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This paper presents a Grasshopper (GH) plugin to evaluate the admissible out-of-plane mechanisms in multi-storey masonry buildings and visually display the possible locations for each admissible mechanism at which the failure can happen. Adopting the macro-block modelling approach, GH components are developed considered a limited number of geometric and construction parameters as inputs that allow the possible mechanisms. These include the quality of the connections between the building walls, applied strengthening devices, and the examined building location within an urban block. Modelling the building, all the potential mechanisms and their possible locations are demonstrated in a user-friendly and readable way. The plugin can finally compute the actual mechanism and its optimised geometry as well as the actual building out-of-plane capacity adopting the limit analysis method.

In this paper a multi-level approach proposed by the Italian Guidelines on Cultural Heritage was adopted to assess the seismic safety of an unreinforced masonry building located in Naples (Italy). In particular, the simplified model of the global seismic response at the territorial scale was used for the first level (LV1), while the nonlinear static (pushover) analysis and the equivalent frame modelling with nonlinear structural-elements were adopted for the more accurate global assessment level (LV3). Different evaluations of the safety indexes are compared in the framework of the LV1 level, with particular attention to their reliability in representing the main aspects of the seismic capacity of the building, in terms of the prevailing failure mechanism and the detection of the weaker direction. The achieved results were compared with those obtained by LV3 assessment level.

An atypical ‘baraccato’ system made of masonry walls encaged in iron frames was realized in the Ischia Island after the earthquake of 1883; an interesting example is represented by the Santa Maria Maddalena Church. Unfortunately, while several experimental and numerical studies can be found in the recent literature for traditional ‘baraccato’ systems (mixed timber and masonry elements), no information is available for iron-framed masonry structures. To fill this gap, the paper presents several parametric non-linear static analyses with reference to, firstly, simple iron-framed masonry panels and, successively, the façade of the Santa Maria Maddalena Church. All the numerical analyses were carried out by means of two modelling approaches with different levels of detail, i.e. finite element (FE) and discrete macro-element (DME) models. The numerical analyses allowed to: assess the reliability of the two models (FE and DME) into predicting similar results for the panels and the church façade with reference to both the unstrengthened and the iron-framed strengthened configurations; analyse the influence of the investigated parameters; evaluate the contribution of the iron frames on the overall behaviour of the strengthened masonry elements; and drive the choice of the most suitable modelling strategy for the whole church.

The concept of vulnerability of the existing building stock is receiving increasing awareness and central importance in the scientific community working in earthquake risk mitigation. This assumes even more relevance when dealing with heritage structures located in relevant seismic hazard zones. This paper aims to identify and describe the earthquake-resistant features found in a unique masonry church in Ischia (Italy), and discuss their effectiveness on the impact of the post-seismic damage through the application of non-linear static analyses. The Santa Maria Maddalena Church represents one of the rare examples in which the technology of the Borbonic casa Baraccata (mixed timber−masonry construction), already well-known in the literature for its use in Italian seismic areas since the eighteenth century, is applied with the non-conventional combination of masonry and iron frames. The church was struck by the recent earthquake of 21 August 2017 with epicentre in Casamicciola Terme. The recorded post-seismic damage of the church evidenced non-relevant structural crack patterns, which are likely to be related to the efficacy of the construction system adopted.

In-plane strength of masonry walls is affected by the resistant mechanisms activated in the walls, i.e., related to flexural or shear behavior. The latter one can occur in the walls according to different failure modes depending on both mortar and unit strengths and on the type of assembling, i.e., ‘regular’ or ‘irregular’ texture. In this paper, a critical review of the existing design formulations for the in-plane strength of masonry walls is firstly presented, with important information on the achievable failure modes depending on the geometrical and mechanical features of the masonry fabric. Then, experimental tests are collected from the literature and a comparison between theoretical and experimental results is carried out. The presented analyses are aimed to highlight the differences between the existing formulations and to identify the most suitable ones.

Unreinforced stone masonry (URSM) buildings without a box-like behaviour are very vulnerable to out-of-plane failure modes in seismic prone areas. These may involve partial or total collapses of walls with severe civil protection implications in terms of hazard to people, structures, and road network in the surroundings. In this paper, an advanced macro-block model accounting for frictional resistances is used to calculate the onset load factors for two classes of local mechanisms in multi-storey URSM buildings: the rocking-sliding and the flexure mechanisms. Based on the application of the kinematic approach of limit analysis, the presented formulations are an upgrade of the load factors identified within the FaMIVE (Failure Mechanism Identification and Vulnerability Evaluation) procedure existing in the literature and developed by the last author. These take into account a revisited evaluation of the in-plane frictional forces for the rocking-sliding mechanisms and the torsion-shear-flexure interactions for the horizontal flexure mechanisms. Moreover, the position of the hinge along the height of the building is identified more accurately, since it can be found at the story level or between two storeys, depending on the accounted mechanism. Other innovative issues concern upgrades of the former formulations for the vertical and horizontal flexure mechanisms. The final perspective of the presented abacus of local mechanisms in multi-storey URSM buildings is the next implementation of the proposed formulations in the FaMIVE procedure, after a sensitivity analysis of the main physical and geometrical parameters affecting the “hierarchy” among the all possible mechanisms. The identification of the most probable mechanisms, through a comprehensive but at the same time relatively rapid assessment, can be very useful for civil protection purposes.

