Numerical modelling of non-confined and confined masonry walls
Abstract
This paper presents a discussion on the behaviour of non-confined and confined masonry walls with different types of horizontal reinforcement when subjected to in-plane horizontal loads, using advanced numerical simulations. An isotropic continuum nonlinear finite element macromodel, based on smeared crack total strain–stress models with scarce parameter input is used to represent previously tested masonry walls. The masonry units, the mortar and the bonding interfaces between the units and mortar have been lumped in continuum elements. The input data is based on experimental results or inverse fitting, with a clearly identification and justification. The results are presented and compared against experimental data, with an emphasis on force–displacement curves and failure modes.
Supplementary resource (1)
Data
February 2015
... Yoshimura et al. [53] and Gouveia and Lourenco [54] found that the ductility and lateral strength of CM walls can be enhanced by providing horizontal and vertical reinforcement. The addition of confining members results in a reduced crack width, and more ductile behavior in CM walls making them more earthquake resistant, [55]. Penna et al. [56] used truss-type reinforcement to examines the effect of bed joint reinforcement on the lateral strength and displacement capacity of masonry walls. ...
... Various FEM studies were conducted to study the nonlinear behaviour of CM walls. Medeiros et al. [55] proposed a nonlinear finite element micro-model based on isotropic continuum that links the values of principal stress and strain through rules governing behavior of the material under tension, compression, and shear, both before and after cracking. However, the results from numerical models for pre-and post-peak stiffness were found to be less accurate when validated with experimental studies. ...
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.
... Research based on detailed micro-modelling of multi-perforated burnt clay brick masonry was studied by Sandoval and Arnau [21]. However, macro-modelling approaches have been generally implemented to represent the global structural behaviour of the CM walls, wherein the masonry units and the joints were modelled as single unit and the material parameters are obtained from the various tests on masonry [22][23][24][25][26][27]. This approach has been generally adopted to minimize computing needs and to simplify modelling. ...
... The FE analysis was carried out using the commercial software package ABAQUS [26]. The surface based cohesive interaction was used which assumes a linear elastic traction separation law prior to damage. ...
The confined masonry (CM) structure consists of load bearing walls strengthened with nominally reinforced concrete tie-elements at the perimeter and other key locations. Various simulation studies using finite element analysis have been performed on CM walls for a better understanding of their response under in-plane and out-of-plane loads. However, for a reliable simulation of response, it is important to define the realistic interaction properties at the wall-to-tie-column interface for CM walls. The current method of defining the wall-to-tie column interaction for numerical simulation is either using monolithic interaction or frictional contact. This simplified assumption results in stiffer or flexible response of the CM walls. Thus, in the present study, the wall-to-tie-column interaction properties were evaluated using experimental and analytical investigation. Initially, flexure (tension) and shear bond tests were conducted on sub-assemblages consisting of masonry and concrete. The tensile and shear bond properties obtained from the experiments were used to calibrate the cohesive and friction interaction properties for numerical analysis. The proposed interaction properties such as bond stiffness, damage initiation, and damage evolution provided better simulation of in-plane response of CM walls.
... The Young's modulus of the masonry in Table 1, obtained from uniaxial compressive tests perpendicular to the bed joints, cannot be used directly for modelling as it results in stiffer responses (Medeiros et al. 2013). This discrepancy arises because the macro-modelling approach attempts to represent anisotropic materials as isotropic. ...
