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Two approaches for the analysis of masonry structures: Micro and macro-modeling
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Two models for the micro- and macro-analysis of masonry structures are presented. For the micromodeling of masonry, an interface failure criterion that includes a straight tension cut-off, the Coulomb friction law and an elliptical cap is proposed. The inelastic behavior includes tensile strength softening, cohesion softening, compressive strength hardening/softening and coupling between tensile and shear failure. It is shown that the model is capable of describing the local interaction of both masonry components and of reproducing, in a detailed manner, observed experimental behavior. For the macro-modeling, an anisotropic continuum model that includes a Rankine type yield surface for tension and a Hill type yield surface for compression is proposed. Anisotropic elasticity is combined with anisotropic plasticity, in such a way that totally different behavior can be predicted along the material axes, both in tension and compression. It is shown that, for sufficiently large structures, the global response of masonry can be well predicted even without the inclusion of the local interaction between the masonry components.
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... Their research aimed to assess the effectiveness of the micro-modeling approach and assess the out-of-plane response of the masonry walls. As defined by Lourenço [12], micro-modeling is where "masonry units and mortar joints are represented by continuum elements, where the unit-mortar interface is represented by a discontinuous constitutive description". A quasi-static (transient dynamic) procedure was used for the numerical study. ...
... Due to the different compression or tensile strength of brick vs. mortar, it is worth noting that mortar joints become the weakest link in masonry walls. According to [12], the unit-mortar interface controls the nonlinear response of the joints, and this is one of the most pertinent features of masonry wall behavior. Different modeling techniques used to simulate the response of masonry structures are depicted schematically in Figure 3. modes will be used later in this article to verify the results that are obtained from the proposed numerical scheme. ...
... The mechanical behavior of masonry buildings has been described using two broad numerical approaches: macro-modeling and micro-modeling [12]. In the macro-modeling method, masonry is analyzed as a uniform material that obtains its average (effective) material properties by a homogenization scheme. ...
A numerical investigation of masonry walls subjected to blast loads is presented in this article. A non-linear finite element model is proposed to describe the structural response of the walls. A unilateral contact–friction law is used in the interfaces of the masonry blocks to provide the discrete failure between the blocks. A continuum damage plasticity model is also used to account for the compressive and tensile failure of the blocks. The main goal of this article is to investigate the different collapse mechanisms that arise as an effect of the blast load parameters and the static load of the wall. Parametric studies are conducted to evaluate the effect of the blast source–wall (standoff) distance and the blast weight on the structural response of the system. It is shown that the traditional in-plane diagonal cracking failure mode may still dominate when a blast action is present, depending on the considered standoff distance and the blast weight when in-plane static loading is also applied to the wall. It is also highlighted that the presence of an opening in the wall may significantly reduce the effect of the blasting action.
... Masonry walls are typically modeled using one of two general approaches, namely: micro-modeling, where the spatial discretization is performed at the detailed level of the brick or block units, head or perpend and bed mortar joints and the surface contact between them; and macro-modeling, where the discretization is made by regarding the material as a composite by establishing a relation between the average masonry stresses and strains and by neglecting the interaction between the brick or block units and mortar [13,16,17]. A detailed representation of masonry using the micro-modeling approach can give better results for small structural elements with highly heterogeneous states of stress and strain, but is usually time consuming and requires large memory for analysis [16]. ...
... Masonry walls are typically modeled using one of two general approaches, namely: micro-modeling, where the spatial discretization is performed at the detailed level of the brick or block units, head or perpend and bed mortar joints and the surface contact between them; and macro-modeling, where the discretization is made by regarding the material as a composite by establishing a relation between the average masonry stresses and strains and by neglecting the interaction between the brick or block units and mortar [13,16,17]. A detailed representation of masonry using the micro-modeling approach can give better results for small structural elements with highly heterogeneous states of stress and strain, but is usually time consuming and requires large memory for analysis [16]. Whereas, the macro-modeling approach is practice oriented and can give reasonable but perhaps less accurate results for modeling masonry walls with comparatively larger dimensions and uniform behavior, and has been used in this research. ...
