Modélisation des murs en maçonnerie sous sollicitations sismiques

Developed. The method is based on the two-dimensional micropolar continuum theory and makes use of the kinematic approach of limit analysis in conjunction with a rigorous homogenization technique. The method is introduced in a general way, with regard to the genericclass of discrete periodic media made of particles of the same type. The case of masonry is presented as application. The homogenised strength domains of masonry columns and walls are retrieved in terms of the generalized stresses and couple stresses of the Cosserat continuum. The formulation of the method based on the Cosserat continuum enables the investigation of the influence of the relative rotation of the particles on the strength of the discrete medium. This influence is illustrated by the application to masonry structures, in comparison with other methods presented in the literature. The development of the homogenisation method continues with its extension to discrete periodic media made of particles disposed along three directions and showing three periodicity vectors. In this case, the approach relies on the three-dimensional micropolar theory. This enables to capture the three-dimensional effect of the relative translations and rotations of the particles constituting the discrete medium. The application to masonry columns and walls shows how the in-plane and out-of-plane actions result coupled in the assessment of masonry strength. The relative rotation of the blocks accentuates this effect, which consistently diminishes the in-plane strength. Masonry walls are finally ascribed to homogenised plates with Cosserat kinematics. A finite element formulation for Cosserat plate models is next developed. The formulation is first presented for elasticity and dynamics. The validation of a specific finite element is made by means of numerical benchmarks and patch tests. The actual use of the element is presented in an application to masonry structures. The natural frequencies of a masonry panel modelled by discrete elements are computed and compared with those given by a homogenisation model implemented in the element. This allows to investigate the role of the in-plane rotations of the blocks and to show their implication towards seismic analyses of masonry structures. The finite element formulation is next extended to the elastoplastic framework. The implementation of the multisurface plasticity theory into the Cosserat finite element is presented. The implementation of this theory is based on a projection algorithm. An important limitation of the classical implementation of this algorithm prevents its use in the framework of multisurface plasticity in efficient way. This limitation is discussed and a solution strategy is proposed. The finite element for Cosserat plate models is finally validated through numerous numerical benchmarks. In conclusion, three different modelling approaches for masonry are proposed and comviipared. A continuum model based on the Cosserat continuum is first presented. The model isconstructed by implementing the homogenised yield criteria computed based on the proposed analytical method into the developed finite element. A homogenisation model based on Cauchy continuum is next introduced. This model is constructed by selecting appropriate constitutive laws and yield criteria from the literature. The performance of those homogenisation models in representing the elastoplastic response of a masonry panel is discussed, based on the comparison with a third analogue discrete elements model. The capability of the three models in predicting the scale effect in the formation of failure mechanisms is investigated in a practical application to masonry structuresDans un premier temps, la méthode est présentée pour le cas bidimensionnel. La méthode est introduite de manière générale, en ce qui concerne les milieux discrets périodiques. L’application à la maçonnerie est ensuite abordée. La résistance homogénéisée de colonnes et murs de maçonnerie est calculée en termes de contraintes et couples-contraintes généralisées du milieu continu de Cosserat. La formulation d’une méthode basée sur le milieu de Cosserat permet la prise en compte de l’influence de la rotation relative des particules du milieu discret. Cette influence est mise en évidence à travers l’application à la maçonnerie, en comparaison avec les autres méthodes présentes dans la littérature. Dans un deuxième temps, la méthode est étendue au cas tridimensionnel. Des milieux discrets périodiques ayant leurs particules disposées le long de trois directions spatiales et montrant trois vecteurs de périodicité sont alors considérés. L’extension de la méthode s’inscrit dans le cadre de la théorie micropolaire tridimensionnelle. Cela permet la prise en compte des effets 3Dde la translation et la rotation relative des particules. L’application aux colonnes et aux murs de maçonnerie montre comment la résistance dans le plan et hors-plan de la maçonnerie sont, par ces effets, couplées. La rotation relative des blocs accentue cette interaction, qui comporte une diminution de la résistance dans-le-plan précédemment calculée. Les murs de maçonnerie sont ici décrits par des modèles de plaque micropolaire. Une formulation aux éléments finis pour des modèles de plaque micropolaire est ensuite développée. Dans un premier temps, la formulation est présentée pour l’élasticité et la dynamique. La validation d’un élément fini spécifique pour le calcul des structures est faite à l’aide d’exemples numériques. L’utilisation de cet élément sur des structures de maçonnerie est ensuite abordée, par l’implémentation d’un modèle d’homogénéisation déjà existant. Les fréquences fondamentales d’un mur maçonné sont ainsi calculées et comparées avec celle obtenues par un modèles aux éléments discrets. L’importance des rotations des blocs dans le plan du mur ainsi que leur participation dans la réponse inertielle du mur vis-à-vis des actions sismiques sont enfin investiguées. Dans un deuxième temps, la formulation aux élements finis est étendue à la plasticité, à travers l’implémentation de la théorie multi-critère pour les milieux de Cosserat. L’implémentation de cette théorie est basée sur un algorithme de projection, dont le schéma itératif de résolution est reporté. Les aspects numériques reliés à l’implémentation de l’algorithme sont examinés. Une importante limitation de l’implémentation classique de l’algoritme est montrée et une nouvelle stratégie de solution est proposée. L’élément fini de Cosserat est donc validé pour la plasticite à l’aide de nombreux exemples numériques. En conclusion, trois approches de modélisation pour les structures de maçonnerie sont proposéeset comparées. Un model continu d’homogénéisation basée sur le milieu de Cosserat est d’abord présenté. Le modèle est construit en introduisant les critères de ruptures homogénéisés calculés dans la première partie du travail dans l’élément fini développé dans la deuxième partie du travail. Un modèle continu basée sur le milieu de Cauchy est ensuite considéré. Ce denier est construit à partir de modèles déjà présents dans la littérature. L’efficacité de ces deux modèles est examinée dans la représentation du comportement élastoplastique d’un mur de maçonnerie. Leur comparaison se base sur un troisième modèle, crée à l’aide des éléments discrets. La capacité des trois modèles de modéliser l’effet d’échelle dans la formation des mécanismes de ruine est enfin investiguée sur une application pratique aux structures de maçonneri

