Tracking localized cracks in the computational analysis of masonry structures

Numerical methods aid significantly the engineering efforts towards the conservation of existing masonry structures and the design of new ones. Among them, macro-mechanical finite element methods based on the smeared crack approach are commonly preferred as an affordable choice for the analysis of large masonry structures. Nevertheless, they usu-ally result in a non-realistic representation of damage as smeared over large areas of the structure, which hampers the correct interpretation of the damage pattern. Additionally, a more critical pathology of this approach is the mesh-dependency, which influences nota-bly the safety and stability predictions. To overcome these limitations, this thesis proposes a novel computational tool based on the {enrichment} of the classical smeared crack approach with a local tracking algorithm. The objective of this localized damage model is the realistic and efficient non-linear anal-ysis of masonry structures with an enhanced representation of cracking. The non-linear behaviour of masonry is simulated through the adoption of a continuum damage mechanics model with two damage indices, allowing the differentiation between the tensile and compressive mechanical responses of masonry. In this context, a novel explicit formulation for the evolution of irreversible strains is proposed and implemented. Two new expressions are derived for the regularization of the tensile and compressive softening responses according to the crack-band approach, ensuring the mesh-size objec-tivity of the damage model. The simulation of the structural behaviour of masonry structures under versatile loading and boundary conditions necessitates some developments in the context of local tracking algorithms. To this end, this thesis presents the enhancement of local tracking algorithms with novel procedures that make possible the simulation of multiple, arbitrary and inter-secting cracking under monotonic and cyclic loading. Additionally, the effect of different crack propagation criteria is investigated and the selection among more than one potential failure planes is tackled. The proposed localized damage model is validated through the simulation of a series of structural examples. These vary from small-scale tests on concrete specimens with few dominant cracks, to medium and large-scale masonry structures with multiple tensile, shear and flexural cracking. The analyses are compared with analytical, experimental and numerical results obtained with alternative methods available in the literature. Overall, the localized damage model developed in this thesis largely improves the mesh-independency of the classical smeared crack approach and reproduces crack patterns and collapse mech-anisms in an efficient and realistic way.Los métodos numéricos son decisivos en la ingeniería para la conservación de estructuras de mampostería existentes y el diseño de estructuras nuevas. Entre ellos, los métodos macro-mecánicos de elementos finitos, basados en el concepto de fisuras distribuidas, son habitualmente los preferidos como opción asequible para el análisis de grandes estructuras de mampostería. Sin embargo, suelen resultar en a una representación poco realista del daño, distribuido en grandes áreas de la estructura, lo que impide la correcta interpretación del patrón de daño. Además, esta metodología presenta una patología más crítica, la dependencia de la malla, que influye notablemente en las predicciones de seguridad y estabilidad. Para superar estas limitaciones, esta tesis propone una nueva herramienta numérica basada en el enriquecimiento del clásico enfoque de fisuras distribuidas con un algoritmo de trazado local. El objetivo de este modelo de daño localizado es el análisis no-lineal de las estructuras de mampostería de manera realista y eficiente con una representación mejora-da de fisuras. El comportamiento no lineal de la mampostería se simula a través de la adopción de un modelo de mecánica de daño continuo con dos índices de daño, permitiendo la diferenciación entre las respuestas mecánicas de tensión y compresión de la mampostería. En este contexto, se propone e implementa una nueva formulación explícita para la evolución de deformaciones irreversibles. Se derivan dos nuevas expresiones para la regularización del ablandamiento de tracción y compresión según el ancho de banda de la fisura, garantizan-do la objetividad del modelo de daño al respecto del tamaño de la malla. La simulación del comportamiento estructural de las estructuras de mampostería en condiciones de carga y contorno generales precisa de algunos desarrollos en el contexto de los algoritmos locales de trazado. Con este objetivo, se presenta la mejora de los algoritmos locales de trazado con nuevos procedimientos que posibilitan la simulación de fisuración múltiple, arbitraria e secante bajo cargas monótonas y cíclicas. Además, se investiga el efecto de diferentes criterios de propagación de fisuras y se aborda la selección entre más de un plano de falla posible. El modelo de daño localizado propuesto se valida mediante la simulación de una serie de ejemplos estructurales. Éstos van desde pruebas a pequeña escala en probetas de hormigón, con pocas fisuras dominantes, hasta estructuras de mampostería de mediana y gran escala con fisuración múltiple de tracción, de cortante y de flexión. Los análisis se comparan con los resultados analíticos, experimentales y numéricos obtenidos con métodos alternativos disponibles en la literatura. El modelo de daño localizado mejora en gran medida la independencia de la malla del clásico método de fisuras distribuidas y reproduce patrones de daño y mecanismos de colapso de una manera eficiente y realist

