Alex Barbat's articles in WoS/Scopus journals

Alex's Barbat Journal Papers is an online archive aimed at collecting, preserving, and disseminating digital copies of the scientific papers published on international journalsshow more

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Seismic and structural response of a framed four level building with RC and steel structure designed according to current Venezuelan codes
R. Ugel, R. Herrera, J. Vielma, A. Barbat, L. Pujades

WIT Transactions on The Built Environment, ISSN 1743-3509 (2013). 132, doi:10.2495/ERES130071

Abstract
This study determines the structural behavior of a four level framed building with composite RC and steel structure designed according Venezuelan seismic codes. The structural system consists of RC frames in the first three levels and steel frames in the fourth. It was performed linear analysis to design all structural elements. Capacity curves and performance points were obtained with pushover analysis. Results showed greater ductility in the X frames’ direction and greater resistance reserve in the external frames. Performing points showed adequate resistance values but low stiffness in two Y frames’ directions. Seismic action is carried on through synthetic accelerograms defined by the seismic codes used in this study. Dynamic analysis is used to compute parameters of ductility, over strength and displacements. In one case the collapse Limit State was reached, implying a general collapse of the building. Incremental dynamic analysis was performed to obtain fragility curves and damage probability matrix; a very high probability of significant lateral displacement and damage was evidenced from this despite a normative design of structural elements.
Abstract
This study determines the structural behavior of a four level framed building with composite RC and steel structure designed according Venezuelan seismic codes. The structural [...]
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Seismic response and torsional effects of RC structure with irregular plant and variations in diaphragms, designed with Venezuelan codes
R. Herrera, J. Vielma, R. Ugel, A. Alfaro, A. Barbat, L. Pujades

WIT Transactions on The Built Environment, ISSN 1743-3509 (2013). 132, doi:10.2495/ERES130071

Abstract
The objective of this study is to determine the seismic response and torsional effects of an existing Reinforced Concrete building with irregular plant and five levels projected according to an older version of Venezuelan seismic design code. Two structures were analysed: the original building and a redesigned version. Nonlinear static analysis and nonlinear 3D dynamic analysis were applied, based on registers of three synthetic accelerograms compatible with the elastic design spectrum for the used code. In 3D analysis, four structures were simulated, with and without rigid diaphragms so as to compare the seismic behaviour of the buildings. Through this nonlinear analysis parameters were determined that define the behaviour of the structure, torsional moments and rotations in columns reached for simulated buildings. Also, to obtain damage fragility curves for five states damage were generated. Results show that the original structure has an inadequate resistant behaviour and a high probability of exceeding the moderate damage state, while the redesigned structure presents good performance under seismic events according to the existing code. It was also observed that maximum torsional effects occur in the entrant corners of the irregular plant, which are reduced in mid-rise buildings by using a rigid diaphragm.
Abstract
The objective of this study is to determine the seismic response and torsional effects of an existing Reinforced Concrete building with irregular plant and five levels projected [...]
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Probabilistic Seismic Damage Assessment of RC Buildings Based on Nonlinear Dynamic Analysis
Y. Vargas, L. Pujades, A. Barbat, J. Hurtado

The Open Civil Engineering Journal (2015). 9, (Suppl. 1, M 12) 344-350

Abstract
The incremental dynamic analysis is a powerful tool for evaluating the seismic vulnerability and risk of buildings. It allows calculating the global damage of structures for different PGAs and representing this result by means of damage curves. Such curves are used by many methods to obtain seismic risk scenarios at urban level. Even if the use of this method in a probabilistic environment requires a relevant computational effort, it should be the reference method for seismic risk evaluation. In this article we propose to assess the seismic expected damage by using nonlinear dynamic analysis. We will obtain damage curves by means of the incremental dynamic analysis combined with the damage index of Park & Ang. The uncertainties related to the mechanical properties of the materials and the seismic action will be considered. The probabilistic damage curves obtained can be used to calculate not only seismic risk scenarios at urban level, but also to estimate economic losses.
Abstract
The incremental dynamic analysis is a powerful tool for evaluating the seismic vulnerability and risk of buildings. It allows calculating the global damage of structures for [...]
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Vulnerability Assessment of Reinforced Concrete Framed Structures Considering the Effect of Structural Characteristics
I. Olteanu, A. Barbat, M. Budescu

The Open Civil Engineering Journal (2015). 9, (Suppl. 1, M 10) 321-329

Abstract
Considering the effects of earthquakes occurred during the last 15 years, this article focusses on finding solutions to minimize the human and economic losses. Several methodologies were developed in order to assess the vulnerability of the built environment with special reference to one of the most suitable structural systems in seismic areas for dwellings, offices or other functionalities, which is the reinforced concrete framed structure. Thus, the present article studies the influence on the vulnerability of reinforced concrete framed structures of geometric structural characteristics like the slab thickness, the building height and the plan configuration. Referring to the slab, it adds supplementary stiffness to the structure that can significantly influence upon its overall failure mechanism. 3D static nonlinear analyses are conducted by means of the SAP2000 computer program. The results are capacity curves which are used to develop the vulnerability curves. Three thicknesses are considered for the slab: 0.1 cm, 0.12 cm and 0.15 m. Medium and high rise structures are considered, with 4, and 8 levels, respectively, in order to determine the influence of the building height on the vulnerability index. Three plan configurations of the buildings are compared: a square one, a rectangular one and an L shaped one. For all the analyzed cases, the corresponding vulnerability curves are compared. The obtained results reveal that more realistic results for the behavior of the structure can be obtained if special attention is given to the structural characteristics, especially during the conceptual design process.
Abstract
Considering the effects of earthquakes occurred during the last 15 years, this article focusses on finding solutions to minimize the human and economic losses. Several methodologies [...]
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Probabilistic seismic risk evaluation of reinforced concrete buildings
Y. Vargas, A. Barbat, L. Pujades, J. Hurtado

Structures and Buildings (Proceedings of the Institution of Civil Engineers) (2013). http://dx.doi.org/10.1680/stbu.12.00031

Abstract
The main objective of this article is to propose a simplified methodology to assess the expected seismic damage in reinforced concrete buildings from a probabilistic point of view by using Monte Carlo simulation. In order to do so, the seismic behaviour of the building was studied by using random capacity obtained by considering the mechanical properties of the materials as random variables. From the capacity curves, the damage states and fragility curves can be obtained, and curves describing the expected seismic damage to the structure as a function of a seismic hazard characteristic can be developed. The latter can be calculated using the capacity spectrum and the demand spectrum according to the methodology proposed by the Risk-UE project. In order to define the seismic demand as a random variable, a set of real accelerograms were obtained from European and Spanish databases in such a way that the mean of their elastic response spectra was similar to an elastic response spectrum selected from Eurocode 8. In order to combine the uncertainties associated with the seismic action and the mechanical properties of materials, two procedures are considered to obtain functions relating the peak ground acceleration to the maximum spectral displacements. The first method is based on a series of non-linear dynamic analyses, while the second is based on the well-known ATC-40 procedure called equal displacement approximation. After applying both procedures, the probability density functions of the maximum displacement at the roof of the building are gathered and compared. The expected structural damage is finally obtained by replacing the spectral displacement calculated using ATC-40 and the incremental dynamic procedure. In the damage functions, the results obtained from incremental static and dynamic analyses are compared and discussed from a probabilistic point of view.
Abstract
The main objective of this article is to propose a simplified methodology to assess the expected seismic damage in reinforced concrete buildings from a probabilistic point [...]
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Seismic performance of waffled-slab floor buildings
J. Vielma, A. Barbat, S. Oller

Structures and Buildings (Proceedings of the Institution of Civil Engineers) (2009). 162, 169–182, doi: 10.1680/stbu.2009.162.3.169

Abstract
The codes used in seismic design of waffled-slab floors buildings (WSFB), such as the Spanish NCSE-02 earthquake-resistant design code, assign them restricted ductility, utilise linear structural analysis based on modal analysis, but also consider the structural ductility concept. Uncertainties arise whenever these codes are applied to the special case of buildings with waffled-slab floors, the ductility of which is doubtful. In many cases, during earthquakes, buildings with restricted ductility are unable to reach the ductility values assumed in the design process, although they may exhibit adequate values of overstrength. This paper therefore studies typical WSFB by applying static incremental non-linear analysis procedures (pushover analysis) in order to calculate their actual structural ductility and overstrength values. Fragility curves corresponding to different damage states and damage probability matrices are also calculated and compared with those of moment-resisting frame buildings (MRFB) in order to obtain useful conclusions for earthquake resistant design. One of the most relevant conclusions of this article is that the use of a better confinement and of ductile steel can only improve the seismic behaviour of MRFB but not that of WSFB.
Abstract
The codes used in seismic design of waffled-slab floors buildings (WSFB), such as the Spanish NCSE-02 earthquake-resistant design code, assign them restricted ductility, [...]
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Probabilistic seismic damage assessment of reinforced concrete buildings considering directionality effects
Y. Vargas, L. Pujades, A. Barbat, J. Hurtado, S. Diaz, D. Hidalgo

Structure and Infrastructure Engineering (2018). 14(6), 817–829, https://doi.org/10.1080/15732479.2017.1385089

Abstract
Most of buildings and structures are usually projected according to two main axes. However, the geographical position of these buildings varies randomly. Such random distributions of the azimuthal positions of structures, in most of the cities, generally, are not accounted for when assessing their seismic risk; certainly, the direction of the seismic loads is another highly random variable. Moreover, an additional important source of uncertainty is related to the structural response, mainly due to the random character of the mechanical properties. There is a consensus that uncertainties must be considered for adequately assessing the seismic risk of structures, but these directionality effects have not been deeply explored so far. In this article, the influence of the high uncertainty involved in these input variables on the expected seismic damage is analysed. Thus, an actual earthquake, which affected the southern part of Spain, is studied. Notably, damages on a group of affected buildings, located close to the epicentre, are analysed and discussed in detail. The results show that the influence of the random azimuthal position of structures is an important source of uncertainty and that it should be taken into account when estimating the expected seismic risk in urban areas.
Abstract
Most of buildings and structures are usually projected according to two main axes. However, the geographical position of these buildings varies randomly. Such random distributions [...]
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Seismic vulnerability and risk evaluation methods for urban areas. A review with application to a pilot area
A. Barbat, M. Carreño, L. Pujades, N. Lantada, O. Cardona, M. Marulanda

Structure and Infrastructure Engineering (2010). 6(1–2), 17–38

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.
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, [...]
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Fourier-based maximum entropy method in stochastic dynamics
J. Hurtado, A. Barbat

Structural Safety (1998). 20, 221-235

Abstract
As the recent research by Trybicki and Sobczyk has demonstrated [1-3] the principle of maximum entropy is a powerful tool for solving stochastic differential equations. In particular, its use in connection with the moment equations generated by the Ito formula provides accurate estimations of the probability density evolution of some oscillators for which conventional methods such as the diverse closure schemes are not applicable. A major computational requirement of the method, however, lies in the need of calculating a large number of multidimensional integrals at each time step -a numerical task for which both accurate and economic algorithms are required. In this paper it is shown that conventional economic integration techniques often lead to numerical collapse of the solution, especially when dealing with higly nonlinear oscillators. A strategy that overcomes this difficulty is proposed. In essence, the integrals are reformulated in terms of multidimensional Fourier transforms, which are solved by an ad hoe FFT algorithm aimed at obtaining only one single "frequency" point. It is demonstrated that the numerical stability and the accuracy of the proposed algorithm are superior to those afforded by other integration schemes.
Abstract
As the recent research by Trybicki and Sobczyk has demonstrated [1-3] the principle of maximum entropy is a powerful tool for solving stochastic differential equations. In [...]
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Improved stochastic linearization method using mixed distributions
J. Hurtado, A. Barbat

Structural Safety (1996). 18(1), 49-62

Abstract
A new procedure for the random vibration analysis of hysteretic structures using stochastic equivalent linearization is reported. Its aim is to improve the prediction of the response obtained by conventional Gaussian linearization technique. To this purpose, mixed discrete-continuous Gaussian distributions are used taking into account the bounded nature of the non-linear restoring force. The simple but important property of the mixed distribution is its linearity, which allows the use of the previous results obtained by the Gaussian hypothesis, avoiding the need of employing non-Gaussian continuous distributions or other time-consuming techniques such as local Monte Carlo simulations. Closed-form expressions of the new linearization coefficients for the Bouc-Wen-Baber model are then provided. The relative weights of the discrete and Gaussian distributions are calculated in dependence of the degree of non-linearity in each time step. The comparison of the results with previously published ones obtained by simulation shows a good agreement, providing a substantial improvement of the method with respect to the conventional Gaussian technique with the same calculation effort.
Abstract
A new procedure for the random vibration analysis of hysteretic structures using stochastic equivalent linearization is reported. Its aim is to improve the prediction of the [...]
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Seismic damage evaluation in urban areas using the capacity spectrum method: Application to Barcelona
A. Barbat, L. Pujades, N. Lantada

Soil Dynamics and Earthquake Engineering (2008). 28, 851–865

Abstract
Conceptual aspects related to seismic vulnerability, damage and risk evaluation are discussed first, together with a short review of the most widely used possibilities for seismic evaluation of structures. The capacity spectrum method and the way of obtaining seismic damage scenarios for urban areas starting from capacity and fragility curves are then discussed. The determination of capacity curves for buildings using non-linear structural analysis tools is then explained, together with a simplified expeditious procedure allowing the development of fragility curves. The seismic risk of the buildings of Barcelona, Spain, is analyzed in the paper, based on the application of the capacity spectrum method. The seismic hazard in the area of the city is described by means of the reduced 5% damped elastic response spectrum. The information on the buildings was obtained by collecting, arranging, improving and completing a broad database of the dwellings and current buildings. The buildings existing in Barcelona are mainly of two types: unreinforced masonry structures and reinforced concrete buildings with waffled-slab floors. The ArcView software was used to create a GIS tool for managing the collected information in order to develop seismic risk scenarios. This study shows that the vulnerability of the buildings is significant in Barcelona and, therefore, in spite of the low-to-moderate seismic hazard in the region, the expected seismic risk is considerable.
Abstract
Conceptual aspects related to seismic vulnerability, damage and risk evaluation are discussed first, together with a short review of the most widely used possibilities for [...]
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An Updated Probabilistic Seismic Hazard Assessment for Romania and Comparison with the Approach and Outcomes of the SHARE Project
F. PAVEL, R. VACAREANU, J. DOUGLAS, M. RADULIAN, C. CIOFLAN, A. BARBAT

Pure and Applied Geophysics (2016). 173, 1881‐1905

Abstract
The probabilistic seismic hazard analysis for Romania is revisited within the framework of the BIGSEES national research project (http://infp.infp.ro/bigsees/default.htm) financed by the Romanian Ministry of Education and Scientific Research in the period 2012–2016. The scope of this project is to provide a refined description of the seismic action for Romanian sites according to the requirements of Eurocode 8. To this aim, the seismicity of all the sources influencing the Romanian territory is updated based on new data acquired in recent years. The groundmotion models used in the analysis, as well as their corresponding weights, are selected based on the results from several recent papers also published within the framework of the BIGSEES project. The seismic hazard analysis for Romania performed in this study are based on the traditional Cornell-McGuire approach. Finally, the results are discussed and compared with the values obtained in the recently completed SHARE research project. The BIGSEES and SHARE results are not directly comparable since the considered soil conditions are different—actual soil classes for BIGSEES and rock for SHARE. Nevertheless, the analyses of the seismic hazard results for 200 sites in Romania reveal considerable differences between the seismic hazard levels obtained in the present study and the SHARE results and point out the need for further analyses and thorough discussions related to the two seismic hazard models, especially in the light of a possible future harmonized hazard map for Europe.
Abstract
The probabilistic seismic hazard analysis for Romania is revisited within the framework of the BIGSEES national research project (http://infp.infp.ro/bigsees/default.htm) [...]
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Failure pressure evaluation of the containment building of a large dry nuclear power plant
A. Barbat, M. Cervera, A. Hanganu, C. Cirauqui, E. Oñate