Quantifying the out-of-plane response of unreinforced masonry walls subjected to relative support motion

TThe supports of out-of-plane loaded unreinforced masonry walls in buildings are subjected to a motion that is filtered and amplified by the building structure and, in some cases, can be significantly different from the ground motion. Moreover, because these walls span one or several storeys, their top and bottom supports are subjected to motions that differ in phase and amplitude. In state-of-the-art assessment procedures for the out-of-plane stability of masonry walls any effect of a relative support motion is neglected. The objective of this paper is to study the effect of the relative support motion on the response of out-of-plane loaded vertically-spanning unreinforced masonry walls. The acceleration capacity of the walls is investigated by means of a discrete element model representative of different wall configurations. A set of ground motions covering a wide range of peak ground acceleration and peak ground displacement is used as input to the simulations. The relative motion between the wall supports is included in the model in a systematic way: firstly, through a motion that is non-synchronous but of equal amplitude; secondly, through a motion that is synchronous but of different amplitude. The effect of the relative support motion is studied on different wall configurations where the elastic modulus of masonry, the wall height-to-thickness ratio, the wall effective thickness and the overburden at the top wall are varied. The study shows that, because of the relative support motion, the acceleration capacity of the walls can drop by 20% and, in the cases where the overburden is high, by more than 50%

Analytical model for the out-of-plane response of vertically spanning unreinforced masonry walls

An analytical model describing the flexural response of vertically spanning out-of-plane loaded unreinforced masonry walls is presented in this paper. The model is based on the second-order Euler-Bernoulli beam theory and captures important characteristics of the out-of-plane response of masonry walls that have been observed in experimental tests and from numerical studies but for which an analytical solution was still lacking: the onset and the evolution of cracking, the peak strength of the out-of-plane loaded walls, and the softening of the response due to P−Δ effects. The model is validated against experimental results, and the comparison shows that the model captures both the prepeak and postpeak response of the walls. From the analytical model of the force-displacement curve, a formula for the maximum out-of-plane strength of the walls is derived, which can be directly applied in engineering practice

