Macromodeling Approach Research Articles

Effective properties of masonry structures and macro-model analysis with experimental verification

Masonry structures are the most prevalent type of buildings worldwide, and a significant portion are situated in seismic-prone areas. Thus, detailed information regarding their seismic strength and vulnerability is needed. The complexity of studying masonry structures lies in defining accurate and efficient models for representing masonry walls. In this context, there is a need for simplified methods that allow the modeling of masonry walls within a 3D structure. This work presents a methodology to define effective masonry properties from numerical analyses on representative volumes, using a damage model informed by experimental tests on units and mortar. These effective material properties serve as input parameters to model masonry walls within a macro-model approach, aiming to accurately capture the in-plane behavior and damage mechanisms with limited computational cost. The methodology is verified with experimental results and applied to real case studies in Cuenca, Ecuador.

Strengthening of historic masonry vaults with CFRP prepreg

Masonry vaults, frequently used in historic buildings to create large openings, have played a critical role in the survival of these buildings to the present day. These structural elements, which have been exposed to destructive effects such as earthquakes for centuries, need strengthening activities in order to transfer cultural heritage to future generations. The use of composite materials with high mechanical properties for strengthening purposes has been a popular method since the beginning of the 21st century, and its effectiveness has been proven. In this study, a masonry vault in the historical redoubts located in Erzurum, Türkiye, was modelled, and the effectiveness of various strengthening scenarios using prepreg composites was investigated. Numerical simulations were conducted with the Finite element method-based macro modelling approach. The investigation revealed that retrofitting arrangements maintained the stress distribution in masonry vaults while reducing maximum tensile stress; intrados reinforcement proved more effective, particularly the intrados-straight retrofit, with a 24% improvement, whereas extrados strengthening showed limited effectiveness.

Out-of-plane behavior of U-shaped unreinforced masonry structures

The out-of-plane behavior of masonry walls is an important aspect of their response, particularly in seismic regions. While previous studies have examined various geometries and materials, there exists a dearth of research on U-shaped walls, specifically with diverse geometric configurations. Moreover, the influence of axial load on out-of-plane behavior remains largely unexplored, limiting practical applications. This study aims to bridge these gaps by comprehensively investigating the out-of-plane behavior of U-shaped walls, focusing on the quantification of variable parameters encompassing geometry and axial load. A three-dimensional finite element model using the macro-modeling approach is used to analyze the structural response of U-shaped masonry walls under out-of-plane loading. The accuracy of the numerical modeling approach has been validated by available experimental test results to demonstrate the effectiveness of the modeling approach in predicting the out-of-plane behavior of U-shaped masonry structures. Subsequently, a series of parametric studies delves into the impacts of distinct geometrical attributes, including thickness, height, and span size, shedding light on the behavior of these walls across diverse geometric configurations. The results indicate that the capacity of the wall at the connection between out-of-plane and cross walls significantly influences the overall behavior and the failure mode. It was found that axial load substantially increases the strength of walls, in order of 1.5–3 times, and the positive effect of axial load was more significant than the secondary effects in most cases, though the significance of secondary effect drastically increases by increasing the height. It is shown that walls with longer span have much better behavior in the presence of axial load. Based on the results, for each specific geometrical parameter, a linear function can be considered for relation between strength and axial load. These findings can provide useful insights for the design and analysis of U-shaped masonry structures, particularly in seismic regions where out-of-plane behavior is a critical factor in their performance.

Conservation-oriented integrated approach for structural stability assessment of complex historic masonry structures

