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The importance of research that addresses the numerous themes of architectural and cultural heritage conservation is a fact that has now been acquired on the national and international scene. The objective of the ongoing research presented is the study and development of infrared thermography as an innovative technique for non-contact, and absolutely non-invasive, investigations for the diagnosis of ancient masonry walls with specific attention to frescoes. In parallel, the devised technique is applied to a case study of very high historical value: the cycles of mural paintings of the Templar Church of San Bevignate in Perugia. Such architectural complex also houses a relevant archeological site which consists of a roman fullonica, part of the museum itinerary. Starting from the thermographic data, both the state of conservation of the precious painting and the seismic safety of the masonry Church – tied to the quality of the brickwork texture – are evaluated. The comparison among thermographic results and the outcomes due to a restoration activity of the painted parts, that took place on 2019 and that is still in progress, are highlighted.

In the present paper we propose a model describing the nonlocal behavior of an elastic body using a peridynamical approach. Indeed, peridynamics is a suitable framework for problems where discontinuities appear naturally, such as fractures, dislocations, or, in general, multiscale materials. In particular, the regional fractional Laplacian is used as the nonlocal operator. Moreover, a combination of the fractional and classical Laplacian operators is used to obtain a better description of the phenomenological response in elasticity. We consider models with linear and nonlinear perturbations. In the linear case, we prove the existence and uniqueness of the solution, while in the nonlinear case the existence of at least two nontrivial solutions of opposite sign is proved. The linear and nonlinear problems are also solved by a numerical approach which estimates the regional fractional Laplacian by means of its singular integral representation. In both cases, a numerical estimation of the solutions is obtained, using in the nonlinear case an approach involving a random variation of an initial guess of the solution. Moreover, in the linear case a parametric analysis is made in order to study the effects of the parameters involved in the model, such as the order of the fractional Laplacian and the mixture law between local and nonlocal behavior.

A multidisciplinary approach embedded with sustainability represents a pathway to design strategies applicable in different cultural contexts. Considering the emissions attributed to building processes, the design of conservation measures is evolving to create high performance both in terms of healthiness and safety. On this, heritage buildings in earthquake-prone cities proved their vulnerability during the recent seismic events. However, the most important aspect of restoration interventions is that the design process must respect the architectural peculiarities of the building. In this regard, the contribution presents the reuse of a heritage building, currently disused, in the novel role of University of Perugia’s plaster cast gallery, in line with the aims declared by the University with the adoption of the “Action Plan for University Sustainability 2021–2023”. Such architecture is part of Palazzo Murena, University of Perugia headquarters, a former monastery designed by Luigi Vanvitelli and completed in 1762 by Carlo Murena. A historical-iconographical investigation, together with a survey, revealed the building origin: a pre-existing architecture, anciently a hospice, included by Vanvitelli in their project. The purpose was the masonries’ reinforcement conceiving, at once, a flexible space according to the adaptive architecture principle: give to buildings configurations new, whole or in part, from the original ones in response to emerging threats. An integrated project was designed to restore the building in order to realize a contemporary museum in which full-height exhibition spaces alternate with the pre-existing ones. In this way, the new Gypso|TechA showcases the academic plasters, actually without a seat matching their cultural value, and through a peculiar layout encodes the collection’s message in a site-specific cognitive process.

Several masonry structures of cultural and historical interest are made with a non-periodic masonry material. In the case of periodic textures, several methods are available to estimate the strength of the masonry; however, in the case of non-periodic masonry, few methods are available, and they are frequently difficult to use. In the present paper we propose using discontinuity layout optimization (DLO) to estimate the failure load and mechanism of a masonry wall made with non-periodic texture. We developed a parametric analysis to account for the main features involved in the estimation of failure: in particular we considered three different textures (periodic, quasi-periodic, and chaotic), variable height-to-width ratio of the wall (from 0 to 3) and of the blocks (from 0.25 to 1), different mechanical properties of mortar joints and blocks, and possible presence of a load on the top. The results highlight the importance of the parameters considered in the analysis, both on the values of the failure load and on the failure mechanism. Therefore, it is found that DLO can be an useful and affordable method in order to assess the mechanical strength of masonry wall made with non-periodic textures.

