Multi-regression analysis to enhance the predictability of the seismic response of buildings

Several methodologies for assessing seismic risk extract information from the statistical relationship between the intensity of ground motions and the structural response. The first group is represented by intensity measures (IMs) whilst the latter by engineering demand parameters (EDPs). The higher the correlation between them, the lesser the uncertainty in estimating seismic damage in structures. In general, IMs are composed by either a single (scalar-based IMs) or a group of features of both the ground motion and the structure (vector-valued IMs); the latter category provides higher efficiency to explain EDPs when compared to the first one. This paper explores how to find new vector-valued IMs, which are highly correlated with EDPs, by means of multi-regression analysis. To do so, probabilistic nonlinear dynamic analyses have been performed by considering a seven-story reinforced concrete building as a testbed. At a first stage, 30 scalar-based IMs have been correlated with 4 EDPs (i.e., 120 groups of IM-EDP pairs have been studied). Afterwards, the structural responses have been classified as elastic, inelastic and a combination of both. It has been analyzed how efficiency behaves when making these classifications. Then, 435 vector-valued IMs have been created to enhance the predictability of the scalar EDPs (i.e., 1740 groups of IM-EDP pairs have been analyzed). Again, the most efficient IMs have been identified. Sufficiency, which is another statistical property desired in IMs, has also been examined. Results show that the efficiency and sufficiency to predict the structural response increase when considering vector-valued IMs. This sophistication has important consequences in terms of design or assessment of civil structures.This research has been partially funded by the European Regional Development Fund (ERDF) of the European Union (EU), through project with reference EFA158/16/POCRISC (INTERREG/POCTEFA. EU) and by the Spanish Research Agency (AEI) of the Spanish Ministry of Science and Innovation (MICIN) through project with reference: PID2020-117374RB-I00/AEI/10.13039/501100011033. The support of these institutions is highly recognized and acknowledged. Yeudy F. Vargas-Alzate has been granted an Individual Fellowship (IF) in the research grant program of the Marie Sklodowska-Curie Actions (MSCA), European Union/European (H2020-MSCA-IF-2017) No 799553. This author is deeply grateful to this institution.Peer ReviewedPostprint (published version

Probabilistic seismic assessment of a high-rise URM building

Several European urban nuclei are constituted by a significant number of ancient structures that belong to constructive typologies in which the seismic demand was not considered in their design at the time. Both, the accurate definition of the mechanical properties of their materials, and a proper seismic demand, are two of the major difficulties in the seismic damage assessment of structures due to their respective large associated uncertainties and variability, respectively. A representative high-rise unreinforced masonry (URM) building of the Eixample district in the city of Barcelona (Spain) is taken as a case-study. The building is modelled as an isolated load-bearing walls system with unidirectional iron beams-brick vaults slabs. The seismic demand variability is addressed by means of different ground motion records, which were selected following the conditional spectrum procedure, and subsequently scaled to different levels of demand (pga) according to the incremental dynamic analysis methodology. On the other hand, and due to the lack of homogeneity and level of knowledge associated with the large diversity of manufacturing and construction techniques, the compressive strength, shear modulus, shear strength and Young modulus are chosen and modelled as random variables in order to encompass the material uncertainties. Sufficient and representative samples are selected from both the population of mechanical properties of materials and the population of incrementally scaled dynamic analyses. Results are categorized in accordance to each of the selected random variables and seismic demand inputs (record and/or pga), providing, in varying degrees, their different correlations and tendencies among them.Postprint (published version

Non-linear static procedures applied to high-rise residential URM buildings

© 2016 Springer Science+Business Media Dordrecht 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.Peer ReviewedPostprint (author's final draft

