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The main objective of this thesis is the probabilistic assessment of the expected seismic damage in steel buildings located in Mexico City. Although a deterministic analysis is performed both, seismic actions and buildings, are considered in a probabilistic way. A broad acceleration database, with 7132 records (3 components) of the 180 stations in the city, 1363 with peak ground acceleration (PGA) above 0.01 g, is analyzed; this analysis, allows having data representative for each one of the 6 seismic zones of the city; the seismic action in each zone is defined by means of 20 accelerograms compatible and with controlled error, in the sense that the mean value and standard deviation of the 20 spectra match well the design spectrum and a predefined error function, respectively. Concerning structures, the study is based on low- (3 stories), mid- (7 stories) and high-rise (13 stories) buildings and on 3 structural configurations: i) Special Moment Frames (SMF) ii) Special Concentrically Braced Frames (SCBF) and (iii) Buckling Restrained Braced Frames (BRBF). The mechanical properties are considered in a probabilistic way by means of appropriate probability distributions; Monte Carlo simulation and Latin hypercube based sampling techniques are used. The deterministic analysis is performed by using mean values of buildings and accelerograms. 2D models, Nonlinear Static Analysis (NLSA), Non Linear Dynamic Analysis (NLDA) and Incremental Dynamic Analysis (IDA) are used. NLSA allows obtaining capacity spectra, fragility curves, mean damage state curves and relations between PGA and the displacement of the performance point. IDA allows obtaining relations among PGA, maximum roof displacement and Park and Ang damage index. The results show that buildings perform properly. However, BRBF show the best performance; SMF the worst. The highest expected damage is obtained for high-rise buildings and, particularly, for SMF buildings; this result is attributed to soft-soil¿s amplification effects, affecting more to high buildings. Uncertainties in the response increase with the severity of the earthquake and they are dominated by uncertainties in the seismic action; however, the influence of uncertainties of the mechanical properties of buildings, although minor, is also significant. Static analysis provides good results, when compared with the ones of the dynamic analysis; but, this consistency is lower for high-rise buildings. The deterministic analysis shows a good consistency with the median values of the probabilistic analysis, although the probabilistic approach allows analyzing uncertainties and, in this sense, it should be preferred. In this thesis, innovative methods for the analysis of the seismic action and for damage assessment have been implemented. Concerning to seismic action, a comprehensive study of directionality effects in Mexico City has been performed; also, the design spectra have been compared with the ones of the recorded accelerograms. Concerning to damage analysis the performance point is obtained by using an energy-balance based method. The parametric model for capacity curves has been applied; this model completely defines capacity curves/spectra with 5 independent parameters. In addition, two damage indices that are compatible with the Park and Ang index have been obtained; these two damage indices are calculated from the capacity curve, in a straightforward way. In addition, a probabilistic assessment of the collapse damage state, is performed. Finally, as a practical and useful contribution, several developments of this thesis, are implemented in an interactive software; it is intended that the computer program, "Probabilistic Seismic Risk" (PSRv1.0), be an easy and efficient tool allowing a fast assessment of the seismic risk., El principal objetivo de esta tesis es la evaluación probabilista del daño esperado en edificios de acero sometidos a las acciones sísmicas de diseño en la Ciudad de México. Aunque se efectúa un análisis determinista, la acción sísmica y los edificios se consideran de forma probabilista. Se analiza una extensa base de datos de aceleración, con 7132 registros (3 componentes) de las 180 estaciones de la ciudad, de los cuales 1363, con aceleraciones pico (PGA) mayor de 0.01 g; este análisis, permite disponer de datos representativos para cada una de las 6 zonas sísmicas de la ciudad. Así, la acción sísmica en cada zona, se define mediante 20 acelerogramas compatibles y con error controlado, de forma que el valor medio y la desviación estándar de los 20 espectros correspondientes, coinciden con el espectro de diseño de cada zona y con una función de error predefinida, respectivamente. Por otra parte, se consideran edificios porticados de 3, 7 y 13 pisos y 3 configuraciones estructurales: i) pórticos especiales resistentes a momento (SMF) ii) pórticos con riostras concéntricas (SCBF) y iii) pórticos con riostras de pandeo restringido (BRBF). Las propiedades mecánicas de las secciones estructurales se consideran de forma probabilista y se usa el método de Monte Carlo y la técnica de muestreo del hipercubo latino. El análisis determinista se efectúa usando valores medios de edificios y acelerogramas. Se usan modelos 2D y análisis no lineal estático (NLSA) y dinámico (NLDA) incremental (IDA). El NLSA, permite obtener espectros de capacidad, curvas de fragilidad, curvas de daño medio y relaciones entre PGA y el desplazamiento del punto de capacidad por demanda, que son fundamentales para comparar