In this paper, an innovative strengthening system for masonry walls made of externally bonded Fabric-Reinforced Cementitious Matrix (FRCM) is presented. Due to the good mechanical properties and the compatibility with the architectural heritage, the FRCM is an adequate alternative to the use of Fiber-Reinforced Polymer (FRP) composites and other traditional techniques. The proposed system is applied to the strengthening of a classical architectural typology in cultural heritage architecture, which is the “in falso” masonry: a load-bearing wall built over a masonry vault, and hence without a direct load path to the ground. A research program, characterized by an experimental campaign, has been started in order to devise and verify an optimal strengthening system that assures for the masonry wall a structural behavior similar to a “wall beam”, so to prevent progressive collapses when the underlying masonry vault loses its carrier function. In particular, rather than the canonical application, consisting in widespread application to the whole surface of the masonry wall, an innovative intervention made of “Green Tape” of composites has been designed and verified by a specifically designed experimental set-up. The main objective of the research is to propose a reinforcement strategy not detrimental to unmovable artistic assets and tied to the safety and robustness of the architectural heritage.

Parametric design, algorithmic modeling, generative design, and associative design are only some of the keywords of a work paradigm that is becoming more and more popular, designed to respond to the complexities of contemporary architecture. Most commonly, such an approach is used for new buildings, but when algorithmic design meets heritage building information modeling (HBIM), the process can take on an even greater centrality—flexibility and control go hand-in-hand, ensuring precious tools for the planning of restoration interventions and management projects. This contribution, oriented to expand the use of these strategies to heritage, deals with the theme of parametric modeling of masonry vaults, a structural–architectural feature that in many forms and combinations characterizes most historic buildings. In particular, the connection of BIM software with algorithmic modeling software can allow the ‘translation’ of complex geometric shapes into elements with full Level of Detail elements (LOD 500) while preserving, at the same time, the algorithmic editing functions. In this paper, it is illustrated as this approach permits the finetuning of the vaults’ details, from time to time, based on different survey strategies (e.g., direct measurements, experimental tests, laser scanners, etc.). In other words, using this new connection in real time, architects can design restoration interventions tied to shapes, geometries, and masonry peculiarities that would otherwise be impossible to manage. An updatable virtualization of the actual state of a heritage building thus becomes affordable for the wider public (LOD G). There is also a valuable benefit for the heritage stakeholders in terms of protection of the architectural value and conscious planning in the restoration practice, especially in the museum field.

Structural identification is one of the most important steps when dealing with historic buildings. Knowledge of the parameters, which define the mechanical properties of these kinds of structures, is fundamental in preparing interventions aimed at their restoration and strengthening, especially if they have suffered damage due to strong events. In particular, by using non-destructive techniques it is possible to estimate the mechanical characteristics of load-bearing structures without compromising the artistic value of the monumental buildings. In this paper, after recalling the main theoretical aspects, the use of elastic waves propagation through impact tests for the characterization of the masonry walls of a monumental building is described. The impact test allowed us to estimate the elastic characteristics of the homogeneous solid equivalent to masonry material. This confirms the great potential of the non-destructive diagnostics suitable for analyzing important structural parameters without affecting the preservation of historical masonry structures.

Photogrammetric surveys via Unmanned Aerial Vehicles are nowadays a valuable tool for historic masonry structures inspection, surveillance, mapping and 3D modeling issues. When structural damage mapping and structural assessment are of interest obtaining accurate and reliable geometric models is a crucial issue. Therefore, the flight plan, the georeferencing and the data processing steps need to be properly designed. In this paper, a procedure for the photogrammetric survey via Unmanned Aerial Vehicles of a masonry structures is used in order to obtain effective visual inspections and a 3D model of a historic masonry arch bridge located along the ancient Via Amerina (Todi, Perugia, Italy). The photogrammetric survey provides a detailed representation of the actual geometry, including lack of volumes and significant cracks along the vault and the spandrel walls, outlining a severe damage state affecting all the structure. Finally, a Total Station and a Laser Scanner were used to compare the results obtained by photogrammetry, highlighting the advantages, the limits and the weaknesses offered by their use.

