Behavior Of Masonry Structures Research Articles

Analysis and prediction of masonry wallette strength under combined compression-bending via stochastic computational modeling

The out-of-plane flexural bending capacity of masonry is a fundamental property for understanding the behavior of masonry structures. This study investigates the behavior of unreinforced masonry wallettes subjected to combined compression-flexural loading using the discrete element method (DEM), and provides a novel framework to estimate the masonry strength. A simplified micro-modeling strategy is utilized to analyze a masonry wallette, including the variation of the mechanical properties in masonry units and joints. Stochastic DEM analyses are performed to simulate brickwork assemblages, assuming a strong unit-weak joint material model typical of most masonry buildings, including historical ones. Once the proposed computational approach is validated against the experimental findings, the effect of spatial and non-spatial variation of mechanical properties is explored. Two failure types are identified: joint failure and brick failure. For each failure mechanism, the variability of the response and the effects of the modeling parameters on the load-carrying capacity is quantified. Afterward, Lasso regression is employed to determine predictive equations in terms of the material properties and vertical pressure on the wallette. The results show that the most important parameters changing the response are the joint tensile strength and the amount of vertical stress for joint failure, whereas the unit tensile strength dominates the response for brick failure. Overall, this research proposes a novel framework adopting validated advanced computational models that feed on simple test results to generate data that is further utilized for training response prediction models for complex structures.

Yığma Yapıların Düzlem İçi Davranışının Kafes Model Yaklaşımı ile Analizi

Yığma yapılarda, malzeme parametrelerindeki belirsizliklerin yanı sıra düzensiz duvar örgü biçimi ve taşıyıcı elemanlarda oluşan hasarlar da göz önünde bulundurulduğunda yapısal davranışının ve taşıma kapasitesinin belirlenmesi oldukça karmaşık bir hale gelmektedir. Bu durumlarda nümerik analizlerde basitleştirilmiş yaklaşımların tercih edilmesi, çözüme pratik olarak ulaşılmasına olanak sağlar. Bu çalışmada, yığma taşıyıcı sistemlerin düzlem içi hasar oluşumları ve taşıma kapasiteleri kafes elemanlardan oluşan sayısal analiz modeli kullanılarak belirlenmeye çalışılmıştır. Yığma yapılarda kullanılması açısından yenilikçi bir yaklaşım olarak önerilen bu yöntemde, sadece uzun ekseni doğrultusunda yük taşıyan çubuk elemanlar kullanılmaktadır. Böylece oluşturulan eşdeğer hesap modeliyle gerçekleştirilen doğrusal olmayan analizler ile yapıda dış yük etkisinde meydana gelebilecek hasarların ve maksimum taşıma kapasitesinin elde edilmesi amaçlanmıştır. Literatürde daha önce incelenen yığma yapıların esas alındığı çalışmada, yöntemin avantajları ve dezavantajları karşılaştırmalı olarak değerlendirilmiştir. Gerçek yapıdaki süneklik tepkisinin tam olarak temsil edilememesine rağmen, maksimum taşıma kapasitesinin ve hasar oluşum bölgelerinin kabul edilebilir düzeyde doğrulukla belirlenebileceği görülmüştür. Yaygın olarak tercih edilen kapsamlı modelleme prosedürlerine bir alternatif olarak önerilen eşdeğer kafes model yaklaşımının umut verici olduğu sonucuna varılmıştır.

Constitutive behaviour of masonry prisms using a full-field measurement technique

To obtain analytical models for the compressive behaviour of masonry structures, it is crucial to accurately measure the compressive strengths of its constituents, i.e., brick and mortar. The mechanical properties and the stress-strain relationship under uniaxial compression are essential for thoroughly investigating and evaluating masonry structures. The present work aims to validate a non-contact measuring technique for obtaining full-scale strain and failure patterns and investigate joint mortar composition's effect on masonry behaviour. Forty masonry prisms were manufactured in this study using two distinct types of brick and five different types of mortar varying according to cement and lime contents. The results showed that 2D Digital Image Correlation (DIC) could generate full-strain assessments of masonry prisms, resulting in a full-scale stress-strain analysis. It was also found that, in the post-peak region, prisms with lower cement content exhibit a more ductile behaviour with strain localisation at the joint mortar level. Based on current experimental results and data from the literature, new analytical relationships were presented to predict masonry mechanical properties and masonry complete stress-strain compressive behaviour.

