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Unreinforced masonry buildings undergoing seismic actions often exhibit local failure mechanisms which represent a serious life-safety hazard, as recent strong earthquakes have shown. Compared to new buildings, older unreinforced masonry buildings are more vulnerable, not only because they have been designed without or with limited seismic loading requirements, but also because horizontal structures and connections amid the walls are not always effective. Also, Out-Of-Plane (OOP) mechanisms can be caused by significant slenderness of the walls even if connections are effective. The purpose of this paper is to derive typological fragility functions for unreinforced masonry walls considering OOP local failure mechanisms. In the case of slender walls with good material properties, the OOP response can be modeled with reference to an assembly of rigid bodies undergoing rocking motion. In particular, depending on its configuration, a wall is assumed either as a single rigid body undergoing simple one-sided rocking or a system of two coupled rigid bodies rocking along their common edge. A set of 44 ground motions from earthquake events occurred from 1972 to 2017 in Italy is used in this study. The likelihood of collapse is calculated via Multiple Stripe Analysis (MSA) from a given wall undergoing a specific ground motion. Then, the single fragility functions are suitably combined to define a typological fragility function for a class of buildings. The procedure is applied to a historical aggregate in the city center of Ferrara (Italy) as a case study. The fragility functions developed in this research can be a helpful tool for assessing seismic damage and economic losses in unreinforced masonry buildings on a regional scale.

The unreinforced masonry buildings can be present frequent local failure mechanisms and represent a serious life-safety hazard as recent strong earthquakes have shown. Compared to new building, existing unreinforced masonry buildings prone to be more vulnerable, not only because they have been designed without seismic or limited loading requirements, but also because horizontal structures and connections amid the walls are not always suitable. Out-of-plane collapse can be caused by important slenderness of walls also when connections are effective. The purpose of this paper is to evaluate fragility functions for unreinforced masonry walls in the presence of local failure mechanisms considering the out-of-plane response. The wall response, very often, can be idealized as rigid bodies undergoing rocking motion. Depending on its configuration, a wall is assumed either as a rigid body undergoing simple one-sided rocking or an assembly of two coupled rigid bodies rocking along their common edge. A set of 44 ground motions from earthquake events occurred from 1972 to 2017 in Italy is used in this study. The likelihood of collapse is calculated via Multiple Stripe Analysis (MSA) from a given wall undergoing a specific ground motion. Later, the single fragility functions are suitably combined to define a typological fragility function for a class of buildings. The procedure is applied to a historical aggregate in the city center of Ferrara (Italy) as a case study. The fragility functions developed in this research can be a very helpful tool for estimating damage and economic loss for unreinforced masonry buildings and for a seismic assessment on a regional scale.

We present here an improvement in the non-uniform rational Bezier spline (NURBS)-based kinematic limit analysis approach, which has proven to be particularly effective for masonry vaults, by adding an innovative mesh adaptation scheme. The procedure is based on the application of the kinematic theorem of limit analysis on a 3D model composed of NURBS rigid blocks. The definition of curved geometries through NURBS surfaces allows using mesh of few elements without modifications of the real geometry. An adjustment of the initial mesh is needed to minimize the kinematic load multiplier. Therefore, a Prey-Predator Algorithm (PPA), an innovative meta-heuristic algorithm based on the natural interaction between a predator and preys, is implemented as core of the mesh adaptation, allowing an efficient evaluation of load-bearing capacity and collapse behavior of masonry vaults. In this work, the standard PPA is further improved by introducing a variable population size, the so-called saw-tooth model, which allows reducing the computational effort without penalizing the evaluation of the objective function. Some numerical examples, which involve a masonry arch, a skew arch, and a horizontally loaded dome, are finally analyzed. For all the cases, a comparison between the proposed PPA and a traditional Genetic Algorithm (GA) is presented.