A damage plasticity macro-model for the static and cyclic in-plane loading analysis of hollow and solid (mortar-filled) lightweight concrete block masonry shear walls is proposed. The model is used to simulate typical wall configurations for both plane walls and walls strengthened or reinforced with mortar infill. As a macro-model, the new damage plasticity method is suitable for practice oriented predictions, and can give reasonably good results with less demand on computation power as compared to typical micro-modeling approaches. Calibration of model parameters and numerical simulation results for typical lightweight concrete block masonry wall configurations performed using the finite element software ABAQUS are presented in the companion paper.
... The second approach is macro-modelling, which treats masonry as a homogenous material governed by isotropic or anisotropic laws. Lourenco [77] suggests using the simplified micro-modelling approach for smaller structures and macro-modelling approach for large masonry structures including CM. Micro-modeling can effectively describe the local interaction of masonry components, while macromodelling can predict the global response of masonry, even without considering local interaction between the masonry components. Eshghi and Pourazin [78] performed pushover analysis using 2D finite element CM models and found that cohesiveness between the RC members and the masonry panel is the primary reason why compressive strut in CM walls differs from strut in RC frames. ...
Confined masonry (CM) is a construction method comprising load bearing masonry walls confined with nominally reinforced concrete (RC) elements at the periphery of walls and other critical building locations. Thanks to its economic feasibility and similar construction practices, it has evolved as a viable alternative to unreinforced masonry (URM) and non-engineered RC construction. CM has gained widespread acceptance in several countries vulnerable to seismic activity, and has also garnered increased attention in other regions due to its demonstrated efficacy during previous earthquakes. The purpose of the paper is to summarize past research studies on various factors influencing CM performance, such as aspect ratio, toothing, longitudinal reinforcement in tie-columns, openings and wall density. Also, the manuscript highlights the existing analytical and numerical techniques used to analyse the CM structures. The review identifies existing knowledge gaps and emphasizes the need for further research to better understand the response of CM structures to seismic forces. Based on the comprehensive review, it was observed that an alternative construction material, including autoclaved aerated concrete (AAC) blocks, fly ash bricks, and lightweight cellular concrete blocks, as potential substitutes for traditional clay bricks in CM construction. It was also observed that the confined masonry has the potential to enhance the seismic performance and resistance of buildings and is a promising construction method. However, more investigation is required to optimize the materials and connections used, as the stiffness of the elements is influenced by the mechanical properties of the materials, as well as their geometry and boundary conditions.
... When using this method, the geometry is divided into simple subunits called finite elements, then each subunit behavior can be determined and system behavior can be understood. The method in question accuracy depends on the accuracy of the data used and the resulting should be predicted [5]. SAP2000, ANSYS for finite element modeling. ...
Existing commercial software (such as ANSYS or other similar software) can be used to efficiently model complicated masonry walls, according to the results of the study. The numerical simulations and calculations used in this study helped to improve our understanding of the structural response of unreinforced and TRM-strengthened masonry walls subjected to diagonal compressive. Masonry constructions are made up of masonry units (brick, stone, marble, etc.) that are joined together using mortar. The models are implemented in ANSYS software to simulate the structural behavior of a tested wall in literature. Brick and mortar are modeled separately in the micro model. The results obtained in the micro modeling and are inconsistent with the experimental study in the literature. The model is implemented in ANSYS and then used to simulate the structural behavior of a group of walls previously tested in a laboratory. The results obtained with the proposed model are in good accord with those obtained in laboratory tests for the five walls considered.
... Following the principles of simplified micro-modeling, the masonry units are expanded to include the 10 mm thickness of the mortar joints. This simplification is made to reduce the complexity of the model, reducing computation time (Lourenço, Rots, and Blaauwendraad 1995) A three-dimensional representation of the cross-vault is created using COMPAS Masonry, an open-source Python-based computational framework for evaluating masonry structures Van Mele 2022). Every single block in the masonry vault has been parametrically generated as a solid mesh, following the vault's stereotomy principles and replicating the discretization visible in the provided AutoCad outline of the vault. ...