A Mouse Model of Pulmonary Metastasis from Spontaneous Osteosarcoma Monitored In Vivo by Luciferase Imaging

BACKGROUND: Osteosarcoma (OSA) is lethal when metastatic after chemotherapy and/or surgical treatment. Thus animal models are necessary to study the OSA metastatic spread and to validate novel therapies able to control the systemic disease. We report the development of a syngeneic (Balb/c) murine OSA model, using a cell line derived from a spontaneous murine tumor. METHODOLOGY: The tumorigenic and metastatic ability of OSA cell lines were assayed after orthotopic injection in mice distal femur. Expression profiling was carried out to characterize the parental and metastatic cell lines. Cells from metastases were propagated and engineered to express Luciferase, in order to follow metastases in vivo. PRINCIPAL FINDINGS: Luciferase bioluminescence allowed to monitor the primary tumor growth and revealed the appearance of spontaneous pulmonary metastases. In vivo assays showed that metastasis is a stable property of metastatic OSA cell lines after both propagation in culture and luciferase trasduction. When compared to parental cell line, both unmodified and genetically marked metastatic cells, showed comparable and stable differential expression of the enpp4, pfn2 and prkcd genes, already associated to the metastatic phenotype in human cancer. CONCLUSIONS: This OSA animal model faithfully recapitulates some of the most important features of the human malignancy, such as lung metastatization. Moreover, the non-invasive imaging allows monitoring the tumor progression in living mice. A great asset of this model is the metastatic phenotype, which is a stable property, not modifiable after genetic manipulation

Shake‑table testing of a stone masonry building aggregate: overview of blind prediction study

City centres of Europe are often composed of unreinforced masonry structural aggregates, whose seismic response is challenging to predict. To advance the state of the art on the seismic response of these aggregates, the Adjacent Interacting Masonry Structures (AIMS) subproject from Horizon 2020 project Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe (SERA) provides shake-table test data of a two-unit, double-leaf stone masonry aggregate subjected to two horizontal components of dynamic excitation. A blind prediction was organized with participants from academia and industry to test modelling approaches and assumptions and to learn about the extent of uncertainty in modelling for such masonry aggregates. The participants were provided with the full set of material and geometrical data, construction details and original seismic input and asked to predict prior to the test the expected seismic response in terms of damage mechanisms, base-shear forces, and roof displacements. The modelling approaches used differ significantly in the level of detail and the modelling assumptions. This paper provides an overview of the adopted modelling approaches and their subsequent predictions. It further discusses the range of assumptions made when modelling masonry walls, floors and connections, and aims at discovering how the common solutions regarding modelling masonry in general, and masonry aggregates in particular, affect the results. The results are evaluated both in terms of damage mechanisms, base shear forces, displacements and interface openings in both directions, and then compared with the experimental results. The modelling approaches featuring Discrete Element Method (DEM) led to the best predictions in terms of displacements, while a submission using rigid block limit analysis led to the best prediction in terms of damage mechanisms. Large coefficients of variation of predicted displacements and general underestimation of displacements in comparison with experimental results, except for DEM models, highlight the need for further consensus building on suitable modelling assumptions for such masonry aggregates

