A non-linear discrete homogenized strategy is used to reproduce out-of-plane two-way bending shake table tests on full-scale unreinforced masonry walls. The numerical strategy represents unreinforced masonry walls as an assemblage of rigid quadrilateral plates connected through non-linear interfaces represented. The material response laws for these non-linear interfaces are derived from a homogenization procedure performed at the meso-scale by a finite-element plate model. This discrete model can simulate masonry orthotropy, full softening behaviour and failure. Bending and torsional deformation modes are represented. The performance of the numerical models in describing the response of the experimentally tested full-scale specimens is presented. The numerical strategy is then used to study the behaviour of unreinforced masonry walls in configurations hitherto untested. Such numerical results are then compared to state-of-the-art analytical approaches. Potential avenues of improvement for the implemented analytical methods are also highlighted.@en

This paper describes a simplified methodology for the assessment of unreinforced masonry (URM) walls under out-of-plane two-way bending seismic action. The methodology involves a force-based check derived from the principle of virtual work. This check is proposed based on experimental observations of significant cracking resistance associated with two-way spanning URM walls, indicating methodologies considering such walls to be pre-cracked or to be non-laterally supported as overly conservative. The methodology incorporates several findings and developments from recent experimental campaigns: ranging from novel characterization tests on masonry couplets to incremental dynamic tests on full-scale buildings. Such incorporations include new formulation to calculate the torsional shear strength of a bed joint and accounting for possible changes in the boundary conditions of an OOP wall during dynamic loading. Testing standards as well as recommendations in several international guidelines for masonry structures addressing the input properties required to implement the proposed methodology are enlisted and reviewed. The methodology requires the definition of the period of vibration of the assessed URM walls, to calculate which plate theory based formulation is provided. Open research questions and potential avenues for further development of the methodology are ultimately highlighted.@en

An experimental programme was conducted on six different batches of unreinforced masonry (URM) considering different unit-mortar combinations to study their behaviour under torsional shear. Experiments performed included a specific characterisation test to measure the torsional shear strength of URM bed joints. Dilatancy measurements during both direct and torsional shear testing of masonry were recorded. Refined finite element modelling was then performed to evaluate whether parameters evaluated from standardised direct shear tests on masonry triplets can be used to estimate the torsional shear strength of URM bed joints. A possible mechanism by which dilatancy can increase the torsional shear resistance of bed joints without affecting the external level of applied normal force is also presented. Based on both experimental and numerical findings, a rational mechanics based formula to evaluate the torsional shear strength of URM bed joints is proposed and validated. This formula represents an improvement on currently used empirical formulation correlating the torsional shear strength of a URM bed joint to their flexural tensile strength.

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This paper presents a benchmark exercise for the seismic assessment of unreinforced masonry (URM) buildings as a follow-up of a blind prediction test organized in the context of the European Conference of Earthquake Engineering Series. The blind prediction exercise was aimed at better defining the open issues in current procedures for modeling and performing seismic analysis of URM buildings, by highlighting the uncertainty that can influence the results. This work presents an overview of the approaches used by different research teams and the scope of predictions. The benchmark structure was a three-story building with traditional European architecture from which two Cases were considered: A) stone masonry walls and flexible horizontal diaphragms and B) brick masonry walls and rigid horizontal diaphragms. A wide range of approaches was used by the participating teams concerning modeling strategies, methods of analysis and criteria for the attainment of limit states, which are here addressed as potential sources for the dispersion of predictions. The results were compared in terms of capacity curves, predicted failure mechanisms compatible with the fulfillment of limit states of near collapse and damage limitation, and related minimum values of peak ground acceleration (PGA). The results show an overall good agreement for damage patterns and collapse mechanisms in both benchmark structures, presenting some differences in the type of failure mode and its extent. However, the scatter of predicted capacity curves and critical PGAs is very high, especially for the Case with brick masonry and rigid diaphragms, indicating that clearer procedures in the building codes are required for professionals.

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Out-of-plane (OOP) mechanisms are one of the major causes of structural collapse in unreinforced masonry (URM) buildings as observed in recent as well as past seismic events. Among such failures, two-way bending mechanisms involving at least one restrained vertical edge constitute a very distinct majority. Nevertheless, very little research pertaining to such mechanisms can be found currently in literature. The paper takes a step forward in this topic through the execution and interpretation of dynamic tests on four full-scale single leaf and one full-scale cavity URM walls. Each tested full-scale specimen consisting of a OOP panel and two return walls, varying in terms of commonly encountered boundary conditions, applied overburden or the presence/absence of an opening. The specimens were subjected to sequences of incremental input motion till collapse and these results are presented in terms of deformed shapes, failure mechanisms and force-displacement hysteretic curves. State of the art analytical techniques based on the method of virtual work are applied to evaluate their reliability as simplified tools for assessing the behaviour of such wall subjected to OOP two-way bending excitation. The testing campaign resulted in all specimens exhibiting a rather brittle response, despite sustaining accelerations of 1 g without any damage.@en

In this paper, a dataset collecting the results of in-plane cyclic tests on unreinforced masonry piers, carried out within different research projects, is presented. The dataset includes brick and block walls with different materials, bed-and head-joint typologies, dimensions, boundary conditions and vertical applied loads. The development of such dataset aims at providing a tool for the improvement of the understanding and the evaluation of the main parameters that may influence and govern the lateral response of the URM piers under seismic excitation. A preliminary investigation on the in-plane lateral strength and displacement capacity, being two of the most significant parameters used in seismic analyses for the design and assessment of masonry buildings, has been proposed. The dataset, that already groups several specimens, is freely shared and might be continuously updated. This source of information of consistent and reliable test results represents a necessary step into the process of definition of shared rules within the scientific and technical community, in particular for the improvement of codified criteria, analytical and numerical models and testing procedures.

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Damage observations from recent seismic events have confirmed that the activation of out-of-plane (OOP) local mechanisms is one of the major causes of structural collapse in unreinforced masonry (URM) buildings. Such failures are mostly due to the attainment of displacement levels incompatible with equilibrium configurations for the kinematic chain of the considered mechanism rather than the exceedance of stress capacity in structural elements. However, very little research can be found currently in literature regarding the two-way bending OOP failure mechanism of walls involving at least one restrained vertical edge despite it being one of the most commonly reported and surveyed cause of structural damage. The paper takes a step towards addressing this lack of knowledge in the form of dynamic testing of full-scale URM masonry walls. In particular, results of three of these tests are reported in this paper: a test on a specimen representing the calcium silicate inner/loadbearing wall, a test representing the clay outer wall, and a cavity wall composed of both leaves together.@en