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.

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.

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.