Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (VI): Discrete Element Approach

ABSTRACT

Although many experimental tests and numerical models are available in the literature, the numerical simulation of the seismic response of existing masonry buildings is still a challenging problem. While the nonlinear behavior of masonry structures is reasonably predictable when the out-of-plane behavior can be considered inhibited, when the in-plane and out-of-plane responses coexist and interact, simplified models seem unable to provide reliable numerical predictions. In this article, taking advantage of the experimental tests carried out in a shaking table on two masonry prototypes at LNEC, a macro-element approach is applied for the numerical simulations of their nonlinear response. The adopted approach allows simulating the nonlinear behavior of masonry structures considering the in-plane and out-of-plane responses. Since it is based on a simple mechanical scheme, explicitly oriented to representing the main failure mechanisms of masonry, its computational cost is greatly reduced with respect to rigorous solutions, namely nonlinear FEM approaches. Two modeling strategies are adopted, namely a regular mesh independent from the real texture of the prototypes and a detailed one coherent with the units disposal. The numerical results are discussed and the correlation between the nonlinear static analyses and the dynamic response is provided.     

Simplified Macro-Model for Infill Masonry Panels

In structural analyses, masonry infill walls are commonly considered to be non structural elements. However, the response of reinforced concrete buildings to earthquake loads can be substantially affected by the influence of infill walls. In this article, an improved numerical model for the simulation of the behavior of masonry infill walls subjected to earthquake loads is proposed and analyzed. First, the proposed model is presented. This is an upgrading of the equivalent bi-diagonal compression strut model, commonly used for the nonlinear behavior of infill masonry panels subjected to cyclic loads. Second, the main results of the calibration analyses obtained with two series of experimental tests are presented and discussed: one on a single frame with one story and one bay tested at the LNEC Laboratory; and the second, on a full-scale four story and three-bay frame tested at the ELSA laboratory.     

Determination of Shear Strength of Masonry Panels Through Different Tests

This study addresses the problem of evaluation of strength of masonry walls. In-plane behavior of masonry panels has been studied under monotonic diagonal-compression and shear-compression loading in quasi-static test facility. The results of 35 laboratory and in situ tests are analyzed to show that in the case of the diagonal compression test results are lower than the strength of masonry walls evaluated trough the shear-compression test, highlighting the problem of choosing the test which best simulates to the real behavior of the masonry when stressed by lateral loads. A presentation is also given of the results of a F.E. investigation for shear strength evaluation of masonry walls. F.E. modeling non-linear procedure was used for the representation of masonry panels. The numerical simulations are compared with experimental results and the reliability of the different finite element models is discussed, thus confirming the different shear strength values measured in the experimental campaign.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (IV): Macro and Micro FEM Based Approaches

ABSTRACT

This article presents a study on the out-of-plane response of two masonry structures without box behavior tested in a shaking table. Two numerical approaches were defined for the evaluation, namely macro-modeling and simplified micro-modeling. As a first step of this study, static nonlinear analyses were performed for the macro models in order to assess the out-of-plane response of masonry structures due to incremental loading. For these analyses, mesh size and material model dependency was discussed. Subsequently, dynamic nonlinear analyses with time integration were carried out, aiming at evaluating the collapse mechanism and at comparing it to the experimental response. Finally, nonlinear static and dynamic analyses were also performed for the simplified micro models. It was observed that these numerical techniques correctly simulate the in-plane response. The collapse mechanism of the stone masonry model is in good agreement with the experimental response. However, there are some inconsistencies regarding the out-of-plane behavior of the brick masonry model, which required further validation.     

Methods and Approaches for Blind Test Predictions of Out-of-Plane Behavior of Masonry Walls: A Numerical Comparative Study

ABSTRACT

Earthquakes cause severe damage to masonry structures due to inertial forces acting in the normal direction to the plane of the walls. The out-of-plane behavior of masonry walls is complex and depends on several parameters, such as material and geometric properties of walls, connections between structural elements, the characteristics of the input motions, among others. Different analytical methods and advanced numerical modeling are usually used for evaluating the out-of-plane behavior of masonry structures. Furthermore, different types of structural analysis can be adopted for this complex behavior, such as limit analysis, pushover, or nonlinear dynamic analysis.