The Slender Rigid Block: Archetype for the Seismic Analysis of Masonry Structures

ABSTRACT The elasto-plastic oscillator, representing the basic model for reinforced concrete and steel structures, shows its inadequacy when dealing with masonry structures. The column, resting on a rigid plane with friction, is shown to be particularly appropriate to model the dynamic behaviour of masonry structures. At this aim, this paper investigates the motion of a slender rigid block (SRB), initially resting in its vertical configuration and hit by a seismic input, represented through a single impulse constituted by a rectangular or sinusoidal half-wave or a simplified sequence of horizontal acceleration pulses, having rectangular or sinusoidal shapes. An accumulation of the rotation of the SRB exists under the action of sequences of opposite acceleration pulses. The dynamic collapse is shown to take place when the column is led to its critical configuration – where the restoring moment of the weight is lost – so that the last pulse can further increase the rotation of the column. Expressing the behaviour of the SRB by means of the force reduction factor, the ratio between the magnitude of the collapse horizontal acceleration and the static strength of the column, the difference between the responses of the column decreases with increasing the number of the pulses of the sequence. A simple definition of the asymptotic failure domain can be obtained with a good approximation with a limited number of pulses. It is possible to evaluate the minimum collapse acceleration intensity of seismic sequences of pulses of any assigned duration able to produce the collapse of the rigid block, representing the seismic strength of the SRB. Finally, the results obtained in the theoretical analysis are compared with the outcomes of more accurate and time-consuming non-linear dynamic or incremental analyses (IDA).

An interface-based detailed micro-model for the failure simulation of masonry structures

This work presents a novel FE-based detailed micro-model approach, referred to as Discontinuous Detailed Micro-Model (DDMM), for the nonlinear analysis of masonry structures subjected to in-plane loading conditions. According to this DDMM, material nonlinearities caused by fracture phenomena at mortar joints are reproduced by means of zero-thickness interface elements placed between all brick/mortar and mortar/mortar interfaces comprised into the volumetric finite element mesh. In particular, the model adopts a novel cohesive-frictional interface model for reproducing the inelastic response under combined shear/compression stresses. The work provides a comprehensive investigation on the well-known nonuniqueness issues usually experienced in similar approaches, providing an effective numerical stabilization strategy. The proposed approach is validated through comparisons with experimental data available in technical literature, involving both tensile and combined shear/compression tests on brick masonry couplets. The results denote that the proposed approach ensures reliable predictions of the failure behavior of masonry structures.

Numerical Analysis of Masonry Structures through a Modified Composite Interface (MCI) Model

This paper presents an innovative modelling approach for evaluating the structural response of new and existing masonry buildings characterized by a periodic arrangement of units and mortar joints. The aim is to provide a calculation tool that allows to model the non-linear behaviour of masonry structures under lateral and vertical loads with a reduced numerical effort, without compromising the accuracy of the results. The proposed model is a typical D-FEM (Discontinuum - Finite Element Model) consisting of deformable blocks, which incorporates several masonry units. The blocks are separated by interface elements placed along predetermined surfaces on which cracks, sliding or crushing planes can develop. The surface layout is conceived to replicate all the fundamental failure mechanisms that can occur in real masonry structures. To adequately describe the non-linear behaviour of the interface elements, a Modified Composite Interface (MCI) model is formulated by modifying the "Combined Cracking-Shearing-Crushing" model originally proposed by Lourenço to simulate the cracking mechanisms along the interface elements of simplified micro-models in FEM analysis. The proposed D-FE model has been already calibrated and validated by the Authors on different masonry panels and, through an Evolutionary Polynomial Regression (EPR), expressions in closed form have been defined to calculate the mechanical parameters of the new MCI model starting from the original CI. Particularly, for each mechanical parameter, six formulas of increasing complexity have been identified through non-linear regression, progressively including a greater number of input variables to increase the precision of results. The aim of this study is to determine the accuracy of these formulas. Numerical analyses are carried out on a population of sixty-four masonry walls already used in the previous calibration phase, modeling each panel with all available equations. This allows to evaluate the average accuracy of each formula and to understand their efficiency in terms of calculation effort and correctness of the results.