Probabilistic seismic assessment of a high-rise URM building

According to the Sendai Framework for Disaster Risk Reduction (2015–2030), disasters have demonstrated that the recovery, rehabilitation and reconstruction phase, which needs to be prepared ahead of a disaster, is a critical opportunity to “Build Back Better”, integrating disaster risk reduction into development measures. In this respect, a significant number of structures, that constitute several European urban nuclei, belong to old constructive typologies, which were designed and built without any consideration for the seismic hazard. One of the most used typologies exhibiting this shortcoming is unreinforced masonry (URM). Therefore, an important step towards increasing resilience of European cities is to deeply understand the seismic behavior of this frequent typology. In order to do so properly, detailed probabilistic nonlinear building models should be developed. However, including the uncertainties associated with this typology is challenging due to the heterogeneity of the different manufacturing techniques, executed under primitive industrial standards, and to the construction techniques, which are dependent on regional uses and criteria in a pre-code scenario. The object of this research is twofold. First, a detailed quantification of the uncertainties related to the mechanical properties of this construction material is conducted. Then, the influence of this variability on the seismic performance of a representative building model of the Eixample district in Barcelona, Spain, is analysed. This building typology represents 72% of the building stock in this district with an average age of 90 years, which means that the construction practice, at that time, was only regulated by early council guidelines that are considered pre-code rules. Specifically, the probabilistic approach is illustrated with a case study performed on an existing seven-story (high-rise) URM. A detailed numerical model of this structure has been developed and randomized taking into account the variability of the material properties. Accordingly, 1000 models were generated and analysed by considering as input different sets of material random variables. The compressive strength, Young modulus, shear modulus and shear strength are chosen and modelled to encompass the material uncertainties. The seismic response of each variant (i.e. selected set of mechanical properties) is obtained through a simplified non-linear static procedure aiming to compare and categorize the influence of the probabilistic input on the seismic performance of the building. Results are presented in terms of correlations between damage parameters and material properties. The analysis carried out shows that the variability in the material properties generates significant uncertainties in the seismic response of URM buildings, leading to over or underestimate expected damage when compared with results based on approaches that do not consider the probabilistic nature of the problem.Peer ReviewedPostprint (published version

Análisis estructural probabilista orientado a evaluación del daño sísmico de edificios de mampostería no reforzada: aplicación a edificios aislados y agregados del distrito del Ensanche de Barcelona