The paper presents a multidisciplinary approach for diagnosing the structural stability of the Takiyya of Ibrahim al-Gulshani in Historic Cairo using geometric and architectural documentation, field survey, laboratory tests, and numerical analyses under static and seismic conditions. The Takiyya, built during the Mamluk period, is an important medieval architectural complex in Egypt and has undergone multiple renovations. The field-testing includes geotechnical and geophysical investigations to evaluate the properties of the bearing soil beneath the monument. A 3D survey using Terrestrial Laser Scanning was employed to record Takiyya’s geometry. Terrestrial photogrammetry and high-resolution images accompanied by an in-situ damage survey were used to document cracking levels, stone weathering, and identification of decay patterns. Laboratory tests were conducted to assess the mineral composition, physical and mechanical properties of the construction materials to enable structural assessments. Data appraisal and integration into architectural drawings was used for mapping degradation patterns and the preservation state of the building. The documentation procedures combined with experiments were then employed to develop a model for structural analysis. Three-dimensional finite element numerical simulations employing macro-modelling approaches were performed for the Takiyya structures under various loading conditions, including modelling the bearing soil, resulting in good agreement with in-situ recorded structure damage patterns. The static and seismic nonlinear analyses helped identify the causes and effects of the current structural deficiencies. The adopted methodologies provided large amounts of information, permitting an improved understanding of existing damage and the assessment of the preservation state of the masonry structure. This project exists thanks to the Egyptian Ministry of Tourism and Antiquities (MoTA) and is funded by World Monument Fund (WMF) through various donors.

A double-strut macro-modelling approach for the in-plane analysis of masonry infilled RC frames with openings

A double-strut macro-modelling approach for the in-plane analysis of masonry infilled RC frames with openings

UNI-axial dynamic tests on a stone masonry subassembly before and after interventions

The present study deals with the seismic response of three-leaf stone masonry subassemblies before and after the application of intervention techniques. In detail, shaking table tests are performed on a scaled substructure in the Laboratory for Earthquake Engineering, at the National Technical University of Athens (NTUA). The substructure consists of two parallel walls. One wall is of rectangular section, whereas the other is provided with a portion of transverse wall at its mid-length. A flexible timber floor rests on the top of the walls. Sine-sweep and dynamic tests are performed perpendicular to the two walls, before and after interventions. The aim of this work is to experimentally study the response of three leaf masonry walls against in-plane and out-of-plane seismic actions, to investigate the effect of the transverse wall to the out-of-plane behavior of walls (and vice versa) and to assess the effect of a selected set of interventions on the behavior of the substructure. The results of this study confirm the vulnerability of three leaf masonry structures, evidenced by the premature detachment of masonry leaves. They prove the significant role of the transverse wall, in reducing the width of the separation cracks observed in the walls subjected to out-of-plane actions followed by an increase of its in-plane damage, as well as the positive effect (in terms of load and deformation capacity) of grouting the walls and enhancing the diaphragm action of the floor. Additionally, the experimental results of this study can serve as a validation tool for the calibration of numerical models and as input for further analytical research. In this paper, the calibration of a smeared crack model that is based on macro-modeling approach is presented, along with a comparison between experimental and numerical results for the specimen before interventions, based on the performed calibration.

The diagonal shear behavior of masonry walls fabricated with historical lime-based mortar and retrofitted with near surface mounted method

The historical monuments in different regions of the world were constructed using local materials. Sarooj was a lime-based mortar utilized extensively in the construction of Unreinforced Masonry (URM) buildings in some Middle Eastern countries in the past centuries. However, few studies have been conducted on the mechanical properties of masonry fabricated with Sarooj and strengthening of the elements in which this type of mortar was used. In the present study, the in-plane shear behavior of URM wallettes fabricated with Sarooj mortar and retrofitted with Near Surface Mounted (NSM) Glass Fiber Reinforced Polymer (GFRP) bars is investigated through an experimental and numerical study. In this regard, first, diagonal shear tests are conducted on square wallettes. The test specimens include bare and retrofitted wallettes. The type of paste used for filling the grooves in the NSM method and the retrofitted face of the wallettes are the main variables whose effects are investigated in the experimental program. In addition to the NSM method, the in-plane behavior of walls retrofitted with a novel technique named Epoxy Filled Joint (EFJ) is investigated in the experimental phase of the present study. Then, through a numerical study, the wallettes retrofitted with the NSM method are simulated in Finite Element (FE) software Abaqus following a macro-modeling approach. The results of the experimental study confirmed that the strengthening of the URM wallettes with the NSM method not only enhanced their ultimate in-plane shear strength, but also improved the ultimate drift capacity of the wallettes. Furthermore, the shear stress-drift curves obtained from the FE model were in good agreement with those obtained from the tests. In addition, the test results showed that the EFJ method significantly increased the in-plane shear strength of the wallettes.