Temporary Shoring System on Masonry Buildings After an Earthquake

Historical masonry structures that make up the cultural assets of a country constitute the identity of the society to which it belongs. For this reason, it should be protected and should be transferred from generation to generation. Earthquakes are threatening action to masonry structures. The force generated by the ground movement may cause shear cracks in masonry structures that may lead to fragmentation and even collapse of the structure. It is necessary to know the earthquake behaviour of masonry structures to be able to apply appropriate temporary shoring system after a damage caused by earthquake in order to prevent the future damages during aftershocks. Thus, the progress of the damages in the building is prevented and it is ensured to survive until detailed investigation or restoration. However, when the applied temporary shoring system designs were examined, the environmental conditions of the building were not taken into account in any guideline on immediate shoring. In this paper, temporary shoring system for 3 traditional houses of Bey District is designed for possible earthquake damages. This district has many registered civil architectures lined side by side along very narrow streets. Some masonry buildings were changed to reinforced concrete with multiple floors. This study includes the registration status of the buildings, their location, the number of floors to be supported, the heights between floors, the height of the forces that can be brought by the adjacent building elements, the width of the street where the facade to be supported, whether there is a window or door opening in the facade to be supported etc. If there are window or door openings, the distances of the opening to the corner points of the building and the distances between the two openings has to be recorded. According to these determinations, possible damages that may occur in the buildings are defined and a temporary shoring system is designed in accordance with the buildings and the surrounding conditions.

Experimental Investigations and Microstructural Characterization of Construction Materials of Historic Multi-Leaf Stone-Masonry Walls

In order to correctly define the pathology of multiple-leaf stonemasonry walls and determine the appropriate interventions for its conservation and preservation, comprehensive studies on its building materials should be carried out since the overall behaviour of masonry structures is highly dependent on the characterization of its construction materials. Consequently, an interdisciplinary procedure for construction material characterization used in multiple-leaf stone-masonry walls in Egypt has been implemented to enrich documentation, conservation and restoration issues of this type of wall. The research methodology integrates experimental data obtained through on-site sampling, conducted tests and analyses, historical information, and field survey observations. The fundamental physical and mechanical properties of the masonry elements were examined by incorporating stone blocks, mortars and core-infill materials. The mineralogical composition and interlocking textures of the collected samples were investigated utilizing a large range of complementary investigation and analysis techniques, including polarizing microscopy, X-ray diffraction (XRD), thermal analysis (TG/DTA), and environmental scanning electron microscope (ESEM) attached to an EDX unit. Through the results thus obtained, a complete characterization of the mineralogical composition; physical–mechanical, chemical, and thermal properties; and the interlocking textures of the construction materials of both the outer and inner-core layers was performed. The outer leaves of the majority of the multiple-leaf stone-masonry walls in medieval architectural heritage were mainly built of well-dressed limestone blocks with nearly uniform dimensions, while the inner-core layer was usually built of stone-rubble infill with bending lime-based mortar. The uniaxial compressive strengths of core infill (corresponding to the inner core layer) and lime-based mortar of the embedded joints are shown to be 85 and 92.5% lower than the limestone units of the outer layer, respectively. Moreover, experimental observations indicate that the inner core layer exhibits the highest porosity values; consequently, deteriorated, loose and cohesionless core infill could greatly affect the durability and thermal resistivity of this kind of wall. The results provide scientific support for investigating the overall structural behaviour of this type of walls and for decision-making in future conservation and restoration strategies.

Steel based retrofitting interventions for existing masonry walls: a comparative numerical investigation

AbstractMasonry buildings constitute a significant portion of the architectural heritage all over the world, also in regions affected by a high seismic hazard. Since this constructional material is characterized by lack of tensile strength, as well as small deformation capacity, masonry structures could result hugely damaged if shaken by seismic forces. In order to avoid collapses and reduce structural damage, innovative retrofitting interventions are necessary to improve the seismic behavior of masonry structures. In this context, steel‐based techniques could be considered among the most suitable solutions. In fact, by using such a high‐performant material, additional strength and ductility may be conferred to existing masonry structures. Based on these premises, the present paper focuses on a numerical investigation of two different retrofitting techniques: the CAM© system and the application of steel grids on both faces of a masonry wall. In particular, on the base of an experimental test carried out within the research project In.CAM.M.I.N.O. on an unreinforced masonry wall tested in condition of constant vertical force and horizontal loads, a reference FE Model has been calibrated in Abaqus by using a macro‐modelling approach with a damage‐plasticity material model for the masonry. Then, based on the reference model, the efficiency of the two systems has been investigated and compared by means of numerical analyses, in order to evaluate the strength and ductility increases obtainable by the application of the two retrofitting techniques.