The aim of this work is to present a simple and practical experimental technique for the estimation of the ultimate shear capacity of perforated in-plane loaded dry joint masonry panels. The test is carried out by using a tilting table; in-scale models of several different perforated walls are assembled and positioned on the tilting table. The table is progressively tilted in quasi-static conditions, in order to reproduce the action of a static horizontal load proportional to masses. As a result, the model collapses for a given tilting angle, which represents the ultimate destabilizing horizontal action. The experimental setup was applied to a series of seven different masonry panels, conceived by different University teams from different countries in the context of a student competition proposed in the occasion of the 10th international Masonry Conference (10th IMC), held at the Technical University of Milan from 9th to 11th July 2018. The aim was to design a running bond shear panel with established height over length ratio, a minimum perforation ratio equal to 30% of the area and clay bricks with given dimensions disposed in either stack or running bond. The winning team was that obtaining the largest inclination angle of the tilting plane activating the collapse of the structure. Three replicates of the same experimental test were repeated in the lab of the Technical University of Milan to reduce experimental scatter of the results. In this paper we present and discuss the outcome of the experimentations carried out, in view of analyzing such results with sophisticated limit analysis approaches in the second part of the paper. The test requires simple and inexpensive instrumentation and can be adopted for a reliable prediction of the behavior of perforated shear walls in-plane loaded, assembled with dry joint bricks and horizontally loaded.

In this paper, the three-dimensional analysis of masonry vaults subjected to differential settlements is presented. A representation through NURBS shell elements is followed. Elements are idealized as rigid blocks and jumps of displacement can occur only at interfaces. Starting from a known displacement at the external boundary, the overall displacement field is determined through standard linear programming formulations. A mesh adaptation governed by a Genetic Algorithm is then applied to find the shape of the mechanism deriving from the settlement. The procedure is here applied on a historical barrel vault and results are compared with previous experimental tests.

In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture . This approach, which is an extension of the standard Virtual Element Method (VEM), facilitates mesh-independent modeling of crack discontinuities and elastic crack-tip singularities on general polygonal meshes . For elastic fracture in the X-VEM, the standard virtual element space is augmented by additional basis functions that are constructed by multiplying standard virtual basis functions by suitable enrichment fields, such as asymptotic mixed-mode crack-tip solutions. The design of the X-VEM requires an extended projector that maps functions lying in the extended virtual element space onto a set spanned by linear polynomials and the enrichment fields. An efficient scheme to compute the mixed-mode stress intensity factors using the domain form of the interaction integral is described. The formulation permits integration of weakly singular functions to be performed over the boundary edges of the element. Numerical experiments are conducted on benchmark mixed-mode linear elastic fracture problems that demonstrate the sound accuracy and optimal convergence in energy of the proposed formulation.

This paper investigates the application of a fast and reliable NURBS-based kinematic limit analysis approach for the assessment of the collapse behaviour of masonry bridges. This approach relies on the description of the geometry of the bridge structure by means of NURBS approximating functions. Starting from the known geometry, an assembly of rigid bodies can be generated, composed by very few elements which still provide an exact representation of the original geometry. The main properties of masonry material are accounted for through homogenisation and an upper-bound formulation for the limit analysis of the obtained mesh is devised. The approach is capable of accurately predicting the load bearing capacity of masonry bridges with arbitrary geometry and load configuration, provided that the initial mesh is adjusted by means of a suitably meta-heuristic approach (i.e., a genetic algorithm) until element edges correctly approximate the actual yield lines of the collapse mechanism.

Infrastructure systems cover an important role for economic activities and emergency response after a disaster, such as an earthquake. Within these systems, bridges represent a crucial component. However, they are often considered a weak link because of their vulnerability to hazards. Indeed, the structural damage of a bridge can create a disconnection in a transportation network or reduce its functionality. A probabilistic approach is the natural environment in which to analyze a complex network system and carry out risk/loss assessment estimations and decision-making processes. This problem presents various computational challenges and usually, sampling-based approaches are used to account for the uncertainty. In this contribution, a prioritization methodology is developed using the matrix-based system reliability (MSR) approach. This method is capable of delivering component failure probabilities and estimating the probabilities of complex system events with parameters sensitivities through efficient matrix calculations.

This paper aims at presenting a new perspective on the modeling of the influence of foundation settlements in masonry structures. We show that it is possible to model in a consistent way the crack pattern and the associated mechanism induced by applied settlements starting from a proper treatment of unilateral contact constraints between contiguous blocks, in which the structure is partitioned after the onset of settlements. We extend two classic variational formulations for the Signorini problem, namely the minimum of the total potential energy and a complementary boundary formulation, to the case of contact between multiple no-tension rigid bodies satisfying Heyman's hypotheses for the limit analysis of masonry structures. The discretization of the proposed variational formulations directly entails two dual linear programming problems. The proposed formulations allow to correctly evaluate the effects of foundation settlements and their influence on the ultimate load bearing capacity of masonry structures.