Assessment of cyclic superposition approaches for the cyclic design of monopiles supporting offshore wind turbines

One of the key design criteria for the design of monopiles supporting offshore wind turbines is limiting the permanent rotation accumulated through its lifetime (Igoe et al., 2022). In geotechnical design practice, macro-modelling approaches are often used to assess the cyclic accumulated rotation. They requires 4 key components: (1) a static model, (2) a cyclic model for accumulating rotation for a given load package, (3) a superposition model for accumulating rotation between different load packages (4) an unloading model to assess the final permanent accumulated rotation once unloaded. The majority of literature focuses on the cyclic models. This paper assesses the effect of using different cyclic superposition models. A new superposition approach is proposed which matches well with the results from a high-quality field test from the literature. The paper compares the permanent accumulated rotation from four widely used semi-empirical cyclic models (Hettler, 1981, Solcyp, 2017; Leblanc et al., 2010a, Klinkvort and Hededal, 2013) used in conjunction with four different superposition approaches. The results demonstrate that the choice of superposition approach can be as important as the choice of cyclic model, which is often overlooked in the literature but is critical for the estimation of accumulated permanent rotation.

Evaluation of the Effect of Change in Support Conditions on the Seismic Behavior of a Historical Masonry Bridge

It is believed that the Yılanlı (or Leylekli) Bridge (bridge with stork or snake figures) in Tokat, a city with high seismicity, was built during the Roman or Byzantine period. Although no structural damage was found on the bridge, which is still open to pedestrian traffic, it is very important to determine the seismic behaviour of the bridge considering the possible earthquakes to which the structure will be exposed. This article presents the seismic response of the historical Yılanlı (Leylekli) Bridge, which has been subjected to unfavourable human-made changes in geometric shape over time. The original and modified shapes of the bridge were modelled using the macro modelling approach in ANSYS finite element software. The structural performance of the models was evaluated in terms of stresses, deformations, and especially cracks on the arch and spandrel walls using nonlinear static and time history analyses. The results of the analysis show that the change in shape, which is not desirable from an architectural and aesthetic point of view, adversely affects the seismic performance of the historical bridge and makes it more vulnerable to possible earthquakes. In addition, the analyses clearly showed that both models are subject to serious structural damage that could lead to a collapse in the event of a potential large magnitude earthquake.

Experimental collapse investigation and nonlinear modeling of a single-span stone masonry arch bridge

Determining appropriate intervention methods for rehabilitation and restoration of historic masonry bridges requires understanding the true behavior of the structural system. The presented study addresses this need by focusing on nonlinear structural behavior of stone masonry arch bridges and investigates the effect of different constitutive material laws, modeling approaches, and multiple spans on simulating the true behavior of the structural system. An extensive experimental program was conducted on a ¼-scaled model of a selected span of the multi-span arch bridge consisting of the arch ring, spandrel walls, and the fill. The model was tested with and without the presence of an in-plane steel bracing system supporting the spandrel walls to study the effect of adjacent spans on the selected span. Line loading applied at the quarter-span was increased with constant increments until. Destructive experimental investigation was followed by numerical studies of the tested specimen by means of both macro and simplified micro modeling approaches with DIANA FEA software utilizing different constitutive material models including Multi-Directional Fixed Crack Model with/without Drucker-Prager plasticity material law and Total Strain Based Fixed Crack Model. Comparison of the experimentally measured values with those of the numerical model validates that both modeling approaches can accurately predict the collapse load and collapse mechanism. Although simplified micro model offers advantages such as capturing the observed local damage states and cracking at masonry joints between the units; the added requirements of time, computational effort, and detailed material knowledge to model such structures accurately, makes macro modeling technique more preferable for masonry bridges having a complex geometry.