Homogenization of Masonry Wall using Sensitivity Analysis

Though masonry buildings are most impacted during earthquakes, and the construction of masonry structure cannot be completely avoided in all part of the earth, there is no proper study regarding the behavior of masonry structure regarding seismic performance analysis and design. Detailed analysis of masonry structures requires a detailed micro-modeling technique using finite element method which requires complex calculation and numerous parameters for analysis. In this paper, an approximated simplified finite element computational technique for non-linear analysis of masonry wall is proposed using sensitivity analysis for the flow parameter of masonry wall using a macro-modeling approach in which the masonry unit and mortar are homogenized into a single panel. An experimental wall in which the nonlinear analysis was performed was considered and numerical simulation using a macro-modeling approach is performed with the experimental properties in ABAQUS Software. With making numerical model, tensile and compressive stress-strain curve were obtained which were used to prepare concrete damage plasticity model for the modelling of masonry wall. The sensitivity analysis was performed for the determination of viscosity parameter and dilation angle. The model is prepared and run with various changing values of viscosity parameter and the one that matches with the experimental result was selected. In the same way, the model is prepared for various changing values of dilation angle and the one that matches with the experimental result was selected. The final model was prepared with the values of dilation angle and viscosity parameters thus prepared and the nonlinear force displacement relation was obtained. Thus obtained, non-linear force displacement curve is compared with the actual experimental force-displacement curve.

A “Smartly Functional” Urban 3D Model: A New Way to Preserve the State of Health and Quality of a Complex Masonry Structure

The 3D model is the primary information of an integrated support system for the assessment of structural safety under vertical loads and seismic vulnerability of a masonry building. The available approaches for evaluating seismic demand and capacity still appear inadequate and today aims to improve the process of knowledge of the seismic behavior of masonry structures and of the reliability of the numerical analysis of evaluation methods. Discrete modeling approaches (macro-elements) can lead to more reliable results if accurate surveys of the geometry and construction details of the masonry structure are used, especially in contexts where advise against the execution of invasive on-site tests for assessments both under vertical and seismic loads, limiting the investigation campaigns. In order to improve digital processes, oriented to the knowledge of the state of health and quality of a masonry structure, this study illustrates a new overture to virtual modeling and assessment of the structural safety of this type of work. The survey and relief methodology here proposed integrates digital data sensors—configured within an IoT (Internet of Things) network—in a geometric model with a level of accurate and precise detail, processed downstream of the laser scanner and photogrammetric survey of the single masonry building, as “S. Domenico Church in the “Sassi” of Matera.

An innovative image processing-based framework for the numerical modelling of cracked masonry structures

A vital aspect when modelling the mechanical behaviour of existing masonry structures is the accuracy in which the geometry of the real structure is transferred in the numerical model. Commonly, the geometry of masonry is captured with traditional techniques (e.g. visual inspection and manual surveying methods), which are labour intensive and error-prone. Over the last ten years, advances in photogrammetry and image processing have started to change the building industry since it is possible to capture rapidly and remotely digital records of objects and features. Although limited work exists in detecting distinct features from masonry structures, up to now there is no automated procedure leading from image-based recording to their numerical modelling. To address this, an innovative framework, based on image-processing, has been developed that automatically extracts geometrical features from masonry structures (i.e. masonry units, mortar, existing cracks and pathologies, etc.) and generate the geometry for their advanced numerical modelling. The proposed watershed-based algorithm initially deconstructs the features of the segmentation, then reconstructs them in the form of shared vertices and edges, and finally converts them to scalable polylines. The polylines extracted are simplified using a contour generalisation procedure. The geometry of the masonry elements is further modified to facilitate the transition to a numerical modelling environment. The proposed framework is tested by comparing the numerical analysis results of an undamaged and a damaged masonry structures, using models generated through manual and the proposed algorithmic approaches. Although the methodology is demonstrated here for use in discrete element modelling, it can be applied to other computational approaches based on the simplified and detailed micro-modelling approach for evaluating the structural behaviour of masonry structures.