The assessment of the seismic performance of unreinforced masonry cross-vaults is still a challenge in numerical analysis, due to complex curved geometries and bond patterns, and uncertainties related to the selection of adequate modeling strategies, including but not limited to that of material properties, damping scheme, and unit/joint idealization. This paper presents the results of a collaborative effort to validate, against the shake table test of both unstrengthened and strengthened masonry cross-vault specimens as part of the SERA Project Blind Prediction and Post-diction Competition, various discontinuum-based numerical approaches. First, the geometry of the cross-vault is created using a Python-based computational framework to accurately represent the brick arrangement and the shape of the vault. Then, the geometry is converted into an assemblage of deformable blocks and analyzed using the Distinct Element Method (DEM). An elasto-softening contact model based on fracture energy is implemented in the masonry joints to simulate crushing, tensile, and shear failures. The performance of the proposed strategy, conceived for the unstrengthened configuration of the tested vault specimen and then adapted to include the presence of cementitious repairs, shows satisfactory agreement with both qualitative and quantitative experimental responses, also revealing critical insights and lessons learned through the blind/post-prediction exercise.
... Block based methods, on the contrary, are able to deal with the particular stereotomy of structures, describing precisely the block interlocking, and have a more clear understanding of the effects of the block dimensions. Among these methods, the Distinct Element Method [5,6,7] is widely adopted in sequential-static and dynamic analyses. ...
... The elastic behavior is formulated based on linear traction-separation behavior, which is related to the damage in the expanded unit material. In general, the linear behavior of expanded units is expressed in the form of an elastic stiffness matrix [25]. ...
... The mechanical behavior of masonry can be investigated using different approaches [34], depending on the balance between accuracy level and both modeling and computation time: a detailed micro-modeling approach considering unit and mortar separately in the spatial discretization and, consequently, distinct constitutive relationships for each material and their interface [1,2,49]; a simplified micro-modeling approach considering expanded units and defining the constitutive relationships for unit and interface, already including the mortar [33,35,51]; and the macro-modeling approach [26,37,46,48,50], in which a constitutive relationship is used for masonry, intended as a homogenized material. The macro-modeling approach is often associated with the equivalent frame modeling strategy [32,38,50] for masonry buildings. ...
The use of new geo-sourced construction materials in seismic areas requires the assessment of the structure ductility in order to properly design the building. This research aims to propose a procedure for behavior factor estimation in case of using a new construction material. In particular, in this paper, the proposed methodology is applied to an unreinforced masonry building in an average-risk seismic zone. Before application for seismic design, the reliability of the selected equivalent frame modeling approach is validated by comparison of dynamic features obtained from both numerical and operational modal analysis. An existing stone masonry building is selected as case study to validate the modeling approach. A measurement campaign provides the structural response to ambient vibrations and structural damping. After validating the model in elastic conditions, the building ductility capacity is estimated using a numerical pushover analysis, for different load combinations and distributions, according to the European design code, under the assumption of perfect plasticity. The proposed procedure provides a behavior factor obtained specifically for the analyzed building, using a relationship between ductility demand and behavior factor deduced from dynamic analysis. The average ductility demand is estimated numerically, for a set of synthetic acceleration signals compatible with the Eurocode elastic response spectrum and a given behavior factor. Finally, it is suggested to verify the near collapse limit state of the building structure not only in terms of target to capacity displacement ratio but also in terms of load ratio, since it can be more restrictive in some instances.
... Micro-modeling represents a distinct approach, wherein micromechanics assume a pivotal role in predicting both localized and overall responses of the masonry while considering interface behavior and damage across different components. This method involves characterizing units and mortar within joints using continuum elements, whereas the interface between units and mortar is modeled using discontinuum elements [46,47]. While this approach indeed offers higher accuracy, its level of complexity and the computational demands it imposes restrict its applicability to scenarios such as smallscale laboratory specimens and structures. ...