Thermography is a non-destructive and non-contact technique allowing, without taking samples, gaining information about several aspects of heritage buildings. This contribution presents the last phase of a research path, started with laboratory tests and now aimed at a real case of great cultural value, which involved the use of the thermal imaging camera to unveil in-depth defects and the wall texture, hidden by valuable plasters or frescoes, in order to correlate the quality of the masonry to its mechanical properties. For this, a method has been devised, made of an original integration of thermographic and post-processing techniques, and recently was applied for the first time to a real case study: the Italian Templar church of San Bevignate, part of an architectural complex from the 13th century located in the city of Perugia. The opportunity to establish the masonry quality of a historical building using non-destructive testing (NDT) represents a little-known possibility to frame not only important factors for the conservation of the frescoes but also information on the seismic vulnerability of historical masonry architectures in order to preserve the artefact from being damaged during the surveys and to plan any effective intervention of restoration and structural reinforcement.

Fiber reinforced composites represent an alternative to traditional techniques for strengthening and retrofitting masonry structures. Within the growing environmental awareness, the development of composite materials to replace conventional synthetic fibers and polymeric matrices has become a crucial issue. In this paper, a novel sustainable composite material consisting in hemp fibers and a natural matrix made of a mix of ground clay bricks and organic binder is proposed. Experimental tests are carried out in order to estimate the mechanical characteristics of the single composite components. The structural performance of polycentric masonry arches strengthened at the extrados first with only natural matrix and then with the bio-composite material (i.e. hemp fibers and biodegradable matrix) is investigated. Single point vertical load tests and tilt tests are carried out in order to assess the effectiveness of the strengthening by comparing the results with those obtained with unstrengthened masonry arches.

This paper presents an integrated approach that combines advanced survey procedures, such as close range photogrammetry based on high resolution images provided by Unmanned Aerial Vehicles, and Ambient Vibration Tests to develop accurate Finite Element models of severely damaged historic masonry structures. The proposed methodology is applied to a masonry arch bridge located in Todi, Central Italy, characterized by severe damage conditions involving diffuse material degradation and structural damages. Two numerical models are developed starting from the digital geometric survey: the first accurately describes the irregular actual geometry due to damage; the second regularizes the boundary surfaces as standard procedure in common practice when detailed survey is not available. The crucial role of the geometric irregularities given by the severe damage state on the dynamic properties of the masonry bridge is demonstrated by comparing the modal parameters of the two models. Furthermore, sensitivity analysis is carried out in order to assess the combined effect of different mechanical characteristics and geometric configurations on the modal properties and to select suitable updating parameters. The overall methodology is completed by a final model updating procedure targeting the experimental modal parameters estimated from Ambient Vibration Tests.

The article deals with the longitudinal waves in a nonlocal elastic rod. Regarding the nonlocal elasticity the Eringeen model has been assumed; the novelty is that this model is described in terms ...

In this paper we derive and solve nonlocal elasticity a model describing the elastic behavior of composite materials, involving the fractional Laplacian operator. In dimension one we consider in (($\mathcal{D}$)) the case of a nonlocal elastic rod restrained at the ends, and we completely solve the problem showing the existence of a unique weak solution and providing natural sufficient conditions under which this solution is actually a classical solution of the problem. For the model (($\mathcal{D}$)) we also perform numerical simulations and a parametric analysis, in order to highlight the response of the rod, in terms of displacements and strains, according to different values of the mechanical characteristics of the material. The main novelty of this approach is the extension of the central difference method by the numerical estimate of the fractional Laplacian operator through a finite-difference quadrature technique. For higher dimensions N ≥ 2 {N\geq 2} we study more general problems for which the existence of weak solutions is proved via variational methods. The obtained results provide an original contribute in the knowledge of composite materials with properties of nonlocal elasticity.