Nuclear Engineering and Design (1998). 180, 251 – 270

Abstract
The evaluation of the failure pressure of the containment building of a large dry PWR-W three loops nuclear power plant, based on computer numerical simulation, is described in this paper. The proposed method considers fully three-dimensional finite element models in order to take into account the effect of the most significant structural characteristics (presence of three buttresses, penetrations, additional reinforcement around the penetrations, etc.), the lack of symmetry of the forces generated by the prestressing system, as well as the nonlinear behaviour of the materials and the sensitivity of the results to uncertainties associated with several parameters. The computational model is completely described, including the constitutive equations for the concrete, the reinforcing steel and prestressing tendons, the spatial discretization—isoparametric elements including the reinforcement are used. The structural models and the analyses performed for their calibration are also described. The influence on the failure pressure of incorporating the foundation slab in the structural model, and the influence of the thermal effects, are discussed. One of the conclusions of the numerical study is that the failure process can be appropriately simulated by means of a structural model which does not include either the foundation slab or the thermal effects. Finally, results of a probabilistic simulation of the failure pressure are given.
Abstract
The evaluation of the failure pressure of the containment building of a large dry PWR-W three loops nuclear power plant, based on computer numerical simulation, is described [...]
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Urban seismic risk index for Medellín, Colombia, based on probabilistic loss and casualties estimations
M. Salgado, D. Romero, C. Velásquez, M. Carreño, O. Cardona, A. Barbat

Natural Hazards (2016). 80(3), 1995‐2021

Abstract
Medellín is the second largest city of Colombia with more than 2 million inhabitants according to the latest census and with more than 240,000 public and private buildings. It is located on an intermediate seismic hazard area according to the seismic zonation of Colombia although no destructive earthquakes have occurred having as a consequence low seismic risk awareness among its inhabitants. Using the results of a fully probabilistic risk assessment of the city with a building by building resolution level and considering the dynamic soil response, average annual losses by sectors as well as casualties and other direct effects are obtained and aggregated at county level. Using the holistic evaluation module of the multi-hazard risk assessment CAPRA platform, EvHo, a comprehensive assessment that considered the social fragility and lack or resilience at county level is performed making use of a set of indicators with the objective of capturing the aggravating conditions of the initial physical impact. The urban seismic risk index, USRi, is obtained at county level which is useful to communicate risk to decision-makers and stakeholders besides making easy identifying potential zones that can be problematic in terms of several dimensions of the vulnerability. This case study is an example of how a multidisciplinary research on disaster risk reduction helps to show how risk analysis can be of high relevance for decision-making processes in disaster risk management.
Abstract
Medellín is the second largest city of Colombia with more than 2 million inhabitants according to the latest census and with more than 240,000 public and private buildings. [...]
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Vulnerability index and capacity spectrum based methods for urban seismic risk evaluation. A comparison
N. Lantada, L. Pujades, A. Barbat

Natural Hazards (2009). 51, 501–524, DOI 10.1007/s11069-007-9212-4

Abstract
This article contributes to the development and application of two latestgeneration methods of seismic risk analysis in urban areas. The first method, namely vulnerability index method (VIM), considers five non-null damage states, defines the action in terms of macroseismic intensity and the seismic quality of the building by means of a vulnerability index. The estimated damage degree is measured by semi-empirical functions. The second method, namely capacity spectrum based method (CSBM), considers four no damage states, defines the seismic action in terms of response spectra and the building vulnerability by means of its capacity spectrum. In order to apply both methods to Barcelona (Spain) and compare the results, a deterministic and a probabilistic hazard scenario with soil effects are used. The deterministic one corresponds to a historic earthquake, while the probabilistic seismic ground motion has a probability of exceedence of 10% in 50 years. Detailed information on the building design has been obtained along years by collecting, arranging, improving, and completing the database of the dwellings of the city. A Geographic Information System (GIS) has been customized allowing storing, analysing, and displaying this large amount of spatial and tabular data of dwellings. The obtained results are highly consistent with the historical and modern evolution of the populated area and show the validity and strength of both methods. Although Barcelona has a low to moderate seismic hazard, its expected seismic risk is significant because of the high vulnerability of its buildings. Cities such as Barcelona, located in a low to moderate seismic hazard region, are usually not aware of the seismic risk. The detailed risk maps obtained offer a great opportunity to guide the decision making in the field of seismic risk prevention and mitigation in Barcelona, and for emergency planning in the city.
Abstract
This article contributes to the development and application of two latestgeneration methods of seismic risk analysis in urban areas. The first method, namely vulnerability [...]
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Robustness of the holistic seismic risk evaluation in urban centers using the USRi
M. Marulanda, O. Cardona, A. Barbat

Natural Hazards (2009). 49, 501–516, DOI 10.1007/s11069-008-9301-z

Abstract
The Urban Seismic Risk index (USRi) published in a previous article (Carreño et al., Nat Hazards 40:137–172, 2007) is a composite indicator that measures risk from an integrated perspective and guides decision-making for identifying the main interdisciplinary factors of vulnerability to be reduced or intervened. The first step of the method is the evaluation of the potential physical damage (hard approach) as a result of the convolution of the seismic hazard with the physical vulnerability of buildings and infrastructure. Subsequently, a set of social context conditions that aggravate the physical effects is also considered (soft approach). According to this procedure, the physical risk index is evaluated for each unit of analysis from existing loss scenarios, whereas the total risk index is obtained by multiplying the former index by an impact factor using an aggravating coefficient, based on variables associated with the socio-economic conditions of each unit of analysis. The USRi has been developed using the underlying holistic and multi-hazard approach of the Urban Risk Index framework proposed for the evaluation of disaster risk in different megacities worldwide. This article presents the sensitivity analysis of the index to different parameters such as input data, weights and transformation functions used for the scaling or normalization of variables. This analysis has been performed using the Monte Carlo simulation to validate the robustness of this composite indicator, understanding as robustness how the cities maintain the ranking as well as predefined risk level ranges, when compared with the deterministic results of risk. Results are shown for different cities of the world.
Abstract
The Urban Seismic Risk index (USRi) published in a previous article (Carreño et al., Nat Hazards 40:137–172, 2007) is a composite indicator that measures risk [...]
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Design and implementation of a voluntary collective earthquake insurance policy to cover low-income homeowners in a developing country
M. Marulanda, O. Cardona, M. Mora, A. Barbat

Natural Hazards (2014). 74, 2071–2088, DOI 10.1007/s11069-014-1291-4

Abstract
Understanding and evaluating disaster risk due to natural hazard events such as earthquakes creates powerful incentives for countries to develop planning options and tools to reduce potential damages. The use of models for earthquake risk evaluation allows obtaining outputs such as the loss exceedance curve, the expected annual loss and the probable maximum loss, which are probabilistic metrics useful for risk analyses, for designing strategies for risk reduction and mitigation, for emergency response strategies and for risk financing. This article presents, based on probabilistic risk models, the design and implementation of a risk transfer instrument to cover the private buildings of the city of Manizales, Colombia. This voluntary collective instrument provides financial protection to both, the estate tax payers and the low-income homeowners through a cross-subsidy strategy; besides, it promotes not only the insurance culture but also the solidarity of the community. The city administration and the insurance industry are promoting this program using the mechanism of the property tax payment. This collective insurance helps the government to access key resources for low-income householders recovery and improve disaster risk management at local level.
Abstract
Understanding and evaluating disaster risk due to natural hazard events such as earthquakes creates powerful incentives for countries to develop planning options and tools [...]
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A disaster risk management performance index
M. Carreño, O. Cardona, A. Barbat

Natural Hazards (2007). 41, 1–20, DOI 10.1007/s11069-006-9008-y

Abstract
The Risk Management Index, RMI, proposed in this paper, brings together a group of indicators that measure risk management performance and effectiveness. These indicators reflect the organizational, development, capacity and institutional actions taken to reduce vulnerability and losses in a given area, to prepare for crisis and to recover efficiently from disasters. This index is designed to assess risk management performance. It provides a quantitative measure of management based on predefined qualitative targets or benchmarks that risk management efforts should aim to achieve. The design of the RMI involved establishing a scale of achievement levels or determining the distance between current conditions and an objective threshold or conditions in a reference country, sub-national region, or city. The proposed RMI is constructed by quantifying four public policies, each of which is described by six indicators. The mentioned policies include the identification of risk, risk reduction, disaster management, and governance and financial protection. Risk identification comprises the individual perception, social representation and objective assessment; risk reduction involves the prevention and mitigation; disaster management comprises response and recovery; and, governance and financial protection policy is related to institutionalization and risk transfer. Results at the urban, national and sub-national levels, which illustrate the application of the RMI in those scales, are finally given.
Abstract
The Risk Management Index, RMI, proposed in this paper, brings together a group of indicators that measure risk management performance and effectiveness. These indicators [...]
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Urban Seismic Risk Evaluation: A Holistic Approach
M. Carreño, O. Cardona, A. Barbat

Natural Hazards (2007). 40, 137–172, DOI 10.1007/s11069-006-0008-8

Abstract
Risk has been defined, for management purposes, as the potential economic, social and environmental consequences of hazardous events that may occur in a specified period of time. However, in the past, the concept of risk has been defined in a fragmentary way in many cases, according to each scientific discipline involved in its appraisal. From the perspective of this article, risk requires a multidisciplinary evaluation that takes into account not only the expected physical damage, the number and type of casualties or economic losses, but also the conditions related to social fragility and lack of resilience conditions, which favour the second order effects (indirect effects) when a hazard event strikes an urban centre. The proposed general method of urban risk evaluation is multi hazard and holistic, that is, an integrated and comprehensive approach to guide decision-making. The evaluation of the potential physical damage (hard approach) as the result of the convolution of hazard and physical vulnerability of buildings and infrastructure is the first step of this method. Subsequently, a set of social context conditions that aggravate the physical effects are also considered (soft approach). In the method here proposed, the holistic risk evaluation is based on urban risk indicators. According to this procedure, a physical risk index is obtained, for each unit of analysis, from existing loss scenarios, whereas the total risk index is obtained by factoring the former index by an impact factor or aggravating coefficient, based on variables associated with the socioeconomic conditions of each unit of analysis. Finally, the proposed method is applied in its single hazard form to the holistic seismic risk evaluation for the cities of Bogota (Colombia) and Barcelona (Spain).
Abstract
Risk has been defined, for management purposes, as the potential economic, social and environmental consequences of hazardous events that may occur in a specified period of [...]
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Framing vulnerability, risk and societal responses: the MOVE framework
J. Birkmann, O. Cardona, M. Carreño, A. Barbat, M. Pelling, S. Schneiderbauer, S. Kienberger, M. Keiler, D. Alexander, P. Zeil, T. Welle

Natural Hazards (2013). 67, 193–211, DOI 10.1007/s11069-013-0558-5

Abstract
The paper deals with the development of a general as well as integrative and holistic framework to systematize and assess vulnerability, risk and adaptation. The framework is a thinking tool meant as a heuristic that outlines key factors and different dimensions that need to be addressed when assessing vulnerability in the context of natural hazards and climate change. The approach underlines that the key factors of such a common framework are related to the exposure of a society or system to a hazard or stressor, the susceptibility of the system or community exposed, and its resilience and adaptive capacity. Additionally, it underlines the necessity to consider key factors and multiple thematic dimensions when assessing vulnerability in the context of natural and socio-natural hazards. In this regard, it shows key linkages between the different concepts used within the disaster risk management (DRM) and climate change adaptation (CCA) research. Further, it helps to illustrate the strong relationships between different concepts used in DRM and CCA. The framework is also a tool for communicating complexity and stresses the need for societal change in order to reduce risk and to promote adaptation. With regard to this, the policy relevance of the framework and first results of its application are outlined. Overall, the framework presented enhances the discussion on how to frame and link vulnerability, disaster risk, risk management and adaptation concepts.
Abstract
The paper deals with the development of a general as well as integrative and holistic framework to systematize and assess vulnerability, risk and adaptation. The framework [...]
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Methodology and applications for the benefit cost analysis of the seismic risk reduction in building portfolios at broadscale
J. Valcárcel, M. Mora, O. Cardona, L. Pujades, A. Barbat, G. Bernal

Natural Hazards (2013). 69, 845–868, DOI 10.1007/s11069-013-0739-2

Abstract
This article presents a methodology for an estimate of the benefit cost ratio of the seismic risk reduction in buildings portfolio at broadscale, for a world region, allowing comparing the results obtained for the countries belonging to that region. This methodology encompasses (1) the generation of a set of random seismic events and the evaluation of the spectral accelerations at the buildings location; (2) the estimation of the buildings built area, the economic value, as well as the classification in structural typologies; (3) the development of vulnerability curves for each typology; (4) the estimation of the annual average loss of the buildings portfolio in the current conditions as well as in the case of a hypothetical structural intervention. The benefit cost ratio is estimated as the difference between the estimates of the present value of these two annual average losses, divided by the retrofitting costs. This methodology has been applied to the portfolio of public schools of 14 countries ofLatinAmerica and the Caribbean, for evaluating the feasibility of the seismic risk reduction at a national scale.
Abstract
This article presents a methodology for an estimate of the benefit cost ratio of the seismic risk reduction in buildings portfolio at broadscale, for a world region, allowing [...]
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Hybrid loss exceedance curve (HLEC) for disaster risk assessment
C. Velásquez, O. Cardona, M. Mora, L. Yamin, A. Barbat, M. Carreño, A. Barbat

Natural Hazards (2014). 72, 455–479, DOI 10.1007/s11069-013-1017-z

Abstract
Taken into account that the natural hazard risk is a contingent liability and, therefore, a sovereign risk for national governments, it is important to assess properly the potential losses to design a suitable risk reduction, retention and transfer strategy. In this article, a disaster risk assessment methodology is proposed based on two approaches: on the one hand, the empiric estimation of losses, using information available from local disaster databases, allowing estimating losses due to small-scale events and, on the other hand, probabilistic evaluations to estimate losses for greater or even catastrophic events, for which information usually is not available due to the lack of historical data. A ‘‘hybrid’’ loss exceedance curve is thus determined, which combines the results of these two approaches and represents the disaster risk in a proper and complete way. This curve merges two components: the corresponding to small and moderate losses, calculated using an inductive and retrospective analysis, and the corresponding to extreme losses, calculated using a deductive and prospective analysis. Applications of this risk assessment technique are given in this article for eleven countries.
Abstract
Taken into account that the natural hazard risk is a contingent liability and, therefore, a sovereign risk for national governments, it is important to assess properly the [...]
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Probabilistic earthquake risk assessment using CAPRA: application to the city of Barcelona, Spain
M. Marulanda, M. Cardona, M. Ordaz, A. Barbat

Natural Hazards (2013). 69(1), 59–84, DOI 10.1007/s11069-013-0685-z

Abstract
The risk evaluation model CAPRA (Comprehensive Approach to Probabilistic Risk Assessment) is a techno-scientific methodology and information platform, composed of tools for evaluating and communicating risk at various territorial levels. The model allows evaluating losses on exposed elements using probabilistic metrics, such as the loss exceedance curve, the expected annual loss and the probable maximum loss, useful for multi-hazard risk analyses. In this article, the process of probabilistic seismic risk analysis is described, explaining the main features of the CAPRA modules of hazard, vulnerability and risk estimation applied to the city of Barcelona, Spain. In addition, according to the physical risk results and the information on the socioeconomic indicators of the city, this article presents the holistic evaluation of seismic risk, which is a valuable result to facilitate the integrated risk management by the different stakeholders involved in risk reduction decision making.
Abstract
The risk evaluation model CAPRA (Comprehensive Approach to Probabilistic Risk Assessment) is a techno-scientific methodology and information platform, composed of tools for [...]
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Seismic performance of buildings with a class of adaptive nonlinear hybrid systems
A. Barbat, J. Rodellar, N. Molinares, E. Ryan

