Abstract

A parametric model for capacity curves and capacity spectra is proposed. The capacity curve is considered to be composed of a linear part and a nonlinear part. The normalized nonlinear part is modelled by means of a cumulative lognormal function. Instead, the cumulative Beta function can be used. Moreover, this new conceptualization of the capacity curves allows defining stiffness and energy functions relative to the total energy loss and stiffness degradation at the ultimate capacity point. Based on these functions, a new damage index is proposed and it is shown that this index, obtained from nonlinear static analysis, is compatible with the Park and Ang index obtained from dynamic analysis. This capacity based damage index allows setting up a fragility model. Specific reinforced concrete buildings are used to illustrate the adequacy of the capacity, damage and fragility models. The usefulness of the models here proposed is highlighted showing how the parametric model is representative for a family of capacity curves having the same normalized nonlinear part and how important variables can be tabulated as empirical functions of the two main parameters defining the capacity model. The availability of this new mathematical model may be a powerful tool for current earthquake engineering research or practice, especially in probabilistic approaches where massive computations are needed.

Abstract

The main goals of this article are to analyze the use of simplified deterministic nonlinear static procedures for assessing the seismic response of buildings and to evaluate the influence that the uncertainties in the mechanical properties of the materials and in the features of the seismic actions have in the uncertainties of the structural response. A reinforced concrete building is used as a guiding case study. In the calculation of the expected spectral displacement, deterministic nonlinear static methods are simple and straightforward. For not severe earthquakes these approaches lead to somewhat conservative but adequate results when compared to more sophisticated procedures involving nonlinear dynamic analyses. Concerning the probabilistic assessment, the strength properties of the materials, concrete and steel, and the seismic action are considered as random variables. TheMonteCarlo method is then used to analyze the structural response of the building. The obtained results show that significant uncertainties are expected; uncertainties in the structural response increase with the severity of the seismic actions. The major influence in the randomness of the structural
response comes from the randomness of the seismic action. A useful example for selected earthquake scenarios is used to illustrate the applicability of the probabilistic approach for assessing expected damage and risk. An important conclusion of this work is the need of broaching the fragility of the buildings and expected damage assessment issues from a probabilistic perspective.

Abstract

The evaluation of the damage caused by horizontal loads, such as seismic action, to existing bridges has received an important attention
in recent years, because it is the first step towards reducing casualties and economic losses. In damage detection and evaluation, the
application of simple and reliable models has been prioritized, because they are necessary in further multi-analyses required by Monte
Carlo simulations. A simplified moment–curvature damage evaluation model, capable of evaluating the expected seismic behavior of RC
highway bridges is proposed in this paper. The damage of a pier is related to the reduction of the cross-sectional moment of inertia of the
bridge piers. Therefore, the evaluation of the damage is based on a non-linear analysis determining the changes of the mentioned moment of inertia. The model was validated using experimental results obtained at the JRC Ispra for the Warth Bridge of Austria and also FEM analyses performed by other authors for the same bridge.

Abstract

This monograph presents the fundamental concepts related to seismic action, the structural response of buildings, the assessment of vulnerability, risk and seismic damage. Some indices proposed by different researchers are also indicated to assess the level of damage suffered by buildings under seismic actions. It also describes the ways to define the seismic action that are appropriate to the structural analysis. Techniques are developed to generate artificial accelerograms, which are necessary to perform the evaluation of the non-linear seismic response through an analysis in time. This evaluation also allows obtaining the level of damage suffered by the structures. The seismic action is focused on the city of Barcelona, ​​Spain, which is located in an area of moderate seismicity and, in addition, does not have seismic records. The seismic action is established by seismic design spectra and artificial accelerograms compatible with said spectra. At the end of this work, the responses spectra considered to define the seismic demand and the artificial accelerograms obtained are shown, which can be used for the evaluation of structures for different seismic intensities and for different locations in Barcelona. Finally, a methodology for assessing the vulnerability and the seismic risk of buildings is described. The methodology is applied in several steps and includes modeling and non-linear analysis of structures. It is focused on obtaining fragility curves, which can be generated both through an empirical evaluation and through an analytical evaluation. The first is based on the damage observed in the buildings of an area after an earthquake occurs, while the second is based on a numerical analysis, where the seismic response of the structure is predicted.

Abstract

In order to ensure that a building structure do not collapse when subjected to the action of strong ground motions, modern codes include prescriptions in order to guarantee the ductile behavior of the elements and of the whole structure. Obviously, it is of special importance for the designer to know during the design process the extent of damage that the structure will suffer under the seismic action specified by the design spectrum and also the probability of occurrence of different states of behaviour. The incremental nonlinear static analysis procedure used in this paper allows formulating a new, simplified, seismic damage index and damage thresholds associated with five limit states. The seismic behavior of a set of regular reinforced concrete buildings designed according to the EC-2/EC-8 prescriptions for a high seismic hazard level is then studied using the proposed damage index and damage states. Fragility curves and damage probability matrices corresponding to the performance point are calculated for the studied buildings. The obtained results show that the collapse damage state is not reached in the buildings designed according the prescriptions of EC-2/EC-8 and also that the damage does not exceed the irreparable damage limit state.

Abstract

Abstract

A methodology for simulating seismic damage of unreinforced mansonry buildings for seismic risk assessment of urban areas is presented in this paper. The methodology is based on the Italian vulnerability index and on the results of a post earthqueke damage survey study whose main result was an observed vulnerability function. The Monte Carlo method was than used to simulate damage probability matrices, fragility curves and vulnerability functions, all of which are the basis of a seismic risk study. The simulation process required the generation of thousands of hypothetical buildings, the analysis of their seismic behaviour and probabilistic studies of the computed results. As an example, probable damage scenarios werw developed for an urban area of Barcelona, Spain.

Abstract

The most relevant seismic vulnerability and risk analysis methods are discussed and compared in this article using, as  a pilot urban area, the city of Barcelona, Spain, where risk studies have been carried out over the last 15 years in the framework of different research projects. Most of the buildings in Barcelona, which have unreinforced masonry structure or reinforced concrete structure with waffled slab floors, show a high degree of vulnerability to earthquakes. The physical seismic risk but also the socio-economic implications of risk are considered in the article. The robustness of the innovative holistic approach, based on indicators related to the physical exposure, the social fragilities and the lack of resilience of urban area, is also proved. Using a geographic information system (GIS), the seismic risk results are described by means of scenarios of expected losses, but also as scenarios of probabilities of occurrence of predefined damage states.