Aiming to evaluate the capabilities of different approaches to similar problems, blind predictions were made using different approaches. For this purpose, two idealized structures were tested on a shaking table and several experts on masonry structures were invited to present blind predictions on the response of the structures, aiming at evaluating the available tools for the out-of-plane assessment of masonry structures. This article presents the results of the blind test predictions and the comparison with the experimental results, namely in terms of formed collapsed mechanisms and control outputs (PGA or maximum displacements), taking into account the selected tools to perform the analysis.     

Effects of Geometrical Features on the Seismic Response of Historical Masonry Towers

ABSTRACT

Historical masonry structures are often located in earthquake-prone regions and the majority of them are considered to be seismically vulnerable and unsafe. Historical masonry towers are slender structures that exhibit unique architectural features and may present many inadequacies in terms of seismic performance. The seismic protection of such typologies of structures and the design of effective retrofitting interventions require a deep understanding of their behavior under horizontal loads. This paper presents the results of the seismic performance evaluation of historical masonry towers located in Northern Italy. A large set of case studies is considered, comprising a significant number of towers with high slenderness and marked inclination. First, a preliminary assessment of the dynamic behavior of the different towers is carried out through eigenfrequency analyses. Then, non-linear dynamic simulations are performed using a real accelerogram with different peak ground accelerations. A damage plasticity material model, exhibiting softening in both tension and compression, is adopted for masonry. The huge amount of results obtained from the non-linear dynamic simulations allows a comparative analysis of the towers to be performed in order to assess their seismic vulnerability and to show the dependence of their structural behavior on some geometrical characteristics, such as slenderness, inclination, and presence of openings and belfry. The evaluation of different response parameters and the examination of tensile damage distributions show the high vulnerability of historical masonry towers under horizontal loads, mainly in the presence of marked inclination and high slenderness. Some general trends of the seismic behavior of the towers are deduced as a function of the main typological features.     

Seismic Analysis of Masonry Gravity Dams Using the Discrete Element Method: Implementation and Application

Much research in recent years has focused on the seismic analysis of concrete and earthfill dams, and few works have addressed the case of masonry dams. The structural behavior of masonry dams is controlled essentially by its discontinuous nature, which may induce significant nonlinear response during an intense earthquake. In this article, a numerical tool based on the Discrete Element Method is presented, aimed at the static, dynamic, and hydromechanical analysis of masonry gravity dams. The use of discontinuous models is mandatory for the study of failure mechanisms involving the masonry discontinuities, the dam-rock interface or the rock mass joints. The Discrete Element Method is able to assemble continuous and discontinuous meshes simultaneously in the same model, providing a versatile tool to consider various assumptions and levels of analysis, ranging from simplified to detailed structural representations. A comprehensive study of the seismic behavior of Lagoa Comprida Dam, located in Portugal, is presented. Both continuous and discontinuous models were developed to assess the main failure mechanisms, including overstress, partial and global sliding, and overturning.     

Stability of Slender Masonry Columns with Circular Cross-Section under Their Own Weight and Eccentric Vertical Load

This work concerns the stability of unreinforced masonry slender circular cross-sectional columns subjected to their own weight and eccentric vertical load. Cantilever columns are examined, considering that the material has infinitely linear elastic behavior in compression and has no tensile strength. For the analysis, an existing numerical model and solution procedure developed for the stability analysis of masonry elements with rectangular cross-section are utilized and adapted to the circular columns. For the instability of the columns, an appropriate criterion that relates the top lateral deflection to the intensity of the applied eccentric vertical load is employed. By considering a reference column, critical buckling load is obtained, behavior of the column interpreted and efficiency of the numerical model emphasized. Performing a nonlinear buckling analysis using a general purpose software on this reference column, obtained results are compared with those of the adapted procedure of the present study. Implementing parametric analyses on reference column, effects of the column slenderness, eccentricity of vertical load, elastic modulus, and self-weight on the buckling load are investigated. Presented calculation procedure provides a useful tool in order to calculate the critical loads or to check the stability of masonry circular columns.     

Comparison of Numerical and Experimental Seismic Responses of FREI-Supported Un-reinforced Brick Masonry Model Building

Comparative study of numerically and experimentally obtained seismic responses of un-reinforced masonry building supported on in-house designed un-bonded fibre reinforced elastomeric isolator (U-FREI) are presented in this article. The effectiveness of U-FREI is established very clearly in terms of controlled dynamic response of the model building. Experimental studies are carried out on a shake table with elaborate instrumentations for measurement of acceleration and displacements at different floor levels. Numerical study of the model building supported on U-FREI is carried out to compare the results with experimental investigation. Multi-linear pivot hysteretic plasticity model is used to simulate the behavior of FREI, while plate elements are used for brick-masonry walls. Experimentally obtained force-displacement curves of FREI are used for defining the properties of multi-linear model representing FREI. The dynamic responses obtained from the numerical studies are compared with those from experimental investigations. This study indicates that the seismic responses of building supported on U-FREI can be numerically evaluated with quite reasonable accuracy. A good numerical model can be judiciously used at the preliminary design stage, followed by actual testing and construction of the base isolated building.     

