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In this paper the actual dynamic behavior of the civic Clock tower of Rotella, a little village in central Italy heavily damaged by the recent 2016 seismic sequence, is thoroughly investigated by means of a detailed numerical model built and calibrated using the experimental modal properties obtained through Ambient Vibration Tests. The goal is to update the uncertain parameters of two behavioral material models applied to the Finite Element Model (elastic moduli, mass densities, constraints, and boundary conditions) to minimize the discrepancy between experimental and numerical dynamic features. A sensitivity analysis was performed with the definition of a metamodel to reduce the computational strain and try to define the necessary parameters to use for the calibration process. Due to the high nonlinear dependency of the objective function of this optimization problem on the parameters, and the likely possibility to get trapped in local minima, a machine learning approach was meant. A fully automated Finite Element Model updating procedure based on genetic algorithms and global optimization is used, leading to tower uncertain parameters identification. The results allowed to create a reference numerical replica of the structure in its actual health state and to assess its dynamic performances allowing better control over their future evolution. [ABSTRACT FROM AUTHOR]

This paper provides a comphrensive review of the critical aspects of nonlinear modeling for evaluating the seismic response of masonry structures, emphasizing the issues relevant to engineering practice. Currently, the specialized technical community shares the opinion that, for a performance-based approach, numerical models are the only tools sufficiently effective to support the seismic assessment of existing buildings. However, their potential often falls short when attempting to accurately describe the behavior of masonry structures. In fact, these structures feature highly complex architectural configurations, different masonry types, and various structural solutions, meaning that extra care is required in numerical modeling. This is especially true when the modelers do not have a solid background in the software chosen and may not be practiced using the vast variety of options offered by the software houses. They are often unaware of the consequences that questionable modeling choices may have on the results obtained by the models. These extremely complex topics are treated in the paper from an engineering practice perspective, providing an in-depth overview of the challenging issues related to the use of different modeling strategies. The paper covers strategies ranging from the Equivalent Frame approach (widely used in common engineering practice) to more refined techniques like 2D and 3D Finite Element procedures based on continuous, discrete, and micro-mechanical approaches. Critical aspects in the modeling of both in- and out-of-plane responses of masonry, as well as the critical issues in wall-to-wall connections and diaphragm roles are investigated. All the examined issues are clarified through numerical examples highlighting also how a consistent and integrated use of different procedures may be beneficial. Finally, some of most relevant challenging issues concerning the use of numerical models in seismic assessment with the nonlinear static approach are presented and discussed. [ABSTRACT FROM AUTHOR]

This paper reports the results of different finite and discrete element simulations on a well-known benchmark of an unreinforced plane masonry structure. Namely, the case study concerns a five floor structural wall, located at the interior of a masonry building, situated in "via Martoglio" in the city of Catania (Italy). The numerical simulations aim to investigate the structural response of the wall subjected to seismic actions by means of a non-linear static analyses. The role of reinforced concrete floor beams within URM walls, their influence on the spandrel elements capacity and the approximation that can affect the model, if the concrete beam non linearity is not engaged, are considered. The benchmark is investigated considering three different structural layouts that have been analysed by means of four numerical approaches. The modelling strategies that have been considered are adaptive NURBS kinematic limit analysis, planar discrete macroelements DME, continuum nonlinear FEM methods and a nonlinear FEM micro-modelling. The results are compared in terms of capacity curves and damage mechanism for each structural layout. As a result, pushover curves and damage patterns appear considerably influenced by the concrete floor beams and their mechanical behaviour. All the considered models denote satisfactory agreement in term of strength and collapse mechanisms, some minor differences are observed in terms of global ductility. [ABSTRACT FROM AUTHOR]