Despite the fact that masonry is one of the oldest and most used building materials, the number of existing studies and experimental data, as well as the applicability of its results (i.e. extrapolation), are substantially lower than those available for much more recent materials, such as concrete or steel. Furthermore, currently in Europe, a large number of residential buildings belong to masonry typologies. These circumstances justify the study of the characteristics and behaviour of the masonry to guide studies on seismic vulnerability. In particular, the Eixample district of Barcelona, in Spain, presents an urban park of functional housing made up 73% of unreinforced masonry structures, solved by means of load-bearing wall systems, without any consideration of seismic action and that, for the most part, exceed 100 years of useful life. These buildings, characteristics of Barcelona, have elements that differentiate them from other buildings of the same construction typology that can be found in other regions of Europe: 1) the number of floors significantly exceeds the average, being able to find buildings with up to 10 or 11 levels; 2) The buildings share dividing walls (e.g. lateral), thereby generating frameworks of buildings known as aggregates; 3) The properties and qualities of the different construction elements are closely linked to the production processes, not yet mechanized, of the time; 4) The level of construction techniques and the qualification of the workforce were very high. In this work, numerical 3D models of isolated structural configurations (i.e. individual building) and in aggregate, of existing buildings have been made, in order to determine and compare the behaviour between the different structural configurations. The buildings have been modelled incorporating the variability of their mechanical parameters and the seismic demand has also been selected taking into account its uncertainty. The structural analysis has been carried out using and comparing different non-linear static calculation procedures and using the incremental non-linear dynamic analysis as a reference. A discussion was carried out comparing the results and the degree of reliability of the different procedures used in relation to the typology of unreinforced masonry buildings. It can be concluded that the simplified methods (i.e. non-linear static) overestimate the damage corresponding to low values of PGA and underestimate the damage for higher values of PGA. Using different criteria, and including the probabilistic consideration of mechanical properties, as well as seismic demand, the foreseeable damage for these structures has been characterized by fragility functions and matrices and damage indices. A study of the correlation between the mechanical parameters and the observed damage is also provided, from which, a high correlation between the obtained results and the variables of interest, is observed, being the Young’s modulus, E, the variable with the highest correlation coefficients. The common difficulties, in any work that involves large samples in relation to the amount of resources and computing time, have been solved through the design of adequate and sufficiently representative samples and by using current computational methods and tools, such as parallel and distributed computing.A pesar de que la mampostería es uno de los materiales de construcción más antiguos y usados, el número de estudios y datos experimentales existentes, así como la aplicabilidad de sus resultados (i.e. extrapolación), son substancialmente inferiores a aquellos disponibles para materiales mucho más recientes, tales como el hormigón o el acero. Además, actualmente en Europa, un gran número de edificaciones habitacionales pertenecen a tipologías de mampostería. Estas circunstancias justifican el estudio de las características y comportamiento de la mampostería para orientar estudios sobre vulnerabilidad sísmica. En particular, el distrito del Ensanche de Barcelona, en España, presenta un parque urbano de viviendas funcionales compuesto en un 73% por estructuras de mampostería no reforzada, resueltas mediante sistemas de muros de carga, sin ninguna consideración de la acción sísmica y que, en su mayoría, sobrepasan 100 años de vida útil. Estos edificios, característicos de Barcelona, tienen elementos que los diferencian de otras edificaciones de la misma tipología constructiva que pueden encontrarse en otras regiones de Europa: 1) el número de plantas supera significativamente la media, pudiendo encontrar edificios con hasta 10 u 11 niveles; 2) Los edificios comparten paredes medianeras (e.g. laterales), generando con ello entramados de edificios conocidos como agregados; 3) Las propiedades y calidades de los distintos elementos constructivos están estrechamente ligados con los procesos de producción, aún no mecanizados, de la época; 4) El nivel de las técnicas constructivas y la cualificación de la mano de obra eran muy elevados. En este trabajo se han realizado modelos numéricos 3D de configuraciones estructurales aisladas (i.e. edificio individual) y en agregado, de edificios existentes, con la finalidad de determinar y comparar el comportamiento entre las distintas configuraciones estructurales. Los edificios se han modelado incorporando la variabilidad de sus parámetros mecánicos y la demanda sísmica también se ha seleccionado teniendo en cuenta su incertidumbre. El análisis estructural se ha realizado utilizando y comparando diferentes procedimientos de cálculo estático no-lineal y utilizando el análisis dinámico no lineal incremental como referencia. Se ha realizado una discusión comparando los resultados y el grado de confiabilidad de los diferentes procedimientos utilizados en relación con la tipología de edificios de mampostería no reforzada. Se concluye que los métodos simplificados (i.e. estáticos no-lineales) sobrestiman el daño correspondiente a valores bajos de PGA, mientras que lo subestiman para valores elevados de PGA. Utilizando diferentes criterios, e incluyendo la consideración probabilista de las propiedades mecánicas, así como de la demanda sísmica, se ha caracterizado el daño predecible para estas estructuras mediante funciones de fragilidad y matrices e índices de daño y también se aporta un estudio de la correlación entre los parámetros mecánicos y el daño observado, a partir del cual se observa que existe una alta correlación entre los resultados obtenidos y las variables aleatorias seleccionadas, siendo el módulo de Young, E, aquella que presenta los coeficientes de correlación más altos. Las dificultades comunes en cualquier trabajo que involucra muestras de gran tamaño en relación con la cantidad de recursos y tiempos de computación, han sido resueltas mediante el diseño de muestras adecuadas y suficientemente representativas, así como el empleo de métodos y herramientas de cómputo actuales, como lo son el cómputo paralelo y distribuido.Postprint (published version