The effects of uncertain geometry on the collapse of masonry arch are considered.Probabilistic models are adopted to describe the geometrical uncertainties.The arch horizontal carrying capacity is evaluated by a limit analysis procedure.Geometrical uncertainties reduce the bearing capacity of the arch.Uncertainties effects are described by a safety factor versus a stereometry parameter. This paper aims to evaluate the effect of the geometrical uncertainties on the collapse condition of the circular masonry arch in presence of horizontal actions. Adopting Heymans hypotheses about the material, a limit analysis based procedure has been developed in order to evaluate the horizontal loads multiplier, taking into account the uncertainties related to the imprecisions of construction, the shape defects of the voussoirs or the deterioration level. The collapse state has been determined in terms of horizontal loads multiplier, whose statistical moments up to second order and probability density functions have been evaluated versus a stereometry parameter. The comparison between the obtained results and those related to the nominal geometry highlighted that the uncertainties effects could reduce significantly the nominal bearing capacity of the structure. Within this context, a safety factor, which takes into account such effects, is introduced.

In this paper the effect of joints structural repointing on single-wythe brickwork masonry using a fiber-reinforced mortar is investigated. Changes in shear strength are evaluated by in-situ tests carried out both on unreinforced and reinforced masonry specimens. The masonry joint shear strength, according to the standard ASTM C 1513, gives local information, while diagonal compression tests provides information on the global masonry shear response. The comparison highlights a good performance in both local and global masonry response, where the shear strength increases.

In this paper an experimental investigation on the dynamic response of masonry structures due to the combined effects of vertical and horizontal seismic components is presented. The motivation of this study started with on-site observations of a special damage state affecting some masonry buildings after the Central Italy earthquake in 2016, which can be ascribed to the interaction of vertical and horizontal components of the seismic action. For this purpose, experimental tests on a two-storey building masonry structure were performed using a shaking table in order to investigate its behaviour to earthquakes with strong vertical component.

In the present paper, the upper bound of the failure surface of quasi-periodic masonry is estimated by means of Discontinuity Layout Optimization (DLO). This allows to overcome the difficulties in using methods which have been tailored for periodic masonry. With this approach, the domain is discretized with a great number of points which are the boundaries possible discontinuities associated with a failure mechanism. The effective pattern of discontinuities at failure is estimated, through usual methods of limit analysis, by minimizing a suitable function. In particular, the present paper shows the first results obtained for a masonry with a quasi-periodic and a random texture, assuming that the discontinuities can appear only in the mortar joints and according to Mohr-Coulomb failure criterion.

Masonry towers constitute a significant part of the European built heritage that, due to their intrinsic geometric slenderness, result particularly vulnerable to horizontal loads. Their seismic assessment requires a numerical model able to reproduce the material nonlinear behavior and to account for the different sources of uncertainties. Among the uncertainties which may affect the reliability of the results, it is possible to list: (i) the building history, its evolution and the structural details, (ii) the masonry construction technique and the material properties and (iii) the boundary condition since in several cases towers are embedded in other buildings (such as churches bell-towers). This paper, to assess the seismic risk of historic masonry towers, investigates the reliability of a probabilistic approach aimed to include some of the sources of uncertainty above mentioned. The employed probabilistic framework was originally introduced in 1991 by Gusella, and it is here discussed by analyzing a representative case study: an historic masonry tower in San Gimignano (Italy). In a first part of the paper the results of ambient vibration tests are employed to tune a numerical model of the tower. The identified numerical model is subsequently employed to perform the non-linear time history analyses that are needed to express the seismic risk of the tower in terms of collapse probability.