Partially grouted reinforced masonry (PG-RM) shear walls have been widely used as structural elements in low- and medium-rise earthquake-resistant buildings. Nonetheless, assessing its shear strength represents a complex task mainly because the partial grouting provides a non-constant cross section, which results in heterogeneous stress–strain patterns. Consequently, refined modeling techniques are needed to reproduce local failure mechanisms taking place in these walls, which significantly influence the global response. In response to this issue, a detailed micro-modeling approach based on the finite element method was proposed in previous studies by the authors. Although the numerical strategy provided accurate results, further validation is required. Therefore, in this study, the experimental results of seven PG-RM shear walls of multi-perforated clay bricks with bed-joint reinforcement are employed as validation cases. These seven walls presented variations in five design parameters. The validated numerical model was then employed to perform a parametric study to assess the influence of the wall aspect ratio, axial pre-compression stress, and horizontal reinforcement ratio on the in-plane lateral behavior of PG-RM shear walls. The obtained results show that the three studied design parameters modified the crack patterns of the walls. Besides, increasing the axial pre-compression stress or reducing the aspect ratio resulted in higher walls' shear strength. Additionally, decreasing the horizontal reinforcement ratio or increasing the aspect ratio generated a higher story-drift ratio at maximum lateral force. Finally, it was corroborated that the positive effect of the axial pre-compression stress on the walls' shear strength decreases inversely proportional to the aspect ratio. [ABSTRACT FROM AUTHOR]

Masonry structures, although classically suitable to withstand gravitational loads, are sensibly vulnerable if subjected to extraordinary actions such as earthquakes, exhibiting cracks even for events of moderate intensity compared to other structural typologies like as reinforced concrete or steel buildings. In the last half-century, the scientific community devoted a consistent effort to the computational analysis of masonry structures in order to develop tools for the prediction (and the assessment) of their structural behavior. Given the complexity of the mechanics of masonry, different approaches and scales of representation of the mechanical behavior of masonry, as well as different strategies of analysis, have been proposed. In this paper, a comprehensive review of the existing modeling strategies for masonry structures, as well as a novel classification of these strategies are presented. Although a fully coherent collocation of all the modeling approaches is substantially impossible due to the peculiar features of each solution proposed, this classification attempts to make some order on the wide scientific production on this field. The modeling strategies are herein classified into four main categories: block-based models, continuum models, geometry-based models, and macroelement models. Each category is comprehensively reviewed. The future challenges of computational analysis of masonry structures are also discussed. [ABSTRACT FROM AUTHOR]

Masonry structures constitute the great majority of buildings in historical centers where construction activities were carried out by adding structural portions to pre-existing ones: as a result, masonry aggregates are currently the most common structural typology in such contexts. The structural behavior of masonry aggregates, which are complex systems of different buildings interacting with each other, is generally affected by several factors, such as the different steps of construction, uncertainties about interlocking between walls, presence of different and irregular masonry textures and multi-leaf walls, which make such a structural typology very difficult to study. During recent seismic events in Italy, a wide number of local collapses has been observed in masonry aggregates of historical centers, highlighting the important role of local mechanisms in the seismic assessment of such structures. In this paper, an efficient software called ANUB-Aggregates (Adaptive Nurbs Upper Bound limit analysis for masonry Aggregates) is proposed for the seismic assessment of partial failure mechanisms in historical masonry aggregates. The theoretical core of this program is a kinematic NURBS-based limit analysis with meta-heuristic mesh adaptation. The use of NURBS allows studying aggregates containing vaulted structures, or any other typology of curved elements, without additional computational effort. Moreover, the mesh adaptation scheme assures the representation of the correct collapse mechanism by finding the real position of fracture lines. Starting from the three-dimensional model of the whole aggregate, the code ANUB-Aggregates provides the analysis of more macro-elements interacting with each other with different interlocking hypotheses, evaluating both simple and complex failure mechanisms. As proof of the effectiveness of this applicative, the analysis of two historical masonry aggregates is presented. [ABSTRACT FROM AUTHOR]

This special issue presents a selection of extended and thoroughly revised papers resulting from the 10th (IMC) International Masonry Conference, which took place at the Technical University of Milan (Politecnico di Milano) in Milan, Italy from 9 to 11 July 2019. [ABSTRACT FROM AUTHOR]