Modelling of masonry walls under seismic loadings

Dans un premier temps, la méthode est présentée pour le cas bidimensionnel. La méthode est introduite de manière générale, en ce qui concerne les milieux discrets périodiques. L’application à la maçonnerie est ensuite abordée. La résistance homogénéisée de colonnes et murs de maçonnerie est calculée en termes de contraintes et couples-contraintes généralisées du milieu continu de Cosserat. La formulation d’une méthode basée sur le milieu de Cosserat permet la prise en compte de l’influence de la rotation relative des particules du milieu discret. Cette influence est mise en évidence à travers l’application à la maçonnerie, en comparaison avec les autres méthodes présentes dans la littérature. Dans un deuxième temps, la méthode est étendue au cas tridimensionnel. Des milieux discrets périodiques ayant leurs particules disposées le long de trois directions spatiales et montrant trois vecteurs de périodicité sont alors considérés. L’extension de la méthode s’inscrit dans le cadre de la théorie micropolaire tridimensionnelle. Cela permet la prise en compte des effets 3Dde la translation et la rotation relative des particules. L’application aux colonnes et aux murs de maçonnerie montre comment la résistance dans le plan et hors-plan de la maçonnerie sont, par ces effets, couplées. La rotation relative des blocs accentue cette interaction, qui comporte une diminution de la résistance dans-le-plan précédemment calculée. Les murs de maçonnerie sont ici décrits par des modèles de plaque micropolaire. Une formulation aux éléments finis pour des modèles de plaque micropolaire est ensuite développée. Dans un premier temps, la formulation est présentée pour l’élasticité et la dynamique. La validation d’un élément fini spécifique pour le calcul des structures est faite à l’aide d’exemples numériques. L’utilisation de cet élément sur des structures de maçonnerie est ensuite abordée, par l’implémentation d’un modèle d’homogénéisation déjà existant. Les fréquences fondamentales d’un mur maçonné sont ainsi calculées et comparées avec celle obtenues par un modèles aux éléments discrets. L’importance des rotations des blocs dans le plan du mur ainsi que leur participation dans la réponse inertielle du mur vis-à-vis des actions sismiques sont enfin investiguées. Dans un deuxième temps, la formulation aux élements finis est étendue à la plasticité, à travers l’implémentation de la théorie multi-critère pour les milieux de Cosserat. L’implémentation de cette théorie est basée sur un algorithme de projection, dont le schéma itératif de résolution est reporté. Les aspects numériques reliés à l’implémentation de l’algorithme sont examinés. Une importante limitation de l’implémentation classique de l’algoritme est montrée et une nouvelle stratégie de solution est proposée. L’élément fini de Cosserat est donc validé pour la plasticite à l’aide de nombreux exemples numériques. En conclusion, trois approches de modélisation pour les structures de maçonnerie sont proposéeset comparées. Un model continu d’homogénéisation basée sur le milieu de Cosserat est d’abord présenté. Le modèle est construit en introduisant les critères de ruptures homogénéisés calculés dans la première partie du travail dans l’élément fini développé dans la deuxième partie du travail. Un modèle continu basée sur le milieu de Cauchy est ensuite considéré. Ce denier est construit à partir de modèles déjà présents dans la littérature. L’efficacité de ces deux modèles est examinée dans la représentation du comportement élastoplastique d’un mur de maçonnerie. Leur comparaison se base sur un troisième modèle, crée à l’aide des éléments discrets. La capacité des trois modèles de modéliser l’effet d’échelle dans la formation des mécanismes de ruine est enfin investiguée sur une application pratique aux structures de maçonnerieDeveloped. The method is based on the two-dimensional micropolar continuum theory and makes use of the kinematic approach of limit analysis in conjunction with a rigorous homogenization technique. The method is introduced in a general way, with regard to the genericclass of discrete periodic media made of particles of the same type. The case of masonry is presented as application. The homogenised strength domains of masonry columns and walls are retrieved in terms of the generalized stresses and couple stresses of the Cosserat continuum. The formulation of the method based on the Cosserat continuum enables the investigation of the influence of the relative rotation of the particles on the strength of the discrete medium. This influence is illustrated by the application to masonry structures, in comparison with other methods presented in the literature. The development of the homogenisation method continues with its extension to discrete periodic media made of particles disposed along three directions and showing three periodicity vectors. In this case, the approach relies on the three-dimensional micropolar theory. This enables to capture the three-dimensional effect of the relative translations and rotations of the particles constituting the discrete medium. The application to masonry columns and walls shows how the in-plane and out-of-plane actions result coupled in the assessment of masonry strength. The relative rotation of the blocks accentuates this effect, which consistently diminishes the in-plane strength. Masonry walls are finally ascribed to homogenised plates with Cosserat kinematics. A finite element formulation for Cosserat plate models is next developed. The formulation is first presented for elasticity and dynamics. The validation of a specific finite element is made by means of numerical benchmarks and patch tests. The actual use of the element is presented in an application to masonry structures. The natural frequencies of a masonry panel modelled by discrete elements are computed and compared with those given by a homogenisation model implemented in the element. This allows to investigate the role of the in-plane rotations of the blocks and to show their implication towards seismic analyses of masonry structures. The finite element formulation is next extended to the elastoplastic framework. The implementation of the multisurface plasticity theory into the Cosserat finite element is presented. The implementation of this theory is based on a projection algorithm. An important limitation of the classical implementation of this algorithm prevents its use in the framework of multisurface plasticity in efficient way. This limitation is discussed and a solution strategy is proposed. The finite element for Cosserat plate models is finally validated through numerous numerical benchmarks. In conclusion, three different modelling approaches for masonry are proposed and comviipared. A continuum model based on the Cosserat continuum is first presented. The model isconstructed by implementing the homogenised yield criteria computed based on the proposed analytical method into the developed finite element. A homogenisation model based on Cauchy continuum is next introduced. This model is constructed by selecting appropriate constitutive laws and yield criteria from the literature. The performance of those homogenisation models in representing the elastoplastic response of a masonry panel is discussed, based on the comparison with a third analogue discrete elements model. The capability of the three models in predicting the scale effect in the formation of failure mechanisms is investigated in a practical application to masonry structure