Tracking localized cracks in the computational analysis of masonry structures

Tesi per compendi de publicacions.Numerical methods aid significantly the engineering efforts towards the conservation of existing masonry structures and the design of new ones. Among them, macro-mechanical finite element methods based on the smeared crack approach are commonly preferred as an affordable choice for the analysis of large masonry structures. Nevertheless, they usu-ally result in a non-realistic representation of damage as smeared over large areas of the structure, which hampers the correct interpretation of the damage pattern. Additionally, a more critical pathology of this approach is the mesh-dependency, which influences nota-bly the safety and stability predictions. To overcome these limitations, this thesis proposes a novel computational tool based on the {enrichment} of the classical smeared crack approach with a local tracking algorithm. The objective of this localized damage model is the realistic and efficient non-linear anal-ysis of masonry structures with an enhanced representation of cracking. The non-linear behaviour of masonry is simulated through the adoption of a continuum damage mechanics model with two damage indices, allowing the differentiation between the tensile and compressive mechanical responses of masonry. In this context, a novel explicit formulation for the evolution of irreversible strains is proposed and implemented. Two new expressions are derived for the regularization of the tensile and compressive softening responses according to the crack-band approach, ensuring the mesh-size objec-tivity of the damage model. The simulation of the structural behaviour of masonry structures under versatile loading and boundary conditions necessitates some developments in the context of local tracking algorithms. To this end, this thesis presents the enhancement of local tracking algorithms with novel procedures that make possible the simulation of multiple, arbitrary and inter-secting cracking under monotonic and cyclic loading. Additionally, the effect of different crack propagation criteria is investigated and the selection among more than one potential failure planes is tackled. The proposed localized damage model is validated through the simulation of a series of structural examples. These vary from small-scale tests on concrete specimens with few dominant cracks, to medium and large-scale masonry structures with multiple tensile, shear and flexural cracking. The analyses are compared with analytical, experimental and numerical results obtained with alternative methods available in the literature. Overall, the localized damage model developed in this thesis largely improves the mesh-independency of the classical smeared crack approach and reproduces crack patterns and collapse mech-anisms in an efficient and realistic way.Los métodos numéricos son decisivos en la ingeniería para la conservación de estructuras de mampostería existentes y el diseño de estructuras nuevas. Entre ellos, los métodos macro-mecánicos de elementos finitos, basados en el concepto de fisuras distribuidas, son habitualmente los preferidos como opción asequible para el análisis de grandes estructuras de mampostería. Sin embargo, suelen resultar en a una representación poco realista del daño, distribuido en grandes áreas de la estructura, lo que impide la correcta interpretación del patrón de daño. Además, esta metodología presenta una patología más crítica, la dependencia de la malla, que influye notablemente en las predicciones de seguridad y estabilidad. Para superar estas limitaciones, esta tesis propone una nueva herramienta numérica basada en el enriquecimiento del clásico enfoque de fisuras distribuidas con un algoritmo de trazado local. El objetivo de este modelo de daño localizado es el análisis no-lineal de las estructuras de mampostería de manera realista y eficiente con una representación mejora-da de fisuras. El comportamiento no lineal de la mampostería se simula a través de la adopción de un modelo de mecánica de daño continuo con dos índices de daño, permitiendo la diferenciación entre las respuestas mecánicas de tensión y compresión de la mampostería. En este contexto, se propone e implementa una nueva formulación explícita para la evolución de deformaciones irreversibles. Se derivan dos nuevas expresiones para la regularización del ablandamiento de tracción y compresión según el ancho de banda de la fisura, garantizan-do la objetividad del modelo de daño al respecto del tamaño de la malla. La simulación del comportamiento estructural de las estructuras de mampostería en condiciones de carga y contorno generales precisa de algunos desarrollos en el contexto de los algoritmos locales de trazado. Con este objetivo, se presenta la mejora de los algoritmos locales de trazado con nuevos procedimientos que posibilitan la simulación de fisuración múltiple, arbitraria e secante bajo cargas monótonas y cíclicas. Además, se investiga el efecto de diferentes criterios de propagación de fisuras y se aborda la selección entre más de un plano de falla posible. El modelo de daño localizado propuesto se valida mediante la simulación de una serie de ejemplos estructurales. Éstos van desde pruebas a pequeña escala en probetas de hormigón, con pocas fisuras dominantes, hasta estructuras de mampostería de mediana y gran escala con fisuración múltiple de tracción, de cortante y de flexión. Los análisis se comparan con los resultados analíticos, experimentales y numéricos obtenidos con métodos alternativos disponibles en la literatura. El modelo de daño localizado mejora en gran medida la independencia de la malla del clásico método de fisuras distribuidas y reproduce patrones de daño y mecanismos de colapso de una manera eficiente y realistaPostprint (published version