In the year 2016 Central Italy has been struck by a series of massive earthquakes of significant intensity, highlighting the need to improve the knowledge on the dynamic behavior of masonry structures excited by ground motions in order to develop useful design solutions to mitigate the seismic vulnerability. For this reason, a research program aimed to improve the dynamic performance of masonry structures by using confined masonry technique was started. A shaking table experimental investigation has been carried out on both unreinforced and confined masonry building models at the ENEA laboratory in Casaccia, Rome, in order to compare the dynamic behavior of the two different construction types.

This paper focuses on the Murena Palace in Perugia, part of an architectural complex designed by Luigi Vanvitelli and completed by Carlo Murena in the 18th century. In the context of the seismic vulnerability assessment of this masonry building, the safety of a construction modulus, which gathers several peculiar features identified within the edifice, is analyzed by means of an integrated architectural-structural approach. This construction modulus, that will be called Vanvitelli&rsquo, s Modulus, is characterized by an intrinsic structural asymmetry with clusters of rooms with masonry vaults, combining different heights, where load bearing walls are standing on top of the vaults. Given these peculiarities, this construction modulus has to be analyzed as a sub-structure with regards to the seismic vulnerability. To this purpose, experimental tests, in particular videoendoscopies and structural monitoring, were conducted to identify geometrical features of walls and vaults, mechanical characteristic of materials and the actual damage condition. From an accurate survey, an innovative parametric approach has been proposed to build the geometrical model of the construction modulus. This has been used, by FEM (finite element method), to perform a structural analysis whose results have been checked by comparison with the actual damage patterns. The proposed integrated architectural-structural approach permits a deeper comprehension of the structural principles that characterize Vanvitelli&rsquo, s construction modulus and to estimate its seismic vulnerability.

The paper is aimed at assessing the shape irregularities effect on the collapse conditions of circular masonry arches in presence of horizontal actions. Historical constructions often present structural elements characterized by irregular shapes, which could affect their bearing capacity if calculated considering the nominal geometry. Some of these irregularities can be ascribed to the arising of deformed states developed over time or, in other cases, directly to technological construction processes. As a first study, the geometrical uncertainties related to construction processes are considered. In order to take into account such irregularities type, a random model of a polycentric arch has been developed.

Heritage buildings, worldwide, are marked by the presence of masonry structural elements often affected by shape irregularities if compared with their initial condition. The trigger factors of such geometrical uncertainties can be ascribed to the over centuries deformation processes, to environmental factors or upstream to the constructive methods. The aim of the present paper is the evaluation of the influence of shape irregularities on the collapse condition of circular masonry arches in presence of horizontal seismic actions. In order to take into account a more reliable estimation of the arches bearing capacity a random generative model is developed considering shape uncertainties. A limit analysis based procedure, referring to Heyman’s theory, is used in order to evaluate the horizontal loads multiplier. Then the collapse condition is studied through a probabilistic approach, by analysing the statistical moments up to second order of the results obtained by a Monte Carlo simulation.

FEM simulations are widely recognized as essential tools in the analysis of the behaviour of dam systems. A detailed representation of the dam structure allows for a better understanding of the local response of important structural elements. The present paper intends to provide a FE modelling procedure of concrete arch-gravity dams. Case of study is the arch-gravity dam of Ridracoli. The vertical construction joints are included in the model as solid elements; their influence on the dynamic properties of the structure is investigate and, adopting the CDP—Concrete Damage Plasticity—model for the filling mortar, elasto-plastic damage time-history analyses are performed. Under MCE—Maximum Credible Earthquake—and varying the water level, the damage parameters evolution is analysed. All simulations integrate the structure-foundation and the fluid-structure interaction by means of rock mass solid and acoustic elements, respectively; moreover, the adopted damping coefficients of rock mass and structure are calibrated on linear elastic dynamic analyses. The inclusion of vertical construction joints into finite element models of dams allows us to verify the local behaviour of such real discontinuities under severe seismic events and therefore to verify the seismic vulnerability assessment of the whole structure.