Recent seismic events in Italy have emphasized the high vulnerability of masonry buildings in historical centers, which were generally erected in continuity to each other over time, resulting in aggregates of constructions. The study of the seismic behavior of masonry aggregates can turn into a very difficult task, usually because of the difficulties to achieve a complete knowledge of geometrical evolutions, state of the connections between structural units, and interventions carried out in the course of time. A wide number of local collapses has been observed after recent earthquakes in Italy, highlighting that collapse under horizontal loads may take place mainly through failure mechanisms of single portions of the aggregate. According to Italian Code, both global and local analyses can be adopted in the seismic assessment of single structural units. Therefore, the aim of this study is to investigate different approaches for the evaluation of the seismic vulnerability of historical masonry aggregates. A masonry aggregate located in the historical center of Arsita (Central Italy), which was hit by the 2009 L’Aquila earthquake, has been chosen as a representative case study and a wide set of local and global analyses has been carried out. Local analyses have been conducted through a new upper-bound limit analysis based on NURBS and mesh adaptation, and a kinematic limit analysis applied to the most common local mechanisms. Global analyses have been performed through pushover analyses using the Equivalent Frame Method, and pushover and nonlinear dynamic analyses on a detailed FE model with appropriate constitutive laws. Finally, a discussion about the effectiveness of the different analysis approaches is presented with reference to the results obtained in this study.

In this contribution we discuss a new framework for the analysis of the bearing capacity of masonry structures, modeled as assemblies of rigid blocks, which allows to correctly take into account the influence of foundation settlements. The crack pattern at failure and the associated mechanism are described by means of a proper treatment of unilateral contact constraints arising between contiguous rigid blocks, in which the structure is partitioned. We extend two classic variational formulations for the Signorini problem, namely the minimum of the total potential energy and a boundary complementary formulation where the unknowns are contact pressures only, to the case of the contact between multiple rigid no-tension masonry bodies, for which Heyman hypotheses are satisfied. The discretization of these two variational formulations leads to two dual linear programming problems. While the first one is classical and maximizes the work of external loads, the second one minimizes the work of constraint reactions for the assigned displacements and it appears new in the literature.

In this paper, we investigate the capability of the recently proposed extended virtual element method (X-VEM) to efficiently and accurately solve the problem of a cracked prismatic beam under pure torsion, mathematically described by the Poisson equation in terms of a scalar stress function. This problem is representative of a wide class of elliptic problems for which classic finite element approximations tend to converge poorly, due to the presence of singularities. The X-VEM is a stabilized Galerkin formulation on arbitrary polygonal meshes derived from the virtual element method (VEM) by augmenting the standard virtual element space with an additional contribution that consists of the product of virtual nodal basis functions with a suitable enrichment function. In addition, an extended projector that maps functions lying in the extended virtual element space onto linear polynomials and the enrichment function is employed. Convergence of the method on both quadrilateral and polygonal meshes for the cracked beam torsion problem is studied by means of numerical experiments. The computed results affirm the sound accuracy of the method and demonstrate a significantly improved convergence rate, both in terms of energy and stress intensity factor, when compared to standard finite element method and VEM.

The aim of this paper is to present an automated procedure for the vulnerability assessment of masonry aggregates under horizontal actions through evaluation of local failure mechanisms. The method is developed as follows: realization of a NURBS model of the whole aggregate, definition of an initial mesh of NURBS rigid elements, upper bound limit analysis with dissipation only on interfaces, and computation of the horizontal load multiplier with progressive mesh adaptation by means of a Genetic Algorithm. A masonry aggregate of the historical center of Arsita (Teramo, Italy) has been chosen as case study.