los resultados de los NLSA y NLDA. El IDA permite obtener relaciones de PGA con el desplazamiento máximo en el techo y con el índice de daño de Park y Ang (IPA). Los resultados muestran un comportamiento adecuado de los edificios; los BRBF son los que tienen un mejor rendimiento y los SMF los que peor. El mayor daño esperado se obtiene para los edificios altos y, en particular, para los no arriostrados (SMF); este resultado se atribuye a la amplificación de la acción sísmica, por efecto de suelos blandos de grandes espesores, afectando más a los edificios altos. La incertidumbre en la respuesta crece con la severidad del terremoto y está dominada por la incertidumbre en la acción sísmica; la influencia de las incertidumbres de las propiedades mecánicas de los edificios, aunque menor, es también significativa. Para los edificios estudiados, en general, el NLSA proporciona buenos resultados comparados con los del NLDA. El análisis determinista muestra una buena consistencia con los valores medianos del probabilista, aunque el análisis probabilista es preferible, ya que permite analizar las incertidumbres. En esta tesis se han desarrollado, implementado y aplicado métodos novedosos para el análisis de la acción sísmica y del daño. En referencia a la acción sísmica, se ha hecho un estudio completo del efecto de direccionalidad en la Ciudad de México. En cuanto al análisis de daño, el cruce entre los espectros de capacidad y de demanda se efectúa usando un método de balance de energías; se ha aplicado el modelo paramétrico de capacidad, que parametriza los espectros de capacidad mediante 5 parámetros independientes y se han obtenido dos índices de daño que son compatibles con el IPA, pero que se evalúan, de forma directa y sencilla, a partir de las curvas de capacidad; además se efectúa una evaluación probabilista del colapso, que permite obtener la frecuencia o tasa anual de colapso. Finalmente, parte de los desarrollos de esta tesis se implementan en un programa interactivo que constituye una contribución práctica y útil de esta tesis; así, el programa "Probabilistic Seismic Risk" (PSRv1.0), pretende ser una herramienta para una evaluación rápida del riesgo sísmico, en térmicos de tasas anuales de excedencia del daño esperado

Esta tesis propone una metodología de evaluación del daño sísmico basada en el método del espectro de capacidad pero con un enfoque probabilista que se apoya en simulaciones Monte Carlo. Así la acción sísmica, la estructura y el daño esperado se consideran y se analizan como variables aleatorias. La metodología, que se valida mediante el análisis dinámico incremental, es una nueva, robusta y potente herramienta de análisis de riesgo tanto a nivel de edificios individuales como a nivel urbano y regional. La validación mediante el análisis dinámico, de hecho, ha supuesto crear también una metodología probabilista basada en el análisis dinámico incremental. El daño esperado puede obtenerse para cualquier intervalo de confianza permitiendo así, a los gestores de la protección civil la elección de los niveles prioritarios o de interés. Como el análisis dinámico incremental requiere acelerogramas, se ha optado por usar registros de terremotos y se ha diseñado una técnica que, para una determinada base de datos, permite optimizar, minimizando la dispersión, el número de acelerogramas compatibles con un determinado espectro de respuesta; de esta forma la incertidumbre en la acción sísmica se considera de una manera adecuada. Aunque a efectos metodológicos, se ha estimado suficiente y adecuado considerar como variables aleatorias gaussianas sólo las propiedades resistentes del hormigón y el acero, con todo se ha introducido también una nueva e interesante forma de incorporar la variabilidad espacial de la resistencia de vigas y columnas. Los desarrollos metodológicos se ilustran con numerosos casos de estudio de edificios existentes y bien documentados. En particular, se han estudiado los edificios de hormigón armado con forjados reticulares, clasificados en altos, de altura mediana y bajos. Este estudio se ha realizado considerando acciones sísmicas compatibles con los espectros previstos en el eurocódigo EC8 para terremotos tipo 1 y tipo 2 y para suelos A, B, C, D y E. La aplicación del método a edificios irregulares ha confirmado la insuficiencia de modelos 2D en estructuras asimétricas. Así, el método probabilista se ha aplicado a dos edificios de especial importancia para escenarios sísmicos de interés. El primero es el hospital de Vielha, para la acción sísmica con un periodo de retorno de 475 años; el segundo es un edificio del Barrio de San Fernando en Lorca, que fue severamente dañado por el terremoto del mes de mayo de 2011. En este segundo caso la acción sísmica se ha definido de forma determinista mediante las dos componentes horizontales de aceleración registradas en la ciudad. En los análisis 3D se ha incorporado el efecto de direccionalidad, concluyendo que edificios del mismo tipo situados en un mismo lugar pueden sufrir daños significativamente distintos dependiendo sólo de su orientación azimutal. Los resultados obtenidos en el caso de Lorca son compatibles con los daños observados lo que contribuye a validar el método probabilista y los desarrollos implementados en esta tesis., This dissertation proposes a methodology for seismic damage assessment based on the capacity spectrum method but with a probabilistic approach which is supported on Monte Carlo simulation. The seismic action, the structure and the expected damage are considered and analyzed