Influence of historic roof structures on the seismic behaviour of masonry structures

Historic buildings are complex structures in which all the composing elements work together. Studies of heritage structures after seismic events have shown that timber roof structures strongly influence the seismic response of masonry structures, being able to reduce or enhance the out-of-plane displacement of the structure. Starting from these observations, three different types of roof structures, from the eighteenth, nineteenth and twentieth centuries, were introduced in the finite-element simulation software SCIA Engineer. The roof structures were subsequently placed on the same eighteenth-century masonry building with a ground floor and two upper floors, respecting its geometric features. Simulations were performed considering successively rigid, hinged or sliding connections between the roof and the masonry structure. At the same time, the traditionally crafted joints of the roof structures were consecutively modelled as hinged, rigid and semi-rigid (determined using three different methods). Ultimately, the top horizontal displacement, inter-storey drift and damage level of the masonry structure were compared. The main aims of this study were to observe if roof structures have an influence on the seismic behaviour of masonry buildings and to determine if selected parameters suffer any changes depending on the roof structure type, the roof–wall connections and joints’ axial stiffness.

Seismic Capacity Assessment of Unreinforced Brick Masonry Building Performed According To Eurocode

Brick Masonry Building with cement sand mortar is a common type of building typology in Nepal. Regardless of being one of the eldest construction technology, the behavior of masonry building is still a matter of study. The uncertainty in the behavior of masonry structures is due to material heterogeneity, complex behavior under different loading conditions and may be due to less research in this arena. Different modeling strategies are used and proposed worldwide to design and to identify the seismic performance of Masonry Building. The analysis strategy ranges from the simple linear method, equivalent frame method, static nonlinear method to dynamic nonlinear, which may be chosen according to engineering design aims and research purpose. In this attempt, authors choose two degrees of freedom 3D model of Unreinforced Brick Masonry Structures which catches both overturning and hysteresis mechanisms due to the shear response implemented by the TREMURI program with static nonlinear procedures. This verified method of modeling and analysis is applied to assess the performance of three different Unreinforced Brick Masonry buildings of the same plans with different numbers of storey.

Assessing the soil-structure interaction effects by direct method on the out-of-plane behavior of masonry structures (case study: Arge-Tabriz)

Soil-Structure Interaction (SSI) is an outstanding factor that influences the linear and nonlinear performance of any structure, and it can be taken into account as one of the most important and effective considerations on the seismic behavior of buildings. On the other hand, historic masonry buildings are specific and important structures, which are significantly affected by SSI. Preservation of these buildings is one of the main demands of every culture and every society; and evaluating the behavior of these buildings under natural events such as earthquake, considering aforementioned SSI phenomenon, is an essential step, in this regard. In this paper, the impact of SSI on the out-of-plane behavior of an ancient building in Iran, named Arge-Tabriz, has been investigated utilizing Finite Element Method (FEM). Modal and nonlinear Time-History (TH) analyses results revealed that SSI has a significant decreasing effect on the acceleration response due to removing the effective mode vectors from the resonance area of the acceleration response spectra. On the contrary, SSI has a remarkable increasing impact on the displacement response of Arg’s walls according to the displacement response spectra.

ÖRNEK BİR YIĞMA BİNA ÜZERİNDE 1998, 2007 VE 2019 TÜRK DEPREM YÖNETMELİKLERİNİN KARŞILAŞTIRMALI OLARAK İRDELENMESİ

In Turkey, masonry structures are still one of the most frequently used structural systems. Since masonry structures have not been built much in recent years, especially in city centers, it seems as they are not considered as a primary option, but the life of new systems is not yet known. However, the masonry building system has been applied for thousands of years. For this reason, there is a possibility that they come into prominence in the future. The behavior of masonry structures under horizontal loads, especially earthquakes, is quite different from that of conventional reinforced concrete frame systems, as vertical load-bearing elements are walls. Thus, masonry structures are either included in seismic codes as a separate section or special regulations about them are published. There have been some changes over time in the regulations regarding the calculation and design of masonry structures in our country. Although there are no significant differences between the 1998 and the 2007 seismic codes, the 2019 seismic code contains significant differences. In this paper, the provisions of the 1998, 2007 seismic codes along with those of the new seismic code that will come into force in 2019 are being compared and studied on a sample building. The seismic code, which will go into effect in 2019, has the changes such as earthquake region and local site class which affect the calculation and design of masonry structures. Based on the results obtained on the sample building assumed to be in Bingol which is the 1st degree earthquake region according to the 2007 code, the base shear force calculated according to the new 2019 code is 38% higher than the value calculated according to the 2007 code and 73% higher than the value calculated according to the 1998 code.