A three-dimensional (3D) general upper-bound limit analysis procedure for the determination of the collapse load of out-of-plane loaded masonry walls with Fiber Reinforced Polymer (FRP) reinforcement strips is presented. The geometry of a given FRP reinforced masonry wall of arbitrary shape is represented by its Non-Uniform Rational B-Spline (NURBS) description in the three-dimensional Euclidean space. The NURBS parameter space is partitioned by means of a number of possible fracture lines and the original reinforced wall geometry is subdivided into an initial set of rigid elements, accordingly. An upper-bound limit analysis formulation, accounting for the main characteristics of both masonry material and FRP reinforcement by means of homogenization techniques, is deduced. Internal dissipation is allowed along element edges only and the effect of vertical loads and membrane stresses is considered as well. Numerical experiments show that a good estimate of the load bearing capacity is obtained provided that the initial arrangement of yield lines is adjusted by means of a suitable Genetic Algorithm (GA).

A new general approach for the limit analysis of out-of-plane loaded masonry walls based on an upper bound formulation is presented. A given masonry wall of generic form presenting openings of arbitrary shape is described through its Non-Uniform Rational B-Spline (NURBS) representation in the three-dimensional Euclidean space. A lattice of nodes is defined in the parameters space together with possible fracture lines. An initial set of rigid elements initially subdividing the original wall geometry is identified accordingly. A homogenized upper bound limit analysis formulation, which takes into account the main characteristics of masonry material such as very low resistance in traction and anisotropic behavior is deduced. Moreover the effect of vertical loads and membrane stresses is considered, assuming internal dissipation allowed exclusively along element edges. A number of technically meaningful examples prove that a good estimate of the collapse load multiplier is obtained, provided that the initial net of yield lines is suitably adjusted by means of a meta-heuristic approach (i.e. a Genetic Algorithm, GA) in order to enforce that element edges accurately represent the actual failure mechanism.

Within the student competition that took place during the 10th International Masonry Conference (10th IMC, 9–11 July 2018, Technical University of Milan, Milan, Italy), a set of tilting plane tests on dry joint masonry shear panels were carried out. Several tests were conducted by means of a tilting table: in-scale models of different perforated masonry shear walls were inclined until the activation of a global collapse mechanism. The ultimate inclination angle is always representative of the maximum shear force that the structure can bear. A total of 7 wall designs WDs, each one proposed by a student team according to some imposed geometrical criteria (8 bricks length, 27 bricks height, 30% minimum percentage of openings), was tested. In this work, numerical simulations aimed at reproducing experimental results obtained during the competition are presented. The problem is studied both in terms of rigid body structures subjected to a finite base rotational settlement and by means of traditional limit analysis. The finite settlement problem is treated incrementally, i.e. by increasing through a small amount the base rotational settlement at each step. On the other hand, limit analysis is performed assuming both associative and non-associative behavior for the masonry material. Finally, in order to better represent the actual behavior of walls during experiments, some simple strategies aimed at including within the numerical models some geometrical imperfections of the bricks and installation defects are devised and their effects are evaluated by means of sensitivity analyses.

We propose a new adaptive NURBS upper-bound limit analysis approach for the assessment of general three-dimensional curved masonry structures, based on different meta-heuristic mesh adaptation schemes. The method, which can easily be integrated within CAD modeling environments, allows to establish the actual failure mechanism and load bearing capacity of a masonry structure by iteratively adjusting a tentative pattern of yield lines, defined upon a suitable initial mesh of NURBS rigid elements, by means of a suitable meta-heuristic algorithm which searches for the minimum collapse load multiplier, thus enforcing the upper-bound theorem of limit analysis. In particular, we investigate and discuss the efficiency of several meta-heuristic algorithms in delivering the optimal solution: a specifically devised Prey Predator Algorithm (PPA) is compared with the Particle Swarm Optimization (PSO) Algorithm, the Firefly Algorithm (FA) and a suitable Genetic Algorithm (GA). Four masonry vaults have been chosen as case studies. In particular, the modified PPA proves to be the most efficient mesh-adjustment scheme for the proposed adaptive NURBS-based limit analysis procedure.

Masonry vaults represent one of the typical structural typologies in historical masonry buildings. The study of the ultimate behavior of masonry vaults, together with the need to design adequate retrofitting techniques, is of high relevance in the optics of the preservation of the cultural heritage. In this paper, a new approach for the limit analysis of masonry construction is applied to FRP reinforced masonry vaults. This approach relies on the representation of geometry through NURBS surfaces, upper bound formulation of limit analysis, idealization of the structure as an assembly of rigid bodies with dissipation allowed only along interfaces, and optimization by means of a mesh adaptation scheme. The presence of FRP strips can be taken into account in easy way, because they can be included simply by adding NURBS surfaces and assigning them an adequate delamination stress value. The efficient mesh adaptation is performed by means of a Prey Predator Algorithm, which has been proven to be very suited for these problems. The strength of the proposed method lies in an accurate estimation of load-bearing capacity and collapse mechanism obtained with a model which requires a very low computational effort.