Numerical Study on the Peak Strength of Masonry Spandrels with Arches

This article presents a numerical study on the force-deformation behavior of masonry spandrels supported on arches which are analyzed using simplified micro models. The model is validated against results from quasi-static cyclic tests on masonry spandrels. A large range of spandrels with different arch geometries, material properties, and axial load ratios are studied. The numerical results are compared to peak strength values predicted with an existing mechanical model. Finally, estimates for the initial stiffness and the spandrel rotation associated with the onset of strength degradation are derived.     

Effectiveness of FRCM Reinforcement Applied to Masonry Walls Subject to Axial Force and Out-Of-Plane Loads Evaluated by Experimental and Numerical Studies

ABSTRACT

An experimental campaign and a numerical analysis devoted to the investigation of the out-of-plane behavior of masonry walls reinforced with Fiber Reinforced Cementitious Matrix (FRCM) are presented here. The main goal of this study is to analyze and evaluate the effectiveness of the strengthening system, by discussing failure modes and capacity of strengthened masonry walls, in order to assess their behavior under out-of-plane horizontal actions, such as, for example, seismic actions. A purposely designed experimental set-up, able to separately and independently apply an axial force and out-of-plane horizontal actions on masonry walls, was used. Experimental results are discussed and compared with the outcomes of nonlinear analyses performed on simplified finite element models of the walls. A proper evaluation of the flexural capacity of FRCM strengthened walls is the first step of the ongoing process of drawing reliable code guidelines leading to a safe design of strengthened masonry structures.     

THREE DIMENSIONAL NONLINEAR BUILDING POUNDING WITH FRICTION DURING EARTHQUAKES

The three dimensional pounding phenomenon of two adjacent buildings during earthquakes with aligned rigid horizontal diaphragms is investigated for the linear and nonlinear structural response. The developed formulation takes into account three dimensional dynamic contact conditions for the velocities and accelerations based on the impulse-momentum relationship, using the coefficient of restitution e and the ratio μ, of tangential to normal impulses, which corresponds to the coefficient of friction under certain conditions. The contact points are determined geometrically from the displacements of the diaphragms' centre of mass. The results of the proposed formulation are compared with those obtained with the Lagrange multipliers approach. Test results are performed for two sets of multi-storey adjacent buildings subjected to real earth-quake motions with elastic and inelastic structural response.     

Experimental and Analytical Investigation on the Corner Failure in Masonry Buildings: Interaction between Rocking-Sliding and Horizontal Flexure

ABSTRACT

The failure mechanism of corners in masonry buildings has frequently been observed in seismic scenarios, but only a few works and no experimental investigations devoted to it are available in the literature. In this aritcle, the experimental behavior of a simple masonry corner is first analyzed, by simulating the seismic horizontal actions through a progressive tilting of the supporting base. Then, the conditions of the onset of two possible failure modes are analytically formulated: they are the rocking-sliding and the horizontal flexure mechanism. A three-dimensional macro-block model with frictional joints is used to analyze these mechanisms, while the crack patterns and the load factors are derived through the kinematic approach of the limit analysis. The evaluation of the in-plane frictional resistances involved by the rocking-sliding mechanism is performed by applying a reliable criterion previously proposed, while for the torsion strength involved in the horizontal flexure mechanism, simplified yield conditions are adopted and a possible criterion is also introduced to take into account the actual reduction of the contact surfaces. Last, the experimental findings are compared and critically interpreted in light of the analytical results and the influence of the main parameters on the prevailing mechanism is highlighted.     

A MICROMECHANICAL INELASTIC MODEL FOR HISTORICAL MASONRY

A micromechanical damage model for the Snite element modelling of historical masonry structures is presented in this article. Masonry is considered as a composite medium made up of a periodic assembly of blocks connected by orthogonal bed and head mortar joints. The constitutive equations, in plane stress, are based on the homogenisation theory and they consider the non linear stress-strain relationship in terms of mean stress and mean strain. Different in-plane damage mechanisms, involving both mortar and blocks, are considered and the damage process is governed by evolution laws based on an energetic approach derived from Fracture Mechanics and on a non-associated Coulomb friction law. The failure domain of the model is analysed both in the equivalent stress and in the principal stress space considering different orientations of the bed joints relative to the loading direction. A comparison with experimental results is provided. A numerical simulation of masonry walls subjected to horizontal forces proportional to their own weight is shown in order to discuss the model's capability of describing the influence of the masonry microstructure on its mechanical behaviour.     

