily determined as functions of daily air temperatures. By means of Monte Carlo simulations and based upon daily output of climate models (daily max. and min. temperatures and water precipitation) yearly maxima of snow loads for various time intervals of 40 years in the period 1980-2100 have been simulated, deriving, via the extreme value theory, the characteristic ground snow loads at the sites. Then, the proposed procedure has been implemented in a more general methodology for snow map updating, in such a way that the influence of gridded data of precipitation, predicted by global climate models, on extreme values of snow loads is duly assessed. Preliminary results demonstrate that the outlined procedure is very promising and allows to estimate the evolution of characteristic ground snow loads and to define updated ground snow load maps for different climate models and scenarios

GPCE-based stochastic inverse methods: A benchmark study from a civil engineer’s perspective

In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of parameters to be calibrated can be obtained; this approach is more informative than a deterministic local minimum point derived from a classical optimization problem. In addition, building a response surface surrogate model could allow one to overcome computational difficulties. Here, the general polynomial chaos expansion (gPCE) theory is adopted with this objective in mind. Owing to the fact that the ability of these methods to identify uncertain inputs depends on several factors linked to the model under investigation, as well as the experiment carried out, the understanding of results is not univocal, often leading to doubtful conclusions. In this paper, the performances and the limitations of three gPCE-based stochastic inverse methods are compared: the Markov Chain Monte Carlo (MCMC), the polynomial chaos expansion-based Kalman Filter (PCE-KF) and a method based on the minimum mean square error (MMSE). Each method is tested on a benchmark comprised of seven models: four analytical abstract models, a one-dimensional static model, a one-dimensional dynamic model and a finite element (FE) model. The benchmark allows the exploration of relevant aspects of problems usually encountered in civil, bridge and infrastructure engineering, highlighting how the degree of non-linearity of the model, the magnitude of the prior uncertainties, the number of random variables characterizing the model, the information content of measurements and the measurement error affect the performance of Bayesian updating. The intention of this paper is to highlight the capabilities and limitations of each method, as well as to promote their critical application to complex case studies in the wider field of smarter and more informed infrastructure systems

Integrating cluster analysis into Multi-Criteria Decision Making for maintenance management of aging culverts

Negligence in relation to aging infrastructure systems could have unintended consequences and is therefore associated with a risk. The assessment of the risk of neglecting maintenance provides valuable information for decision making in maintenance management. However, infrastructure systems are interdependent and interconnected systems of systems characterized by hierarchical levels and a multiplicity of failure scenarios. Assessment methodologies are needed that can capture the multidimensional aspect of risk and simplify the risk assessment, while also improving the understanding and interpretation of the results. This paper proposes to integrate the multi-criteria decision analysis with data mining techniques to perform the risk assessment of aging infrastructures. The analysis is characterized by two phases. First, an intra failure scenario risk assessment is performed. Then, the results are aggregated to carry out an inter failure scenario risk assessment. A cluster analysis based on the k-medoids algorithm is applied to reduce the number of alternatives and identify those which dominate the decision problem. The proposed approach is applied to a system of aging culverts of the German waterways network. Results show that the procedure allows to simplify the analysis and improve communication with infrastructure stakeholders

Statistical Parameters of Steel Rebars of Reinforced Concrete Existing Structures

Historical and cognitive investigations supported by in-situ and/or laboratory tests are needed for a robust reliability assessment of existing structures. Indeed, an adequate knowledge of material properties and their statistical description is the basis for carrying out accurate reliability analyses and verifications on the investigated structures. In this paper, a procedure for the definition of pdfs of mechanical parameters of steel rebars is proposed based on secondary experimental test data. This information is very helpful for the reliability assessment of existing r.c. buildings, where estimation of statistical parameters of mechanical properties of steel reinforcement is very difficult. In fact. It must be highlighted on the one hand that direct information about the examined structure are commonly not sufficient, on the other hand that the number of rebar samples extracted from the structure, if available, is so limited that it does not allow a complete statistical analysis. The first step has been the collection of experimental acceptance tests carried out by Department of Civil and Industrial Engineering of University of Pisa on steel rebars of reinforced concrete (r.c.) structures during the 1960s. The yield strength and the tensile strength are extrapolated for each sample defining a significant database of experimental test results for existing r.c. structures. Then, probability distribution models for the mechanical properties of steel reinforcement have been defined as already done by the authors for concrete strength. A cluster analysis has been carried out based on the Gaussian Mixture Model applying the Expectation-Maximization algorithm to identify homogeneous material classes and their associated pdfs of material mechanical parameters. The main advantage of proposed procedure consists in its “blindness”, In fact, not requiring subjective information like pre-classification of data, the methodology is not sensitive to alterations caused by engineering judgement or by inexact identification of declared strength class of the tested samples, due for example to downgraded materials