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.     

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.     

Definition of Seismic Input for Out-of-Plane Response of Masonry Walls: I. Parametric Study

Response of masonry walls to out-of-plane excitation is a complex, yet inadequately addressed theme in seismic analysis. The seismic input expected on an out-of-plane wall (or a generic “secondary system”) in a masonry building is the ground excitation filtered by the in-plane response of the walls and the floor diaphragm response. More generally, the dynamic response of the primary structure, which can be nonlinear, contributes to the filtering phenomenon. The current article delves into the details and results of several nonlinear dynamic time-history analyses executed within a parametric framework. The study addresses masonry structures with rigid diaphragm response to lateral loads. The scope of the parametric study is to demonstrate the influence of inelastic structural response on the seismic response of secondary systems and eventually develop an expression to estimate the seismic input on secondary systems that explicitly accounts for the level of inelasticity in the primary structure in terms of the displacement ductility demand. The proposed formulation is discussed in the companion article.     

Review of Different Pushover Analysis Methods Applied to Masonry Buildings and Comparison with Nonlinear Dynamic Analysis

This article presents the comparison among different nonlinear seismic analysis methods applied to masonry buildings, i.e., pushover analyses with invariant lateral force distributions, adaptive pushover analysis and nonlinear dynamic analysis. The study focuses on the influence of lateral force distribution on the results of the pushover analysis. Two simple benchmark case studies are considered for the purpose of the research, i.e., a four-wall masonry building prototype without floor rigid diaphragms and a two-wall system with a cross-vault. The comparative study offers a useful review of pushover analysis methods for masonry structures and shows advantages and possible limitations of each approach.     

In-Plane Seismic Response Analyses of a Historical Brick Masonry Building Using Equivalent Frame and 3D FEM Modeling Approaches

ABSTRACT

This article aims at contributing to the seismic performance assessment of a historic brick masonry building by finding a strength reduction coefficient through the use of linear and nonlinear modeling approaches, using Finite Element Method and Equivalent Frame modeling. To reduce the uncertainties, ambient vibration tests (AVT) were implemented. Series of simulations was performed using nonlinear dynamic analyses and incremental dynamic analysis curves were compared with the pushover curves. Results indicate that the mass-proportional pushover curve meets the mean of results obtained from IDA and the strength reduction coefficient falls into the range given in EN 1998–1 for unreinforced masonry.     

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.     

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.     

Review of Out-of-Plane Seismic Assessment Techniques Applied To Existing Masonry Buildings

ABSTRACT

Observations after strong earthquakes show that out-of-plane failure of unreinforced masonry elements probably constitutes the most serious life-safety hazard for this type of construction. Existing unreinforced masonry buildings tend to be more vulnerable than new buildings, not only because they have been designed to little or no seismic loading requirements, but also because connections among load-bearing walls and with horizontal structures are not always adequate. Consequently, several types of mechanisms can be activated due to separation from the rest of the construction. Even when connections are effective, out-of-plane failure can be induced by excessive vertical and/or horizontal slenderness of walls (length/thickness ratio). The awareness of such vulnerability has encouraged research in the field, which is summarized in this article. An outline of past research on force-based and displacement-based assessment is given and their translation into international codes is summarized. Strong and weak points of codified assessment procedures are presented through a comparison with parametric nonlinear dynamic analyses of three recurring out-of-plane mechanisms. The assessment strategies are marked by substantial scatter, which can be reduced through an energy-based assessment.     

Simple Homogenization-Topology Optimization Approach for the Pushover Analysis of Masonry Walls

ABSTRACT

A topology optimized rigid triangular FE macro-model with non-linear homogenized interfaces for the pushover analysis of in plane loaded masonry is presented. The shape of the mesh and the position of the interfaces is evaluated through a topology optimization approach that detects the main compressive stress fluxes in the structure. Different values of the horizontal action are considered to derive an adaptive mesh or an optimal discretization that is suitable for multiple loads. Masonry properties are calibrated by means of a homogenization approach in the nonlinear range. To tackle elastic and inelastic deformations, interfaces are assumed to behave as elasto-plastic with softening in both tension and compression, with orthotropic behavior. The two-step procedure competes favorably with classic equivalent frame approaches because it does not require a-priori assumptions on the mesh and on the length of the rigid offsets. An example of technical relevance is discussed, relying into a multi-story masonry wall loaded up to failure.     