Application of the MACRO Model Approach to the Interpretation Management of Creative Tourism in the form of Coffee in Khao Kho Sub-district Phetchabun Province

The goal of this study was to spread information about interpretative management of creative coffee tourism using the MACRO model approach and to create new strategies for promoting coffee-based creative tourism in Khao Kho Subdistrict, Khao Kho District, and Phetchabun Province. The 40 people who are interested in taking part in the project of utilizing the MACRO model approach to transmit Khao Kho Arabica Coffee tour guides from beginning to finish and the 40 people who are coffee growers in the Khao Kho Sub-district of Phetchabun Province are the target demographics. The tools used in this research are; 1) a creative guide utilizing the MACRO model method to promote coffee-based community creative tourism, and 2)interpretative activities and a guidebook for tourism from source to mouth Using the MACRO model approach, Khao Kho Arabica coffee is a form used to interview project participants. The results showed that utilizing MACRO model approach with an IOC value of 0.89, guidelines and interpretative activities for tourism from source to mouth, Khao Kho Arabica coffee goods, which are values that may be used, and the final product after that, the researcher has improved and then communicated to the group of coffee producers and interested parties the guidebook and interpretative tourist activities from the beginning to the mouth, Khao Kho Arabica coffee goods. According to the transfer findings, participants in the project were highly satisfied with their engagement in the project of transferring the handbook and interpreting tourism activities, with an average of 4.66 and a standard deviation of 0.47. Participating in the activity encourages participants to construct a learning process through group brainstorming to create a body of information they can use to advance their careers and share with the general public.

A New Macromodeling Method Based on Deep Gated Recurrent Unit Regularized With Gaussian Dropout for Nonlinear Circuits

In this paper, for the first time, the deep gated recurrent unit (Deep GRU) is used as a new macromodeling approach for nonlinear circuits. Similar to Long Short-Term Memory (LSTM), the GRU has gating units that control the information flow and makes the network less prone to the vanishing gradient problem. Having a smaller number of gates causes GRU to have fewer parameters compared to LSTM leading to better model accuracy. Using the gates leads gradient formulations to have additive nature which helps them to be more resistant to vanishing and consequently learn long sequences of data. The proposed macromodeling method is capable of modeling nonlinear circuits more accurately and using fewer parameters compared to the conventional LSTM macromodeling method. To further improve the GRU performance, a regularization technique called Gaussian dropout is applied in this paper on deep GRU (GDGRU) to reduce the overfitting problem resulting in better test error. Additionally, the models obtained from the proposed techniques are remarkably faster than the original transistor-level models. To verify the superiority of the proposed method, time-domain modeling of three nonlinear circuits is provided. For these circuits, the comparisons of the accuracy and speed between the conventional recurrent neural network (RNN), the LSTM, and the proposed macromodeling methods are provided.

Earthquake response and damage patterns assessment of two historical masonry churches with bell tower

The earthquake response of two historical masonry churches is investigated through a finite element macro-modelling approach and non-linear dynamic analyses. The main aim of the study is to evaluate the church walls effects on the seismic performance and damage patterns of slender bell towers, which are analyzed also in the isolated configuration to perform a comprehensive comparison with the confined counterpart. The results of the numerical simulations point out that both the churches, which present different sizes, structural features and dynamic properties, are highly vulnerable to low-to-moderate seismic actions and the bell tower is one of the most critical elements, suffering widespread damage due to also the interactions effects with the neighboring church walls. The presence of shorter adjacent structural elements significantly modifies the main structural dynamic characteristics, seismic response and damage patterns of the bell tower. For both the confined towers, the first cracks originate in the connection regions with the adjacent church walls: on the other hand, for both the isolated towers, the first cracks originate mainly at the base. An advance of damage onset is also detected in the case of confined towers with respect to isolated towers. At the end of the numerical analyses, for both the case studies, the confined configurations show more remarkable damage patterns and larger values of energy density dissipated by tensile damage than the isolated ones, presenting relevant cracks concentrations mostly near the connection regions with the church walls and in the middle-upper part of the bell tower. The results of this study emphasize the paramount importance of taking into account the interactions effects with the surrounding church walls for a proper damage and failure mechanisms assessment of bell towers within the church context: simplified analyses performed on isolated configurations without considering such interaction effects may lead to significant underestimations of damage for the bell tower inside the church.