Seismic assessment of high-rise URM buildings: a probabilistic approach

The definition of the seismic demand and the correct characterization of the mechanical properties of the materials are two of the major difficulties in the seismic damage assessment of unreinforced masonry buildings due to the large uncertainties and variability that they present. A seven-story unreinforced masonry building in Barcelona, Spain, is taken as a case-study and modeled as an isolated solid clay structure with unidirectional iron beams-brick vaults slabs and load-bearing walls. In order to overcome the material definition shortcomings, the compressive strength, Young modulus, shear modulus and shear strength are modeled as random variables. On the other hand, the seismic demand variability is addressed through a set of different ground motions selected with the conditional spectrum method and subsequently scaled to different levels of demand (pga) as the incremental dynamic analysis methodology suggests. Due to computational and time limitations, a sufficiently representative sample is selected firstly from the population of mechanical properties, and secondly from the population of dynamics analyses for each direction of analysis. The obtained results show the correlation and different grades of influence for each of the selected random variables and levels of seismic demand (pga).Postprint (published version

Seismic vulnerability of building aggregates in Barcelona

Almost half of the housing buildings of Barcelona were built before 1940. In the Eixample district, approximately the 65% of the buildings fit the main features of a building design based on unreinforced masonry (URM) without any consideration of the seismic action. The buildings of the Eixample district are not isolated, quite the opposite, they are built as a part of a squared aggregate (113,3m per 113,3m) which includes approximately 22 buildings. Since 1960, the major part of the demolished URM buildings has been substituted by reinforced concrete (RC) buildings. As a consequence of this substitution, we expect a change in the seismic vulnerability of the buildings aggregate. In order to evaluate changes in the dynamic behavior of an aggregate, we performed different pushover analysis using the TreMuri software. A comparison of results corresponding to aggregates of URM-buildings and aggregates including RC-buildings is presented.Postprint (published version

Seismic damage assessment of URM buildings: a comparison of non-linear static procedures

In the scientific literature, a significant number of non-linear procedures are proposed in order to evaluate the seismic vulnerability of a building. In this work, and in the context of the Risk-UE methodology, a complete comparison of six representative nonlinear procedures, applied to an unreinforced building, has been performed. The incremental dynamic analysis has been considered in order to provide a reference for comparisons. Additionally, the evaluation of the applicability and reliability of the nonlinear static procedures has been performed and, some simple modifications, oriented to improve their use, have been proposed. The seismic demand has been conveniently defined applying the conditional spectrum approach procedure. Two different methodologies were used in order to define the fragility curves. Accordingly, a complete comparison of the calculated damage indices and the damage curves, corresponding to the different considered peak ground acceleration values, has been undertaken. The comparison results let know that the damage curves obtained by performing the non-linear procedures and by applying the Risk-UE methodology tend to overestimate the damage corresponding to low values of the PGA while the damage related to higher values of the PGA is underestimated.Postprint (published version

Seismic vulnerability of building aggregates in Barcelona

Almost half of the housing buildings of Barcelona were built before 1940. In the Eixample district, approximately the 65% of the buildings fit the main features of a building design based on unreinforced masonry (URM) without any consideration of the seismic action. The buildings of the Eixample district are not isolated, quite the opposite, they are built as a part of a squared aggregate (113,3m per 113,3m) which includes approximately 22 buildings. Since 1960, the major part of the demolished URM buildings has been substituted by reinforced concrete (RC) buildings. As a consequence of this substitution, we expect a change in the seismic vulnerability of the buildings aggregate. In order to evaluate changes in the dynamic behavior of an aggregate, we performed different pushover analysis using the TreMuri software. A comparison of results corresponding to aggregates of URM-buildings and aggregates including RC-buildings is presented

Non-linear static procedures applied to high-rise residential URM buildings

© 2016 Springer Science+Business Media Dordrecht 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.Peer Reviewe