In the present paper, mechanical characteristics of masonry wall covered with plaster are estimated by means of thermography. Masonry wall samples have been purposely built with different textures: periodic, quasi-periodic and random. All the samples are covered with plaster. By means of a thermographic camera, images have been taken and the texture have been estimated and compared to the exact ones. The elastic characteristics have been estimated by means of homogenization, imposing boundary conditions in terms of displacements and forces. The effect of different parameters involved in the response has been evaluated.

The use of equivalent beam models to estimate the dynamical characteristics of complex tall buildings has been investigated by several authors. The main reason is the structural response estimation to stochastic loads, such as wind and earthquake, using a reduced number of degrees of freedom, which reduces the computational costs and therefore gives the designer an effective tool to explore a number of possible structural solutions. In this paper, a novel approach to calibrate the mechanical and dynamical features of a complete 3D Timoshenko beam, i.e., describing bending, shear and torsional behavior, is proposed. This approach is based on explicitly considering the sub-structures of the tall building. In particular, the frames, shear walls and lattice sub-systems are modeled as equivalent beams, constrained by means of rigid diaphragms at different floors. The overall dynamic features of the tall building are obtained by equating the deformation energy of an equivalent sandwich beam with that of the selected sub-structures. Finally, the 3D Timoshenko equivalent beam parameters are calibrated by minimizing a suitable function of modal natural frequencies and static displacements. The closed form modal solution of the equivalent beam model is used to obtain the response to stochastic loads.

In this paper, the effect of geometric irregularities on the dynamic response of circular masonry arches is considered. Irregular geometries are obtained through a random generation of the key geometric parameters, and the effect of these irregularities is shown by modelling the dynamic response to ground motion. The masonry arch is modelled as a four-link mechanism, i.e., a system made of three rigid blocks hinged at their ends, where the position of the hinges at the instant of activation of the motion is determined through limit analysis. Lagrange’s non-linear equations of motion have been solved through numerical integration. The results show that geometrical uncertainties produce an alteration of the mechanical features of the rigid blocks which may reduce the seismic capacity.

This paper aims to evaluate the limit equilibrium condition and the minimum thickness of masonry arches in presence of horizontal loads. The analysis fits into the frame of limit analysis referring to Heyman's theory. Two types of arches are analysed, the circular and pointed one. The loading system consists of vertical and horizontal loads, which refer respectively to the self-weight of the voussoirs and to the seismic actions. The collapse mechanism and the corresponding horizontal load multiplier are determined, in the condition of rigid abutments, as functions of the geometrical features of the structure. The results are supported by some simple experimental tests and a sensitivity analysis, which considers the effect of geometrical irregularities on the load multiplier.

Wind loads on structures are commonly described as stationary phenomena that occur in neutral atmospheric conditions at the synoptic scale with velocity profiles in equilibrium with the atmospheric boundary layer. Nevertheless, structural systems can be also affected by thunderstorm outflows, which are non-stationary local phenomena at the mesoscale that occur in convective conditions with totally different velocity profiles with respect to synoptic winds. This paper presents a non-stationary probabilistic model that describes the wind velocity fluctuations experienced during a thunderstorm in order to estimate its effects on the dynamic structural response. The model is first calibrated on a typical thunderstorm recorded in the north-west italian coast and it is used to generate virtual time histories in a Monte Carlo simulation approach. The potential influence of the wind load non-stationary features on the peak structural response is investigated using single degree of freedom parametric analysis and statistical estimation.

The paper proposes an approach to model the geometrical uncertainty in case of curves in space. After highlighting the importance of the geometrical uncertainty in various fields of mechanics, the random set of “irregular or imperfect curves” is analysed in the natural or intrinsic reference system by the formulas of Serret–Frenet. It is shown that the Riccati’s random differential operator, in complex domain, describes this random set. The curvature and torsion are modelled by weakly homogeneous random functions with discrete spectrum. Numerical results show the application of the proposed approach.