Two earthquakes struck the NW region of Albanian territory on 21 September 2019 (Mw = 5.6) and on 26 November 2019 (Mw = 6.4). The epicenters of the seismic activity were located offshore NW Durrës, one of Albania's most populated cities, located 30 km from the capital Tirana. Various aftershocks followed subsequently. While there were no reported injuries, a number of buildings sustained significant damage near the epicenter following the initial event. Subsequently, during the second event, there was loss of life and extensive damage to civilian structures, resulting in multiple collapses. This study focuses on the earthquake damages observed in residential and public buildings in the earthquake-affected region. The earthquakes predominantly affected low-rise masonry buildings, while the newly constructed RC structures built according to the latest seismic rules were almost unaffected. The commonly encountered building typologies in the region, together with photos showing the amount of destruction are presented here. As observed by the authors during the reconnaissance visit to the stricken area, examples of various damage patterns are presented, along with a technically substantiated description of the reasons for those damages. Although modern buildings during recent earthquakes in the region show acceptable performance, the detailed surveys from the Durrës Earthquakes showed that there is still an important level of deficiency in current masonry buildings built by conventional methods and materials. This problem may reoccur in future earthquakes that may hit other rural regions of Albania, which must be focused on systematically in the near future.
The demand for advanced nonlinear time‐history and seismic collapse simulations of old unreinforced masonry (URM) constructions to support informed risk evaluation and mitigation plans is rapidly increasing in the structural engineering profession. On one hand, offering cutting‐edge solutions based on the latest advances is challenging for practitioners, given the reduced timeframe usually available for projects and the specialized knowledge required. On the other hand, researchers frequently face difficulties in accessing old buildings and gathering key data required in complex numerical collapse analysis strategies. In this work, a pragmatic approach for evaluation of the earthquake collapse response of vulnerable old URM churches typical of the Northern Netherlands, now exposed to low‐magnitude induced seismicity due to gas extraction, is presented. To bridge the gap between academic and industry applications, an integrated framework is proposed that combines archival and onsite research, code‐based prescriptions, geometrical characterization and simplified discrete element modeling. Main outcomes include the identification of recurrent damage patterns for five old URM churches erected during the 11th, 13th, 14th, and 19th centuries, representative of key traditional multi‐leaf and cavity‐wall structural types, as well as relevant failure mechanisms and collapsed debris distributions for seismic signals of varying intensities. Produced results constitute a solid foundation of data on which to base the design of ad‐hoc retrofits and development of tailored risk assessment models. This study opens a new line of inquiry while discussing practical challenges and research questions which arose, to be of interest to both applied researchers and structural engineering professionals.
This paper describes a series of biaxial compression tests on half-scale brickwork. Tests were performed on square brickwork panels with the principal compressive stresses oriented at various angles to the bed joints, and a failure surface was obtained in terms of these parameters. Two distinct modes of failure were observed depending on the ratio of the principal stresses, with the influence of the bed joints being significant only when one principal stress predominated.
A fracture theory for a heterogenous aggregate material which exhibits a gradual strain-softening due to microcracking and
contains aggregate pieces that are not necessarily small compared to structural dimensions is developed. Only Mode I is considered.