Confined brick masonry structures have garnered considerable attention as an effective solution for earthquake-prone regions due to their robust construction, efficient wall-to-column connections, and optimised utilisation of material strength. Within the realm of building design and construction, openings play a pivotal role, serving as essential elements for facilitating natural light and fresh air into the structure. However, the presence of openings within confined brick masonry walls causes a significant reduction in their seismic resistance. Hence, striking the right balance between these openings and structural strength is crucial. For this purpose, it is necessary to investigate the influence of size, shape, and position of the openings in confined brick masonry walls on their seismic performance. In this work, a comprehensive finite element macro-model is adopted that treats the wall and tie members as a unified system. A concrete damage plasticity approach is employed to predict damage progression in confined brick masonry walls. Using a pushover analysis in finite element framework, the ultimate strength, stiffness, and energy absorption capacity of confined brick masonry with different types of openings is assessed. Furthermore, a parametric study is conducted incorporating various scenarios, such as aspect ratios of confined brick masonry walls, diverse shapes of opening and variations in the positions of windows, doors, and combinations of both openings. Based on the results, simplified equations are developed to facilitate analytical estimation of ultimate strength, along with recommendations for optimising opening shape, size, and placement to enhance the design of confined brick masonry walls with openings. The study highlights that larger openings in confined brick masonry walls diminish ultimate strength, stiffness, and energy dissipation due to reduced load distribution and increased stress concentrations. Openings smaller than 10% of the masonry area maintain load paths, but larger openings require additional support. Rectangular openings with greater height than width exhibit superior performance. Furthermore, the positioning of windows significantly influences wall strength, with placements farther from the loading point proving favorable. Door placement also impacts ultimate strength, with central placement compromising stiffness. Combining window openings with a centrally located door maintains consistent ultimate strength but affects stiffness. Overall, this research contributes to a better understanding of the seismic behaviour of confined brick masonry structures with openings, offering valuable insights for engineers and architects working in regions susceptible to seismic activity.
... Following two earthquakes in Turkey in 2011, Piroglu et al. [22] examined buildings and found that enclosed masonry structures without seismic measures showed no significant damage. Subsequent studies [23,24] using numerical analysis have further explored these observations. Shake table experiments, an indispensable method, have also been conducted using scaled models of actual structures, demonstrating the effectiveness of seismic retrofitting measures [25]. ...
Frequent seismic events have demonstrated that building collapse is primarily caused by the loss of load-bearing capacity in vertical structural members. In response to this risk, various national design codes have been established. This study conducted field investigations at an earthquake site in Luding County, Sichuan Province, which was struck at a magnitude of 6.8 on 5 September 2022. In this case, the lower x-direction load-bearing wall of the Tianyi Hotel suffered severe shear damage, and the building was on the verge of collapse. However, no obvious damage was seen in the elementary school dormitory. Numerical simulation analysis revealed that during the earthquake, the buildings primarily experienced y-direction displacement in the x-direction, with significant differences in the stress state among different axes. In the model of Tianyi Hotel, the x-direction load-bearing walls suffered shear damage, while the frame columns were still in the elastic stage. At this point, the shear force of the walls was 6–9 times that of the frame columns. Comparing the damage characteristics of the two buildings during the earthquake, it was found that different structural forms lead to different internal force distributions. This phenomenon is further interpreted through the principle of “deformation saturation”, with core structural components being modeled and tested using quasi-static experiments. The results indicated substantial differences in material properties among different structural forms, including variations in lateral stiffness, ultimate load-bearing capacity, and maximum displacement. Moreover, at the same floor level, components with smaller ultimate displacements are decisive of the overall structural stability. To ensure seismic resilience and stability, it is essential to consider not only the load-bearing capacity but also the rational arrangement and cooperative interactions between different components to achieve a balanced distribution of overall stiffness. This approach significantly enhances the building’s resistance to collapse.
... Various openings present in the structures are one of the causes of the non-linearity, resulting in localized failure and significant difficulties in modelling. Numerous models for the simulation of the behaviour of CM structures are based on the finite element method (FEM) (Eshghi & Pourazin, 2009;Medeiros et al., 2013;Okail et al., 2016). Lang et al. (2014) introduced a micro-modeling strategy for CM, leveraging the Discrete Element Method (DEM). ...
This research investigates the development of a simplified micro-modelling technique for the nonlinear analysis of confined masonry (CM) walls. The primary objective of this research is to compare this novel modelling approach with the conventional finite element modelling (FEM) technique implemented in ETABS, utilizing identical modelling parameters. Furthermore, this research extends to modelling a full-scale CM building and conducting a comprehensive seismic performance assessment. In the simplified micro-modelling methodology, distinct elements represent the individual units and mortar within the brick joints. Concrete damage plasticity (CDP) models are applied, incorporating diverse elastic and inelastic parameters to represent the brick and concrete tie elements accurately. The reinforced elements are modelled using truss elements, providing a macro-level understanding of the structural behaviour. Simultaneously, FEM is executed within the ETABS platform, employing a layered technique that allows for macro-level wall modelling. The numerical results obtained through both modelling techniques are compared with the experimental results in the existing literature, establishing the validity and efficacy of the simplified micro-modelling approach. The convergence between the two modelling methodologies is pivotal, as the same model is subsequently utilized to validate the FEM technique in ETABS. This validation process is a foundation for conducting a seismic performance assessment of CM buildings. The findings of this research endeavour hold significant implications for the earthquake and masonry structure research community, offering valuable insights and methodologies for enhancing the seismic resilience of CM structures.