as random variables. The method, which is validated through incremental dynamic analysis, is a new, robust and powerful tool for risk analysis that can be applied to individual buildings, but also at urban and regional scales. In fact, the validation through dynamic analyses has involved creating also a probabilistic method for damage assessment, based on incremental dynamic analysis. The expected damage can be obtained for any confidence interval thus allowing the civil protection managers choosing the levels of priority or interest. As incremental dynamic analyses require accelerograms, the use of earthquake records has been preferred and it has been developed a specific technique that, for a given database, minimizes the dispersion and optimizes the number of accelerograms compatible with a given response spectrum; in this way, the uncertainties in the seismic action are considered in an appropriate manner. Although for methodological purposes it was estimated sufficient and adequate to consider only the strength properties of concrete and steel as Gaussian random variables, yet a new and interesting way to incorporate the spatial variability of the strength of beams and columns has been also proposed. The methodological developments are illustrated with numerous case studies of existing and well documented buildings. Specifically, reinforced concrete buildings with waffle slabs, classified as low-rise, mid-rise and high-rise, have been studied. This study has been conducted considering seismic actions compatible with the response spectra foreseen in the Eurocode EC8 for type 1 and type 2 earthquakes and soil classes A, B, C, D and E. The application of the method to irregular buildings confirmed the insufficiency of 2D models for asymmetric structures. Thus, the probabilistic method has been applied to two buildings of special importance for seismic scenarios of interest. The first one is the hospital of Vielha considering the seismic action with a return period of 475 years; the second one is a building located in the neighborhood of San Fernando in Lorca, which was severely damaged by the earthquake of May 2011. In this second case the seismic action has been defined deterministically by means of the two horizontal accelerograms recorded in the city. In 3D analyses the directionality effect is considered, concluding that buildings of the same type located in the same place can suffer significantly different damages depending only of their azimuthal angle. The results obtained in the case of Lorca are compatible with the observed damage. This fact supports the validity of the probabilistic method as well as that of the developments implemented in this thesis.

The present research commences with a revision of the concepts of hazard, vulnerability, and risk. This is a basic requirement for the construction of the theoretical framework herein developed. A revision of commonly used concepts is offered in order to identify gaps and fine-tune definitions that will help in the search to offer a coherent and integrated theoretical framework. Approaches developed in the natural, applied, and social sciences are discussed and a criticism of these is offered. It is argued that conceptual fragmentation and inconsistency have been two of the reasons why risk reduction has been in good part unsuccessful in a large number of countries. The lack of an adequate conceptual basis has impeded adequate interventions.Risk is understood in terms of potentially dangerous events and the vulnerability of exposed social elements. This type of analysis is linked into decision-making processes, and the difficulties associated with the implementation of risk reduction public policies are made explicit. Inherent uncertainty and reductionist approaches help explain this problem. Moreover, factors such as risk perception of decision-makers; legal contexts that impede preventive actions, and the general problem of levels of risk tolerance and acceptability also come into play.The traditional approach to evaluating urban seismic risk is revised. This involves a consideration of the physical effects and damage to be expected in exposed elements under determined seismic conditions. Modern techniques for seismic vulnerability estimates and knowledge in the area of loss and damage are summarized. And, the better approach to physical urban seismic risk evaluation from the perspective of the author is provided.A coherent and consistent conceptual risk model is provided based on complex non-lineal dynamic systems theory. This allows an explanation of the concept of crisis, instability and adaptability relating this to the concepts of disaster, vulnerability, risk and prevention. Urban centres are seen as complex dynamic systems. Two holistic urban seismic risk-modeling techniques are then proposed. The first methodology is based on relative indicators using hierarchical and pairwise analytical processes. The second methodology employs neural networks and fuzzy sets approaches. The two methodologies take into account the physical, economic, social and institutional variables, which allow a multidisciplinary approach to seismic risk assessment. The methods are subsequently employed in the estimation of seismic risk in the city of Bogotá, Colombia.Finally, a risk management strategy is proposed as a planning tool, and a global proposal is made for facing collective risk, which is a clearly significant contemporary technical and social problem. Recommendations are made, as regards needed future studies and research.