In this paper, we propose the extended virtual element method (X-VEM) to treat singularities and crack discontinuities that arise in the Laplace problem. The virtual element method (VEM) is a stabilized Galerkin formulation on arbitrary polytopal meshes, wherein the basis functions are implicit (virtual)—they are not known explicitly nor do they need to be computed within the problem domain. Suitable projection operators are used to decompose the bilinear form on each element into two parts: a consistent term that reproduces the first-order polynomial space and a correction term that ensures stability. A similar approach is pursued in the X-VEM with a few notable extensions. To capture singularities and discontinuities in the discrete space, we augment the standard virtual element space with an additional contribution that consists of the product of virtual nodal basis (partition-of-unity) functions with enrichment functions. For discontinuities, basis functions are discontinuous across the crack and for singularities a weakly singular enrichment function that satisfies the Laplace equation is chosen. For the Laplace problem with a singularity, we devise an extended projector that maps functions that lie in the extended virtual element space onto linear polynomials and the enrichment function, whereas for the discontinuous problem, the consistent element stiffness matrix has a block-structure that is readily computed. An adaptive homogeneous numerical integration method is used to accurately and efficiently (no element-partitioning is required) compute integrals with integrands that are weakly singular. Once the element projection matrix is computed, the same steps as in the standard VEM are followed to compute the element stabilization matrix. Numerical experiments are performed on quadrilateral and polygonal (convex and nonconvex elements) meshes for the problem of an L -shaped domain with a corner singularity and the problem of a cracked membrane under mode III loading, and results are presented that affirm the sound accuracy and demonstrate the optimal rates of convergence in the L 2 norm and energy of the proposed method.

In this paper, the first result on the collapse behavior of reinforced masonry domes under seismic loads is presented. A certain masonry dome is modeled through NURBS surfaces, which have the great advantage to represent accurately complex geometries. The obtained NURBS model is imported in the MATLAB® environment, in which an initial NURBS mesh is defined. An upper bound limit analysis is applied: each element is idealized as rigid block and eventual plastic dissipation is allowed only along element edges. The minimum of the kinematic multipliers is found by optimizing the NURBS mesh (i.e. modifying the position of fracture lines) through a meta-heuristic algorithm (e.g. a Genetic Algorithm). A reinforcing system made by FRCM fibers is included through additional NURBS surfaces: each new surface represents a strip and exhibits only a tensile contribute in the evaluation of plastic dissipation. The dome of the church of Anime Sante, which collapsed during the L’Aquila earthquake in 2009, is considered as meaningful case study. A standard disposition of FRCM fibers, typically designed for incrementing the vertical load bearing capacity, has been hypothesized. The reinforced dome is analyzed under a horizontal acceleration linear in height and constant in plane and a comparison between the unreinforced and the reinforced case is presented.

The aim of this paper is to study the vulnerability to horizontal loads of a severely damaged masonry arch bridge located in the province of Ascoli Piceno (Marche, Italy). The bridge is a traditional single-span masonry arch designated as road bridge. A wide fracture line has been observed along the longitudinal direction. The arch has been studied by applying two distribution of horizontal loads directed in the longitudinal and the transversal directions separately. A new upper bound limit analysis recently developed by the cooperation of the Polytechnic University of Milan and the University of Ferrara has been adopted. For the case of horizontal load acting along the longitudinal direction, the capacity curve and the associated fragility curve are presented.