... Although such tests have been insightful in understanding the response of CBM structures, carrying out parametric experimental studies can be costly and time-consuming (Quiroz et al. 2014;Cruz and Pérez-Gavilán 2015). On the other hand, advances in numerical modeling techniques, like the finite element (FE) method, have offered efficient, robust, and less expensive technique for understanding CBM structures (Medeiros et al. 2013;Naciri et al. 2021). Using a robust numerical technique, one can assess various designs, such as the effect of opening sizes, opening location, aspect ratio, and different materials on the response of CBM structures. ...
Confined brick masonry (CBM) structures have demonstrated success in seismic regions due to their straightforward construction and efficient wall-to-column connections. However, there is not enough comprehensive understanding about how these structures respond to changes in geometry and material. Addressing this gap, our study employs a robust numerical technique, utilizing an integrated finite element macro-model. In this approach, we treat wall and tie members as a unified entity, enhancing computational efficiency. The concrete damage plasticity method is applied to predict the evolution of CBM wall damage, with a subsequent pushover analysis conducted to ascertain seismic capacity and response reduction factor. This factor is further used as a criterion to appraise the performance and seismic response of CBM walls. An extensive parametric study is carried out that compares the response of CBM wall with reinforced concrete (RC) infill wall, examines the impact of different opening sizes and confinement schemes around openings in CBM walls, and considers various masonry material properties. The study presents insights into damage propagation of CBM walls under seismic action particularly for cases of opening, confinement around opening, and material type. Findings indicate the superiority of CBM structures over RC infill walls, especially in earthquake-prone regions. Crucially, confinement around openings is identified as a pivotal factor in restoring lost strength, with Scheme A and E emerging as structurally and economically viable optimal confinement schemes. Furthermore, this study underscores the importance of selecting appropriate masonry type and mortar mix proportions in designing CBM walls for seismic resistance.
... In recent years, much of the research on CM has been centred on mechanical characterization, primarily through quasi-static and shake table tests, as well as the advancement of modelling approaches [17][18][19][20][21][22][23]. With well-established mechanical characterization findings, the focus has now shifted towards the development of innovative retrofitting solutions [24][25][26]. ...
This paper investigates the dynamic characteristics and Finite element model updating of two confined masonry buildings in Messina, constructed in the aftermath of the devastating 1908 earthquake. The study addresses the need for advanced research in this field to enhance the understanding of the dynamic behaviour of confined masonry structures. The authors identified the modal parameters of the buildings from ambient vibration tests. Finite element models have been developed and fine-tuned in a second step to optimize the agreement between the simulated and observed modal parameters. The optimized parameters are then compared with the outcomes of nondestructive tests on masonry and reinforced concrete. This research addresses the modelling issues when dealing with confined masonry structures, offering guidance to engineers to select the modelling parameters. The paper emphasizes the substantial stiffening effect introduced by confined masonry, as evidenced by the optimized Young's modulus of masonry, which is almost two and a half times higher than values obtained from flat jack tests. To accurately represent the interaction between reinforced concrete ties and masonry panels within equivalent frame models, it becomes crucial to adequately overstate the masonry stiffness to capture the mutual coupling between structural components.
... Para representar el comportamiento de la mampostería se pueden trabajar tres tipos de estrategias diferentes según el nivel de detalle y el problema físico a representar, la primera es a través de un mesomodelo detallado donde se representen cada uno de los componentes: mortero, ladrillo e interfaz ladrillo-mortero, la segunda es mediante un meso-modelo simplificado donde la interfaz ladrillomortero se analiza dentro de la misma unidad a través de una homogenización de los dos elementos y la última estrategia es mediante un macro modelo que representa el problema como un material homogéneo (Abdellatif et al., 2019;Campbell & Durán, 2017;Freddi & Royer-Carfagni, 2011;Lourenço, 1996;Lourenço et al., 2007;Lourenço & Silva, 2020;Marques et al., 2020;Medeiros et al., 2013aMedeiros et al., , 2013bObaidat et al., 2017;Shadlou et al., 2020;Smoljanović et al., 2017;Zucchini & Lourenço, 2009) El presente trabajo utilizó un meso-modelo simplificado para representar el comportamiento de la mampostería postensada no adherida, a través de la homogenización del material se logró obtener un comportamiento aproximado del comportamiento mecánico de los muros de mampostería postensada no adherida ...