In masonry buildings without a box-type behaviour and subjected to seismic loadings, in-plane and out-of-plane failure mechanisms can take place where frictional resistances might play a predominant role. In this paper a detailed limit analysis of a simple out-of-plane failure mechanism is developed according to static force-based and displacement-based approaches. The main goal is to point out the great importance of the stabilizing role of friction between interlocked walls compared to other extrinsic or intrinsic loading capacities, e.g. the effect of tie-rods and simply supported horizontal diaphragms with frictional resistance. The sensitivity of the load multiplier to these strength parameters is investigated both at the onset of the rocking mechanism and after the hinge formation and a parametric analysis is carried out for the first condition. The results are obtained with reference to different combinations of loading conditions, including the detrimental effect of the static thrust of masonry vaults. Comparative results and pushover curves are developed to evaluate the loading and displacement capacities for each case analyzed and some experimental work is presented to validate the analytical results.

The corner failure is one of the most typical local mechanisms in masonry buildings vulnerable to earthquakes. The seismic assessment of this mechanism is poorly studied in the literature and in this paper it is addressed by means of both nonlinear static and dynamic analyses of rocking rigid blocks. The static approach is based on the displacement-based method and is aimed at predicting the onset of the 3D failure mechanism and its evolution through incremental kinematic analysis. This approach also considers the presence of a thrusting roof and the stabilizing contribution of frictional resistances exerted within interlocked walls. The capacity in terms of both forces and displacements is compared with the seismic demand through the construction of acceleration–displacement response spectra, with some originality. The nonlinear dynamic approach is based on the seminal Housner’s work on rocking rigid blocks and considers the influence of transverse walls, roof overloads and outward thrust, all included in an updated equation of one-sided motion. In particular, the process of defining an equivalent prismatic block, representative of the original corner geometry, is presented to convert the 3D dynamic problem into a 2D rocking motion. The wide suitability and advantage of such modeling approaches to assess the seismic response of rocking masonry structures with reference to specific limit states are demonstrated through a real case study, i.e. the collapse of a corner in a masonry school building during the 2016–2017 Central Italy seismic sequence. The compared results provide a good agreement of predictions in terms of both onset and overturning conditions, for which the static model appears to be more conservative than the dynamic one.

In this paper a macro-block model accounting for frictional resistances is presented to assess the lateral strength of a multi-storey masonry block wall. The kinematic approach of limit analysis is used to define the load factor causing the onset of rocking-sliding mechanism under in-plane horizontal loading. A dry frictional contact condition is assumed at the rigid block interfaces, according to the Coulomb's law with non-associated flow rule. The key aspect of the proposed approach is the introduction of a criterion to evaluate the contribution of the actual frictional resistances depending on the inclination angle of the crack line. An accurate assessment of the frictional resistances is also obtained by distinguishing two different contributions (the wall own weight and additional vertical loads) and their application points. Hence, a sensitivity analysis is performed with respect to the overloading condition, the friction coefficient, and geometrical parameters such as the shape ratios of the wall and the unit block and the number of rows. The analytical results of the proposed model are also validated against results from other existing macro and micro-block modelling approaches in terms of load factor. The comparison confirms the reliability of the proposed model that allows, with similar results, great simplification of the computational effort with respect to micro-block models.

The failure mode of a free corner in masonry buildings, still poorly investigated, is one of the most common failure mechanisms occurring and clearly recognizable in the aftermath of a seismic event. It is characterized by the formation of a masonry wedge, mainly due to the thrust of roof elements in addition to inertial forces, and it generally involves rocking-sliding motions along the cracks on the interlocked orthogonal walls. The onset of this failure mode is herein analyzed by means of an upgraded macro-block model, based on the kinematic approach of limit analysis and accounting for the influence of frictional resistances on the collapse load multiplier and the related crack pattern. An original criterion weighting the role of rocking vs. sliding motion on the collapse load factor is developed and a formulation with general applicability is obtained. Several parametric analyses are performed in order to highlight the influence of geometrical, mechanical and loading parameters (with and without openings) on the seismic capacity of the corner. The reliability of the proposed model and solution procedure is confirmed through the comparison with the results provided by other macro-block models existing in the literature. The final perspective is the next implementation of the proposed model in FaMIVE (Failure Mechanism Identification and Vulnerability Evaluation) applicative.

In this paper the seismic vulnerability assessment of a case study of masonry building located in Naples has been performed. First, a simplified analysis approach foreseen in the Italian Guidelines on Cultural Heritage, aligned with the Technical Codes for Constructions and based on a statistical evaluation of seismic behavior of masonry buildings, has been applied. Then, the achieved results have been compared with the more refined approach of nonlinear static analysis carried out by means of the TREMURI structural program. This is based on the schematization of masonry elements with the macro-element technique and the results are reported in terms of damage and collapse mechanisms of masonry walls, pushover curves and seismic safety index. The model with the additional assumption of all the floor diaphragms as completely rigid has also been analyzed and compared with the model with flexible horizontal structures. The comparison among results has allowed to have a clear indication of the seismic safety of the investigated building, useful to program future retrofitting interventions.