LOCALIZATION ANALYSIS OF AN ORTHOTROPIC MULTI-SURFACE PLASTICITY MODEL UNDER UNIAXIAL STRESS

Numerical simulations of masonry structures are often based on continuum macromodelling approaches that need constitutive laws able to phenomenologically reproduce the behavior of the material. To capture the deformation process up to failure, appropriate softening laws are needed to take into account the contraction of the yield stress domain caused by cracking and crushing. It is well known that softening may lead to localization of inelastic strain. This paper focuses on localization analysis of an orthotropic macro-scale model in the framework of multi-surface plasticity, which describes the in-plane behavior of masonry structures. Preliminary results reported in this short paper are limited to uniaxial stress states. Analytical localization conditions are first derived for uniaxial stress states with principal axes aligned with the material axes of orthotropy. Then, localization analysis is extended to an arbitrary angle between the principal stress axes and the axes of orthotropy.

High-resolution monitoring of the initial development of cracks in experimental masonry shear walls and their reproduction in finite element models

Induced seismicity in the north of the Netherlands has recently exposed unprepared, unreinforced masonry structures to considerable earthquake hazard. While the ultimate-limit state capacity of the structures is vital to assess the individual’s risk, their behaviour during more frequent, lighter earthquakes leading to ‘light damage’, has shown to be strongly linked to economical losses and societal unrest. To study the effect of these repeated light earthquakes, the behaviour of masonry structures, typical of the region, needs to be investigated when subjected to multiple small cycles. In particular, insight into the potential aggravation of the light damage is sought. Hence, shear walls of replicated clay brick masonry have been tested in the laboratory and exposed to a high number of low in-plane drift cycles. The experiments show, under inspection with high-resolution Digital Image Correlation, how stair-case, diagonal cracks initially distribute in multiple cracks running in joints at the centre of the walls, but later localise into a single, visible, wider crack. The tests are used to establish an interval over which light damage can be expected for these types of walls.Furthermore, this initial distribution of strains in ‘bands’ and subsequent localisation, previously observed only with computational finite element models and which could not be verified experimentally, is compared and reproduced with improved models both at the composite continuum scale (macro-model) and the brick-to-brick micro scale. The models are calibrated based on the quasi-static, cyclic experimental results and later used for extrapolation in dynamic nonlinear settings to assess the influence of natural ground motion excitations.

Stochastic strength prediction of masonry structures: a methodological approach or a way forward?

Today, there are several computational models to predict the mechanical behaviour of masonry structures subjected to external loading. Such models require the input of material parameters to describe the mechanical behaviour and strength of masonry constructions. Although such masonry material parameters are characterised by stochastic-probabilistic nature, engineers are assigning the same material properties throughout the structure to be analysed. The aim of this paper is to propose a methodology which considers material spatial variability and stochastic strength prediction for masonry structures. The methodology is illustrated on a case study covering the in-plane behaviour of a low bond strength masonry wall panel containing an opening. A 2D non-linear computational model based on the Discrete Element Method (DEM) is used. The computational results are compared against those obtained from the experimental findings in terms of failure mode and structural capacity. It is shown that computational models which consider the spatial variability of masonry material properties better predict the load carrying capacity, stiffness and failure mode of the masonry structures. These observations provide new insights into structural behaviour of masonry constructions and lead to suggestions for improving assessment techniques for masonry structures.

Application of asymptotic expansion homogenization in vibration analysis of masonry structures using finite elements

The asymptotic expansion homogenization (AEH) method, which is a rigorous mathematical homogenization theory, is applied here to the modeling of the mechanical behavior of masonry structures for practical dynamic analysis applications. A homogenization process reduces the modeling complexity associated with a detailed component representation of masonry structures and permits the use of a continuous macro-scale model. The method is validated and demonstrated through several applications to masonry structures with the aid of the commercial finite element software ABAQUS in conjunction with a simple self-made program to automate the procedure. The obtained equivalent elastic coefficients for the continuous macro-scale model are used to evaluate the performance of AEH method in determining natural frequencies and modal shapes of various masonry panels and structures. Comparison of results between analyses based on the AEH model and the discrete element model demonstrates the high potential of the AEH model in the seismic analysis of masonry structures.