Abstract

The paper introduces a new global damage evaluation method which leads to a meaningful global damage index. A numerical procedure for the prediction of local and global damage in civil engineering structures using the finite element method and a continuum damage model, is presented. The method is adequate for the computation of the limit load in reinforced concrete (RC) structures and for the prediction of the failure mechanisms. Details of the applied damage model are given together with a description of the finite element implementation and the procedure for computing the global damage parameters. Examples of applications of the methodology to the nonlinear analysis of a range of RC structures, are presented.

Abstract

The seismic risk of the buildings of Barcelona, Spain, is analyzed by using a method based on the capacity spectrum. The seismic hazard in the area of the city is described by means of the reduced 5% damped elastic response spectrum. Obtaining fragility curves for the most important building types of an urban center requires an important amount of information about the structures and the use of nonlinear structural analysis tools. The information on the buildings of Barcelona was obtainedby collecting, arranging, improving, and completing the database of the housing and current buildings. The buildings existing in Barcelona are mainly of two types: unreinforced masonry structures and reinforced concrete buildings with waffled slab floors. In addition, the Arc-View software was used to create a GIS tool for managing the collected information to develop seismic risk scenarios. This study shows that the vulnerability of the buildings is significant and therefore, in spite of the medium to low seismic hazard in the area of the city, the expected seismic risk is considerable.

Abstract

In this article, the nonlinear constitutive behavior is considered in the geometrically nonlinear formulation for beams proposed by Simo and Vu-Quoc. The displacement based method is employed in solving the resulting nonlinear problem in the static case. Thermodynamically consistent three-dimensional constitutive laws are used in describing the material behavior, leading to a more precise estimation of the energy dissipated by the structures. The simple mixing rule is also applied in modeling materials which are composed by several simple components. An appropriated cross sectional analysis is implemented under the assumption and limitations of the planarity of the beam cross sections. Special attention is paid to the development of a method for defining the global damage state of a structure based on a scalar damage index capable of describing the residual strength and the load carrying capacity. Several numerical examples, including composite materials and strain localization, are presented and discussed.

Abstract

A fully geometric and constitutive nonlinear model for the description of the dynamic behavior of beam structures is developed. The proposed formulation is based on the geometrically exact formulation for beams due to Simo but, in this article an intermediate curved reference configuration is considered. The resulting deformation map belongs to a nonlinear differential manifold and, therefore, an appropriated version of Newmark’s scheme is used in updating the kinematics variables. Each material point of the cross-section is assumed to be composed of several simple materials with their own constitutive laws. The mixing rule is used to describe the resulting composite. An explicit expression for the objective measure of the strain rate acting on each material point is deduced in this article. Details about its numerical implementation in the time-stepping scheme are also addressed. Viscosity is included at the constitutive level by means of a thermodynamically consistent visco damage model developed in terms of the material description of the First Piola Kirchhoff stress vector. The constitutive part of the tangent tensor is deduced including the effect of rate dependent inelasticity. Finally, several numerical examples, validating the proposed formulation, are given.

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

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

Recently proposed capacity-based damage indices and parametric models for capacity curves are applied to frame steel buildings located in soft soils of the Mexico City. To do that, the seismic performance of 2D models of low-, mid- and high-rise buildings is assessed. Deterministic and probabilistic nonlinear static and incremental dynamic analyses are implemented. Monte Carlo simulations and the Latin Hypercube sampling technique are used. Seismic actions are selected among accelerograms recorded in the study area. Spectral matching techniques are applied, so that the acceleration time histories have a predefined mean response spectrum and controlled error. The design spectrum of the Mexican seismic code for the zone is used as target spectrum. The well-known Park and Ang damage index allows calibrating the capacity-based damage index. Both damage indices take into account the contribution to damage of the stiffness degradation and of the energy dissipation. Damage states and fragility curves are also obtained and discussed in detail. The results reveal the versatility, robustness and reliability of the parametric model for capacity curves, which allow modelling the nonlinear part of the capacity curves by the cumulative integral of a cumulative lognormal function. However, these new capacitybased damage index and capacity models have been tested for and applied to 2D frame buildings only; they have not been applied to 3D building models yet. The Park and Ang and the capacity-based damage indices show that for the analysed buildings, the contribution to damage of the stiffness degradation is in the range 66–77% and that of energy loss is in the range 29–34%. The lowest contribution of energy dissipation (29%) is found for the low-rise, more rigid, building. The energy contribution would raise with the ductility of the building and with the duration of the strong ground motion. High-rise frame buildings in soft soils of Mexico City show the worst performance so that the use of adequate braced frames to control the displacements could be recommended.

Abstract

The vulnerability index method, in its version developed in the framework of the European project Risk-UE, has been adapted and applied in this article, to evaluate the seismic risk for the city of Barcelona (Spain) through a GIS based tool. According to this method, which defines five damage states, the action is expressed in terms of the macroseismic intensity and the seismic quality of the buildings by means of a vulnerability index. The probabilities of damage states are obtained considering a binomial or beta-equivalent probability distribution. The most relevant seismic risk evaluation results obtained, for current buildings and monuments of Barcelona, are given in the article as scenarios of expected losses.

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

Between the late nineteenth century and the early twentieth century, Barcelona was expanded, occupying the terrains connecting the old walled city and the nearby towns of the plateau of Barcelona. At that time, a large number of unreinforced masonry buildings were constructed and nowadays many of them are still used as dwellings. Though built individually, these buildings are connected to adjacent buildings, forming blocks composed of aggregates. In order to analyze the seismic behavior of isolated buildings and aggregates, two typical central buildings and one typical corner building have been chosen. The two central buildings and the corner building are referred as C1, C2, and E buildings. Two corner buildings and two central buildings have been connected in order to simulate a block side. This aggregate is referred as AGG and it is composed by the following sequence of individual buildings: E-C1-C2-E. Original plans and drawings of existing buildings are then used to model these buildings. The modeled buildings have five stories. Standard pushover analyses lead to evaluate their seismic performance by means of capacity spectra and fragility curves. The analysis has been carried out in the parallel (Ux) and transversal (Uy) directions to the street. Then, a capacity spectrum based method is used to analyze the seismic behavior of these buildings considered as individual buildings and as an aggregate. Two earthquake scenarios are considered. The first one is a deterministic scenario which is based on a historical earthquake occurred in 1824, 25 km away from the city and the second one is a probabilistic scenario, which represents the ground motion with a probability of occurrence of 10% in 50 years. The soil local effects have been also considered and both scenarios have been used to assess the expected damage. Four non-null damage states are considered: slight (1), moderate (2), severe (3) and extensive-to-collapse (4). For the type of soil where most of the buildings are, and in the Ux direction, the four buildings show a similar behavior. The mean damage grade is 2.3 for the deterministic scenario and 2.7 for the probabilistic one. This means that moderate to severe damage is expected in both cases; furthermore, in the case of the deterministic scenario more than 10% of the buildings would suffer extensive-to-collapse damage and nearly 20% for the probabilistic scenario, confirming the high vulnerability of such buildings. The differences in the expected damage are due to the significant different characteristics of the response spectra of the earthquake scenarios in the range of the fundamental periods of the buildings.