Capacity Of Unreinforced Masonry Walls Research Articles

Out-of-Plane lateral load capacity of unreinforced masonry walls

ABSTRACT This study tests two full-scale unreinforced masonry (URM) walls under constant axial stress and cyclic out-of-plane lateral loads and proposes mathematical models to predict their rocking and toe crushingstrengths based on the elasticity and plasticity theorems of concrete. The two specimens were designed to simulate a non-perforated URM wall without opening and a URM wall with a door opening. Parallel walls with a length of 590 mm and thickness of 190 mm were constructed at the both ends of the walls in the out-of-plane direction, producing a barbell-shaped section. Test results showed that the URM wall specimens were initially governed by the rocking rotation and then ultimately failed with compressive toe crushing. The value of the equivalent damping coefficient mostly remained constant up to the occurrence of rocking rotation, beyond which it gradually increased. The effect of a door opening on the out-of-plane seismic response of the URM wall was insignificant because the applied lateral loads were resisted mainly by the in-plane action of the auxiliary parallel walls. The proposed models accurately estimated the rocking and toe crushing strengths of URM walls under out-of-plane lateral loads.

Probabilistic approach to assess URM walls with openings using discrete rigid block analysis (D-RBA)

This study aims to improve our current understanding of the seismic assessment of load-bearing unreinforced masonry (URM) systems by proposing a probabilistic computational modeling framework using the discrete element method (DEM). The main objective is to predict the structural behavior and capacity of URM walls with openings subjected to lateral loading, considering uncertainties in material properties. The proposed modeling strategy represents masonry as an assembly of rigid blocks interacting along their boundaries by adopting the point-contact hypothesis. Fracture energy-based softening contact models are implemented into a commercial discrete element code (3DEC) to better simulate both the pre- and post-peak behavior of masonry. The results highlight the influence of material properties on the force capacity, displacement capacity (drift limits), and collapse mechanisms of walls with openings. Based on the applied non-spatial probabilistic analyses, the most commonly observed failure mechanisms are further assessed using a simplified macro-block formulation. As a result, practical, yet necessary, inferences are made, providing valuable contributions. Furthermore, the validated discontinuum analysis framework is demonstrated as an accurate structural analysis strategy and a useful approach to simulating the potential collapse mechanism of load-bearing URM structures.

Simplified Approach for In-Plane Strength Capacity of URM Walls by Using Lower-Bound Limit Analysis and Predefined Damage Patterns

In this study, a two-phase simplified approach is proposed to predict the in-plane strength capacity of unreinforced masonry (URM) walls. In the first phase, in-plane damage and failure patterns of URM walls are determined from available observational (field) data, experimental data and also from numerical analysis data. Then, a set of rules are proposed to estimate damage and failure patterns of URM wall panels. In the second phase, this valuable information is employed to develop a simplified numerical model with a coarse mesh for the masonry wall, which is consistent with the crack formation at the ultimate state. Then, lower-bound limit analysis approach is used to predict the failure load of the wall without any detailed micro-element analysis. At the final stage, the proposed approach is verified by comparing the numerical results with experimental data from URM wall tests. By the assistance of this approach, it becomes possible to estimate the lateral capacities of ordinary, non-engineered URM walls and buildings from damage patterns at failure state. As an ultimate goal, this structural information can be used for seismic risk assessment of regions where the building typology considered in this study governs the building stock.

Influence of openings on two-way bending capacity of unreinforced masonry walls

Perforated unreinforced masonry (URM) walls in out-of-plane (OOP) two-way bending are commonly encountered in natural hazard investigations. However, related research is rather limited. This study focuses on the influence of openings on the two-way bending capacity of URM walls. An experimental database about the perforated URM walls in OOP two-way bending was created. A brief review of the experimental results show that the arrangement of the opening area can significantly affect the two-way bending capacity of walls (defined as the peak pressure on the wall net area): when the opening area is non-covered and non-loaded, the two-way bending capacity of the perforated wall is higher than that of its solid counterpart; when the opening area is covered with timber or glass plates loaded as the rest of the wall, the two-way bending capacity of the perforated wall is lower than that of the corresponding solid wall. These observations from the experiments were confirmed by an analytical estimation using the Yield Line Method (YLM). Next, to study the influence of openings on the two-way bending capacity, a numerical study has been carried out by employing the 3D simplified brick-to-brick modelling approach. The results of calibration and validation show that this modelling approach can precisely predict the two-way bending capacity and crack patterns. By applying the validated numerical models, the influence of the arrangement for the opening area from the experimental results and YLM evaluation was confirmed. Further, a parametric study focusing mainly on cases with the opening area non-covered and non-loaded was conducted. The influence of the geometric parameters of openings, namely, the opening size, shape and position was investigated on walls with different aspect ratios. Results show that the two-way bending capacity increases as the opening size or aspect ratio (height to width) increase, but it is insensitive to the opening position. Eventually, based on the numerical results, analytical equations were proposed to account for the influence of the considered parameters on the two-way bending capacity. A comparison with the Australian Standard (AS3700) indicates that the proposed equations incorporate more opening parameters such as opening shape.