Nonlinear numerical modelling of complex masonry heritage structures considering history-related phenomena in staged construction analysis and material uncertainty in seismic assessment

This material may be downloaded for personal use only. Any other use requires prior permission of the American Society of Civil Engineers. This material may be found at https://ascelibrary.org/doi/abs/10.1061/%28ASCE%29CF.1943-5509.0001494.This paper presents the systematic use of numerical analysis as a tool for addressing some of the most common challenges encountered in the structural analysis of complex historical masonry structures, i.e. the description of the effects of history-related phenomena and the un-certainty of material properties. The numerical strategy is based on the use of a constitutive model able to describe time-dependent strain accumulation, as well as damaging behaviour un-der different stress states. This constitutive model is combined with a crack-tracking technique to represent tensile crack localization. The numerical model is applied to the study of two im-portant monuments in Spain, i.e. the Mallorca Cathedral and the church of the Poblet Monas-tery. The staged construction analysis of the first case study allows understanding the reasons of its current deformed condition, i.e. critical construction process, strain accumulation given by long-term creep phenomena, and nonlinear geometric effects. The structural analysis of the second case study allows the structural diagnosis of the existing deformation and cracking pat-terns given by architectural alterations, insufficient buttressing of the naves, and past earth-quakes. The application of a probabilistic analysis to the church of the Poblet monastery allows considering the effects of the uncertainties of material properties and numerical parameters in the seismic vulnerability assessment.The authors would like to thank the Ministry of Science, Innovation and Universities (MCIU) of the Spanish Government, the State Agency of Research (AEI) and the European Regional Development Fund (ERDF) through the SEVERUS project (Multilevel evaluation of seismic vulnerability and risk mitigation of masonry buildings in resilient historical urban cen-tres ref. num. RTI2018-099589-BI00).Peer ReviewedPostprint (author's final draft

Seismic vulnerability assessment method for vernacular architecture considering uncertainty