Rapid Diagnosis of Crack Patterns of Masonry Buildings Subjected to Landslide-Induced Settlements by Using the Load Path Method

One of the main difficulties, when dealing with landslide structural vulnerability, is the diagnosis of the causes of the crack pattern. This is also due to the excessive complexity of models based on classical structural mechanics that makes them inappropriate especially when there is the necessity to perform a rapid vulnerability assessment at the territorial scale. This is why in this article a new approach for the rapid diagnosis of crack patterns of masonry buildings subjected to landslide-induced settlements is proposed. This approach is based on the Load Path Method, recently applied to the interpretation of the behavior of masonry buildings subjected to landslide-induced settlements.     

RESPONSE OF UNREINFORCED MASONRY BUILDINGS

Abstract

A summary of dynamic measurements are presented that illustrate relations between linear seismic demand and true nonlinear response of unreinforced masonry buildings with flexible diaphragms and rocking piers subjected to a series of simulated earthquake motions.     

OUT-OF-PLANE SEISMIC RESISTANCE OF MASONRY WALLS

Seismic vulnerability of unreinforced masonry buildings is studied by means of simplified out-of-plane collapse mechanisms that take into account connections with transversal walls. According to experimental evidence, the analysis assumes that failure is reached with a rigid body motion of a part of the facade that falls down. Two classes of mechanism are examined: the overturning of the facade due either to a vertical crack at the connection or a diagonal crack on the transversal wall, both defined resorting to a simple model of masonry fabric, viewed as a regular assembly of rigid blocks and elastic plastic joints with friction but no cohesion. The use of simplified mechanisms give rise to an explicit evaluation of the seismic resistance to changes in the geometry and in the masonry fabrics, that could be used by practising engineers. This formulation is developed for both static horizontal actions and ground velocity peak, in the belief that the latter probably gives a better approximation of seismic action, while also providing, by comparison with the results of static forces, an estimate of the behaviour factor for unreinforced masonry. Eventually, the analytical forecasts are compared with numerical results obtained by means of the distinct element method.     

Experimental Study on Postponing the Deboning of FRP Sheets in Masonry Walls

ABSTRACT

A large number of buildings all around the world are constructed of unreinforced masonry. These structures do not act well during earthquakes because of their vulnerable behavior. In last two decades, fiber-reinforced polymers (FRPs) has been used widely in seismic rehabilitation and strengthening unreinforced concrete and masonry structures. One important issue in using FRP composites for strengthening masonry walls is the inopportune debonding of composites from the wall surface; thus, in this article new methods are proposed to further delay the mentioned debonding issue. For this purpose, 13 masonry panels with 100x870x870 mm dimension are strengthened by using carbon and glass FRPs (CFRPs and GFRPs). A variety of strengthening methods such as surface preparation, boring, grooving, nailing, and plaster are used to mount FRP composites to the walls. For each specimen subjected to diagonal compression test, the loading level along with tensile and compressive diagonal displacements are evaluated. In order to assess the effect of FRP composites, four unreinforced masonry walls are tested as well. The results show 110% increase in ductility index of reinforced specimens compared to the unreinforced ones.     

Seismic Assessment of a Historical Masonry Building in Switzerland: The “Ancien Hôpital De Sion”

This article presents the results of the evaluation of the seismic safety of the Ancien Hôpital de Sion, an important Swiss architectural heritage building, situated in the Canton of Valais, the region with the highest seismic hazard in Switzerland. Three-dimensional Applied Element (AEM) modeling of the whole structure has been performed and validated. The adopted modeling strategy, together with nonlinear dynamic analysis, was able to represent the actual behavior and failure mechanisms typical of complex masonry structures, in addition to a good computational efficiency compared to other available numerical approaches. The local collapse mechanisms have been also studied through a kinematic limit analysis based on rigid block rotation. Both linear and nonlinear approaches have been followed together with the capacity spectrum method. The results provided by the different methodologies have been compared with the aim to provide possible insights concerning a general procedure for the assessment of the safety of such type of structures.