Journal of Structural Control (1994). 1(1-2), 117-141

Abstract
A class of hybrid control system which combines a passive nonlinear base isolator with an active controller is analyzed. The passive component of the system has a hysteretic behaviour. A single control force is applied on the structural base by means of a new adaptive control strategy, not requiring knowledge of the system parameters and the excitation and able to handle the typical nonlinearities associated with base isolators. A numerical study is performed to assess the improvement of the behaviour of buildings equipped with this control system.
Abstract
A class of hybrid control system which combines a passive nonlinear base isolator with an active controller is analyzed. The passive component of the system has a hysteretic [...]
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Nonlinear Response of Structures with Sliding Base lsolation
. L.Bozzo, A. Barbat

Journal of Structural Control (1995). 2(2), 59-77

Abstract
It is accepted that sliding or friction base isolation systems effectively protect structures subjected to severe earthquakes. Precise modeling of the sliding connection is, however, still difficult since various parameters influence the friction coefficient. Simplified models, such as those based on a constant friction coefficient, are convenient to understand the behavior of sliding structures and to identify general trends. However, this article shows that for final structural designs (and in particular if the building enters in the nonlinear range) these trends should be used carefully. The purpose oí the article is to discuss the general behavior of structures supported on sliding connections and to describe a simple numeric model to take into account variations in the friction coefficient. The numeric model enables to represent complex force-displacement relationships for the sliding bearings. The model is used to perform a preliminary evaluation of the influence in the response caused by changes in the friction coefficient for elastic and elasto-plastic structures. The variations in the friction coefficient are obtained from experimental testing for a class of teflon-based connections.
Abstract
It is accepted that sliding or friction base isolation systems effectively protect structures subjected to severe earthquakes. Precise modeling of the sliding connection is, [...]
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Deterministic and Probabilistic Earthquake Scenarios for the Seismic Risk Analysis of URM Buildings
J. Avila-Haro, J. González-Drigo, Y. Vargas, L. Pujades, A. Barbat

Key Engineering Materials (2013). 525-526, 537-540, doi:10.4028/www.scientific.net/KEM.525-526.537

Abstract
Barcelona, as well as a large number of cities in the Mediterranean basin, has a housing stock composed of a large number of unreinforced brick masonry buildings. Motivated by different factors, the enlargement of the city (Eixample in Catalan) was held from the second half of the 19th century and the beginning of the 20th, a period in which a large number of buildings of this type were built, many of which are still used as dwellings. Although the buildings were built individually, some of them are linked to adjacent buildings by the side walls. This feature leads to the analysis of the buildings as isolated structures and also as an aggregate. Barcelona is located in a seismic region of low to moderate hazard, with macroseismic intensity between the grades VI and VII of the European macroseismic scale EMS'98. Based on the deterministic and probabilistic response spectra for the different types of soils present in Barcelona obtained in the work of Irizarry (2004), the seismic risk of four individual buildings and an aggregate is evaluated. The buildings are modeled and analyzed using the TREMURI program and MATLAB routines under the guidance of RISK-UE project.
Abstract
Barcelona, as well as a large number of cities in the Mediterranean basin, has a housing stock composed of a large number of unreinforced brick masonry buildings. Motivated [...]
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Dynamic System Characterization via Eigenvalue Orbits
J. Marczyk, J. Rodellar, A. Barbat

JOURNAL OF GUIDANCE , CONTROL , AND DYNAMICS (1999). 22(3), 447-454, doi.org/10.2514/2.4417

Abstract
A new model-free approach for the description of general dynamicalsystems with unknownstructure, order, and excitation is introduced. The approach is based on the new concept of eigenvalue orbit. The eigenorbits are obtained by building an associated linear time-variant system through a matrix that relates the output measurements in a moving horizon window and viewing the trajectories of its time-varying eigenvalues. How the eigenorbits may be computed from the measurements and used for the characterization of the original system is shown. The basic properties of the eigenorbits are presented via a series of theorems for the case of a discrete-time, linear timeinvariant system. A set of examples are included to illustrate these properties for more general classes of systems and to suggest some practical issues that can be drawn from the orbits.
Abstract
A new model-free approach for the description of general dynamicalsystems with unknownstructure, order, and excitation is introduced. The approach is based on the new concept [...]
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Computational Tool for Post-Earthquake Evaluation of Damage in Buildings
M. Carreño, O. Cardona, A. Barbat

Earthquake Spectra (2010). 26(1), 63–86

Abstract
A method and a computational tool oriented to assist the damage and safety evaluation of buildings after strong earthquakes is described in this article. The input of the model is the subjective and incomplete information on the building state, obtained by inspectors which are possibly not expert professionals of the field of building safety. The damage levels of the structural components are usually described by linguistic qualifications which can be adequately processed by computational intelligence techniques based on neuro-fuzzy systems what facilitate the complex and urgent tasks of engineering decision-making on the building occupancy after a seismic disaster. The hybrid neuro-fuzzy system used is based on a special three-layer feedforward artificial neural network and fuzzy rule bases and is an effective tool during the emergency response phase providing decisions about safety, habitability, and reparability of the buildings. Examples of application of the computer program are given for two different building classes.
Abstract
A method and a computational tool oriented to assist the damage and safety evaluation of buildings after strong earthquakes is described in this article. The input of the [...]
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New methodology for urban seismic risk assessment from a holistic perspective
M. Carreño, O. Cardona, A. Barbat

Bulletin of Earthquake Engineering (2012). 10, 547–565, DOI 10.1007/s10518-011-9302-2

Abstract
The seismic risk evaluation usually works with a fragmented concept of risk, which depends on the scientific discipline in charge of the assessment. To achieve an effective performance of the risk management, it is necessary to define risk as the potential economic, social and environmental consequences due to a hazardous phenomenon in a period of time. This article presents a methodology which evaluates the seismic risk from a holistic perspective, which means, it takes into account the expected physical damage and also the conditions related to social fragility and lack of resilience, which favour the second order effects when a hazard event strikes an urban centre. This seeks to obtain results which are useful in the decision making process for risk reduction. The proposed method for urban seismic risk evaluation uses the fuzzy sets theory in order to handle qualitative concepts and variables involved in the assessment, the physical risk level and aggravation level, related to the social fragility and the lack of resilience, are evaluated and finally a total risk level is determinate.
Abstract
The seismic risk evaluation usually works with a fragmented concept of risk, which depends on the scientific discipline in charge of the assessment. To achieve an effective [...]
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Procedures Based on Composite FEM Technology for the Resolution of Concrete-Framed Structures with Masonry in-fills: Comparison with Mexican Building Code
C. Escudero, S. Oller, X. Martinez, A. Barbat

Journal of Engineering Mechanics, ASCE (2017). 143(9), 04017080-1 -- 04017080-19

Abstract
The construction of confined masonry buildings has become a good choice to meet the housing needs of low-income families in big cities. Despite this, current building codes for such construction allow the use of highly simplified analysis techniques that have hardly changed in the last 40 years. This paper is based on numerical simulation and discusses the need to combine and improve existing techniques in finite-element method (FEM) analysis for composite materials, to assess the overall structural behavior of reinforced concrete structures with masonry in-fills, and consequently to support the derivation of rational rules for analysis and design. Through the use of a simple yet powerful shell finite element (FE), state-of-the-art theories of mixtures to analyze composite materials, a computational tool to generate the volume fraction of composites, and the Mexican building code, this paper attempts to be a guide to numerical reproduction of the overall behavior of confined masonry structures.
Abstract
The construction of confined masonry buildings has become a good choice to meet the housing needs of low-income families in big cities. Despite this, current building codes [...]
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Predictive control of structures
J. Rodellar, A. Barbat, J. Martín-Sánchez

Journal of Engineering Mechanics, ASCE (1987). 113(6), 797-812

Abstract
Different continuous-time approches have been proposed in recent years to formulate active control algorithms to reduce the response of civil engineering structures under dynamic excitations. In this paper, a general formulation of a new discrete-time control methodology is presented and applied to structural control. This methodology, based on the concept of predictive control, is discussed and compared to the optima! control methodology by means of numerical examples.
Abstract
Different continuous-time approches have been proposed in recent years to formulate active control algorithms to reduce the response of civil engineering structures under [...]
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New Tension-Compression Damage Model for Complex Analysis of Concrete Structures
J. Paredes, S. Oller, A. Barbat

Journal of Engineering Mechanics, ASCE (2016). 142(10), 04016072, doi: 10.1061/(ASCE)EM.1943-7889.0001130

Abstract
A new damage model, based on continuum damage mechanics and simulating the opening, closing, and reopening of cracks in concrete using only one surface of discontinuity, is proposed in this article. The model complies with the thermodynamics principles of nonreversible, isothermal, and adiabatic processes. Two scalar internal variables have been defined: a tensile damage variable d+ and a compressive damage variable d−; the threshold of damage is controlled by only one surface of discontinuity and a new parameter controlling the damage variable that should be activated. This new parameter represents the ratio of tensile stress to compressive stress in the damaged material. The continuity of response under complex loads, which is one of the aims of this work, is ensured. An adequate response under different types of loads leads to the conclusion that the proposed model provides a powerful tool to numerically analyze reinforced concrete structures. Validation and illustrative examples are included in the article.
Abstract
A new damage model, based on continuum damage mechanics and simulating the opening, closing, and reopening of cracks in concrete using only one surface of discontinuity, [...]
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ACTIVE CONTROL OF NONLINEAR BASE-ISOLATED BUILDINGS
A. Barbat, J. Rodellar, E. Ryan, N. Molinares

Journal of Engineering Mechanics, ASCE (1995). 121(6), 676-684

Abstract
A hybrid seismic control system for building structures is considered, which combines a class of passive nonlinear base isolator with an active control system. The active control forces are applied to the structural base with the objective of reducing its absolute displacements. An adaptive control law is formulated to compute the control forces to assure a form of stable behavior of the system under seismic excitation and in the presence of uncertainties in the characteristics of the building and the base isolator. Numerical simulations are performed to assess the effectiveness of the hybrid control system. The global behavior of the structurebase-isolator system is such that the absolute base displacement is significantly reduced, the price paid being a slight increase of the response of the structure.
Abstract
A hybrid seismic control system for building structures is considered, which combines a class of passive nonlinear base isolator with an active control system. The active [...]
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High Damping Rubber Model for Energy Dissipating Devices
P. Mata, R. Boroschek, A. Barbat, S. Oller

Journal of Earthquake Engineering (2007). 11, 231–256, DOI: 10.1080/13632460601123214

Abstract
This work presents the results of a study carried out to characterize the mechanical response of a high damping rubber to be used in designing and constructing energy dissipating devices and base isolators for controling strong vibrations in civil engineering structures. A new parametric model of the elastomer is proposed to be employed in the design procedure and structural analysis of passive controlled structures. The parameters of the model are calibrated using experimental data obtained from tests on rubber specimens under different loading paths. The main dissipating energy mechanisms of the rubber are identified. The proposed model is able to reproduce those main mechanisms as well as geometric second order effects such as tension stiffening due to the effect of axial strains in the response. The response predicted by the proposed model is compared with that obtained from experimental tests and from the Kelvin and plasticity models.
Abstract
This work presents the results of a study carried out to characterize the mechanical response of a high damping rubber to be used in designing and constructing energy dissipating [...]
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Earthquake Loss Assessment for Integrated Disaster Risk Management
O. Cardona, M. Ordaz, L. Yamin, M. Marulanda, A. Barbat

Journal of Earthquake Engineering (2008). 12(S2), 48–59, DOI: 10.1080/13632460802013495

Abstract
Understanding probable losses and reconstruction costs due to earthquakes creates powerful incentives for countries to develop planning options and tools to cope with risk, including allocating the sustained budgetary resources necessary to reduce those potential damages and safeguard development. A specific catastrophic risk model has been developed to evaluate, building by building, the probabilistic losses and pure premiums of different portfolios, taking into account the seismic microzonation of cities. This model has been used to evaluate the fiscal contingency liabilities of the government and to build an optimal structure for risk transfer and retention, considering contingent credits, reserve funds, insurance/reinsurance, and cat bonds. Lastly, the model allows the evaluation of an exceedance probability curve of benefit-cost ratio, providing an innovative and ground-breaking tool for decision makers to analyze the net benefits of the risk mitigation strategies, such as earthquake retrofitting and seismic code enforcement. This article describes the model and the derived abovementioned tools, using the results of loss scenarios and the strategies implemented in some earthquake prone urban centers.
Abstract
Understanding probable losses and reconstruction costs due to earthquakes creates powerful incentives for countries to develop planning options and tools to cope with risk, [...]
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Estimation of Probabilistic Seismic Losses and the Public Economic Resilience—An Approach for a Macroeconomic Impact Evaluation
O. Cardona, M. Ordaz, M. Marulanda, A. Barbat

Journal of Earthquake Engineering (2008). 12(S2), 60–70, DOI: 10.1080/13632460802013511

Abstract
The Disaster Deficit Index (DDI) measures country risk from a macroeconomic and financial perspective, according to possible catastrophic events. The DDI captures the relationship between the demand for contingent resources to cover the maximum probable losses and the public sector’s economic resilience; that is, the availability of internal and external funds for restoring affected inventories. For calculating potential losses, the model follows the insurance industry in establishing a probable loss, based on the critical impacts during a given period of exposure, and for the economic resilience the model computes the country’s financial ability to cope with the situation taking into account: the insurance and reinsurance payments; the reserve funds for disasters; the funds that may be received as aid and donations; the possible value of new taxes; the margin for budgetary reallocations; the feasible value of external credit; and the internal credit the country may obtain. Access to these resources has limitations and costs that must be taken into account as feasible values according to the macroeconomic and financial conditions of the country. This article presents the model of DDI and proposes it as a simple way of measuring a country’s fiscal exposure and potential deficit—or contingency liabilities—in case of extreme disasters to guide the governmental decisionmaking from economic, financial, and disaster risk reduction perspectives.
Abstract
The Disaster Deficit Index (DDI) measures country risk from a macroeconomic and financial perspective, according to possible catastrophic events. The DDI captures the relationship [...]
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VISCOUS DAMAGE MODEL FOR TIMOSHENKO BEAM STRUCTURES
A. Barbat, S. Oller, E. Oñate, A. Hanganu

International Journal of Solids Structures (1997). 34(30), 3953-3976

Abstract
A local damage constitutive model based on Kachanov’s theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The model takes into account viscous effects, thus allowing damping to be considered in a rigorous way. A damage index based on potential energy criteria, useful in evaluating the behaviour of structures or of parts of structures, is proposed. The procedure is applied to estimate the damage produced by seismic actions in reinforced concrete building structures, whose response is computed by using a non-linear Newmark-type incremental time integration scheme. Three numerical examples are included; one of them compares results obtained by using the proposed model with results of a laboratory test.
Abstract
A local damage constitutive model based on Kachanov’s theory is used within a finite element frame and applied to the case of 2D and 3D Timoshenko beam elements. The [...]
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Analysis of Ultra Low Cycle Fatigue problems with the Barcelona plastic damage model and a new isotropic hardening law
X. Martínez, S. Oller, L. Barbu, A. Barbat, A. Jesus

International Journal of Fatigue (2015). 73, 132–142, http://dx.doi.org/10. 1016/j.ijfatigue.2014.11.013