The paper deals with the differences between effective and homogeneous solution in case of dynamic of continuous media with random micro-structure. In particular, these differences, called “residuals”, are considered for the dynamic linear problem of the Euler-Bernoulli's beam with random Young's modulus . The differential operator with random coefficient, that describes the eigenvalues problem, is taken into account. The convergence to the effective solution is analysed by introducing two measures: the normalized error between apparent and effective Young's moduli and between the modes shapes. The obtained results permit to highlight the dependence of the residuals from the micro-structure dimensionless length and the effect of the modes order; these aspects should be considered in the homogenization of dynamic behaviour of random heterogeneous composites. The assessment of the Rapresentative Volume Element (RVE) by convergence of the Statistical Volume Element (SVE) is also discussed.

Wind action on structures is commonly estimated under the stationary assumption that is related to the phenomena that occur in neutral atmospheric conditions at the synoptic scale with velocity profiles in equilibrium with the atmospheric boundary layer. Nevertheless, when thunderstorm outflows are concerned the wind induced load description should take into account its inherent non-stationary features. In this paper a non-stationary model is proposed to describe wind velocity fluctuations of a typical thunderstorm in the northern Italian coast. This model can be obtained by modulating both amplitude and frequency of a stationary process. First, experimental time histories are used to calibrate the non-stationary model, then a parametric dynamic response study to stationary and non-stationary wind loads is finally investigated.

In the present paper, the elastic mechanical characteristics of masonry samples, whose texture isnot visible due to plaster, are estimated by means of homogenization technique applied through thermographicimages. In particular, three masonry samples with different textures have been purposely built. The textureschosen were periodic, quasi-periodic and random. Theimages, taken with a thermocamera, have been analyzed in order to identify the texture. An homogenization technique, based on the application of appropriate boundary conditions, has been used. The mechanical characteristics obtained using the textures identiedusing photographic images and thermographic imageshave been compared. The in uence of some parameters(such as the dimensions of the structural element usedin morphological operator) are analysed. The obtainedresults permits to point out the reliability of the masonry elastic characteristics assessment by the proposedprocedure.

This paper concerns the homogenization of the dynamic response of Euler Bernoulli'sbeam with random Young's modulus. Considering the eigenvalue problem, specialattention is dedicated to the homogenization residuals (correctors) analysis, i.e. thedfference between the random heterogeneous solution and the homogenized solution.Several correlation (mixing) laws of the Young's modulus are considered anda dimensionless characteristic scale length, based on the correlation length, is introduced. The effects of the mixing law on the residuals are analyzed using numericalapproaches both for sampling the random Young' modulus and for examining thebeam eigenvalue problem. Two measurements are introduced to estimate the residualsbetween apparent and effective solution: the normalized difference of Young'smodulus and the normalized difference of modes' shape. The effect of the mode'sorder is also highlighted with reference to forced vibrations.

In this paper the estimation of masonry characteristics by means of thermographic images, enhanced by sampling Kantorovich algorithm, is taken into account. In particular, the convergence of the Statistical Volume Element (SVE) to the Representative Volume Element (RVE) is analyzed. It is found that the enhancement, obtained by the proposed procedure, allows a faster convergence of SVE to RVE and a reduced coefficient of variation of the estimates obtained using a partition of the image with windows of smaller dimensions. Moreover, the effects of the uncertainties in the parameters involved in the reconstruction of texture from thermographic image, such as those used in morphological operators employed in digital image processing, involving the environmental conditions of the samples and the properties of the kernel utilized in the image enhancement algorithm, have been studied in order to assess their influence on the estimated mechanical characteristics. The performed analyses contribute to increase the reliability of the thermography as tool for identifying of masonries covered with plaster or frescoes, which is a very frequent case in vulnerability analysis of historical buildings.

This work is aimed at evaluating the collapse displacement of masonry arch subjected to spreading supports. This is achieved through a general application of the virtual works principle. The problem is described in a finite displacements formulation and investigated with a probabilistic approach, also considering the effects of the geometrical uncertainties. This aspect is related to the imperfections of the voussoirs, which affect the structural shape. The comparison between the numerical and experimental results, derived both by the literature and laboratory tests, confirms that the geometrical irregularities can significantly affect the results obtained on the nominal structural geometry. Moreover, the disagreement observed in the experimental tests is explained.