La modelación numérica de la mampostería puede resultar compleja debido a que es un material compuesto heterogéneo y anisótropo, además si se requiere representar un presfuerzo longitudinal paralelo al eje del muro implicaría un factor adicional al análisis y evaluación estructural. En esta investigación se modeló a través de un software comercial de elementos finitos un muro de mampostería postensada con bloques de arcilla bajo carga laterales monotónicas. Se evidenció a través de un análisis de sensibilidad que a partir de una división de 72 elementos finitos el error relativo supera la tolerancia de 0.5 % y se obtiene los resultados de desplazamiento respecto a la carga incrementando gradualmente de manera monotónica. Los resultados del comportamiento mecánico de la modelación numérica presentaron una tendencia similar a los datos experimentales obtenidos en una anterior investigación, sin embargo, fue necesario calibrar el modelo numérico a través de las propiedades mecánicas del material encontradas previamente.
This study investigated the efficacy of a strengthening technique, employing bed joint reinforcement alongside mortar wallposts and a pioneering approach by combining in-plane and out-of-plane loading in cyclic tests to comprehensively evaluate masonry wall behavior. The investigation started with scrutinizing two full-scale walls under the combined cyclic loading and a single-story 3D building under shaking table test. This paper investigated the efficiency of mortar wallpost, which was built during the construction of walls, in bearing out-of-plane loads under simultaneous out-of-plane and in-plane cyclic loading conditions, as well as shaking table tests. Additionally, the performance of specimens subjected to the proposed simultaneous out-of-plane and in-plane cyclic loading was compared to the results from shaking table tests. The findings indicate that longer walls with mortar wallpost performed similarly to shorter walls without wallposts. Therefore, the wallposts were successful in reducing the free span of the wall, effectively transferring forces to the wall, and not interfering with the in-plane behavior of the frame. The mortar wallposts are thus applicable and effective in masonry materials. Moreover, comparing the results from cyclic and shaking table tests shows that cyclic tests can conservatively predict the seismic behavior of walls and serve as a cost-effective alternative when shaking table tests are not available.
The paper addresses the possibilities and research needs with respect to advanced testing and numerical analysis of masonry structures, with a focus in cyclic behaviour. A complete masonry characterization is sought, in terms of modern deformation controlled test set-ups, which is a key aspect for modern, non-linear, computer simulations. In addition, the aspects related to masonry innovation and to construction needs are also addressed.
Attention is given to the mechanical properties of concrete block masonry, with respect to its compressive and tensile strength. These properties are important parameters in the in-plane lateral behaviour of masonry walls, determining their resistance and ductility. Such properties play also a central role when analytical and numerical analysis is used for simulating or predicting the behaviour of masonry structures. The influence of two selected parameters on the mechanical properties of masonry is discussed, namely the geometry of the units and the filling of the vertical joints. Results show that masonry under compression behaves as a homogeneous material and the stress-strain diagrams can be represented by a parabola similarly to what is suggested for structural concrete. in case of tensile strength, filling of vertical joints appears to influence considerably the tensile strength. The filling of the vertical joints increased the strength but lead to a more brittle behaviour.
The mechanics of masonry structures have been for long underdeveloped in comparison with other fields of knowledge, presently, nonlinear analysis being a very popular field in research. Masonry is a composite material made with units and mortar, which presents a clear microstructure. The issue of mechanical data necessary for advanced nonlinear analysis is addressed first, with a set of recommendations. Then, the possibilities of using micromodelling strategies replicating units and joints are addressed, with a focus on an interface finite element model for cyclic loading and a limit analysis model. Finally, homogenisation techniques are addressed, with a focus on a model based on a polynomial expansion of the microstress field. Application examples of the different models are also given.