Abstract
This paper presents a plastic-damage formulation and a new isotropic hardening law, based on the Barcelona plastic damage model initially proposed by Lubliner et al. (1989) [1], which is capable of predicting steel failure due to Ultra Low Cycle Fatigue (ULCF). This failure mechanism is obtained when the material is subjected to cyclic loads and breaks after applying a very low number of cycles, usually less than hundreds. The failure is driven by the plastic response of the material, and it is often predicted based on the plastic strains applied to it. The model proposed in this work has been formulated with the objective of predicting accurately the plastic behavior of the material, as well as its failure due to ULCF. This is achieved taking into account the fracture energy dissipated during the whole loading process. This approach allows the simulation of ULCF when it takes place due to regular cyclic loads or non-regular cyclic loads, as it is the case of seismic loads. Several simulations are conducted in order to show the capabilities of the formulation to reproduce the mechanical response of steel when it is subjected to regular and non-regular cyclic loads. The formulation is validated comparing the numerical results with several experimental tests made o n X52 steel specimens. The agreement between the numerical and experimental results asses the validity of the proposed model to predict the plastic behavior of steel and its failure due to Ultra Low Cycle Fatigue.
Abstract
This paper presents a plastic-damage formulation and a new isotropic hardening law, based on the Barcelona plastic damage model initially proposed by Lubliner et al. (1989) [...]
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Validation on large scale tests of a new hardening–softening law for the Barcelona plastic damage model
L. Barbu, X. Martinez, S. Oller, A. Barbat

International Journal of Fatigue (2015). 81, 213- 226, doi:10.1016/j.ijfatigue.2015.07.031

Abstract
This paper presents the results of finite element simulations made on a bent pipe subjected to an in-plane variable cyclic displacement combined with internal pressure. Special emphasis is put on the capacity of the model to illustrate different failure modes depending on the internal pressure applied on the pipe. The results of the numerical analyses will be compared to experimental ones. The constitutive model used for the simulation of Ultra Low Cycle Fatigue (ULCF) loading and the hardening–softening law used are only briefly touched upon. The monotonic behavior of a large diameter pipe, as obtained from the constitutive model proposed, is also shown and compared to experimental results under two different loading conditions. The total axial load at failure for this case resulted in less than 10% error as compared to the experiments. Regarding the ULCF in-plane bending simulations conducted on a 16-in. 90º elbow, the results were in good agreement with the experimental test in terms of force–displacement hysteresis loops and total fatigue life of the specimen. An analysis of the dependence of the failure mode to the internal pressure applied has been conducted, showing that the formulation is capable of obtaining both habitual failure types.
Abstract
This paper presents the results of finite element simulations made on a bent pipe subjected to an in-plane variable cyclic displacement combined with internal pressure. Special [...]
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Behaviour of the interface between concrete and FRP using serial/ parallel mixing theory
M. Molina, J. Cruz, S. Oller, A. Barbat, L. Gil

INGENIERÍA E INVESTIGACIÓN (2011). 31(3), 26-39

Abstract
Experimental research has shown that one of the key factors affecting the behaviour of reinforced concrete structures strengthened with externally-bonded fibre-reinforced polymer (FRP) is the bonding behaviour between concrete and FRP laminates. As a complement to experimentation, this paper proposed the use of serial/parallel mixing theory in numerical simulation, which is a tool for studying the behaviour of the concrete-FRP epoxy interface. An example is presented which analyses beam test simulation results and compares them with the experimental results.
Abstract
Experimental research has shown that one of the key factors affecting the behaviour of reinforced concrete structures strengthened with externally-bonded fibre-reinforced [...]
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FINITE ELEMENT ANALYSIS OF BASE ISOLATED BUILDINGS SUBJECTED TO EARTHQUAKE LOADS
O. Salomón, S. Oller, A. Barbat

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (1999). 46, 1741-1761

Abstract
A finite element formulation modelling hyperelastic quasi-incompressible rubber-like materials (elastomers) is developed which takes into account large displacements and large elastic strains as well as inelastic effects. The capacity of laminated rubber-like materials to support high loads in compression and large displacements in shear is the principal reason for their use in devices for seismic base isolation of structures. The energy-dissipation capacity of these devices is increased by using high damping rubber, which is an elastomer incorporating carbon black particles, or having lead-plug insertion. The Ogden strain energy function has been used as a basis for the material model implemented in a total Lagrangian formulation, the strain being decomposed into its deviatory and volumetric parts and the pressure variable being condensed at element level. Mooney-Rivlin and neo-Hooke strain energy functions can also be used by simply changing the parameters of the model. The stress-strain hysteresis, which appears when these devices are subjected to dynamic or quasi-static cyclic loads, has been modelled by frequency dependent viscoelastic and plastic constitutive models. The bearings have been modelled by means of an equivalent single element capable of describing the composite behaviour of the actual isolation system. The proposed model is validated using available experimental results and it is proved to be a powerful tool in dealing with different bearings. Finally, results for a six-storey base isolated building subjected to the El Centro earthquake are given.
Abstract
A finite element formulation modelling hyperelastic quasi-incompressible rubber-like materials (elastomers) is developed which takes into account large displacements and large [...]
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Non-linear seismic analysis of RC structures with energy-dissipating devices
P. Mata, A. Barbat, S. Oller, R. Boroschek

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2009). 78, 1037–1075

Abstract
The poor performance of some reinforced concrete (RC) structures during strong earthquakes has alerted about the need of improving their seismic behavior, especially when they are designed according to obsolete codes and show low structural damping, important second-order effects and low ductility, among other defects. These characteristics allow proposing the use of energy-dissipating devices for improving their seismic behavior. In this work, the non-linear dynamic response of RC buildings with energy dissipators is studied using advanced computational techniques. A fully geometric and constitutive non-linear model for the description of the dynamic behavior of framed structures is developed. The model is based on the geometrically exact formulation for beams in finite deformation. Points on the cross section are composed of several simple materials. The mixing theory is used to treat the resulting composite. A specific type of element is proposed for modeling the dissipators including the corresponding constitutive relations. Special attention is paid to the development of local and global damage indices for describing the performance of the buildings. Finally, numerical tests are presented for validating the ability of the model for reproducing the non-linear seismic response of buildings with dissipators.
Abstract
The poor performance of some reinforced concrete (RC) structures during strong earthquakes has alerted about the need of improving their seismic behavior, especially when [...]
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SSP algorithm for linear and non-linear dynamic response simulation
F. López-Almansa, A. Barbat, J. Rodellar

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (1988). 26, 2687-2706

Abstract
A direct integration algorithm to solve the spatially discretized equations of motion of a structure is proposed. This algorithm formulates the equations of motion in state space and uses their analytical solution to derive a recursive discrete-time equation. The proposed structural state procedure (SSP) can be considered as a generalization for multi-degree-of-freedom systems of the Duhamel's integral used for single-degree-of-freedom systems. It can be noted that the proposed SSP algorithm does not need a previous modal uncoupling of the equations of motion and consequently it does not require any hypothesis about damping. SSP is shown to be stable and to give accurate results with a reasonable computation time. Stability and accuracy essentially depend on the computation of the system matrix. The SSP algorithm is combined with an iterative scheme to obtain the response of structures with non-linear behaviour. Two examples of application of SSP are included: seismic response of a building structure with linear behaviour and free vibration of a non-linear system with imposed initial conditions.
Abstract
A direct integration algorithm to solve the spatially discretized equations of motion of a structure is proposed. This algorithm formulates the equations of motion in state [...]
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Comparing observed damages and losses with modelled ones using a probabilistic approach: The Lorca 2011 case
M. Salgado-Galvez, A. Barbat, O. Cardona, M. Carreño

International Journal of Disaster Risk Reduction (2016). 19, 355– 365, DOI: 10.1016/j.ijdrr.2016.09.008

Abstract
A loss and damage assessment was performed for the buildings of Lorca, Spain, considering an earthquake hazard scenario with similar characteristics to those of a real event which occurred on May 11th, 2011, in terms of epicentre, depth and magnitude while also considering the local soil response. This low-to moderate earthquake caused severe damage and disruption in the region and especially on the city. A building by building resolution database was developed and used for damage and loss assessment. The portfolio of buildings was characterized by means of indexes capturing information from a structural point of view such as age, main construction materials, number of stories, and building class as well as others related to age and vulnerability classes. A replacement cost approach was selected for the analysis in order to calculate the direct losses incurred by the event. Seismic hazard and vulnerability were modelled in a probabilistic way, considering their inherent uncertainties which were also taken into account in the damage and loss calculation process. Losses have been expressed in terms of the mean damage ratio of each dwelling and since the analysis has been performed on a geographical information system platform, the distribution of the damage and its categories was mapped for the entire urban centre. The simulated damages and losses were compared with the observed ones reported by the local authorities and institutions that inspected the city after the event.
Abstract
A loss and damage assessment was performed for the buildings of Lorca, Spain, considering an earthquake hazard scenario with similar characteristics to those of a real event [...]
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Seismic and wind vulnerability assessment for the GAR-13 global risk assessment
L. Yamin, A. Hurtado, A. Barbat, O. Cardona

International Journal of Disaster Risk Reduction (2014). 10, 452 – 460, http://dx.doi.org/10.101 6/j.ijdrr.2014.05.007

Abstract
A general methodology to evaluate vulnerability functions suitable for a probabilistic global risk assessment is proposed. The methodology is partially based in the methodological approach of the Multi-hazard Loss Estimation Methodology (Hazus) developed by the Federal Emergency Management Agency (FEMA). The vulnerability assessment process considers the resolution, information and limitations established for both the hazard and exposure models adopted. Seismic and wind vulnerability functions are estimated for each one of the building classes defined in typical global exposure databases. They consider possible variations according to the design level in different regions of the world which accounts for variations of the expected quality of construction and the design code compliance level. In addition, a consistent, expert opinion based methodology is proposed in order to assign particular vulnerability functions to building classes according to the development level of each country, the city complexity and the hazard level of the region. The proposed set of vulnerability functions and the assignment procedure were used for the probabilistic global risk assessment made in the framework of the UNISDR’s Global Assessment Report on Disaster Risk Reduction, GAR 2013. Recommendations for the refinement of the methodological approach are included for future global or scaled regional risk assessments.
Abstract
A general methodology to evaluate vulnerability functions suitable for a probabilistic global risk assessment is proposed. The methodology is partially based in the methodological [...]
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RETROSPECTIVE ASSESSMENT OF RISK FROM NATURAL HAZARDS
C. Velásquez, O. Cardona, M. Carreño, A. Barbat

International Journal of Disaster Risk Reduction (2014). 10, 477–489, http://dx.doi.org/ 10.1016/j.ijdrr.2014.05.005

Abstract
The existing disaster databases allow analyzing losses produced by previous events and assessing the risk to natural hazard in a similar way as the insurance industry does for vehicles, health, etc., if the conditions and trends are maintained. Among the existing disaster databases, we selected DesInventar whose vast majority of records correspond to “small” events; this selection is of special interest as these small events are often ignored because, individually, they only stroke a few assets accounting for low economic losses. Nevertheless, their accumulated effect can have a significant impact over the economic and fiscal sustainability of urban areas, regions or countries. Also, considering the difficulties involved in assessing risk for those small disasters, like the lack of general models and the elevated susceptibility to local variables of the results, this approach can give answers so far unavailable. The methodology herein proposed has been applied to the assessment of risk (in the terms of the loss exceedance curve) in 23 countries.
Abstract
The existing disaster databases allow analyzing losses produced by previous events and assessing the risk to natural hazard in a similar way as the insurance industry does [...]
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Holistic Disaster Risk Evaluation for the Urban Risk Management Plan of Manizales, Colombia
M. Carreño, O. Cardona, A. Barbat, D. Suarez, M. Perez, L. Narvaez

International Journal of Disaster Risk Science (2017). 8, 258–269, DOI 10.1007/s13753-01 7-0136-7

Abstract
Disaster risk depends on both the physical vulnerability and a wide range of social, economic, and environmental aspects of a society. For a better risk understanding, a holistic or integrated perspective was considered when risk was assessed for the city of Manizales, Colombia. This assessment accounts not only for the expected physical damage and loss, but also for the socioeconomic vulnerability factors that favor second order effects in a disaster. This comprehensive approach allows the identification of different aspects related to physical vulnerability, social fragility, and lack of resilience that can be improved, thus enhancing integrated disaster risk management actions. The outcomes of this comprehensive assessment are currently being used as input to update the disaster risk management plan of Manizales.
Abstract
Disaster risk depends on both the physical vulnerability and a wide range of social, economic, and environmental aspects of a society. For a better risk understanding, a holistic [...]
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Modernist Unreinforced Masonry (URM) Buildings of Barcelona: Seismic Vulnerability and Risk Assessment
R. González-Drigo, A. Avila-Haro, A. Barbat, L. Pujades, Y. Vargas, S. Lagomarsino, S. Cattari

INTERNATIONAL JOURNAL FOR ARCHITECTURAL HERITAGE (2015). 9, 214-230

Abstract
The main objective of this work is to assess the vulnerability and seismic risk of typical existing modernist unreinforced masonry (URM) modernist buildings and aggregates situated in the Eixample district of Barcelona, part of the architectural heritage of the city. The context of the analysis is the methodology proposed by the Risk-UE project. The buildings are characterized by their capacity spectrum and the earthquake demand is defined by the 5% damped elastic response spectrum, considering deterministic and probabilistic earthquake scenarios. A discussion addresses the basis of the seismic damage states probabilities and the calculated damage index. An important research effort has been focused on the buildings modeling. All the architectural elements and their mechanical properties have been studied and evaluated accurately. It has been evidenced that a detailed and complete knowledge of all the structural elements existing in this type of buildings influence directly their behavior and hence the calculations and the results. The analysis of the isolated buildings and of the aggregate building has been performed for both mentioned seismic scenarios. Finally, a complete discussion of the results is included.
Abstract
The main objective of this work is to assess the vulnerability and seismic risk of typical existing modernist unreinforced masonry (URM) modernist buildings and aggregates [...]
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Probabilistic estimation of annual lost economic production due to premature deaths because of earthquakes
M. Salgado-Galvez, G. Bernal, A. Barbat, M. Carreño, O. Cardona

Human and Ecological Risk Assessment , (2016). 22(2), 543-557, DOI: 10.1080/10807039.2015.1095072

Abstract
A methodology to estimate, in a probabilistic way, the annual cost to society of premature deaths because of earthquakes is proposed in this article. The methodology makes use of results obtained by means of prospective and probabilistic seismic risk assessments where expected deaths caused by the collapse of buildings are obtained. Those results, combined with demographic and macroeconomic indicators such as the age distribution, life expectancy at birth, and per capita gross domestic product, are used to estimate the cost to society in terms of lost productivity due to premature mortality because of earthquakes. The proposed methodology does not attempt to estimate nor assign a cost to human lives at any stage, but the one associated to lost productivity at the societal level. One of the descriptors of the methodology is part of the components of the disability adjusted life year, a widely used metric in the public health field that estimates the burden of diseases based mostly on historical data. As an example, the methodology is applied to Medellín, the second largest city of Colombia, finding that the cost of lost productivity due to premature mortality because of earthquakes has a similar order of magnitude to the direct physical losses in the public and private building stock calculated in a previous probabilistic seismic risk assessment.
Abstract
A methodology to estimate, in a probabilistic way, the annual cost to society of premature deaths because of earthquakes is proposed in this article. The methodology makes [...]
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Holistic Urban Seismic Risk Evaluation of Megacities: Application and Robustness
M. Carreño, O. Cardona, M. Marulanda, A. Barbat

Geotechnical, Geological, and Earthquake Engineering (2009). 7, 167-183, DOI 10.1007/978-1-4020-8609-0_10

Abstract
The holistic evaluation of disaster risk is achieved affecting the physical risk with an impact factor, obtained from contextual conditions, such as the socioeconomic fragility and the lack of resilience, that aggravate the initial physical loss scenario. Available data about these conditions at urban level are necessary to apply the method. Abrief explanation of the model is made in this work to illustrate the benefits of this approach that contributes to the effectiveness of disaster risk management, inviting to the action and identifying the hard and soft weaknesses of urban centres.
Abstract
The holistic evaluation of disaster risk is achieved affecting the physical risk with an impact factor, obtained from contextual conditions, such as the socioeconomic fragility [...]
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A laminated structural finite element for the behavior of large non-linear reinforced concrete structures
C. Escudero, S. Oller, X. Martinez, A. Barbat

