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A unified formulation is presented for non-linear time history, static pushover and limit analysis of historic masonry structures modelled as 2D assemblages of rigid blocks interacting at no-tension, frictional contact interfaces. The dynamic, incremental static and limit analysis problems are formulated as mathematical programming problems which are equivalent to the equations system governing equilibrium, kinematics and contact failure. Available algorithms from the field of mathematical programming, contact dynamics and limit analysis are used to tackle the contact problems between rigid blocks in a unified framework. To evaluate the accuracy and computational efficiency of the implemented formulation, applications to numerical case studies from the literature are presented. The case studies comprise rigid blocks under earthquake excitation, varying lateral static loads and sliding motion. A set of two leaves wall panels and an arch-pillars system are also analysed to compare failure mechanisms, displacement capacity and magnitudes of lateral loads promoting the collapse.

In this manuscript, it is presented, a case-study about the assessment of the seismic behaviour of Veronicas Market. Its structure, initially constituted by steel trusses supported on masonry walls, was subsequently modified by the addition of a mezzanine supported on reinforced concrete piers. Applying the capacity spectrum method, based on an updated nonlinear finite element model, the performance levels of both the original and modified structure have been compared to assess the effects originated by the change in the transmission mechanism of the seismic loads., En este artículo, se presenta, un caso en estudio sobre la evaluación del comportamiento sísmico del Mercado de Verónicas. Su estructura, originalmente constituida por cerchas metálica apoyadas sobre muros de fábrica fue posteriormente modificada por la incorporación de una entreplanta con pilares de hormigón armado. Aplicando el método del espectro de capacidad, con base en un modelo calibrado no-lineal de elementos finitos, se han comparado los niveles de desempeño de la estructura original y modificada para valorar los efectos originados por el cambio en el mecanismo de transmisión de las cargas sísmicas.

This paper deals with the vulnerability assessment of historic masonry structures subjected to settlements using rigid block modelling. A 2-D rigid block model with unilateral elastic contacts and finite friction is developed for the evaluation of the displacement capacity in the large displacement regime by push-down analysis. A variational formulation of the rigid block model is adopted, which relies on associative behavior for displacement rates. Under this assumption, the equation systems governing the behavior of the rigid block model can be uncoupled into two equivalent force and displacement-based problems, thus reducing computational costs. The numerical model was validated against the results of an ad-hoc experimental campaign on small scale tuff panels and against the tests on a small-scale masonry facade subjected to moving supports, from the literature. Applications of the proposed modelling approach are presented to the assessment of a full scale, monumental masonry facade. Following classic force-displacement methods that are used in the case of seismic actions, capacity curves are proposed for the damage assessment induced by settlements. Those state the relation between the base reaction at the moving supports and the displacement of a control point, which is obtained from the push-down analysis. Finally, comparisons with empirical assessment methods from the literature are presented.

In this manuscript, it is presented, a case-study about the assessment of the seismic behaviour of Veronicas Market. Its structure, initially constituted by steel trusses supported on masonry walls, was subsequently modified by the addition of a mezzanine supported on reinforced concrete piers. Applying the capacity spectrum method, based on an updated nonlinear finite element model, the performance levels of both the original and modified structure have been compared to assess the effects originated by the change in the transmission mechanism of the seismic loads. En este artículo, se presenta, un caso en estudio sobre la evaluación del comportamiento sísmico del Mercado de Verónicas. Su estructura, originalmente constituida por cerchas metálica apoyadas sobre muros de fábrica fue posteriormente modificada por la incorporación de una entreplanta con pilares de hormigón armado. Aplicando el método del espectro de capacidad, con base en un modelo calibrado no-lineal de elementos finitos, se han comparado los niveles de desempeño de la estructura original y modificada para valorar los efectos originados por el cambio en el mecanismo de transmisión de las cargas sísmicas.

The aim of this paper is to show to what extent a simple constitutive model can adequately describe the collapse mechanisms of historic masonry structures under horizontal seismic loads. Referring to block masonry, the paper presents the formulation and the numerical implementation of a constitutive relationship for modeling masonry structures regarded at a macroscopic scale as homogenized anisotropic continuum. The macroscopic model is shown to retain memory of the mechanical characteristics of the joints and of the shape of the blocks. The overall mechanical properties display anisotropy and singularities in the yield surface, arising from the discrete nature of the block structure and the geometrical arrangement of the units. The model is formulated in the framework of multi-surface plasticity. It is implemented in a FE code by means of a minimization algorithm directly derived from the Haar-Karman principle. A sensitivity analysis to mechanical and geometrical parameters was carried out to show the influence on the predicted response of small-scale wall components from the literature. The model is then used for the analysis of a numerical case study which is representative of a masonry church subjected to horizontal seismic action. The result of the model will be compared with those obtained by a rigid block model (RBM) of the same small-scale masonry prototypes and of the church building. In the paper, the results of the two models are discussed and analyzed in the way to highlight the weakness and the potentiality of the two different approaches.

In this paper we present the study of an archaeological structure in Pompeii and we detail the difficulties encountered applying the Italian standards and guideline when designing the new roofing structure. Following the latest Italian standards and guidelines, about the assessment and mitigation of seismic risk of cultural heritage, the analysis of the Insula has been carried out. In particular, among all the studied structures, the attention was focused on the covering of the main hall where a prototype of a roofing structure covering a portion of the hall was installed near the remaining ruins of the house. Numerical models have been developed in order to track the effect of these new roofing structures on this ancient masonry structure.

U radu se razmatra dinamičko ponašanje blokovima zidanog minareta povijesne džamije u Istanbulu i metoda protupotresne sanacije. S obzirom na visoku seizmičku aktivnost regije, za određivanje bočnih pomaka i načina otkazivanja uslijed seizmičkih djelovanja odabran je prostorni model konačnih elemenata. Provedene analize pokazuju da se najveća oštećenja obično pojavljuju u podnožju i donjem dijelu minareta, te da se ojačavanjem tih dijelova trakama od polimera armiranog vlaknima (engl. FRP - Fiber Reinforced Polymer) poboljšava otpornost na bočne sile. Postignuti rezultati su u smislu seizmičke zaštite obećavajući., The dynamic behaviour of block masonry minaret of a historical mosque in Istanbul is analyzed, and a seismic retrofit method is proposed. Due to high seismicity of the region, a 3D finite element model is used to determine lateral displacements and failure modes under seismic load. The analyses show that the highest damage usually occurs at the base and the lower part of the minaret, and that lateral behaviour can be improved by strengthening these sections with fiber reinforced polymer (FRP) sheets. The results obtained are promising in terms of seismic protection.

The paper describes the methodology applied to assess the state of preservation of the tallest historic tower in Mantua, the “Gabbia” tower, after the earthquakes of May 2012. An extensive investigation program—including visual inspection, sonic and flat jack tests, operational modal testing and structural modeling—has been planned to support the future preservation actions of the tower. The paper focuses especially on the information collected during on-site survey and dynamic tests and describes how these results can be employed and cross-correlated to assess the structural condition and seismic vulnerability of the tower.