The behavior of masonry shear walls is fundamental in the design of masonry buildings subjected to different actions, namely of seismic nature. The usage of unreinforced, confined or reinforced masonry is currently subjected to a strong debate in Europe due to the new codes. In particular, the part of Eurocode 8 (Design of structures for earthquake resistance) related to masonry structures is only a limited compromise for the different countries. A large testing program was started at University of Minho in order to clarify issues regarding confined masonry and unfilled vertical joints. Confined masonry is assumed as a hybrid material joining masonry with small section horizontal and vertical lightly reinforced concrete elements. This project, partly sponsored by the light-weight concrete block industry, aims at defining adequate structural solutions for regions of low to high seismicity in Portugal. This paper discusses the results of the experimental program, consisting mainly of masonry walls subjected to cyclic actions and constant pre-compression. Sixteen specimens are considered, being the shear strength, ductility, energy dissipation and stiffness discussed. The key aspects under discussion are: (a) the possibility of replacing the filling of the vertical joints by interlocking and horizontal bed joint reinforcement, (b) the need for filling vertical joints in confined masonry solutions.
An innovative system for reinforced concrete masonry walls based on the combination of vertical and horizontal trussed reinforcement is proposed. The mechanical characterization of the seismic behavior of such reinforced masonry walls is based on static cyclic tests carried out on panels with appropriate geometry. The influence of the factors influencing the in-plane cyclic behavior of concrete masonry walls, such as the horizontal reinforcement, precompression, and masonry bond pattern, is discussed. The results are analyzed in terms of failure modes and force versus displacement diagrams, from which the seismic performance is assessed based on the ductility and energy capacity dissipation. The results stressed that the increase on the precompression level leads to a stiffer and more brittle lateral behavior of the masonry walls. The presence of horizontal reinforcement ensures better control and better distribution of cracking, even if only a marginal increase of lateral strength was found in the particular testing program.
Flexural and shear strengths of reinforced masonry shear walls are examined, based on experimental results obtained from 22 6-ft by 6-ft masonry wall specimens. These results are summarized and current design formulas examined. It is found that the simple flexure theory based on the plane-section assumption can be applied to square wall panels with good accuracy. Moreover, it appears to be consistently conservative. The 1988 Uniform Building Code specifications for the shear strength tend to be very conservative for the square wall panels studied and less conservative for walls with lower aspect ratios. Furthermore, the code specifications tend to overestimate the shear strength contributed by the horizontal reinforcement and neglect the influence of axial stress. Hence, a new shear formula that takes into account the influence of axial stress and flexural reinforcement is proposed. The formula appears to have good correlation with experimental results obtained in this study as well as those of others.
The seismic resistance of story-height reinforced masonry shear walls has been evaluated experimentally to examine the influence of the applied axial stress and the amount of vertical and horizontal reinforcement on the lateral resistance, failure mechanism, ductility, and energy-dissipation capability of a wall panel. The results obtained from 16 concrete masonry specimens are summarized in this paper. It has been shown that the flexural strength increases with the applied axial stress and the amount of the vertical reinforcement present. The shear strength dominated by diagonal cracking increases with the amount of vertical and horizontal steel, as well as with the tensile strength of masonry and the applied axial stress. However, the axial stress has a more significant influence on the flexural strength than on the shear strength. Furthermore, increasing the amount of vertical and horizontal reinforcement can substantially improve the postcracked ductility and energy-dissipation capability of a shear-dominated specimen.
Results of tests conducted for combined and confined masonry walls are reported in this paper. The cyclic testing followed the protocol established by Mexican guidelines for masonry structures (NTCM-2004), which is similar to that used worldwide for the cyclic testing of wall structures. Resisting mechanisms and deformation characteristics of such walls were evaluated. Indicative values of useful parameters for analysis and design were also defined. In addition, it was verified if such a system is earthquake-resistant according to NTCM-2004 guidelines.
An improved micro-mechanical model for masonry homogenisation in the non-linear domain, is proposed and validated by comparison with experimental and numerical results available in the literature. Suitably chosen deformation mechanisms, coupled with damage and plasticity models, can simulate the behaviour of a basic periodic cell up to complete degradation and failure. The micro-mechanical model can be implemented in any standard finite element program as a user supplied subroutine defining the mechanical behaviour of an equivalent homogenised material. This work shows that, with the proposed model, it is possible to capture and reproduce the fundamental features of a masonry shear wall up to collapse with a coarse finite element mesh. The main advantage of such homogenisation approach is obviously the possibility to simulate real complex structures while taking into consideration the arrangement of units and mortar, which would otherwise require impractical amount of finite elements and computer resources.