Numerical study on the nonlinear thermomechanical behaviour of refractory masonry with dry joints

Refractory masonry with dry joints is widely employed as a protective lining in industrial applications requiring high-temperature treatments. The thermal and mechanical behaviour of alumina spinel refractory masonry is investigated for a wide range of mechanical loading conditions at ambient and high temperature up to 1500 °C within the framework of the ATHOR project. This paper discusses the different numerical analysis approaches for the simulation of the experimental results. Micro and macro modelling approaches show good agreement with the large scale uniaxial and biaxial compression tests for loading and unloading at the ambient temperature. Simulations carried out for large scale uniaxial and biaxial creep tests as well as biaxial relaxation tests at 1500 °C show good agreement. The numerical results indicate the ability of these modelling approaches to represent the complex thermomechanical behaviour of the refractory masonry. Both methods demonstrate an orthotropic and highly nonlinear behaviour of the refractory masonry as observed in the experimental campaign. The numerical outcome, validated with experimental results demonstrate compatibility between micro and macro modelling approach that can be employed to evaluate local and global behaviour of large industrial installations.

Preliminary structural and seismic performance assessment of the Mosque-Cathedral of Cordoba: The Abd al-Rahman I sector

This manuscript discusses some preliminary results on the structural and the seismic performance of the Mosque-Cathedral of Cordoba, a UNESCO World Heritage. The area is characterized by a moderate seismic hazard. The building was built from the 8th to the 16th century and it has undergone several transformations. Owing to the complexity of the building, this work has focused on the assessment of the Abd al-Rahman I sector, which is the most aged part of the complex. For that, first, a 3D numerical finite element model of the sector has been done in the OpenSees framework and calibrated. To do so, an experimental non-destructive campaign has been carried out. Second, the model has been used to evaluate the structural behaviour, under vertical and horizontal loads, considering different scenarios. Finally, the crack patterns and the seismic safety have been obtained. The results showed that the numerical damage obtained for the gravitational loads is in good agreement with the data collected from the in situ surveys. Also, particular attention should be paid to the cymatiums, as they are the most demanded part of the system. Regarding its seismic performance, the building presents a higher capacity in the direction of the arcades. For the seismic demand, slight damage is expected in both principal directions of the building, which could be easily repaired. Damage concentration is expected in the contact between the perimetral wall and the arcades. This work has expanded the study of the features of the Mosque-Cathedral of Cordoba to the structural and seismic analysis with advanced numerical FE computing, which has not been done to date. To the authors’ knowledge, this is the first time that a macro-modelling approach with solid elements is presented for the seismic assessment of heritage buildings using the OpenSees framework. The methodology to do so is also presented. Apart from showing how advanced numerical analyses can provide useful information to assess the existing damage on monumental buildings, this work aims at contributing to the assessment of the vulnerability and the safety of one of the most emblematic mosque-like buildings of the world.

Comparison of different numerical modelling approaches for the assessment of the out-of-plane behaviour of two-leaf stone masonry walls

This work compares the ability of different numerical modelling approaches to simulate the out-of-plane behaviour of two-leaf stone masonry walls with different masonry bond configurations: an irregular drystone stone masonry wall and a masonry wall with roughly cut regular stone units. Finite element modelling, considering both a micro and macro-modelling approach, and the distinct element method have been compared in this study, which intends to (i) provide an insight regarding parameter estimation and the calibration procedure for each modelling approach considered; (ii) highlight their pros and cons of the selected modelling strategies; (iii) further expand the existing literature addressing the numerical modelling of two-leaf stone masonry walls.

Dynamic progressive collapse response of multi-storey frame structures with masonry infills

The response of reinforced concrete (RC) frame building structures to exceptional events like explosions or impacts causing the loss of a primary structural element depends on the robustness of the structural configuration. In the case of a sudden column loss, the resisting mechanism of the involved spans substantially changes, while a progressive collapse mechanism can develop under the arising dynamic loads. The presence of masonry infill walls can substantially modify the overall response to a sudden column loss scenario. In this context, this paper investigates the response of reinforced concrete frame structures undergoing instantaneous column losses in order to assess the influence of masonry infills on the progressive collapse response under dynamic load demands. A recently formulated equivalent-strut macro-modelling approach is employed to reproduce the mechanical interaction between infill walls and the frames. A ten-storey, six-bays 2D reinforced concrete frame is selected as a case study structure considering different reinforcement layouts (seismic or non-seismic design) and column loss scenarios (central column or corner column loss). The simulations are carried out using the fiber-section beam/column elements available in the OpenSees software platform, as they can account for the arching mechanism developing in the post-cracked regime. The dynamic responses of the case-study tests to the sudden column loss scenarios are assessed with and without the inclusion of masonry infills within the structural models. Results demonstrate that masonry infills introduce a substantial modification of the resisting mechanism and of the dynamic response, limiting the propagation of progressive collapse in most of the considered cases.