In this paper a homogenization procedure for theestimation of the failure surface of a quasi-periodic masonry,based on a mean stresses approach through the analysis ofthe Statistically Equivalent Periodic Unit Cell (SEPUC), isshown. The mean stresses approach consists in the identificationof critical states for the homogenized continuum bymeans of an overall failure criterion, function of the meanstress state of each constituent. These macroscopic tensorsare evaluated in the elastic field. The SEPUC definition refersto a statistical criterion applied to a population of PeriodicUnit Cells (PUCs) generated taking into account the geometricalfeatures of the quasi-periodic texture; moreover itis validated on the basis of the homogenized elastic propertiesin terms of components and Frobenius norm of theelastic matrix. By a multi-objective optimization approach, the obtained results highlight that the proposed SEPUC can be used to estimate the failure surface.

The convergence of the elastic coecients residuals compared to the homogeneous solution, at varying size of the representative volume sample, is analysed in this work in the case of random two-dimensional media. In particular,it is considered the case of the masonry material which can be considered a heterogeneous solid with two phases (stones or bricks and mortar). Moreover,in relation to the peculiarities related to its eective realization, the masonrypresents a quasi-periodic micro-structure. A procedure of numerical generation of wall portions has been developed by varying not only the scale ratio but also the mechanical ratio, between the characteristics of the stone andmortar, and the geometrical ratio, relative to the stones dimensions. Comparing to the homogeneous solution, the convergence of residuals has beenhighlighted in terms of probability density function and static moments, upto the second order, of the stiness coecients, log-Euclidean distance between matrices and closet isotropic material.

This study presents the results of the static and dynamic assessment of the dome of the Basilica of Santa Maria degli Angeli in Assisi, designed by Galeazzo Alessi. The first section is devoted to an overview of the masonry domes designed by the Italian architect and focuses on the structural solutions adopted in the several cases described to better understand Alessi’s designing skills. In the second part, the drum-dome system is analyzed in order to attain a structural assessment. The static assessment is performed by means of limit analysis and finite element model approaches with non-linear mechanical behavior. The obtained results are consistent with the detected crack pattern and confirm the suitability of the reinforcement steel rings applied to the drum. The seismic assessment has been performed by response spectrum analysis. Due to the lack of specific information, a probabilistic approach for the material mechanical properties was used. The results obtained highlight an adequate seismic response...

In this paper the estimation of residuals for the homogenized solution in elastic problem is taken into account. The case of the beam with Young's modulus randomly varying along the axis is considered. The analysis is performed by means of numerical simulation which is validated by comparison with particular solutions reported in the literature. The convergence to the homogenized solution and the behavior of the residuals are studied in terms of the parameter ɛ , which represents the ratio between the microscopic and the macroscopic scale. After validation with the literature results, the procedure is used to analyze the influence on the convergence of the correlation law of Young's modulus with log-normal distribution. Moreover the particular case of the two-phase beam is considered. The effect of different boundary conditions is also investigated.

The paper presents a method to estimate the Statistically Equivalent Periodic Unit Cell (SEPUC) corresponding to a masonry with quasi-periodic texture. The identification of the texture and the constituent phases (unit blocks and mortar joints) is achieved by means of digital image processing techniques applied to color image of the masonry wall. A statistical analysis of geometrical parameters (width and height of blocks, thickness and length of mortar joints) allows to estimate their probability distribution and to identify the typology of the texture. Subsequently a Monte Carlo analysis is performed using several tentative SEPUCs generated with different dimensions of blocks and joints according to the estimated distributions. A criterion was eventually proposed to identify, among the numerically generated ones, the SEPUC which is more suitable to model the behavior of masonry wall. The SEPUC is analyzed with techniques available for periodic texture, applying periodic boundary conditions, in order to estimate the equivalent elastic stiffness. The proposed method is validated comparing the results in the elastic range obtained with SEPUC and those obtained imposing essential and natural boundary conditions on the original texture.