In-plane lateral load transfer capacity of unreinforced masonry walls considering presence of openings

This study proposes mathematical models for the prediction of the in-plane lateral load capacity of unreinforced masonry (URM) walls considering potential failure modes and the presence of openings. The rocking strength is derived from the elasticity theorem for the compound stress condition under the assumption that rocking begins when the stresses at the extreme tensile fiber reach the tensile resistance capacity of the masonry. For toe crushing strength, the equivalent rectangular stress block specified in federal emergency management agency (FEMA) 273 is considered in the calculation of resultant compressive forces. The sliding and diagonal shear crack strengths are formulated based on the upper-bound theorem of concrete plasticity. The proposed models account for the effects of door or window openings on the failure mode and lateral load capacity of URM walls. The reliability of the proposed models is verified by comparing with test datasets comprising 202 URM walls without opening, 3 walls with door opening, and 4 walls with window opening. The proposed models confirm that URM walls are initially governed by the rocking rotation and subsequently ultimately fail via different mechanisms. It is also found that the empirical design equations specified in FEMA 273 and new zealand society for earthquake engineering (NZSEE) overestimate the rocking strength of URM walls and that their predicted their lateral load capacity significantly deviates from the test data. The proposed model results present comparatively better agreement with the test results. The mean and standard deviation of the ratios between the experimental and predicted results are 0.93 and 0.20, respectively, for URM walls without openings, and 0.92 and 0.14 respectively, for URM walls with openings. The proposed models rationally consider the effect of openings on the transition of the failure modes and the consequent reduction in the lateral load capacity.

Influence of aspect ratio and pre-compression on force capacity of unreinforced masonry walls in out-of-plane two-way bending

Out-of-plane (OOP) failure of unreinforced masonry (URM) walls in two-way bending was widely observed after natural hazards such as earthquakes. Of various crucial factors influencing the force capacity of URM walls in OOP two-way bending (force capacity being defined as the wall peak force in terms of pressure), the pre-compression and aspect ratio (defined as the wall height to length with the height kept constant) have not been sufficiently studied. To better understand their influence, an extensive numerical study was conducted by employing a detailed 3D brick-to-brick modelling method. First, a set of monotonic quasi-static tests on full-scale walls was taken as references for calibration and validation. The numerical results matched well with the experimental results in terms of initial stiffness, force capacity and crack pattern. Afterwards, the validated model was adopted to carry out a parametric study. Results show that the force capacity of the URM walls in OOP two-way bending is exponentially related to the aspect ratio and linearly related to the pre-compression. Besides, the influence of the pre-compression and aspect ratio on the force capacity can be interdependent. Additionally, when the pre-compression is relatively low, a wall does not crack in a localized manner into several rigid plane plates at the force capacity. Instead, the deformed shape of the wall approximates a curved surface, indicating distributed rather than localized cracking at force capacity. Furthermore, the force capacity is much higher than the residual force when the rigid-plates crack pattern is formed in the post-peak stage. The parametric study also shows that torsional failure of bed joints is the predominant failure mechanism for URM walls in OOP two-way bending, and its contribution to the force capacity generally increases as the pre-compression or aspect ratio increases. Finally, the numerical results were compared with the predictions by three major analytical formulations, namely Eurocode 6, Australian Standard for Masonry Structures (AS 3700) and Willis et al. (2006). As a result, the relations between the force capacity and the aspect ratio or pre-compression derived from the numerical models could not be accurately predicted by the analytical formulations. Based on previous results, recommendations on improving the analytical formulations were proposed.

Experimental behaviour of unreinforced and reinforced concrete block masonry walls under uniaxial compression

This paper presents the details of experimental investigations on the compressive strength of full scale hollow concrete block masonry walls. Comparison of load carrying capacity of unreinforced masonry walls with reinforced masonry walls have been studied as part of this study. The failure mechanism of reinforced hollow concrete block masonry (RHCBM) walls and unreinforced hollow concrete block masonry (URHCBM) walls have been studied. It is observed that the load carrying capacity of RHCBM walls are about 39.40% higher compared to URHCBM walls which is due to presence of marginal amount of reinforcement (about 0.12% of cross sectional area) and grout.