Finite Elements in Analysis and Design (2016). 119, 78–94

Abstract
In order to correctly predict the kinematics of complex structures, analysis using three-dimensional finite elements (3DFEs) seems to be the best alternative. However, simulation of large multi-layered structures with many plies can be una ordable with 3DFEs because of the excessive computational cost, especially for non-linear materials. In addition, the discretization of very thin layers can lead to highly distorted FEs carrying numerical issues, therefore, reduced models arise as an a ordable solution. This paper describes a new finite element formulation to perform numerical simulations of laminated reinforced concrete structures. The intention of this work is that the proposed scheme can be applied in the analysis of real-life structures where a high amount of computational resources are needed to fulfill the meshing requirements, hence the resulting formulation has to be a compromise between simplicity and efficiency. So that, the condensation of a dimension (thickness), mandatory to model three-dimensional structures with twodimensional finite elements (2DFEs), leads to refer all layers contained within such FEs to a plane, which is typically named middle plane or geometrical plane, since its sole function is to serve as a geometrical reference. This work is based on the assumption that the geometrical plane has to be distinguished from a mechanical plane, which is where the resultant sti ness of all layers is contained. It is also assumed in this work that the mechanical plane changes its position due to non-linear response of the component materials.
Abstract
In order to correctly predict the kinematics of complex structures, analysis using three-dimensional finite elements (3DFEs) seems to be the best alternative. However, simulation [...]
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Energy damage index based on capacity and response spectra
S. , L. Pujades, A. Barbat, Y. Vargas, D. Hidalgo-Leiva

Engineering Structures (2017). 152, 424–436

Abstract
To assess the expected seismic damage of a structure, non-linear dynamic analysis and the damage index of Park-Ang have been often used. Depending on the size of the structure and on the duration of the record, the computational effort in dynamic analyses is usually high. In this research a new damage index is proposed based on nonlinear static analysis. The damage index is a linear combination of two energy functions: 1) the strain energy associated to the stiffness variation and the ductility of the structure and 2) the energy dissipated associated to hysteretic cycles. These two energy functions are obtained from the capacity curve of the structure and from the energy balance with the spectral acceleration. To show the ability of the index to represent damage, low-rise steel buildings subjected to seismic actions expected in Mexico City are studied. The results obtained with the new method show a good agreement with those calculated by means of dynamic analyses using the Park-Ang damage index. In average, the Park-Ang damage index is well fitted by the combination of 62% of the strain energy and 38% of the energy dissipated by hysteresis. Moreover, this new damage index allows linking damage to certain characteristics of the seismic actions as, for instance, intensity and duration of the applied seismic action. Therefore, the new approach results in a practice and powerful tool for estimating the seismic damage in buildings, especially when considering probabilistic approaches, where massive computations are needed.
Abstract
To assess the expected seismic damage of a structure, non-linear dynamic analysis and the damage index of Park-Ang have been often used. Depending on the size of the structure [...]
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Two-scale approach for the nonlinear dynamic analysis of RC structures with local non-prismatic parts
P. Mata, A. Barbat, S. Oller

Engineering Structures (2008). 30, 3667–3680

Abstract
There is general agreement in the fact that fully three-dimensional (3D) numerical techniques provide the most precise tools for simulating the behavior of RC buildings even when their computational costs for real structures became them unpractical. Moreover, one-dimensional formulations (1D) are rather limited for predicting the mechanical behavior of framed structures which present local weakness that can determine their global responses, such as it is the case of poor detailed joints of RC buildings in seismic zones or precast concrete structures. An alternative approach, combining both simplicity and computational efficiency, is given by coupling reduced models for prismatic elements with full 3D models for the zones corresponding to connecting joints. In this work, a two-scale approach is developed for obtaining the nonlinear dynamic response of RC buildings with local non-prismatic parts. At global scale level all the elements are rods; however, if local parts with complex geometry appear, the corresponding elements are analyzed considering fully 3D models which constitute the local scale level. The dimensional-coupling between scales is performed imposing the kinematics hypothesis of the beam model on surface-interfaces of the 3D model. An iterative Newton-Raphson scheme which considers the interaction between scales is developed to obtain the response at global level. The tangential stiffness of the local models are obtained numerically. Computationally, the problem is managed by means of a master-slave approach, where the global scale problem acts as the master and the local models are the slaves; iterative communication between scales considers internal forces and moments as well as tangential tensors. The process stops when global convergence is achieved. From the computational point of view, the developed method is implemented in a parallelized scheme, where the master and slave problems are solved independently by different programs thus minimizing the intervention on existing codes specific for beams and solids. Finally, numerical examples are included.
Abstract
There is general agreement in the fact that fully three-dimensional (3D) numerical techniques provide the most precise tools for simulating the behavior of RC buildings even [...]
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A compression–tension concrete damage model, applied to a wind turbine reinforced concrete tower
J. Paredes, A. Barbat, S. Oller

Engineering Structures (2011). 33, 3559–3569

Abstract
Structures subjected to cyclic loads show alternative tension–compression stress states; in such a case, even if certain damage (fracture) is reached during the tension cycle, the computational model of the structure should maintain its capacity to withstand subsequent compression based only on the contact effect in the damaged area (opening, closing and reopening of cracks). In order to control this behavior, a phenomenological constitutive model able to consider the contact as a structural limitation is required. From the constitutive point of view, geomaterials have different damage thresholds for tension and compression and, from the structural point of view, it must be ensured that the material damaged in tension still resist compression. In this case, it is accepted that cracks behave as a contact surface at the structural level. To meet the above mentioned phenomenology, a modification of the damage model differentiated in tension and compression proposed by Faria et al. [Faria R, Oliver J, Cervera M. A strainbased plastic viscous-damage model for massive concrete structures. Int J Solids Struct 1998; 35:1533–58] is performed in this paper, considering independent strength thresholds in each of these processes, controlled with two independent discontinuity threshold functions. Also, in this work an elasto-plastic constitutive model is used to represent the behaviour of the steel bars.
Abstract
Structures subjected to cyclic loads show alternative tension–compression stress states; in such a case, even if certain damage (fracture) is reached during the [...]
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Equivalent linearization of the Bouc–Wen hysteretic model
J. Hurtado, A. Barbat

Engineering Structures (2000). 22, 1121–1132

Abstract
The smooth endochronic hysteretic Bouc–Wen model is studied from the point of view of random vibration. The sources of the errors of the method of equivalent linearization applied to this model using the hypothesis of joint Gaussian behaviour are examined. The method of linearization for softening hysteretic models proposed by the authors, which is based on a combination of Dirac and Gauss densities, is developed and applied to the Bouc–Wen model under a variety of conditions. It is shown that the method gives excellent estimations of the response statistics without increasing the computational effort required by the conventional technique.
Abstract
The smooth endochronic hysteretic Bouc–Wen model is studied from the point of view of random vibration. The sources of the errors of the method of equivalent linearization [...]
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Seismic damage evaluation of reinforced concrete buildings with slit walls
S. Baetu, A. Barbat, I. Ciongradi, G. Baetu

ENGINEERING COMPUTATIONS (2015). 32(6), 1661-1690

Abstract
The purpose of this paper is to investigate a reinforced concrete multi-storey building with dissipative structural walls. These walls can improve the behaviour of a tall multi-storey building. The damage of a building with dissipative walls is compared with that of a building with solid walls. The comparative nonlinear dynamic analysis is performed by means of the SAP2000 software, using a layer model. In order to increase the seismic performance of a building with structural walls is to create slit zones with short connections into the walls. The short connections are introduced as a link element with multi-linear pivot hysteretic plasticity behaviour. The hysteretic rules and parameters of these short connections were proposed by the authors and used in this study. Using the proposed computational model for the slit wall, a seismic analysis of a multi-storey building with slit walls was done. From the results obtained, the advantages of the proposed model are observed. Unlike other studies on slit walls with short connections, which are focused mostly on the nonlinear dynamic behaviour of the short connections, in this paper the authors take into consideration the whole structural system, wall, connections and frames.
Abstract
The purpose of this paper is to investigate a reinforced concrete multi-storey building with dissipative structural walls. These walls can improve the behaviour of a tall [...]
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Seismic damage evaluation of reinforced concrete slit walls
S. Baetu, A. Barbat, I. Ciongradi

ENGINEERING COMPUTATIONS (2015). 32(2), 424-451

Abstract
The purpose of this paper is to investigate a dissipative reinforced concrete structural wall that can improve the behavior of a tall multi-storey building, evaluating the damage it undergoes in comparison with that of a solid wall. The comparative nonlinear dynamic analysis between a dissipative and a solid wall is performed by means of SAP2000 software and using a layered model. The solution to increase the seismic performance of a reinforced concrete structural wall is to create a slit zone with short connections. These are introduced as a link element with multi-linear pivot hysteretic plasticity behavior. The behavior of these short connections is modeled using the finite element software ANSYS 12. The authors propose to evaluate the damage of reinforced concrete slit walls with short connections using seismic analysis. Using the proposed computational model, a seismic analysis of the dissipative wall belonging to a multi-storey building was performed. From the results obtained, the advantages of the proposed model are observed. The proposed computational model consumes low processing resources and reduces the processing time for a dynamic pushover analysis. Unlike other studies on slit walls with short connections, which are focussed mostly on the nonlinear dynamic behavior of the short connections, in this paper the authors take into consideration the whole structural system, wall and connections.
Abstract
The purpose of this paper is to investigate a dissipative reinforced concrete structural wall that can improve the behavior of a tall multi-storey building, evaluating the [...]
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Active control of building structures under measured seismic loads
J. Rodellar, A. Barbat

ENGINEERING COMPUTATIONS (1985). 2, 128-134

Abstract
The concept of active control has been introduced in recent years in order to reduce the seismic response of structures. A predictive control methodology is used to formulate a discrete-time structural control algorithm. This algorithm computes the control forces by using not only the information provided by the structural response but also that given by the measurement of the seismic ground acceleration. Results for checking the effectiveness of the control algorithm in reducing the structural response are presented.
Abstract
The concept of active control has been introduced in recent years in order to reduce the seismic response of structures. A predictive control methodology is used to formulate [...]
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Plastic-damage analysis of reinforced concrete frames
J. Faleiro, S. Oller, A. Barbat

ENGINEERING COMPUTATIONS (2010). 27(1), 57-83

Abstract
The purpose of this paper is to develop an improved analytical model for predicting the damage response of multi-storey reinforced concrete frames modelled as an elastic beam-column with two inelastic hinges at its ends. The damage is evaluated in the hinges, using the concentrated damage concepts and a new member damage evaluation method for frame members, which leads to a meaningful global damage index of the structure. A numerical procedure for predicting the damage indices of the structures using matrix structural analysis, plastic theory and continuum damage model is also developed. The method is adequate for the prediction of the failure mechanisms. Using the proposed framework, various numerical examples are included. Based on the obtained results, advantages and limitation of the proposed model are observed. The proposed numerical model is useful to solve multi-storey reinforced concrete frames using a procedure that combines structural finite elements (beams) with moment-curvature constitutive models derived from classic stress-strain ones. It is an inexpensive and reliable procedure to model the frame structures.
Abstract
The purpose of this paper is to develop an improved analytical model for predicting the damage response of multi-storey reinforced concrete frames modelled as an elastic beam-column [...]
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FLEXIBILITY-BASED LINEAR DYNAMIC ANALYSIS OF COMPLEX STRUCTURES WITH CURVED-3D MEMBERS
C. Molins, P. Roca, A. Barbat

Earthquake Engineering and Structural Dynamics (1998). 27, 731-747

Abstract
A fexibility-based formulation of a new mass matrix for the dynamic analysis of spatial frames consisting of curved elements with variable cross-sections is presented. The main characteristic of such formulations is the exact equilibrium of forces at any interior point, with no additional hypotheses about the distribution of displacements, strains or stresses. Accordingly, the derived element mass matrix takes into account the exact sti ness and mass distribution throughout each element. In validation tests, results obtained with this method are compared with those obtained by other numerical or analytical formulations, showing the accuracy of the proposed method. The comparison of experimental results for a multispan arch bridge subjected to a dynamic load with those achieved by means of the proposed method are nally included to illustrate its eciency in the treatment of complex structures.
Abstract
A fexibility-based formulation of a new mass matrix for the dynamic analysis of spatial frames consisting of curved elements with variable cross-sections is presented. The [...]
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A method to estimate intensity occurrence probabilities in low seismic activity regions
J. Egozcue, A. Barbat, J. Canas, J. Miquel

Earthquake Engineering and Structural Dynamics (1991). 20, 43-60

Abstract
The estimation of site intensity occurrence probabilities in low seismic activity regions has been studied from different points of view. However, no method has been definitively established because several problems arise when macroseismic historical data are incomplete and the active zones are not well determined. The purpose of this paper is to present a method that estimates site occurrence probabilities and, at the same time, measures the uncertainties inherent in these probabilities in low activity regions. The region to be studied is divided into very broad seismic zones. An exponential intensity probability law is adjusted for each zone and the degree of uncertainty in the assumed incompleteness of the catalogue is evaluated for each intensity. These probabilities are used to establish what may be termed 'prior site occurrence models'. A Bayesian method is used to improve 'prior models' and to obtain the 'posterior site occurrence models'. Epicentre locations are used to recover spatial information lost in the prior broad zoning. This Bayesian correction permits the use of specific attenuation for different events and may take into account, by means of conservative criteria, epicentre location errors. Following Bayesian methods, probabilities are assumed to be random variables and their distribution may be used to estímate the degree of uncertainty arising from (a) the statistical variance of estimators, (b) catalogue incompleteness and (e) mismatch of data to prior assumptions such as Poisson distribution for events and exponential distribution for intensíties. The results are maps of probability and uncertainty for each intensity. These maps exhibit better spatial definition than those obtained by means of simple, broad zones. Sorne results for Catalonia (NE of Spain) are shown.
Abstract
The estimation of site intensity occurrence probabilities in low seismic activity regions has been studied from different points of view. However, no method has been definitively [...]
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Prioritizing interventions to reduce seismic vulnerability in school facilities in Colombia
M. Mora, J. Valcárcel, O. Cardona, A. Barbat, L. Pujades, G. Bernal

Earthquake Spectra (2015). 31(4), 2535-2552, DOI: 10.1193/040412 EQS151T

Abstract
Colombian seismic code NSR-98 establishes the requirement for the seismic vulnerability analysis and, if necessary, the strengthening of public facilities (schools). Due to the investments required by risk reduction programs, it is necessary to establish criteria for assigning priorities for the interventions. This article proposes a methodology for obtaining a Benefit-Cost Ratio (BCR) at the subnational level, by assessing the expected annual average loss of the built area of public schools and the retrofitting cost. The BCR is estimated as the difference between the estimates of the net present value for status quo and retrofitted states, these two divided by the retrofitting costs. According to the BCR, 47.3% of the total school built area of Colombia should be retrofitted where the retrofitting costs correspond to 25% of the total investment. Proposed BCR is useful for prioritizing regions in function of the feasibility of reducing the seismic vulnerability of the schools.
Abstract
Colombian seismic code NSR-98 establishes the requirement for the seismic vulnerability analysis and, if necessary, the strengthening of public facilities (schools). Due to [...]
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Damage scenarios simulation for seismic risk assessment in urban zones
A. Barbat, F. Moya, J. Canas

Earthquake Spectra (1996). 12(3), 371-394

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
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 [...]
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Revealing the socioeconomic impact of small disasters in Colombia using the DesInventar database
M. Marulanda, O. Cardona, A. Barbat