This chapter discusses two advanced numerical approaches for the analysis of fiber reinforced polymer (FRP)-reinforced masonries, namely a novel adaptive upper bound limit analysis (UBLA) and a nonlinear procedure with rigid elements based on sequential quadratic programming. Both are tools for an effective structural analysis of FRP-reinfoced masonry, requiring a preliminary homogenization of the masonry material at the mesoscale. When dealing with the UB limit analysis approach, a genetic algorithm (GA)—nonuniform rational b-spline (NURBS)-based general framework suitable for a mesh adaptation—applied to curved masonry structures is discussed. A given FRP-reinforced masonry vault can be geometrically represented by a NURBS parametric surface, and a NURBS mesh of the given surface can be generated. Each element of the mesh is a NURBS surface itself and can be idealized as a rigid body. An UBLA formulation, which takes into account the main characteristics of masonry material and FRP reinforcement, is deduced, with internal dissipation allowed exclusively along element interfaces. GA helps in progressively adjusting the shape of the NURBS elements to closely approximate the real failure mechanism activating. When dealing with the nonlinear approach, finite element discretization without mesh adaptation constituted by both rigid wedge elements (masonry) and rigid triangular elements (FRP) interconnected by nonlinear homogenized interfaces is discussed. The step-by-step nonlinear problem is solved as constrained minimization of the quadratic energy function. Both approaches are capable of well predicting the load-bearing capacity of any kind of FRP-reinforced masonry structure (in particular, vaults of arbitrary shape, which are the most complex), with the nonlinear model having the additional features of accurately predicting initial stiffness, postpeak behavior, and displacements at failure. Both approaches are benchmarked through a number of numerical simulations applied to FRP-reinforced masonry structures tested in experiments taken from the literature.

The ultimate limit state behavior of masonry domes under axisymmetric gravity loads is nowadays well known and it has been proved how a generalization of the thrush line method used successfully for arches is quite effective also in this case. However, the behavior of a dome under horizontal loads, which is important in case of seismic action, becomes incredibly hard to tackle and still remains an open issue. The present paper aims at presenting a fast and reliable automatized kinematic limit analysis approach able to accurately predict the actual behavior of masonry domes subjected to horizontal static loads. The model uses a rough discretization of the dome obtained by means of few rigid-infinitely resistant NURBS generated elements, adapting step by step the initial mesh in order to progressively overlap the element edges (where all dissipation is lumped) with the hinges forming the failure mechanism. The adoption of a rough mesh makes the code extremely fast, much more competitive than a standard FE model, allowing at the same time to approximate the actual geometry and load distributions in an extremely accurate way. The utilization of geometries obtained with laser scanner acquisitions is straightforward and the presence of pre-existing cracks can be accounted for as well. Three complex case studies are analyzed in detail to benchmark the approach proposed, relying into existing domes belonging to the Italian cultural heritage. The first example has the geometrical parameters of a typical late Renaissance dome, the Cathedral of Montepulciano, the second is the dome of Anime Sante church (collapsed during the L’Aquila 2009 earthquake with a paradigmatic failure mechanism) and the last is the dome of Caracalla baths, whose causes of collapse remain still unknown. In all cases inspected, the approach proposed quickly provides collapse accelerations and active failure mechanisms at a fraction of the time needed by non-linear FE analyses, providing interesting hints into the actual behavior of such kind of structures under horizontal loads.

Two constitutive models representative of two well-known modeling techniques for superelastic shape-memory wires are reviewed. The first model has been proposed by Kim and Aberayatne in the framework of finite thermo-elasticity with non-convex energy [1]. In the present article this model has been modified in order to take into account the difference between elastic moduli of austenite and martensite and to introduce the isothermal approximation proposed in [1]. The second model has been developed by Auricchio et al. within the theory of irreversible thermodynamics with internal variables [2]. Both models are temperature and strain rate dependent and they take into account thermal effects. The focus in this article is on investigating how the two models compare with experimental data obtained from testing superelastic NiTi wires used in the design of a prototypal anti-seismic device [3, 4]. After model calibration and numerical implementation, numerical simulations based on the two models are compared wit...

In this paper, numerical insights on the seismic behavior of a non-isolated historical masonry tower are presented and discussed. The tower under study is the main tower of the fortress of San Felice sul Panaro, a town located near the city of Modena (Italy). Such a tower is surrounded by adjacent structural elements and, therefore, is not isolated. This historical monument has been hit by the devastating seismic sequence occurred in May 2012 in the Northern part of the Emilia region (the so-called “Emilia earthquake”), showing a huge and widespread damage. Here, in order to understand the behavior of the structure, its interaction with the adjacent buildings and the reasons of the occurred damage, advanced numerical analyses (both nonlinear static and dynamic) are performed on a 3D finite element model with different levels of constraint supplied by the adjacent structural elements and a detailed comparison between the simulated damage and the actual one is carried out. The results of the conducted numerical campaign show a good agreement with the actual crack pattern, particularly for the model of the tower that considers the adjacent structural elements.

