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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

There is a general interest in civil engineering to quantify the damage produced in structures by catastrophic actions. It would be convenient, from a practical point of view, to describe the state of a structure by means of a single figure that clarifies whether the structure is capable of supporting the service charges or not; if it will survive to another extraordinary load in the future; how does the present damaged state influence in its future behavior; where the most damaged points are located; what capacity of resistance remains in each point; and, in general, all kind of information that help to make design or repair decisions. The authors have proposed a solution to this problem in the specific case of earthquakes acting upon reinforced concrete building structures. A methodology has been formulated for the definition of an index of damage that can be typified for all the structures belonging to the same class and that allows classifying them according to their seismic vulnerability. In the monograph, simple beam structures are first studied in order to better describe the concepts involved and the parameters that influence the solution to the problem. The developed methodology, which models the structures using the finite element method, is directly and easily extended to shells, plates or 3D solids. The fundamental idea of ​​this work is to apply constitutive equations formulated in 3D at a material point instead of using constitutive laws formulated in generalized forces-displacements such as, for example, bending moment-curvature, shear force-angular distortion, etc. This allows modeling the behavior of composite materials directly since for each component material its own constitutive law is considered. In this way, it is sufficient to have a single 3D constitutive model and a methodology to calculate the components of the stress and strain tensors at any point of the beam section.

Abstract

The main objective of this monograph is to evaluate the overall damage index of framed reinforced concrete structures using different models. In order to achieve this objective it is necessary to identify the parameters that most influence the seismic behavior of reinforced concrete buildings and to propose alternatives for the calculation of some of them. In this context, procedures for calculating variables such as the yielding curvature due to inelastic shear are indicated. The methods for assessing the seismic damage in framed reinforced concrete structures are analyzed, and the correlation between the results obtained with different models in several structures with different reinforcement is studied. Based on this analysis, a simplified methodology for evaluating seismic damage using a global (or overall) index is proposed. The seismic action in most damage evaluation methods is defined by means of accelerograms. Very few methods calculate the damage defining the action by means of response spectra. Although there is no theoretical justification for the possibility of using modal analysis in the context of inelastic analysis, in the seismic analysis of structures this type of calculation is included in all seismic design regulations in the world. The proposed calculation method uses response spectra, is easy to use, can be applied to any type of earthquake, determines the zones that are going to enter into the non-linear range, the maximum lateral displacement that is expected and indicates the overall damage index of the structure.

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In this monograph, a complete review of the state of the art of the seismic vulnerability of motorway bridges is carried out. The work begins with a review of the damage caused by the last major earthquakes in the world. Next, the theoretical framework of the methods of evaluation of the seismic vulnerability of structures is described. Then, different methodologies for the evaluation of the seismic vulnerability of bridges are examined in detail. Advances in assessing their seismic vulnerability should be sought using expert judgment, the study of damage data associated with past earthquakes and the numerical simulation of bridge response. For this reason, in the monograph the seismic vulnerability evaluation methods are classified into the following groups: (1) methods based on vulnerability indexes; (2) methods that use structural analysis; (3) methods based on statistical evaluations and expert opinion; and (4) methods that use the observed damage statistics. Finally, some of the main methods for obtaining the indices that characterize the importance of motorway bridges are described, as well as indices for the evaluation of the liquefaction effect.

Abstract

In this monograph, we study the definition of possible damage in bridges by using simplified structural models. The state-of-the-art of the seismic vulnerability of bridges is first discussed and the theoretical background of the methods to evaluate their vulnerability is commented. The existing methodologies to evaluate the vulnerability of bridges are then described in detail; The methods are classified as: (1) methods based on the vulnerability index; (2) methods based on structural analyses; (3) methods based on expert opinion and statistical evaluations; and (4) methods based on statistical evaluations of the observed damages. A simplified methodology to estimate the seismic vulnerability of reinforced concrete bridges with simple pier bent and elastic girders is then proposed. The methodology is applied to an existing bridge, built 30 years ago. The elastic and the non-linear procedures of evaluation are first discussed. The non-linear procedure includes an analytical methodology to estimate the local damage in the piers, using a continuous damage model, and the global damage of the bridge. Thereinafter, a numerical process allows considering artificial seismic actions compatible with the velocity spectrum of deterministic records. Finally, an application of the proposed analytical procedure to estimate the seismic vulnerability of the real bridge is given. The obtained damage results show that the studied bridge would suffer only a minor damage when  a seismic action similar to that of the expected seismic scenario is considered. The proposed methodology is compared with previous experimental results and with analytical results obtained by using commercial codes. It is shown that the proposed simplified methodology is less computational time consuming and that it provides reliable values of the maximum damage suffered by the bridge piers.

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.

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