Capacity of unreinforced masonry walls in out-of-plane two-way bending: A review of analytical formulations

Investigations of post-seismic events show that the collapse of walls in out-of-plane (OOP) two-way bending can be one of the most predominant failure mechanisms for unreinforced masonry (URM) structures. To assess the force capacity of URM walls in OOP two-way bending, various analytical formulations have been developed during past decades. However, the accuracy and the application range of these analytical formulations have been evaluated against only a limited number of experiments. For this purpose, a dataset of 46 testing specimens from 8 international testing campaigns was created and used to evaluate current analytical formulations, namely Eurocode 6 based on the yield line method, Australian Standard AS3700 based on the virtual work method, and two other virtual work formulations related to AS3700. A general comparison shows that within the listed dataset, AS3700 overall provides the most accurate predictions. More specifically, AS3700 is the most accurate assessing walls assumed to be partially clamped and walls with openings. Testing specimens were divided into groups to study the influence of crucial factors, such as material properties, boundary conditions, pre-compression, aspect ratio and openings. However, only in a few cases clear trends were identified from the testing data. Sensitivity studies were carried out to reveal how the analytical formulations assess the influence of the crucial factors on the force capacity of the walls. Results expose drawbacks and limitations of the considered analytical formulations. Eventually, potential directions for improving the accuracy and the application range of the analytical formulations are pointed out.

Effects of size and position of openings on in-plane capacity of unreinforced masonry walls

In recent earthquakes, unreinforced masonry (URM) structures built of masonry walls containing openings such as doors and windows have been shown to have poor seismic capacity. However, although different sizes and positions of openings are known to reduce the stiffness and strength of URM walls, the relationships between the size and position of openings and seismic capacity of the walls are not clear. Therefore, a series of numerical analyses has, for the first time, explored many possible opening sizes and opening positions under simulated seismic loading to identify their impact on the in-plane behaviour of URM walls. The numerical models were built using the code “3DEC” which is based on the discrete element method (DEM). The key feature of the DEM is that it allows the development of large displacements between elements with contacts being recognized automatically during the analysis. Thus, this numerical method can capture the whole degradation progress from the initial cracking of the masonry walls right through to collapse, with the bricks being modelled as rigid blocks and the mortar as Coulomb-slip joints with zero thickness. Both load-based and displacement-based quasi-static pushover analysis procedures have been studied and the modelling methodology and the calibration of numerical models is described. The results from the analyses, the crack patterns and collapse mechanisms of the masonry walls are identified and discussed, and a key output from this work is the characterization of the relationships between the sizes and positions of openings and the in-plane performance of URM walls.

Strengthening unreinforced masonry walls using natural hemp fibers

This paper presents an experimental setup to study the effectiveness of using natural hemp fibers for enhancing the out of plane flexural capacity of unreinforced masonry walls. Wall specimens are constructed using normal-weight hollow concrete masonry units, and then hemp fiber fabrics are externally applied for strengthening. Performance of the hemp reinforced wall units is gauged by examining the flexural capacity, ductility, and failure modes of the wall specimens. A sensitivity analysis is conducted to investigate the effects of different strengthening configurations on the capacity of strengthened wall sections. Experimental results show that both the flexural capacity and ductility of the walls increase with an increase in reinforcement ratio.

On the out-of-plane flexural design of reinforced masonry walls

Out-of-plane flexural capacity of masonry is enhanced due to the presence of vertical compression up to a certain level. Most international design standards include the vertical load contribution to the flexural capacity of unreinforced masonry walls; however, the treatment of reinforced masonry design in such standards ranges from completely disregarding to partly accounting for the effect of vertical load to the resistance of out-of-plane loading. Furthermore, consideration of the effects of aspect ratio and boundary conditions on the out-of-plane response of reinforced masonry amongst the design standards is also not consistent. This paper presents a series of studies on the sensitivity to vertical compression, aspect ratio and boundary conditions of the out-of-plane flexure of reinforced masonry walls using a recently validated explicit finite element (EFE) model and provides a comparative assessment of the results predicted from the EFE and provisions of four international design standards. It is shown that disregarding the vertical load makes predictions of two-way out-of-plane flexural response extremely conservative in some standards; however, prediction of one-way vertical bending is reasonable in all standards. The results suggest that there exists a strong case for including the aspect ratio, boundary conditions and vertical compression for appropriate two-way bending design of reinforced masonry walls subject to out-of-plane loading.