A new approach for the limit analysis of masonry vaults retrofitted with fiber-reinforced polymers (FRP) based on an upper bound formulation is presented in this paper. In particular, a new...

A new approach for limit analysis of masonry vaults retrofitted with fiber-reinforced polymers (FRPs) based on an upper bound formulation is presented. Part I of this paper was devoted to d...

Summary Recent seismic events have provided evidence that damage to masonry infills can lead not only to large economic losses but also to significant injuries and even fatalities. The estimation of damage of such elements and the corresponding consequences within the performance-based earthquake engineering framework requires the construction of reliable fragility functions. In this paper, drift-based fragility functions are developed for in-plane loaded masonry infills, derived from a comprehensive experimental data set gathered from current literature, comprising 152 masonry infills with different geometries and built with different types of masonry blocks, when tested under lateral cyclic loading. Three damage states associated with the structural performance and reparability of masonry infill walls are defined. The effect of mortar compression strength, masonry prism compression strength, and presence of openings is evaluated and incorporated for damage states where their influence is found to be statistically significant. Uncertainty due to specimen-to-specimen variability and sample size is quantified and included in the proposed fragility functions. It is concluded that prism strength and mortar strength are better indicators of the fragility of masonry infills than the type of bricks/blocks used, whose influence, in general, is not statistically significant for all damage states. Finally, the presence of openings is also shown to have statistically relevant impact on the level of interstory drift ratio triggering the lower damage states.

This contribution is devoted to assess the capability of a new upper-bound approach for the limit analysis of FRP-reinforced masonry arches by comparing it to both experimental tests and a number of existing numerical procedures. The approach is based on an idea previously presented by the Authors and relies on the representation of the geometry of both the arch and of FRP reinforcement through Non Uniform Rational B-Spline (NURBS) functions. This allows generating a rigid body assembly starting from the assigned geometry composed by very few elements which still provide an exact representation of the original shape. A homogenized kinematic formulation for the limit analysis of the obtained rigid blocks assembly is derived, which accounts for the main properties of masonry material. FRP material is included exploiting the Italian CNR Recommendations for the design of FRP based reinforcing interventions. The approach is capable of accurately predicting the load bearing capacity of masonry arches of arbitrary geometry, provided that the initial mesh is adjusted by means of a suitably devised Genetic Algorithm (GA) until the active interfaces among blocks (e.g. hinges) closely approximate the actual failure mechanism.

The aim of this paper is to study the statics of the stellar (i.e. star-shaped) vault of the church of Santa Maria del Monte in Cagliari. This church, which was built during the second half of the 16th century, is a beautiful example of Gothic-Catalan style and the ribbed stellar vault is one of the most representative of this type in the town of Cagliari. A comparison between a static finite element non-linear analysis carried out with the commercial code Diana and a limit analysis performed with a method recently developed by the research team of the University of Ferrara is presented.

From the NURBS 3D model of a generic masonry vault to a rigid body assembly.Kinematic limit analysis based on a homogenized upper bound formulation.Dissipation allowed along element edges only.Optimization of the rigid body assembly through a suitable Genetic Algorithm.Fast determination of the load bearing capacity and failure mechanism of the masonry vault. The present paper proposes a new Genetic Algorithm NURBS-based approach for the limit analysis of masonry vaults based on an upper bound formulation. A given masonry vault geometry can be represented by a NURBS (Non-Uniform Rational B-Spline) parametric surface and a NURBS mesh of the given surface can be generated. Each element of the mesh is a NURBS surface itself and can be idealized as a rigid body. An upper bound limit analysis formulation, which takes into account the main characteristics of masonry material is deduced, with internal dissipation allowed exclusively along element edges. The approach is capable of well predicting the load bearing capacity of any masonry vault of generic shape. It is proved that, even by using a mesh constituted by very few elements, a good estimate of the collapse load multiplier is obtained provided that the initial mesh is adjusted by means of a meta-heuristic approach (i.e. a Genetic Algorithm, GA) in order to enforce that element edges accurately represent the actual failure mechanism. The proposed method turns out to be both accurate and much less computationally expensive than existing methods for the limit analysis of masonry vaults.