Built vernacular heritage embraces buildings that are not designed by specialists, but are part of a process that involves many people over many generations and relies on empirical knowledge. Its value as a key-element for cultural identity is unquestionable. However, precisely due to its empirical and traditional nature, it is often seen as an obsolete and unsafe way of construction, which leads to its progressive abandonment. This lack of proper construction details and poor maintenance increases the seismic vulnerability of the vernacular heritage. There is an evident need for simplified easy-to-use seismic vulnerability assessment methods for vernacular architecture, given the generalized lack of resources that can be normally assigned to its study and preservation. Most of the times, visual inspection will be the only tool available to carry out the assessment.Postprint (published version

Cylindrical samples of brick masonry with aerial lime mortar under compression: experimental and numerical study

This research presents an experimental and numerical study focusing on the compression test of cylindrical samples core drilled from existing masonry walls. This method is suitable for the minor destructive assessment of the mechanical properties of historical masonry, like that composed of aerial lime mortar joints and solid clay bricks. This particular material combination, frequently found in the vast majority of the built cultural heritage, was utilized to build representative specimens that were stored in the laboratory for one year until their testing. Cylindrical samples of 150 mm diameter were extracted from the masonry walls by using a dry core-drilling procedure, and then regularized to be tested under compression in the laboratory. A comparison is presented between the experimental results on cylindrical samples and those obtained from standard compression tests on prismatic samples consisting in stack bond prisms. Numerical simulations by finite element micro-modelling of the compression tests on the core samples were carried out to investigate the experimental behaviour of the specimens and evaluate the compressive strength of the material from this nonstandard technique. The combined experimental and numerical study allows the assessment of important mechanical parameters for the compressive characterisation of masonry composed of aerial lime mortar joints and solid clay bricks.Peer ReviewedPostprint (author's final draft

Challenges, tools and applications of tracking algorithms in the numerical modelling of cracks in concrete and masonry structures

The final publication is available at Springer via http://dx.doi.org/10.1007/s11831-018-9274-3The importance of crack propagation in the structural behaviour of concrete and masonry structures has led to the development of a wide range of finite element methods for crack simulation. A common standpoint in many of them is the use of tracking algorithms, which identify and designate the location of cracks within the analysed structure. In this way, the crack modelling techniques, smeared or discrete, are applied only to a restricted part of the discretized domain. This paper presents a review of finite element approaches to cracking focusing on the development and use of tracking algorithms. These are presented in four categories according to the information necessary for the definition and storage of the crack-path. In addition to that, the most utilised criteria for the selection of the crack propagation direction are summarized. The various algorithmic issues involved in the development of a tracking algorithm are discussed through the presentation of a local tracking algorithm based on the smeared crack approach. Challenges such as the modelling of arbitrary and multiple cracks propagating towards more than one direction, as well as multi-directional and intersecting cracking, are detailed. The presented numerical model is applied to the analysis of small- and large-scale masonry and concrete structures under monotonic and cyclic loading.Peer ReviewedPostprint (author's final draft

Assessment of structural damage in historical constructions using numerical models : the case of the church of the Poblet Monastery

This paper presents the assessment of the structural damage and stability of the church of the Royal Monastery of Santa Maria de Poblet, one of the UNESCO World Heritage sites in Spain. The structure presents damage affecting mostly the main nave and lateral aisles, including cracking in the vaults and significant deformation in the clerestory walls and the barrel vault of the main nave. Following the historical survey, a sophisticated finite element model was used for the structural analysis of a damaged bay of the church. The 3D model was developed on the basis of the results of a terrestrial laser-scanning survey. In this way, the current deformed state of the structure was taken into consideration in the performed analyses. A continuum damage model allowed a realistic representation of the masonry behavior under tension and compression, which is a key factor for the assessment of masonry structures. The simulation of past reported or possible actions i.e. earthquakes, structural alterations and settlements provided valuable information on the causes of the present deformation and damage of the church. The influence of the material parameters in the structural response was evaluated with a detailed parametrical analysis. The paper ends with the graphic statics solution for the structure and a comparison with the equivalent finite element analysis outcomesPeer ReviewedPostprint (author’s final draft