Numerical study on factors that influence the in‐plane drift capacity of unreinforced masonry walls

SummaryDisplacement‐based assessment procedures require as input reliable estimates of the deformation capacity of all structural elements. For unreinforced masonry (URM) walls, current design codes specify the in‐plane deformation capacity as empirical equations of interstory drift. National codes differ with regard to the parameters that are considered in these empirical drift capacity equations, but the inhomogeneity of datasets on URM wall tests renders it difficult to validate the hypotheses with the currently available experimental data. This paper contributes to the future development of such empirical relationships by investigating the sensitivity of the drift capacity to the shear span, the aspect ratio, the axial load ratio, and the size of the wall. For this purpose, finite element models of URM walls are developed in Abaqus/Explicit and validated against a set of experimental results. The results show that the axial load ratio, the shear span, and the wall size are among the factors that influence the drift capacity the most. Empirical equations are mainly derived from test results on small walls, and the numerical results suggest that this can lead to a significant overestimation of the drift capacity for larger walls.

Increase of load‐carrying capacity of masonry with textile reinforced rendering / Erhöhung der Tragfähigkeit von Mauerwerk mit textilbewehrtem Putz

AbstractContemporary externally bonded structural upgrading schemes for masonry structures employ Fiber Reinforced Polymer (FRP) systems (a technique that was extended from concrete to masonry structures) and technical textiles (structural fiber grids) embedded in inorganic matrices. The latter account for a multitude of systems depending on the type of grid – fiber material, bundle treatment (dry, coated or even impregnated), grid geometry, manufacturing method etc. – and matrix – binder (e.g. cement or lime), rheology etc. – resulting in the derivation of many different acronyms (FRCM, TRM, CMG, IMG or other – see for definitions below). The mechanical behavior of such systems and their interaction with different substrates may vary significantly (e.g. dry vs. impregnated fiber grids embedded in mortars). This paper aims to summarize all reported efforts to increase the load‐carrying and/or deformation capacity of unreinforced masonry walls against in‐plane loading and second‐order phenomena (eccentric compressive loading).

Deformation capacity of unreinforced masonry walls subjected to in-plane loading: a state-of-the-art review

A research project on the deformation capacity of unreinforced masonry structures is underway at the Institute of Structural Engineering of ETH Zurich. The development of the basic building blocks for the displacement-based design of unreinforced masonry structures is the objective of the present research project, which should be seen as a first step in an initiative to investigate the limits of the deformation capacity of unreinforced masonry walls. This paper presents a summary review of previous experimental and analytical studies on the deformation capacity of unreinforced masonry walls subjected to in-plane loading. This review is the first phase of the aforementioned research program. A summary of 71 shear tests on unreinforced masonry walls is presented in the form of a database, along with the statistical analysis and discussion of the tests results. Furthermore, three different computational approaches for structural masonry, i.e. micro-modelling, macro-modelling and macro-element discretization, are discussed, and a review of macro-elements for the in-plane response of unreinforced masonry walls is presented. The reviewed models are discussed and a set of conclusions is given. Special attention is devoted to the deformation capacity parameter throughout the paper. Finally, the paper shows the limitations of our current state of knowledge of the deformation capacity of structural masonry.

Displacement-Based Assessment of the Seismic Capacity of Unreinforced Masonry Walls in Bending

In this paper, the displacement-based analysis procedure for the seismic assessment of unreinforced masonry walls in bending is refi ned to account for the dynamic response behaviour of the masonry building. The fi ltering effects in a masonry building are fi rst determined in accordance with the in-plane force-displacement properties of the supporting walls. The fi ltered excitations transmitted to the upper fl oors in the building are then used for analysis of the walls’ out-of-plane fl exural behaviour using traditional force-based (static and dynamic) analysis techniques. These results are then compared to displacement-based analytical predictions to highlight the potential conservatism of using only strength to assess the seismic resistance of masonry walls in bending

Strengthening of Unreinforced Masonry Walls Using FRPs

An experimental program conducted at the University of Alberta showed that externally applied fiber reinforced polymers (FRPs) are effective in increasing the load-carrying capacity of unreinforced masonry walls that are subjected to out-of-plane flexural loads. Ten walls with a height of 4 m were used to conduct 13 tests in two series. Both undamaged and slightly damaged walls were tested. The following experimental parameters were investigated: (1) type of fiber reinforcement; (2) amount of fiber reinforcement; (3) layout of fiber reinforcement; (4) effects of moderate compressive axial load; and (5) cyclic behavior. This paper briefly reviews the existing rehabilitation methods available and explains why the use of FRPs as external reinforcement is a possible alternative. The test setup and instrumentation of the specimens are described followed by a discussion of the results. The general behavior of the specimens is discussed with emphasis on the load deflection and strain characteristics. The modes of failure are identified and categorized. Finally, a simple analytical model is proposed and compared with the test results followed by a summary of the major results.