Investigations on unreinforced masonry (URM) walls subjected to natural hazards, such as earthquakes and wind loads, identify the out-of-plane (OOP) failure as one of the most common failure mechanisms. Concerning the OOP failure, two types of failure mechanisms can be distinguished in URM walls: one-way bending in which lateral edges of walls are not supported; two-way bending in which at least one lateral edge of walls is supported in addition to the supports at the top and bottom. Compared with walls in one-way bending, walls in two-way bending are more widely encountered in practice considering that the lateral edges of walls are usually connected with pillars or return walls. Therefore, the failure of URM walls in OOP two-way bending can be more common. Even so, research on the geometric parameters that can have a major influence on the two-way bending capacity of URM walls, such as the aspect ratio, pre-compression and opening, is quite scarce. Due to a lack of experimental evidence and systematic numerical study, the current analytical formulations, namely the Yield Line Method (YLM) incorporated in the European Standard Eurocode 6, and the Virtual Work Method (VWM) incorporated in the Australian Standard AS3700 and Dutch Practical Guideline NEN-NPR 9998, assessing these geometric parameters can be limited in accuracy and application range. This thesis aims at improving the analytical formulations assessing the influence of geometric parameters on the two-way bending capacity of URM walls. As a starting point, the accuracy and application range of the current analytical formulations are assessed and geometric parameters having a crucial influence on the two-way bending capacity are revealed (Chapter 2). A dataset of 46 testing specimens from 8 international testing campaigns is created and used for the assessment. The analytical formulations based on the VWM are found to return the most accurate predictions for the testing specimens. Even so, drawbacks and limitations are identified for the VWM. Besides, the precompression, wall aspect ratio and openings are identified to have a crucial influence on the two-way bending capacity of URM walls....@en

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.

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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.

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Research has shown that lateral boundary conditions can have a large influence on the force capacity of two-way spanning unreinforced masonry (URM) walls subjected to out-of-plane (OOP) loading. Differently than laterally free one-way spanning walls, they show a higher force capacity, which however is underestimated by current analytical formulations. By means of nonlinear finite element analyses adopting a detailed 3D brick-to-brick model, the influence of lateral boundary conditions on two-way out-of-plane failure of a single wythe masonry wall is studied. Results indicate that the cracking pattern varies as lateral boundaries become stiffer, accordingly the force capacity increases. Numerical results are compared with analytical formulation proposed in the Australian Standard AS3700. These preliminary results will serve to evaluate how to consider the lateral boundary conditions, provided by the wall-to-wall connection, for two-way spanning walls in existing buildings.@en

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.

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