Force-Based Beam Finite Element (FE) for the Pushover Analysis of Masonry Buildings

A simplified approach for analyzing the nonlinear response of masonry buildings, based on the equivalent frame modeling procedure and on the nonlinear equivalent static analyses, is presented. A nonlinear beam finite element (FE) is formulated in the framework of a force-based approach, where the stress fields are expanded along the beam local axis, and introduced in a global displacement-based FE code. In order to model the nonlinear constitutive response of the masonry material, the lumped hinge approach is adopted and both flexural and shear plastic hinges are located at the two end nodes of the beam. A classical elastic-plastic constitutive relationship describes the nonlinear response of the hinges, the evolution of the plastic variables being governed by the Kuhn-Tucker and consistency conditions. An efficient element state determination procedure is implemented, which condenses the local deformation residual into the global residual vector, thus avoiding the need to perform the inner loops for computing the element nonlinear response. The comparison with some relevant experimental and real full-scale masonry walls is presented, obtaining a very good agreement with the available results, both in terms of global pushover curves and damage distributions.     

Window opening effects on structural behavior of historical masonry Fatih Mosque

Structural walls of old historical structures are either blind or have openings for functional requirements. It is well known that in and out of plane responses of structural walls are affected by the size, locations, and arrangements of such openings. The purpose of this investigation is to study the window opening effects on static and seismic behaviors of historical masonry old mosques. Fatih Mosque, which was converted from a church, constructed in 914 in Trabzon, Turkey, is selected for this purpose. The mosque is being restored. Structural exterior walls of the mosque were made using stone and mortar materials. When the plaster on the walls was removed during the restoration, 12 window openings were found as blind on the exterior structural walls of the mosque. Within the scope of restoration works, it is aimed to open such blind windows. In order to investigate the effects of the window openings on the structural behavior of the mosque, 3D solid and finite elements models of the mosque with and without window openings are initially developed. The experimental dynamic characteristics such as frequency, damping ratio, and mode shapes of the current situation of the mosque, where some windows openings are blind, are determined using Ambient Vibration Testing. Then, the finite element model of the current situation of the mosque is updated using the experimental dynamic characteristics. The static and seismic time history analyses of the updated finite element model with and without window openings are carried out. Structural behaviors of the mosque with and without window openings are compared considering displacement and stress propagations.     

Comparative Seismic Risk Assessment of Basilica-type Churches

ABSTRACT

This paper discusses the seismic risk assessment of a Basilica-type church according to the provisions of the Italian Guidelines. A comparison between the results obtained with local and global approaches is reported, based on a knowledge process aimed to characterize the geometric and mechanical parameters required for a reliable structural analysis. To perform the global analyses the finite element technique was employed, with proper assumptions to account for the nonlinear behavior of masonry. Illustrating a case study, the paper critically discusses about the employability of pushover analysis methods for the seismic assessment of basilica-type churches.     

Interaction Curves for In-Plane and Out-of-Plane Behaviors of Unreinforced Masonry Walls

Different types of macro-elements have been proposed to simulate the behavior of unreinforced masonry (URM) structures under seismic loads. In many of these, macro-elements URM walls are replaced with beam elements with different hysteretic behaviors. The effect of out-of-plane loading or change of gravity load due to the overturning moment is usually not considered in the behavior of these macro-elements. This article presents interaction curves for bidirectional loadings of unreinforced masonry walls to investigate the importance of these factors. Two parameters are systematically changed to derive the interaction curves for a wall with specific dimensions, including compressive traction atop the wall to represent gravity loading, and loading angle that represents a combination of in-plane and out-of-plane earthquake loadings. Interaction curves are developed considering various possible failure modes for bricks and mortar, including tension, crushing and a combination of shear and compression/tension failures. The proposed interaction curves show the initiation of failure of URM walls as a function of compressive traction and loading angle. Several examples are presented for URM walls with different aspect ratios to aid in understanding the effects of various parameters on the derived interaction curves. Finally, for a specific case, the derived interaction curve is compared with nonlinear finite element results and ASCE41. The results show that, as a simplified method, the derived interaction curves can be used for the preliminary evaluation of URM walls under bidirectional loadings.     