Disasters (2010). 34(2), 552 − 570

Abstract
Small disasters are usually the product of climate variability and climate change. Analysis of them illustrates that they increase difficulties for local development—frequently affecting the livelihoods of poor people and perpetuating their level of poverty and human insecurity—and entail challenges for a country’s development. In contrast to extreme events, small disasters are often invisible at the national level and their effects are not considered as relevant from a macroeconomic standpoint. Nevertheless, their accumulated impact causes economic, environmental and social problems. This paper presents the results of an evaluation of the DesInventar database, developed in 1994 by the Network for Social Studies in Disaster Prevention in Latin America. In addition, it proposes a new version of the Local Disaster Index developed in 2005 within the framework of the Disaster Risk and Management Indicators Program for the Americas, with the support of the Inter-American Development Bank.
Abstract
Small disasters are usually the product of climate variability and climate change. Analysis of them illustrates that they increase difficulties for local development—frequently [...]
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Disaster risk from a macroeconomic perspective: a metric for fiscal vulnerability evaluation
O. Cardona, M. Ordaz, M. Marulanda, M. Carreño, A. Barbat

Disasters (2010). 34(4), 1064 − 1083

Abstract
The Disaster Deficit Index (DDI) measures macroeconomic and financial risk in a country according to possible catastrophic scenario events. Extreme disasters can generate financial deficit due to sudden and elevated need of resources to restore affected inventories. The DDI captures the relationship between the economic loss that a country could experience when a catastrophic event occurs and the availability of funds to address the situation. The proposed model utilises the procedures of the insurance industry in establishing probable losses, based on critical impacts during a given period of exposure; for economic resilience, the model allows one to calculate the country’s financial ability to cope with a critical impact. There are limitations and costs associated with access to resources that one must consider as feasible values according to the country’s macroeconomic and financial conditions. This paper presents the DDI model and the results of its application to 19 countries of the Americas and aims to guide governmental decision-making in disaster risk reduction.
Abstract
The Disaster Deficit Index (DDI) measures macroeconomic and financial risk in a country according to possible catastrophic scenario events. Extreme disasters can generate [...]
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A numerical procedure simulating RC structures reinforced with FRP using the serial/parallel mixing theory
X. Martinez, S. Oller, F. Rastellini, A. Barbat

Computers and Structures (2008). 86, 1604–1618

Abstract
The use of fiber reinforced polymers (FRP) to reinforce and retrofit reinforced concrete (RC) structures has become one of the main applications of composites in civil engineering. This paper describes a procedure, based on a finite element formulation, that can be used to perform numerical simulations of RC structures reinforced with FRP. Composites are treated using the serial/parallel mixing theory, which deduces the composite behavior from the constitutive equations of its components. A new construction-stages algorithm is developed for simulating retrofitted structures. The performance of the proposed formulation is proved comparing numerical and experimental results. Finally, the developed code is used to obtain the optimum FRP reinforcement configuration for a RC frame structure.
Abstract
The use of fiber reinforced polymers (FRP) to reinforce and retrofit reinforced concrete (RC) structures has become one of the main applications of composites in civil engineering. [...]
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Plastic–damage seismic model for reinforced concrete frames
J. Faleiro, S. Oller, A. Barbat

Computers and Structures (2008). 86, 581–597

Abstract
A plastic–damage model for reinforced concrete frames is developed in this article, based on the classical plastic model and the continuum damage model. The plastic–damage constitutive law is implemented into a beam model for framed structures, in which these are described by elastic beams and columns with two inelastic hinges at their ends. A numerical procedure for predicting the member and global damage in framed structures using the matrix analysis is developed. Additionally, the article introduces a damage index useful in evaluating the state of structural members and a meaningful global damage index for whole structure. The plastic–damage model, together with the member and global damage indices, are adequate for the computation of the limit load of reinforced concrete frames subjected to seismic actions. Examples of applications of the methodology to the non-linear analysis of reinforced concrete framed structures are finally given.
Abstract
A plastic–damage model for reinforced concrete frames is developed in this article, based on the classical plastic model and the continuum damage model. The plastic–damage [...]
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EFFECTIVENESS OF BLOCK ITERATIVE SCHEMES IN COMPUTING THE SEISMIC RESPONSE OF BUILDINGS WITH NONLINEAR BASE ISOLATION
A. Barbat, N. Molinares, R. Codina

Computers and Structures (1996). 58(1), 133-141

Abstract
The conventional form of solving the equations of motion governing the seismic response of building structures with nonlinear base isolation consists of using monolithic step by step integrationmethods. As an alternative, the application of a block iterative scheme is examined in this paper. After describing the particularities of the equations of motion of the structure with base isolation, different block iterative schemes are described. Their effectiveness is discussed and compared with that of monolithic step by step integration methods. Adequate examples are used with the aim of performing numerical comparisons.
Abstract
The conventional form of solving the equations of motion governing the seismic response of building structures with nonlinear base isolation consists of using monolithic step [...]
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Parameter identification of large-scale magnetorheological dampers in a benchmark building
A. Bahar, F. Pozo, L. Acho, J. Rodellar, A. Barbat

Computers and Structures (2010). 88, 198–206

Abstract
Magnetorheological (MR) dampers are devices that can be used for vibration reduction in structures. However, to use these devices in an effective way, a precise modeling is required. In this sense, in this paper we consider a modified parameter identification method of large-scale magnetorheological dampers which are represented using the normalized Bouc–Wen model. The main benefit of the proposed identification algorithm is the accuracy of the parameter estimation. The validation of the parameter identification method has been carried out using a black box model of an MR damper in a smart base-isolated benchmark building. Magnetorheological dampers are used in this numerical platform both as isolation bearings as well as semi-active control devices.
Abstract
Magnetorheological (MR) dampers are devices that can be used for vibration reduction in structures. However, to use these devices in an effective way, a precise modeling is [...]
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Hierarchical semi-active control of base-isolated structures using a new inverse model of magnetorheological dampers
A. Bahar, F. Pozo, L. Acho, J. Rodellar, A. Barbat

Computers and Structures (2010). 88, 483–496

Abstract
Magnetorheological (MR) dampers have received special attention as semi-active devices for mitigation of structural vibrations. Because of the inherent nonlinearity of these devices, it is difficult to obtain a reasonable mathematical inverse model. This paper is concerned with two related concepts. On one hand, it presents a new inverse model of MR dampers based on the normalized Bouc–Wen model. On the other hand, it considers a hybrid seismic control system for building structures, which combines a class of passive nonlinear base isolator with a semi-active control system. In this application, the MR damper is used as a semi-active device in which the voltage is updated by a feedback control loop. The management of MR dampers is performed in a hierarchical way according to the desired control force, the actual force of the dampers and its capacity to react. The control is applied to a numerical three-dimensional benchmark problem which is used by the structural control community as a state-of-the-art model for numerical experiments of seismic control attenuation. The performance indices show that the proposed semi-active controller behaves satisfactorily.
Abstract
Magnetorheological (MR) dampers have received special attention as semi-active devices for mitigation of structural vibrations. Because of the inherent nonlinearity of these [...]
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A finite element methodology for local/global damage evaluation in civil engineering structures
A. Hanganu, E. Oñate, A. Barbat

Computers and Structures (2002). 80, 1667–1687

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 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 [...]
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Performance of Buildings under Earthquakes in Barcelona, Spain
A. Barbat, L. Pujades, N. Lantada

Computer-Aided Civil and Infrastructure Engineering (2006). 21, 573–593

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
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 [...]
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Static analysis of beam structures under nonlinear geometric and constitutive behavior
P. Mata, S. Oller, A. Barbat

Computer Methods in Applied Mechanics and Enginering (2007). 196, 4458–4478

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
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 [...]
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Dynamic analysis of beam structures considering geometric and constitutive nonlinearity
P. Mata, S. Oller, A. Barbat

Computer Methods in Applied Mechanics and Enginering (2008). 197, 857–878

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
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 [...]
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Moment–curvature damage model for bridges subjected to seismic loads
S. Oller, A. Barbat

Computer Methods in Applied Mechanics and Enginering (2006). 195, 4490–4511

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 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 [...]
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Capacity, fragility and damage in reinforced concrete buildings: a probabilistic approach
Y. Vargas, L. Pujades, A. Barbat, J. Hurtado

Bulletin of Earthquake Engineering (2013). 11(6), 2007-2032

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 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 [...]
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Capacity, damage and fragility models for steel buildings: a probabilistic approach
S. Díaz, L. Pujades, A. Barbat, D. Hidalgo-Leiva, Y. Vargas-Alzate

Bulletin of Earthquake Engineering (2018). 16, 1209–1243, https://doi.org/10.1007/s10518-017-0237-0

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
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 [...]
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Seismic hazard and risk scenarios for Barcelona, Spain, using the Risk-UE vulnerability index method
N. Lantada, J. Irizarry, A. Barbat, X. Goula, A. Roca, T. Susagna, L. Pujades

Bulletin of Earthquake Engineering (2010). 8, 201–229, DOI 10.1007/s10518-009-9148-z

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
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 [...]
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Parametric model for capacity curves
L. PUJADES, Y. Vargas-Alzate, A. Barbat, J. González-Drigo

Bulletin of Earthquake Engineering (2012). 10(1), 331-349

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
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 [...]
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Seismic performance of a block of buildings representative of the typical construction in the Eixample district in Barcelona (Spain)
L. Pujades, A. Barbat, R. González-Drigo, J. Avila-Haro, S. Lagomarsino

Bulletin of Earthquake Engineering (2012). 10(1), 331-349

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.
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 [...]
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Non-linear static procedures applied to high-rise residential URM buildings
R. González-Drigo, J. Avila-Haro, L. Pujades, A. Barbat

Bulletin of Earthquake Engineering (2016). DOI 10.1007/s10518-016-9951-2

Abstract
In this work, the vulnerability of an unreinforced masonry building, evaluated on the one hand by using the incremental dynamic analysis, and on the other hand by using nine representative non-linear static incremental procedures, is compared. For comparison reasons among the different non-linear static procedures, the obtained incremental dynamic analyses results are used as reference values. The aim of this analysis is to evaluate the applicability and reliability of the diverse non-linear static procedures for unreinforced masonry buildings, and to propose modifications oriented to improve their use in this typology of structures. For this purpose, a fully representative unreinforced masonry building of the dominating building type in the Eixample district of Barcelona, is analyzed. Furthermore, the conditional spectrum approach procedure has been applied with the aim to conveniently define the seismic demand. Regarding the definition of the fragility curves, two different methodologies were used for each non-linear static procedure and incremental dynamic analyzes. Subsequently, the corresponding damage indices as well as the damage curves were calculated and compared for the different considered peak ground acceleration values. The results of this comparison seem to confirm that the damage curves obtained by performing the NSP and by applying the Risk-UE methodology overestimate the damage corresponding to low values of the PGA and underestimate the damage for higher values of the PGA.
Abstract
In this work, the vulnerability of an unreinforced masonry building, evaluated on the one hand by using the incremental dynamic analysis, and on the other hand by using nine [...]
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Ground-Shaking Scenarios and Urban Risk Evaluation of Barcelona using the Risk-UE Capacity Spectrum Based Method
J. Irizarry, L. Lantada, L. Pujades, A. Barbat, X. Goula, T. Susagna, A. Roca

Bulletin of Earthquake Engineering (2011). 9, 441–466, DOI 10.1007/s10518-010-9222-6

Abstract
The Capacity Spectrum Based Method (CSBM) developed in the framework of the European project Risk-UE has been applied to evaluate the seismic risk for the city of Barcelona, Spain. Accordingly, four damage states are defined for the buildings, the action is expressed in terms of spectral values and the seismic quality of the buildings, that is, their vulnerability, is evaluated by means of capacity spectra. The probabilities of the damage states are obtained considering a lognormal probability distribution. The most relevant seismic risk evaluation results obtained for Barcelona, Spain, are given in the article as scenarios of expected losses.
Abstract
The Capacity Spectrum Based Method (CSBM) developed in the framework of the European project Risk-UE has been applied to evaluate the seismic risk for the city of Barcelona, [...]
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SEISMIC SAFETY OF LOW DUCTILITY STRUCTURES USED IN SPAIN
J. Vielma, A. Barbat, S. Oller

Bulletin of Earthquake Engineering (2010). 8, 135–155, DOI 10.1007/s10518-009-9127-4

Abstract
The most important aspects of the design, seismic damage evaluation and safety assessment of structures with low ductility like waffle slabs buildings or flat beams framed buildings are examined in this work. These reinforced concrete structural typologies are the most used in Spain for new buildings but many seismic codes do not recommend them in seismic areas. Their expected seismic performance and safety are evaluated herein by means of incremental non linear structural analysis (pushover analysis) and incremental dynamic analysis which provides capacity curves allowing evaluating their seismic behaviour. The seismic hazard is described by means of the reduced 5% damped elastic response spectrum of the Spanish seismic design code. The most important results of the study are the fragility curves calculated for the mentioned building types, which allow obtaining the probability of different damage states of the structures as well as damage probability matrices. The results, which show high vulnerability of the studied low ductility building classes, are compared with those corresponding to ductile framed structures.
Abstract
The most important aspects of the design, seismic damage evaluation and safety assessment of structures with low ductility like waffle slabs buildings or flat beams framed [...]
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APPLICATION OF QUALITATIVE REASONING IN ENGINEERING
L. Bozzo, A. Barbat, L. Torres

Applied Artificial Intelligence (1998). 12, 29-48

Abstract
Qualitative reasoning is an alternative problem-solving technique useful for the conceptual design of structures. Qualitative reasoning represents the relationships between parameters in a model, and a search computation assigns values represented by intervals and relevant points in the behavior. The traditional difference between analysis and design or input and output parameters in a procedural computation is not existent in qualitative reasoning, since all the parameters in a model are equally represented. Qualitative reasoning derives values for parameters even with incomplete and imprecise knowledge about the model. This work presents a qualitative structural analysis framework, suitable for the evaluation of conceptual designs as well as for tutoring systems. The framework has been implemented in a computer program called Agrippa using the computer language Prolog. Based on a representation of fundamental principles of equilibrium, compatibility, and force-deformation and an incomplete knowledge of geometry and topology, Agrippa derives the signs and relative magnitude of forces and displacements for three-dimensional models of structures.
Abstract
Qualitative reasoning is an alternative problem-solving technique useful for the conceptual design of structures. Qualitative reasoning represents the relationships between [...]
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Adaptive Control of Uncertain Coupled Mechanical Systems with Application to Base-Isolated Structures
J. Rodellar, E. Ryan, A. Barbat

APPLIED MATHEMATICS AND COMPUTATION (1995). 70, 299-314

Abstract
A problem of feedback stabilization is addressed for a class of uncertain nonlinear mechanical systems with n degrees of freedom and nc < n control inputs. Each system of the class has the structure of two coupled subsystems with nc and nr degrees of freedom, respectively, a prototype being an uncertain base isolated building structure with n degrees of freedom actively controlled via actuators applying forces to specific degrees of freedom of the base movement, nc < n in number. A nonlinear adaptive feedback strategy is described, which, under appropriate assumptions on the system uncertainties, guarantees a form of practical stability of the zero state. Numerical simulations are also presented to illustrate the application of the control strategy to a base isolated building.
Abstract
A problem of feedback stabilization is addressed for a class of uncertain nonlinear mechanical systems with n degrees of freedom and nc < n control inputs. Each system [...]
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Constitutive and Geometric Nonlinear Models for the Seismic Analysis of RC Structures with Energy Dissipators
P. Mata, A. Barbat, S. Oller, R. Boroschek

Archives of Computational Methods in Engineering (2008). 15, 489–539, DOI 10.1007/s11831-008-9024-z