The fracture is modeled as a blunt smeard crack band, which is justified by the random nature of the microstructure. Simple
triaxial stress-strain relations which model the strain-softening and describe the effect of gradual microcracking in the
crack band are derived. It is shown that it is easier to use compliance rather than stiffness matrices and that it suffices
to adjust a single diagonal term of the complicance matrix. The limiting case of this matrix for complete (continuous) cracking
is shown to be identical to the inverse of the well-known stiffness matrix for a perfectly cracked material. The material
fracture properties are characterized by only three parameters—fracture energy, uniaxial strength limit and width of the crack
band (fracture process zone), while the strain-softening modulus is a function of these parameters. A method of determining
the fracture energy from measured complete stres-strain relations is also given. Triaxial stress effects on fracture can be
taken into account. The theory is verified by comparisons with numerous experimental data from the literature. Satisfactory
fits of maximum load data as well as resistance curves are achieved and values of the three material parameters involved,
namely the fracture energy, the strength, and the width of crack band front, are determined from test data. The optimum value
of the latter width is found to be about 3 aggregate sizes, which is also justified as the minimum acceptable for a homogeneous
continuum modeling. The method of implementing the theory in a finite element code is also indicated, and rules for achieving
objectivity of results with regard to the analyst's choice of element size are given. Finally, a simple formula is derived
to predict from the tensile strength and aggregate size the fracture energy, as well as the strain-softening modulus. A statistical
analysis of the errors reveals a drastic improvement compared to the linear fracture theory as well as the strength theory.
The applicability of fracture mechanics to concrete is thus solidly established.
On présente une théorie de la rupture pour un matériau hétérogène à granulats qui montre une déformation avec radoucissement
causé par microfissuration et qui renferme des granulats dont les dimensions peuvent n'être pas petites par rapport à celles
de la structure. On ne considère que le mode I. La rupture est modélisée comme une bande de microfissures parallèles à front
obtus, ce qui se justifie par le caractère aléatoire de la microfissuration. On déduit des relations simples de contrainte/déformation
triaxiales qui modélisent des déformations à radoucissement et décrivent l'effet de la microfissuration graduelle dans la
zone de fissures parallèles. On démontre qu'il est plus facile d'utiliser les matrices de compliance que de rigidité et qu'il
suffit d'ajuster un simple élément diagonal de la matrice de compliance. On verra qu'à la limite cette matrice pour une fissuration
continue est identique à l'inverse de la bien connue matrice de rigidité pour un matériau parfaitement fissuré. Les propriétés
de rupture du matériau ne sont caractérisées que par trois paramètres: énergie de rupture, limite de résistance uniaxiale
et largeur de la bande de fissuration (zone où intervient la rupture), le module de radoucissement de déformation étant une
fonction de ces paramètres. On donne aussi une méthode pour déterminer l'énergie de rupture d'après les relations complètes
contrainte/déformation mesurées. On peut prendre en compte les effets sur la rupture des contraintes triaxiales.
La théorie se vérifie au moyen de comparaisons avec les nombreux résultats expérimentaux publiés. On obtient de bonnes concordances
tant pour les données de charges maximales que pour les courbes de résistance; les valeurs des trois paramètres de matériau
en jeu, soit, l'énergie de rupture, la résistance, la largeur du front de la bande fissuration sont déterminées d'après les
résultats d'essai. Il apparaît que la valeur optimale du dernier paramètre est d'environ trois fois la dimension d'un granulat,
ce qui se justifie également comme le minimum acceptable pour une modélisation d'un milieu homogène continu. On indique aussi
la méthode pour utiliser la théorie dans un code d'éléments finis et les règles pour atteindre à l'objectivité des résultats
à l'égard du choix de la dimension d'un élément par l'aanlyste. Enfin, on dérive une formule simple de prévision de l'énergie
de rupture d'après la résistance en traction et la dimension du granulat, ainsi que du module d'atténuation de déformation.
L'analyse statistique des erreurs met en évidence un progrès radical sur la théorie de la rupture linéaire, ainsi que sur
la théorie de la résistance. Ainsi établit-on solidement la possibilité d'appliquer au béton la mécanique de la rupture.
Soils having cohesion and internal friction are often considered to be perfectly plastic solids. A consistent approach has been proposed on the basis of the mathematical theory of perfect plasticity, and several interesting results were obtained. However, such an idealized treatment will often result in a marked difference between prediction and experimental fact. In particular, the strong dependence of the volume change under shearing action on the prior history of the soil cannot be properly taken into account. It is suggested herein that soil be treated as a work-hardening material which may reach the perfectly plastic state. A remarkable qualitative agreement is then obtained with the known behavior of soils in triaxial tests; additional study along similar lines appears most promising.