Seismic Assessment of the Lima Cathedral Bell Towers via Kinematic and Nonlinear Static Pushover Analyses

ABSTRACT

The protection of cultural heritage against earthquake induced actions is one of the main challenges the earthquake engineering science and practice are facing. This article presents a seismic assessment study on one of the most ancient colonial buildings present in Peru, the Cathedral of Lima, focusing on its towers. A historical review highlighted how these structures, together with the whole Cathedral, suffered intense damage and partial collapse during previous earthquakes. In order to identify the structure main deficiencies, both linear kinematic analyses and nonlinear static analyses have been performed. Different nonlinear finite element models have been created to evaluate the influence of the adjacent walls. Different load distributions have been compared to evaluate how simplified patterns could provide results close to load distributions taken from a modal analysis of the complex. A simple retrofit strategy, consisting on the introduction of steel ties, has also been studied as a reference. Results show good correlation between kinematic and pushover analyses. The construction, when compared to the requirements of the national code for new buildings, results significantly vulnerable, pointing out the need to accept some structural damage even after seismic retrofit.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (III): Two-Step FEM Approach

ABSTRACT

This article presents numerical simulations of two full-scale masonry structures which were tested on the shaking table within the scope of the workshop “Methods and challenges on the out-of-plane assessment of existing masonry buildings”. The numerical models have been developed on the basis of the blind-prediction models which have been improved after the publication of the test results. The solution procedure is divided into two steps with separate numerical simulations for each one. In the first step the collapse mechanism of the structure is determined by means of pushover analysis using a continuum, plasticity-based model. In the second step the dynamic response of the structure is simulated using a multibody model approach and frictional contacts. Results of the tests show reasonable, yet far from perfect predictive capabilities of the used numerical methods.     

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.     

Seismic Behavior Prediction of Flanged Unreinforced Masonry (FURM) Walls

In most available studies, unreinforced masonry (URM) walls are idealized as rectangular sections, while in reality walls have effective sectional shapes such as C, I, T, and L. In this article, the results of experimental and analytical assessment of flange effects on the behavior of I- and C-shaped URM walls are reported. Four clay brick walls at half scale were tested. Two specimens were designed with I- and C-shaped sections, and for comparison, two additional specimens were designed without flanges. The tests showed that under constant axial load the strength of the I-shaped wall increases, but that of the C-shaped wall decreases, because of out-of-plane distortion effects. Despite the loss of strength, both flanged walls indicated almost similar initial stiffness, deformation capacity, and mode of failure in comparison with walls without flanges. A mixed-mode analytical model is proposed to predict the lateral force displacement curve of flanged URM (FURM) walls. The proposed analytical model is based on section analysis of the walls and shows good agreement with previous experimental results.     

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.     

Displacement-Based Design of an Energy Dissipating System for Seismic Upgrading of Existing Masonry Structures

A displacement-based method for the design of an energy dissipating system is proposed in this article. The device, which is composed of added concrete walls equipped with hysteretic Added Damping and Stiffness (ADAS) dampers, is aimed at upgrading the seismic behavior of existing masonry structures. The design method is based upon a simplified model of the overall structure-dissipating system. The proposed displacement-based design procedure was tested by means of inelastic response-time history analyses considering different masonry structures. The results of the analyses were compared with the seismic behavior expected from the design.     

Out-of-Plane Seismic Response of Unreinforced Masonry Walls: Conceptual Discussion,Research Needs,and Modeling Issues

ABSTRACT

Modeling unreinforced masonry walls, subjected to seismic loads applied normal to their plane, has received much attention in the past. Yet, there is a general lack of conformance with regard to what aspects of seismic response a computational model should reflect. Boundary conditions are certainly an important aspect, as the response can involve two-way bending or just one-way bending and, in the second case, along vertical or horizontal directions. In this respect, flexural restraint of wall intersections can be significant in addition to size and placement of openings. Moreover, in-plane damage can modify the boundary conditions and the overall out-of-plane performance. Proper modeling of actions is also relevant, as they can be a result of distortions imposed upon wall elements and/or inertial forces along the span of a wall. Axial forces can markedly affect the out-of-plane response of the wall, particularly vertical compressive forces, which can enhance out-of-plane strength. The outcome of static verifications can be more conservative than that of dynamic analyses, but the latter are much more complex to carry out. These topics are discussed with reference to previous research, observations in the field and in the laboratory, as well as numerical analyses on three-dimensional models.