Abstract
Nowadays, the use of energy dissipating devices to improve the seismic response of RC structures constitutes a mature branch of the innovative procedures in earthquake engineering. However, even though the benefits derived from this technique are well known and widely accepted, the numerical methods for the simulation of the nonlinear seismic response of RC structures with passive control devices is a field in which new developments are continuously preformed both in computational mechanics and earthquake engineering. In this work, a state of the art of the advanced models for the numerical simulation of the nonlinear dynamic response of RC structures with passive energy dissipating devices subjected to seismic loading is made. The most commonly used passive energy dissipating devices are described, together with their dissipative mechanisms as well as with the numerical procedures used in modeling RC structures provided with such devices. The most important approaches for the formulation of beam models for RC structures are reviewed, with emphasis on the theory and numerics of formulations that consider both geometric and constitutive sources on nonlinearity. In the same manner, a more complete treatment is given to the constitutive nonlinearity in the context of fiber-like approaches including the corresponding cross sectional analysis. Special attention is paid to the use of damage indices able of estimating the remaining load carrying capacity of structures after a seismic action. Finally, nonlinear constitutive and geometric formulations for RC beam elements are examined, together with energy dissipating devices formulated as simpler beams with adequate constitutive laws. Numerical examples allow to illustrate the capacities of the presented formulations.
Abstract
Nowadays, the use of energy dissipating devices to improve the seismic response of RC structures constitutes a mature branch of the innovative procedures in earthquake engineering. [...]
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Seismic Analysis of Base Isolated Buildings
A. Barbat, L. Bozzo

Archives of Computational Methods in Engineering (1997). 4(2) , 153-192

Abstract
This paper presents a survey of the numerical simulation of base isolation systems for the vibration control of buildings and their equipment, primarilly against earthquakes. Base isolation has received much attention in the recent twenty years and many buildings have been protected using this technology. The article focusses mainly on the different numerical methods used in the analysis of base isolated buildings. The conventional form of solving the equations of motion governing the seismic response of building structures with nonlinear base isolation consists of using monolithic step by step integration methods. As an effcient alternative, static condensation and block iterative schemes can be applied. The particularities of the equations of motion of buildings equiped with various base isolation systems are described. The linear theory of base isolated buildings is then presented. After this, numerical solution techniques for the analysis of the seismic response of buildings with isolation systems are developed in detail in the paper. Finally, numerical results for elastic and inelastic structures are described. A complete set of references coverning a wide range of studies is included.
Abstract
This paper presents a survey of the numerical simulation of base isolation systems for the vibration control of buildings and their equipment, primarilly against earthquakes. [...]
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Monte Carlo Techniques in Computational Stochastic Mechanics
A. Barbat, J. Hurtado

Archives of Computational Methods in Engineering (1998). 5(1) 3-30

Abstract
A state of the art on simulation methods in stochastic structural analysis is presented. The purpose of the paper is to review some of the di erent methods available for analysing the effects of randomness of models and data in structural analysis. While most of these techniques can be grouped under the general name of Monte Carlo methods, the several published algorithms are more suitable to some objectives of analysis than to others in each case. These objectives have been classiffed into the following cathegories: (1), The Statistical Description of the structural scattering, a primary analysis in which the uncertain parameters are treated as random variables; (2) The consideration of the spatial variability of the random parameters, that must then be modelled as Random Fields (Stochastic Finite Elements); (3) The advanced Monte Carlo methods for calculating the usually very low failure probabilities (Reliability Analysis) and, (4), a deterministic technique that depart from the random nature of the above methods, but which can be linked with them in some cases, known as the Response Surface Method. All of these techniques are critically examined and discussed. The concluding remarks point out some research needs in the field from the authors' point of view.
Abstract
A state of the art on simulation methods in stochastic structural analysis is presented. The purpose of the paper is to review some of the di erent methods available for [...]
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Análisis dinámico probabilista de edificios de acero sometidos a sismos de larga duración
S. Díaz, . L.G.Pujades, A. Barbat, D. Hidalgo, Y. Vargas

Rev. int. métodos numér. cálc. diseño ing. (2018). Vol. 34, (1), 6

Abstract
The probabilistic analysis of the seismic performance of a structure requires quantifying the uncertainties of the involved variables and parameters, including the seismic action and mechanical properties of its elements. In this article, the seismic performance of high-rise, mid-rise and low-rise of steel buildings, subjected to long duration seismic actions like those of Mexico City, is analyzed. The analysis is conducted by using a probabilistic approach. The seismic actions are selected to be compatible with the design spectra of the Mexican seismic code for soft soils and long duration earthquakes, characteristic for this region. The dynamic analyses are performed by using Monte Carlo simulations. The strength and ductility of the beams and columns are considered random variables; the seismic actions are also modelled in a probabilistic way. The damage index of Park and Ang is used. The results show that the uncertainties expected in the response are significant, being the randomness of the seismic action the main cause. From the comparison between the mean values of the probabilistic approach and those corresponding to the deterministic case, a good consistency of the result obtained for low-rise and mid-rise buildings is observed. Nevertheless, the consistency is lower in the case of high-rise buildings. The analyzed low-rise and mid-rise buildings show a good seismic performance to seismic actions, but the high-rise buildings show slight or moderate damage. It is concluded that the probabilistic approach provides a more complete information on the structural response.
Abstract
The probabilistic analysis of the seismic performance of a structure requires quantifying the uncertainties of the involved variables and parameters, including the seismic [...]
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Evaluación probabilista del riesgo sísmico de estructuras con base en la degradación de rigidez
A. Barbat, Y. Vargas, L. Pujades, J. Hurtado

Rev. int. métodos numér. cálc. diseño ing. (2016). Vol. 32, (1)

Abstract
The incremental dynamic analysis is a powerful tool for evaluating the seismic vulnerability and risk of buildings. It allows calculating the global damage of structures for different peak ground accelerations, PGA, and representing this result by means of damage curves. Such curves are currently used to obtain seismic risk scenarios at urban level. Even if the application of this method in a probabilistic environment requires a relevant computational effort, this has to be the reference method for determining those curves. Nevertheless, it would be of high practical interest to have a simpler method based, for instance, on pushover analysis, for assessing the seismic vulnerability and risk of buildings, which allows obtaining results similar to those based on the incremental dynamic analysis. Referring to the capacity-spectrum-based-methods, expert opinions have been used in previous researches for defining damage states thresholds starting from the yielding and the ultimate spectral displacement identified in the bilinear capacity spectrum. Therefore, we propose in this article a new procedure for defining the damage states thresholds, based on the stiffness degradation of reinforced concrete building, and a fully probabilistic approach is tackled by means of Monte Carlo simulations. It is demonstrated in the paper that the obtained results are in good agreement with those calculated using the incremental dynamic analysis.
Abstract
The incremental dynamic analysis is a powerful tool for evaluating the seismic vulnerability and risk of buildings. It allows calculating the global damage of structures for [...]
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Evaluación probabilista del riesgo sísmico en Lorca mediante simulaciones de escenarios
M. Salgado-Gálvez, M. Carreño, A. Barbat, O. Cardona

Rev. int. métodos numér. cálc. diseño ing. (2016). Vol. 32, (2)

Abstract
A comprehensive and probabilistic seismic risk assessment has been performed for the buildings of Lorca, the most affected city in the region of Murcia, Spain, after the May 2011 earthquake. Seismic hazard is represented through a set of stochastic scenarios that allow accounting for small, moderate and extreme events in the future losses, also through spectral transfer functions the dynamic soil response has been considered. A building by building resolution level database has been used allowing the disaggregation of risk results in several categories besides allowing the generation of risk maps to visualize the geographical distribution of the future losses. For each of the identified building classes a vulnerability function has been assigned to determine the expected losses for different acceleration levels. Risk results have been obtained in terms of the loss exceedance curve from where other probabilistic risk metrics such as the average annual loss and the probable maximum loss can be derived. Risk results are useful for the decision-makers in the fields of emergency planning, existent building retrofitting schemes and financial protection through traditional insurance and reinsurance schemes or with alternative risk transfer instruments.
Abstract
A comprehensive and probabilistic seismic risk assessment has been performed for the buildings of Lorca, the most affected city in the region of Murcia, Spain, after the May [...]
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Evaluación probabilista de la capacidad, fragilidad y daño sísmico de edificios de hormigón armado
Y. Vargas, L. Pujades, A. Barbat, J. Hurtado

Rev. int. métodos numér. cálc. diseño ing. (2013). Vol. 29, (2)

Abstract
Currently, many structures existing in seismic areas are highly vulnerable because they have been built without the use of seismic design codes or by using outdated codes. Often, methods for assessing the vulnerability of the structures do not take into account that their seismic behavior is dynamic and highly nonlinear and, moreover, that the structural characteristics and action have large uncertainties. This article aims to assess the vulnerability of structures taking into account that the mechanical properties of materials and the seismic action are random variables, by using advanced techniques based on the Monte Carlo method and on the nonlinear stochastic dynamics. The results obtained with these techniques are compared with those corresponding to a standard vulnerability assessment, based on deterministic models, in order to highlight the differences between both approaches. The main conclusion of this work is the need to address the vulnerability assessment problem from a probabilistic perspective which, combined with advanced nonlinear static and dynamic structural analysis techniques, provides a powerful tool giving information impossible to be captured by means of deterministic models. Finally, detailed results obtained for a building with waffle slabs, which is a structural typology widely used in Spain, are included and discussed.
Abstract
Currently, many structures existing in seismic areas are highly vulnerable because they have been built without the use of seismic design codes or by using outdated codes. [...]
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Evaluación de la habitabilidad de edificios afectados por sismo utilizando la teoría de conjuntos difusos y las redes neuronales artificiales
M. Carreño, O. Cardona, A. Barbat

Rev. int. métodos numér. cálc. diseño ing. (2011). Vol. 27, (4)

Abstract
The fuzzy sets theory and the artificial neural networks are computational intelligence tools which are nowadays widely used in earthquake engineering. This paper develops a method and a computer program which use these computational intelligence tools in order to support the damage and safety evaluation of buildings after strong earthquakes. The model uses an artificial neural network with three layers and a Kohonen learning algorithm, it also uses fuzzy sets in order to manage subjective information such as linguistic qualification of the damage levels in buildings and a fuzzy rule base to support the decision making process. All these techniques are incorporated in the developed computer program. The input data is the subjective and incomplete information about the building state obtained by possibly non experienced evaluators in the field of the seismic performance of buildings. The proposed method is implemented in a tool especially useful in the emergency response phase, when it supports the decision making regarding the building habitability and reparability. In order to show its effectiveness, two examples are included for two different types of buildings.
Abstract
The fuzzy sets theory and the artificial neural networks are computational intelligence tools which are nowadays widely used in earthquake engineering. This paper develops [...]
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Método numérico para la evaluación holística del riesgo sísmico utilizando la teoría de conjuntos difusos
M. Carreño, A. Barbat, O. Cardona

Rev. int. métodos numér. cálc. diseño ing. (2014). Vol. 30, (1)

Abstract
The fuzzy set theory offers a bridge between the symbolic and numerical processing, allowing managing qualitative concepts useful in the decision-making process related to the seismic risk management and, in general, to the disaster risk management. Its use in the seismic risk evaluation is necessary in the cases where the data required to apply a conventional method of assessing risk are not available or are insufficient. One possible solution, considered in this article, is to replace the missing information by expert opinions and to process the resulting qualitative variables and linguistic qualifications instead of numerical values. This process is based on the fuzzy set theory. In order to achieve an effective management, the risk must be defined as the potential physical, economic, social and environmental consequences which occur due to hazards in a given period of time. From this holistic perspective and using the fuzzy set theory, the proposed numerical method calculates a level of the physical risk and level of the aggravating conditions related to social fragility and to the lack of resilience, to determine a total risk level. In the article are included two examples of application of the proposed method and the obtained results are compared with those corresponding to a conventional method of holistic evaluation.
Abstract
The fuzzy set theory offers a bridge between the symbolic and numerical processing, allowing managing qualitative concepts useful in the decision-making process related to [...]
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A new strategy for thevulnerability study of buildings exposed to open-airexplosions
. F. Zárate, . V.E. Cardoso, A. Barbat, . S. Botello

Rev. int. métodos numér. cálc. diseño ing. (2017). Vol. 33, (4)

Abstract
In this paper, a new methodology is described to evaluate the effect of open air explosions on equivalent structures to the facades of buildings. The structural damage is defined by vulnerability surfaces that are a function of the explosion magnitude, the distance to the structure and the detonation damage index developed in this article. The proposed index considers the structural load capacity degradation, the fracturing and the loss material due to the explosion. The structure is modeled by means of discrete elements (DEM) which allows describing the multifracturing state. The load capacity of the structure is quantified by a virtual compression test on the damaged structure. The forces on the structure caused by the explosion are modeled by a semi-empirical methodology, which avoids the fluid-dynamic analysis and reduces the computation time.
Abstract
In this paper, a new methodology is described to evaluate the effect of open air explosions on equivalent structures to the facades of buildings. The structural damage is [...]
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Estudio numérico-experimental de la interfaz hormigón-epoxi-FRP para una estructura reforzada sometida a doble corte
M. Molina, J. Cruz, S. Oller, A. Barbat, L. Gil

Rev. int. métodos numér. cálc. diseño ing. (2012). Vol. 28, (2)

Abstract
The strengthening of concrete structures with laminates of carbon fibers CFRP (Carbon Fibers Reinforced Polymer) began in the 1980s. Nowdays, this technology is one of the most promising one because of the good mechanical properties of laminates and their easy hand-work. Laminates are bonded to the concrete structure by means of epoxy resins. The load-carrying capacity of the strengthening depends directly on the proper behavior of the interface laminate-concrete. While the concrete is capable of transferring stresses to the laminate, this one becomes in charge and collaborates to the strength mechanism of the structure. The safety factor of the reinforcement can be guaranteed if we can predict the behavior at the interface between both materials. In this work we present a pure shear test and a simulation three-dimensional to characterize the behavior of the interface between the laminate and the concrete.
Abstract
The strengthening of concrete structures with laminates of carbon fibers CFRP (Carbon Fibers Reinforced Polymer) began in the 1980s. Nowdays, this technology is one of the [...]
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Control digital predictivo de la respuesta sísmica de estructuras
J. Rodellar, A. Barbat

Rev. int. métodos numér. cálc. diseño ing. (1985). Vol. 1, (1)

Abstract
En este artículo se desarrolla un controlador digital predictivo con aplicación en la reducción de la respuesta sísmica de estructuras. Su eficacia se comprueba controlando la respuesta de un modelo de reactor nuclear.
Abstract
En este artículo se desarrolla un controlador digital predictivo con aplicación en la reducción de la respuesta sísmica de estructuras. Su eficacia [...]
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Evaluación holística del riesgo sísmico en zonas urbanas
A. Barbat, M. Carreño, O. Cardona, M. Marulanda

Rev. int. métodos numér. cálc. diseño ing. (2011). Vol. 27, (1)

Abstract
Risk has been defined, for management purposes, as the potential economic, social and environmental consequences of hazardous events that may occur in a specified period of time. In the past, the concept of risk has been defined in many cases in a fragmentary way, according to each scientific discipline involved in its appraisal. A framework and a multidisciplinary risk evaluation model is proposed in this article that take into account not only the expected physical damage, the number and type of casualties or the economic losses, but also the conditions related to soial fragility and lack of resilience which favor second order effects (or indirect effects) when an earthquake strikes an urban centre. Thus, the mentioned evaluation is holistic, that is based on an integrated and comprehensive approach, made by using indicatos andoriented towards guiding decision-making. Th conceptual framework and the model proposed are also valid for their applicationto multihazard risk evaluation, although this article has been focused on the evaluation of the seismic riskk. The first step in obtaining the Urban Seismic Risk index (USRi) consists of calculating a Physical Risk index for each unit of analysis starting form existing physical risk scenarios. An impact factor, associated with a set of socio-economic and lack of resilience conditions of the community, is applied in a second step to the physical risk index in order to obtain the USRi. It has been demostrated that the proponed holistic evaluationmodel of the seismic risk in robust, provideing stable and reliable values of the USRi. Finally, numerical simulation results of the seismic risk obtained with the proposed model are given in the article for the cities of Bogota (Colombia), Barcelona (Spain) and Manila (The Phillipines).
Abstract
Risk has been defined, for management purposes, as the potential economic, social and environmental consequences of hazardous events that may occur in a specified period of [...]
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Comportamiento sísmico de edificios con un sistema no lineal de control híbrido
A. Barbat, J. Rodellar, .. Ryan, N. Molinares