An operationally simple strength criterion for anisotropic materials is developed from a scalar function of two strength tensors. Differing from existing quadratic approximations of failure surfaces, the present theory satisfies the invariant requirements of coordinate transforma tion, treats interaction terms as independent components, takes into account the difference in strengths due to positive and negative stresses, and can be specialized to account for different material symmetries, multi-dimensional space, and multi-axial stresses. The measured off-axis uniaxial and pure shear data are shown to be in good agreement with the predicted values based on the present theory.
A theory is suggested which describes, on a macroscopic scale, the yielding and plastic flow of an anisotropic metal. The type of anisotropy considered is that resulting from preferred orientation. A yield criterion is postulated on general grounds which is similar in form to the Huber-Mises criterion for isotropic metals, but which contains six parameters specifying the state of anisotropy. By using von Mises' concept (1928) of a plastic potential, associated relations are then found between the stress and strain-increment tensors. The theory is applied to experiments of Korber & Hoff (1928) on the necking under uniaxial tension of thin strips cut from rolled sheet. It is shown, in full agreement with experimental data, that there are generally two, equally possible, necking directions whose orientation depends on the angle between the strip axis and the rolling direction. As a second example, pure torsion of a thin-walled cylinder is analyzed. With increasing twist anisotropy is developed. In accordance with recent observations by Swift (1947), the theory predicts changes in length of the cylinder. The theory is also applied to determine the earing positions in cups deep-drawn from rolled sheet.
Stress-strain relations are given for an initially isotropic material,
which is macroscopically homogeneous, volume is considered to be composed of
various portions, which can be represented by subelements showing secondary creep
and isotropic work handening in plastic deformation. If the condition is imposed
that all subelements of an element of volume are subjected to the same total
strain, it is demonstrated that the inelastic stress-strain relations of the
material show anisotropic strain-hardening, creep recovery, and primary and
secondary creep due to the nonuniform energy dissipation in deformation of the
subelements. Only quasi-static deformations under isothermal conditions are
considered. The theory is restricted to small total strains. (auth)
The rate formulation and an unconditionally stable integration algorithm for a single-surface hardening anisotropic elastoplasticity model are developed to obtain an effective medium constitutive model for a class of periodic elastoplastic composites. Because the plasticity model features an intrinsically anisotropic failure criterion and hardening law, it requires more material parameters (15) than does its isotropic analogue (2). To address this issue and to assess how well the new model serves as an effective medium constitutive model for a class of composites, results from numerical elastoplastic homogenization computations are utilized for free-parameter estimation. It is shown that the new model provides a good fit to the homogenization data, and the model's excellent performance in a two-dimensional finite element setting is demonstrated by performing computations involving in-plane loading of an elastoplastic masonry wall. The wall is modelled first as a heterogeneous medium with all of its microstructure, and subsequently as a homogeneous effective medium with the new plasticity model.
Algorithms based upon the notion of return mapping have been developed for the Hill yield function of anisotropic plasticity. The relative accuracy of two algorithms is assessed by means of iso-error maps. The choice of the algorithm turns out to be much more critical for the orthotropic Hill criterion than for the underlying isotropic von Mises plasticity model. A tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operator. The model has been applied to three shell/plate structures.
Rate-independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non-smooth fashion are considered in detail. It is shown that the standard Kuhn-Tucker optimality conditions lead to the only computationally useful characterization of plastic loading. On the computational side, an unconditionally convergent return mapping algorithm is developed which places no restrictions (aside from convexity) on the functional forms of the yield condition, flow rule and hardening law. The proposed general purpose procedure is amenable to exact linearization leading to a closed-form expression of the so-called consistent (algorithmic) tangent moduli. For viscoplasticity, a closed-form algorithm is developed based on the rate-independent solution. The methodology is applied to structural elements in which the elastic domain possesses a non-smooth boundary. Numerical simulations are presented that illustrate the excellent performance of the algorithm.