Seismic fragility assessment of low-rise reinforced concrete frame: A comparative study of bare and infill model

Most of the residential structures designed in Nepal are low-rise reinforced concrete (RC) frames. They are designed following the guidelines given in the Nepal Building Code, especially, the mandatory rule of thumb. In analyzing and designing most of the reinforced concrete structures in the urban and semi urban areas of Nepal, only bare frame model is considered. The additional effect caused by the infill walls are neglected. In this research, a comparative seismic fragility assessment of low-rise RC frame is conducted. Two cases are assumed; with and without the consideration of the unreinforced masonry infill. Macro modelling approach is followed for modelling the infill effect. Results clearly indicate that the inclusion of the infills drastically reduce the roof displacement compared to the bare frame model during a seismic shaking. This is attributed to the fact that the inclusion of the infill imparts more stiffness to the structure during a seismic-shaking compared to the bare frame model and hence the displacement is reduced. Furthermore, seismic fragility of the frame structure is also overstated when the effect of infill is not taken into consideration. The inclusion of infills reduced the structural fragility to significant extent. In this regard, the bare frame model was found to be more vulnerable to seismic shaking compared to the infill model.

Topology Optimization of the FRP for strengthening of masonry barrel vaults

Composite materials are commonly used to preserve historical structures for future generations. The optimum use of composite materials in strengthening masonry buildings and structural elements is a critical issue that needs solutions. This study aimed to determine the effect of optimal reinforcement arrangements on masonry vaults. Numerical models were created using a 3D macro modelling approach and validated with experimental and numerical data from the literature. The study compared the effectiveness of three strengthening procedures using carbon or glass fibre-reinforced fabric materials on masonry vaults under different loads, aiming to determine the most effective procedure, material type, and amount. Results showed that the intrados strengthening procedure was more effective than the extrados, and carbon fibre-reinforced fabric material was generally more effective than glass fibre-reinforced fabric material. The research demonstrates that using significantly less material can still achieve high efficacy. Additionally, the article presents various suggestions for practical situations.

Failure mechanisms and behaviour of adobe masonry buildings: A case study

Non-linear static analyses are amongst engineering community one of the most common analysis approaches for the seismic assessment of existing buildings, due to a good trade-off between information needed and results produced to assess structural safety. Pushover analyses, in fact, can provide hindsight onto structural behaviour well into the non-linear range, up unto conditions of collapse initiation and structural failure.Reliable information concerning the material’s mechanical behaviour – especially in the non-linear range - is, however, required – something which is challenging for earth-based materials, such as adobe masonry, due to the acknowledged variation of their mechanical properties.In this paper, a non-linear constitutive law for adobe masonry, numerically calibrated using experimental results and defined within the widely used computer program SAP2000®, a Finite Element software package commonly used by practicing engineers for building design and structural verification, is proposed. A total strain crack-based macro-modelling approach was pursued, and mechanical properties were validated through numerical modelling and comparison with values available in literature.The proposed constitutive model, whose reliability was proven by good agreement with experimental data, is then used to evaluate the expected seismic performance of a real case study given by an adobe building in central Portugal, representative of the city of Aveiro’s earthen heritage. Therefore, starting from this application, more hindsight over the structural behaviour of Portuguese adobe masonry buildings under failure conditions was provided, also showing the implemented model suitability for large scale structural analysis in the SAP2000® software. Sensitivity analyses are run in Finite Element environment and the structural behaviour considering different boundary conditions of the building, namely isolated and aggregate conditions, is assessed through a multi-criteria approach accounting for displacement and acceleration capacity, drift levels and safety against in-plane and out-of-plane failures.