Rev. int. métodos numér. cálc. diseño ing. (1993). Vol. 9, (2)

Abstract
En el artículo se propone una clase de sistema hibrido de control antisísmico de edificios que combina un sistema pasivo de aislamiento de base con comportamiento no lineal con uno , activo. La componente pasiva del sistema está constituida por un aparato de apoyo que puede ser de tipo histerético, de tipo friccional, o una combinación de los dos. Las fuerzas de control activo se aplican sobre la base y tienen como objetivo la reducción de su desplazamiento. Se desarrolla una ley de control adaptativo que garantiza una forma de comportamiento estable del sistema frente a las incertidumbres tanto en las características del edificio como en las de la excitación sismica así como frente a las no linealidades. La reducción del desplazamiento de la base estructural puede provocar un ligero empeoramiento del comportamiento dinámico del edificio con respecto al del caso puramente pasivo. Sin embargo, su comportamiento global mejora cuando se considera el sistema híbrido, especialmente para excitaciones con frecuencias predominantes para las cuales la respuesta de la estructura con control pasivo es máxima. La eficacia del procedimiento propuesto en solucionar el problema formulado se ilustra mediante estudios numéricos.
Abstract
En el artículo se propone una clase de sistema hibrido de control antisísmico de edificios que combina un sistema pasivo de aislamiento de base con comportamiento no lineal [...]
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Análisis numérico de estructuras de hormigón reforzadas con FRP por medio de la teoría de mezclas serie/paralelo
M. Molina, S. Oller, A. Barbat, X. Martínez

Rev. int. métodos numér. cálc. diseño ing. (2010). Vol. 26, (2)

Abstract
The numerical simulation of composite materials is a field under continuous development. Its application to structural design has shown important improvements, leading to a better simulation of strengthened structures. This paper uses the serial/parallel mixing theory to predict the mechanical behavior of composites. This theory uses the constitutive equations of the component materials to obtain the composite performance. The advantages provided by this formulation to simulate concrete structures reinforced or retrofitted with Fiber Reinforced Polymers (FRP) will be shown from the analysis of several finite element models, consisting of a set of concrete frames with different strengthening configurations. The results obtained will show that the use of this theory to simulate FRP reinforced structures improves their analysis and design.
Abstract
The numerical simulation of composite materials is a field under continuous development. Its application to structural design has shown important improvements, leading to [...]
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Evaluacion de la presión de fallo del edificio de contencion de una central nuclear tipo PWR-W tres lazos. Parte II: Simulacion numérica
A. Barbat, M. Cervera, C. Cirauqui, A. Hanganu, E. Oñate

Rev. int. métodos numér. cálc. diseño ing. (1995). Vol. 11, (3)

Abstract
En este articulo se presentan los resultados de la simulación numérica efectuada para evaluar la presión de fallo debida a un accidente del edificio de contención de una central nuclear PWR- W tres lazos. El modelo computacional tridimensional de elementos finitos utilizado ha sido descrito en la primera parte del artículo1. En esta segunda parte se analiza la influencia que tiene sobre la presión de fallo de la contención tanto la inclusión en el modelo estructural de la losa de cimentación como los efectos térmicos. El estudio numérico demuestra que puede llevarse a cabo la simulación del proceso de fallo utilizando un modelo estructural que no incluya la losa de cimentación y la carga de temperatura. Finalmente, se presentan y se discuten los resultados de un estudio probabilista de simulación de la presión de fallo y se resumen las conclusiones.
Abstract
En este articulo se presentan los resultados de la simulación numérica efectuada para evaluar la presión de fallo debida a un accidente del edificio de [...]
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Evaluacion de la presión de fallo del edificio de contencion de una central nuclear tipo PWR-W tres lazos. Parte I: Metodología
M. Cervera, A. Barbat, A. Hanganu, E. Oñate, C. Cirauqui

Rev. int. métodos numér. cálc. diseño ing. (1995). Vol. 11, (2)

Abstract
Se presenta en este artículo la metodología seguida para la evaluación de la presión de fallo del edificio de contención de una central nuclear PWR-W tres lazos. El análisis debe ser totalmente tridimensional para permitir la consideración de los elementos estructurales más significativos, tener en cuenta el comportamiento no lineal de los materiales y estudiar la sensibilidad de los resultados ante ciertas incertidumbres asociadas a algunos parámetros. El modelo computacional incluye las ecuaciones constitutivas para el hormigón y las armaduras de acero, la discretización espacial (elementos isoparamétricos con armado) y la resolución del problema estructural no lineal mediante algoritmos incrementales-iterativos con aceleradores de convergencia. Se describen los modelos estructurales utilizados y los análisis llevados a cabo para su calibración.
Abstract
Se presenta en este artículo la metodología seguida para la evaluación de la presión de fallo del edificio de contención de una central nuclear PWR-W tres lazos. El análisis [...]
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Cálculo de la respuesta dinámica de estructuras mediante un procedimiento de estado
A. Barbat, J. Rodellar, F. Almansa, J. Carrera

Rev. int. métodos numér. cálc. diseño ing. (1987). Vol. 3, (3)

Abstract
A procedure for computing the dynamic response of elastic linear structure is developed. The method is based on the state representation the equations of motion. The algorithm stability and accuracy compare favourably with those of step-by-step integration procedures. The proposed approach does not require any restriction on the type of dampingmatrix. The methodology isillustrated by two examples: seismic response of a dam and calculation of a building structure.
Abstract
A procedure for computing the dynamic response of elastic linear structure is developed. The method is based on the state representation the equations of motion. The algorithm [...]
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Una formulación matricial generalizada. Parte 2: Analisis dinamico
. C.Molins, P. Roca, A. Barbat

Rev. int. métodos numér. cálc. diseño ing. (1995). Vol. 11, (1)

Abstract
Se describe una formulación para el análisis dinámico de estructuras formadas por entramados espaciales de elementos de directriz curva y sección variable, cuyo desarrollo se basa en la Formulación Matricial Generalizada (FGM) presentada en una comunicación anterior. El aspecto más notable de la extensión de la FMG al análisis dinámico reside en la construcción de una matriz de masa elemental que, por una parte, no requiere ninguna hipótesis complementaria sobre el campo de movimientos y, por otra parte, permite considerar de forma exacta la distribución de rigidez y masa interior de los elementos. Ello parte de la previa definición de una matriz de masa seccional. Se ha realizado una comparación, para algunas estructuras sencillas, de los resultados obtenidos mediante la formulación presentada y los obtenidos por otros autores a través de distintas formulaciones. De ésta se desprenden la eficiencia y exactitud del método propuesto y, en particular, de la formulación que se realiza de la matriz de masa.
Abstract
Se describe una formulación para el análisis dinámico de estructuras formadas por entramados espaciales de elementos de directriz curva y sección variable, cuyo desarrollo [...]
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Simulación de acelerogramas compatibles con espectros de energía sísmica inducida
J. Hurtado, A. Barbat, J. Canas

Rev. int. métodos numér. cálc. diseño ing. (1996). Vol. 12, (1)

Abstract
En este artículo se presenta un estudio sobre el espectro de energía inducida en las estructuras sometidas a acciones sísmicas. En primer lugar se discuten las variables que influyen en dicho espectro, con base en las relaciones que guarda el mismo con otras medidas de la acción sísmica. En segundo lugar, se presenta un procedimiento que permite estimar un espectro suavizado de diseño, basado en la regresión sobre los registros de las dos componentes horizontales de 56 sismos diferentes. Finalmente, se describe un método para simular acelerogramas compatibles con un espectro de energía prescrito y se presenta un ejemplo que ilustra la utilidad del método para la evaluación del daño sísmico.
Abstract
En este artículo se presenta un estudio sobre el espectro de energía inducida en las estructuras sometidas a acciones sísmicas. En primer lugar se discuten las variables [...]
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Simulacion de escenarios de daño sísmico en zonas urbanas
F. Yépez, A. Barbat, J. Canas

Rev. int. métodos numér. cálc. diseño ing. (1996). Vol. 12, (3)

Abstract
A methodology to perform a damage simulation procedure for existing non-reinforced masonry buildings in an urban zone is presented in this paper. By simulating the behaviour of thousands of hypothetical buildings and performing probabilistic studies of the computed results, damage probability matrices and vulnerability functions are obtained, which are the bases for vulnerability and seimic risk evaluations. The fundamentals of the presented methodology are the italian vulnerability index and the results of a post-earthquake survey damage study. As an example, an urban zone of Barcelona is examinated and probable damage scenarios are developped.
Abstract
A methodology to perform a damage simulation procedure for existing non-reinforced masonry buildings in an urban zone is presented in this paper. By simulating the behaviour [...]
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Un método de evaluación del daño sísmico en estructuras de hormigón armado
S. Oller, B. Luccioni, A. Barbat

Rev. int. métodos numér. cálc. diseño ing. (1996). Vol. 12, (2)

Abstract
En este artículo se presenta un método que permite evaluar el daño sísmico global en estructuras de barras de hormigón armado. Se denomina estado dañado de un punto del sólido a aquel estado termodinámico resultante de la entrada del material en estado de comportamiento no lineal. A partir del concepto de daño local en un punto del sólido, se deduce por extensión el índice de daño global estructural. Se utiliza la técnica de elementos finitos para aproximar el campo de desplazamientos. Se trabaja con un elemento de barra Timoshenko en 3-D subdividido en capas entrecruzadas (fibras), donde en cada una de ellas se aplica un modelo constitutivo general formulado en tensión-deformación. Esto último permite incluir cualquier fenómeno que acerque más la simulación numérica a la realidad del problema (plasticidad, degradación de rigidez, problemas viscosos, etc.). Al final se incluyen ejemplos de cálculo que demuestran la capacidad del método numérico que se presenta, para la obtensión del nivel de daño global en las estructuras.
Abstract
En este artículo se presenta un método que permite evaluar el daño sísmico global en estructuras de barras de hormigón armado. Se denomina estado dañado de un punto [...]
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Evaluación probabilista del riesgo sísmico en zonas urbanas
A. Barbat, U. Mena, F. Yépez

Rev. int. métodos numér. cálc. diseño ing. (1998). Vol. 14, (2)

Abstract
A methodology to evaluate the vulnerability and seismic risk of existing building structures in an urban area developed within a probabilistic scheme. It uses numerical procedures for the analysis of the non-linear seismic behaviour of structures and optimized sampling method and probabilistic models for the description of the obtained results. Occurrence probabilities for different damage levels of the structures in risk, corresponding to a giiven exposure period are thus obtained. From ail economical point of view, annual losses and minimum earthquake insurance taxes are evaluated. The proposed method is applied td the assessment of the seismic risk of a complete urban are a, located in the central part bf Barcelona, Spain, in which mostly unreiilforced masonry buildings and non-ductile reinforced concrete buildings are the most common building types. The method has been implemented, in a modular format in a Geographical Inforinatioil System, with the objetive of obtaining seismic risk scenarios.
Abstract
A methodology to evaluate the vulnerability and seismic risk of existing building structures in an urban area developed within a probabilistic scheme. It uses numerical procedures [...]
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Simulación numérica de elastómeros multi-fase en estiramientos principales
O. Salomón, S. Oller, A. Barbat

Rev. int. métodos numér. cálc. diseño ing. (2000). Vol. 16, (1)

Abstract
En este trabajo se propone un modelo hiperelástico generalizado para el análisis de elastómeros milti-fase. El modelo se desarrolla en grandes deformaciones en función de los estiramientos principales. Debido a la cuasi-incomprensibilidad de los elastómeros, se supone un comportamiento diferente para las partes volumétrica y desviadora de la deformación. Se utiliza teoría de mezclas para incorporar las expresiones constitutivas básicas propuestas para cadqa material, viscoelasticidad para el caucho y elastoplasticidad para las partículas agregadas, en un formulación de sólido compuesto.
Abstract
En este trabajo se propone un modelo hiperelástico generalizado para el análisis de elastómeros milti-fase. El modelo se desarrolla en grandes deformaciones en función [...]
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Análisis sísmico de edificios con dispositivos de aislamiento de base elastoméricos
O. Salomón, S. Oller, A. Barbat

Rev. int. métodos numér. cálc. diseño ing. (2000). Vol. 16, (2)

Abstract
Los sistemas de aislamiento sísmico de base desacoplan parcialmente una estructura de los movimientos del terreno por medio de dispositivos colocados entre la estructura y su cimentación. De los diversos tipos de dispositivos desarrollados, los más utilizados son lo de elastómero laminado que están constituidos por capas alternadas de elastómero y acero. Este artículo es una contribución al tratamiento numérico conjunto de las estructuras con sus dispositivos de aislamiento de base de elastómeros laminados.
Abstract
Los sistemas de aislamiento sísmico de base desacoplan parcialmente una estructura de los movimientos del terreno por medio de dispositivos colocados entre la estructura [...]
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Evaluación del daño sísmico en puentes de hormigón armado
C. Gómez, S. Oller, A. Barbat

Rev. int. métodos numér. cálc. diseño ing. (2002). Vol. 18, (2)

Abstract
La estimacion del daño producido por la accion sísmica en puentes existentes ha cobrado interes en los ultimos años, no solo para tratar de disminuir el numero de víctimas sino tambien para reducir los drasticos costos generados en diversos sectores economicos. En la caracterizacion y evaluacion del daño se han priorizado los metodos de aplicacion simple y conﬁable, ya que son una herramienta util en casos de analisis multiples relacionados con la simulacion por Monte Carlo. Optando por este camino, en este artículo se presenta una propuesta de analisis simpliﬁcado del daño ocasionado por terremotos en puentes de autopista de hormigon armado. Se muestra la formulacion basica del modelo dinamico propuesto y el procedimiento de evaluacion del daño estructural, basado en el calculo de la inercia dañada de los pilares del puente para la estimacion de su degradacion. Se dan ejemplos de calculo que muestran la ﬁabilidad y eﬁcacia del modelo propuesto.
Abstract
La estimacion del daño producido por la accion sísmica en puentes existentes ha cobrado interes en los ultimos años, no solo para tratar de disminuir el numero de víctimas [...]
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Evaluación de vulnerabilidad sísmica del puente Warth (Austria) mediante un modelo simplificado
C. Gómez, S. Oller, A. Barbat

Rev. int. métodos numér. cálc. diseño ing. (2002). Vol. 18, (3)

Abstract
En la actualidad existen muchos puentes, construidos hace veinte o treinta años, que han sido proyectados aplicando normativas que luego han sido actualizadas, tanto en lo referente a la peligrosidad como a los métodos de cálculo. Para estas estructuras son necesarias herramientas de evaluación confiables que permitan evaluar su futuro comportamiento sísmico. En busca de ese objetivo, en un trabajo previo los autores han propuesto un método de análisis basado en la determinación de la degradación máxima de las pilas del puente. En este artículo se aplica la metodología para la evaluación de la vulnerabilidad sísmica del Puente Warth, Austria, construido hace 30 años bajo requisitos de diseño ahora obsoletos. Para esta estructura se realizaron varias simulaciones porMonte Carlo, considerando las incertidumbres asociadas a los parámetros de definición de la peligrosidad sísmica y a las características estructurales. A través de los resultados obtenidos se define el comportamiento futuro de la estructura para un posible escenario sísmico y se comprueba la bondad y confiabilidad del modelo simplificado propuesto.
Abstract
En la actualidad existen muchos puentes, construidos hace veinte o treinta años, que han sido proyectados aplicando normativas que luego han sido actualizadas, tanto en lo [...]
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Barbat, Alex 3531
Universitat Politècnica de...

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