Experimental setup and numerical evaluation of the compression test on thin tiles for masonry timbrel vaults

Compressive tests on clay tiles used in historical masonry timbrel vaults are hindered by the relatively small thickness of the specimens, resulting in buckling or confinement problems depending on the loading direction. This paper presents an experimental campaign and a numerical validation of a novel testing setup for estimating the compressive strength of thin clay tiles used in timbrel vaults. The experimental campaign focuses on two different types corresponding to historical and modern handmade tiles. Experimental and numerical results show that the proposed test setup can be used for the estimation of the compressive strength of thin clay tiles.The authors gratefully acknowledge the financial support from the Ministry of Science, Innovation and Universities of the Spanish Government (MCIU), the State Agency of Research (AEI) as well as that of the ERDF (European Regional Development Fund) through the project SEVERUS (Multilevel evaluation of seismic vulnerability and risk mitigation of masonry buildings in resilient historical urban centres, ref. Num. RTI2018-099589-B-I00). Support from MCIU through a predoctoral grant awarded to the first author is also gratefully acknowledged.Peer ReviewedObjectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats SosteniblesObjectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles::11.4 - Redoblar els esforços per a protegir i salvaguardar el patrimoni cultural i natural del mónPostprint (published version

Out-of-plane seismic response and failure mechanism of masonry structures using finite elements with enhanced strain accuracy

The out-of-plane response is a complex and at the same time key aspect of the seismic vulnerability of masonry structures. It depends on several factors, some of which are the material properties, the quality of the walls, the geometry of the structure, the connections between structural elements and the stiffness of the diaphragms. During the last years, a wide variety of numerical methods has been employed to assess the out-of-plane behaviour of unreinforced masonry structures. Finite element macro-modelling approaches are among the most famous as they allow modelling large structures at a reasonable computational cost. However, macro-modelling approaches may result in a non-realistic representation of localized cracks and a dependency of the numerical solution on the finite element mesh. Mixed strain/displacement finite elements have been recently proposed as a remedy to the above nu-merical pathologies. Due to the independent interpolation of strains and displacements these finite element formulations are characterized by an enhanced accuracy in strain localization and crack propagation problems, being at the same time practically mesh independent. For these reasons, mixed finite elements are employed in this work for the out-of-plane assessment of unreinforced masonry struc-tures, being at the same time their first real-scale application. A full-scale experimental campaign of two masonry structures, a stone and a brick one, subjected to shaking-table tests is chosen as reference benchmark. Their structural response under seismic actions is numerically assessed through nonlinear static analysis. The proposed approach is validated through the comparison of the numerical results with the experimental ones, as well as with the results obtained using standard irreducible finite ele-ments.Peer ReviewedPostprint (author's final draft

Analytical derivation of seismic fragility curves for historical masonry structures based on stochastic analysis of uncertain material parameters

This is an Accepted Manuscript of an article published by Taylor & Francis Group in International Journal of Architectural Heritage on 2019, available online at: http://www.tandfonline.com/10.1080/15583058.2019.1638992This work presents a probabilistic method to assess the seismic vulnerability of historical masonry structures, such as churches or cathedrals, including uncertainty analysis of the material parameters. The proposed approach considers the pushover analysis using the finite element method for the structural evaluation of the seismic behaviour of masonry structures. A stochastic analysis based on Monte Carlo simulation investigates the effect of the uncertainty of the structural members’ mechanical parameters on the evaluation of the seismic fragility. The method is applied to the seismic assessment of the bay structure of Santa Maria del Mar church in Barcelona, Spain. This case study is characterised by complex geometry and material heterogeneity, and shows to be sensitive enough to the uncertainty of the material properties to experience two possible collapse mechanisms in case of an earthquake. The study presents how to derive analytical seismic fragility curves by considering the uncertainties regarding the material properties and the different types of collapse mechanism.Peer ReviewedPostprint (author's final draft