Tri-linear model for the out-of-plane seismic assessment of unreinforced masonry walls

A new model describing the response of vertically-spanning unreinforced masonry walls subjected to out-of-plane loading is presented. The model approximates the real behaviour of the walls by a tri-linear force-displacement relationship, which is suitable for engineering practice. Differently from the existing tri-linear models, which are mainly based on experimentally calibrated parameters, the present one relies on principles of mechanics. Its fully analytical formulation provides the potential for using it in the assessment of unreinforced masonry for a wide range of wall configurations and boundary conditions. The comparison of model simulations with experimental results from shake table tests documented in the literature validates the model for cantilever and parapet walls

Trilinear Model for the Out-of-Plane Seismic Assessment of Vertically Spanning Unreinforced Masonry Walls

Out-of-plane failure of masonry walls is often responsible for the partial collapse of unreinforced masonry structures. Modeling the out-of-plane response of these walls is therefore key in the assessment of existing buildings. The paper presents a new trilinear model describing the force-displacement response of vertically spanning unreinforced masonry walls subjected to out-of-plane loading. Different factors that affect the response of the walls are captured by the model: the support conditions, the level of applied axial load, the slenderness ratio, and the deformability of the wall. The model is validated against experimental results from shake table tests. The force and displacement parameters of the model are described by analytical expressions that are derived from a mechanical model previously developed for unreinforced masonry. They offer an alternative to existing trilinear models in which corner displacements are mainly defined by empirical relationships

Evaluation of force-based and displacement-based out-of-plane seismic assessment methods for unreinforced masonry walls through refined model simulations

The performance of force-based and displacement-based seismic assessment methods for the life-safety limit state check of out-of-plane loaded unreinforced masonry walls is evaluated on the basis of refined numerical simulations. For this purpose, a discrete element model of a vertically spanning wall is built and validated against experimental results from static and dynamic test conditions. The model is then analysed for a large range of wall configurations. For each configuration, a static pushover analysis and a series of incremental dynamic analyses are run, the latter permitting to determine the capacity of the wall under dynamic loading. The accuracy of the assessment methods in predicting the acceleration at which the walls collapse is evaluated. It is found that the displacement-based method is more accurate, robust, and safe than the force-based method. The comparison also shows that for walls characterised by a relatively high ratio of axial load to Euler's critical load, both assessment methods lead to an overestimation of the wall capacity. As a remedy, a modification to the methods based on a recently developed mechanical model is put forward and tested. For the force-based method, it is additionally suggested to set for walls with relatively high overburden ratios the behaviour factor equal to 1. To ensure reproducibility of this study, all input and output files of the numerical simulations are made publicly available