Masonry arches are vulnerable to seismic actions. Over the last few years, extensive research has been carried out to develop strategies and methods for their seismic assessment and strengthening. The application of constant horizontal accelerations to masonry arches is a well-known quasi-static method, which approximates dynamic loading effects and quantifies their stability, while tilting plane testing is a cheap and effective strategy for experimentation of arches made of dry-stack masonry. Also, the common strengthening techniques for masonry arches are mainly focusing on achieving full strength of the system rather than stability. Through experimentation of a dry-stack masonry arch it has been shown that the capacity of an arch can be increased, and the failure controlled by defining hinge positions through reinforcement. This paper utilizes experimentally obtained results to introduce: (1) static friction and resulting mechanisms; and (2) the post-minimum mechanism reinforcement requirements into the two-dimensional limit analysis-based kinematic collapse load calculator (KCLC) software designed for the static seismic analysis of dry-stack masonry arches. Computational results are validated against a series of experimental observations based on tilt plane tests and good agreement is obtained. Discrete element models to represent the masonry arch with different hinge configurations are also developed to establish a validation trifecta. The limiting mechanism to activate collapse of arches subjected to hinge control is investigated and insights into the optimal reinforcement to be installed in the arch are derived. It is envisaged that the current modelling approach can be used by engineers to understand stability under horizontal loads and develop strengthening criteria for masonry arches of their care. [ABSTRACT FROM AUTHOR]

The need for seismic protection of structures located in earthquake prone areas of developing countries has motivated several investigations of low-cost seismic isolators in recent years. One of the most promising device is the Unbonded Fiber Reinforced Elastomeric Isolator (UFREI): in UFREIs no bonding or fastening is provided between the bearing and top–bottom supports and expensive thick steel plates are not required. The behavior of UFREIs is characterized by rollover and full-contact deformations under horizontal loads: the former decreases the effective stiffness of the isolation system, thus reducing the seismic demand, while the latter plays a key role in generating a hardening phase, thus limiting the horizontal displacement of the isolator under severe earthquakes. Such remarkable advantages highlight a great potential for world-wide UFREIs applications. However, until now there is no representative UFREI model available in structural analysis software codes. In this work, a comprehensive but simple UFREI model is implemented in an ABAQUS user element (UEL), taking into account non-linear, hardening and hysteretic behavior of the bearing: in addition, multiple DOFs are considered to simulate the complex 3D behavior of UFREIs, which is characterized by horizontal and vertical displacements, rotation and torsion. The effectiveness of the UEL model is evaluated performing 3D FE dynamic time history analyses on a rigid slab supported by four different types of UFREI. The results show that the UEL model can reasonably fit the behavior of the detailed FE model, significantly reducing the computational efforts of the analyses. The UEL model proposed in this study can be particularly suitable for 3D dynamic time history analyses of complex base isolated structures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A mechanistic model with rigid elements and interfaces suitable for the non-linear dynamic analysis of full scale 3D masonry buildings is presented. The model relies into two steps: in the first step, a simplified homogenization is performed at the meso-scale to deduce the mechanical properties of a macroscopic material, to be used in structural applications; the second step relies into the implementation of a Rigid Body and Spring Model (RBSM) constituted by rigid elements linked with homogenized interfaces. In the homogenization step, a running bond elementary cell is discretized with 24 three-node plane-stress elastic triangular elements and non-linear interfaces representing mortar joints. It is shown how the mechanical problem in the unit cell is characterized by few displacement variables and how homogenized stress-strain curves can be evaluated by means of a semi-analytical approach. The second step relies on the implementation of the homogenized curves into a RBSM, where an entire masonry structure can be analyzed in the non-linear dynamic range through a discretization with rigid elements and inelastic interfaces. Non-linear structural analyses are conducted on a church façade interconnected with a portion of the perpendicular walls and on a small masonry building, for which experimental and numerical data are available in the literature, in order to show how quite reliable results may be obtained with a limited computational effort. [ABSTRACT FROM AUTHOR]

A very simple kinetic model for natural rubber (NR) and polybutadiene (PB) blends is presented. The model is characterized by a completely uncoupled curing between NR and PB, NR being modeled with a primary vulcanization and a subsequent de-vulcanization and PB only by a simple first order model of vulcanization. The assumptions made are roughly in agreement with the actual experimental behavior of the constituent materials in a rheometer chamber, where PB exhibits a quite stable behavior even at high curing temperatures and long vulcanization times. As a result of the simplifications assumed into the curing model adopted, the numerical approach uses only on three kinetic constants, two for NR and one for PB. Such assumptions allow for a quite straightforward determination of the kinetic constants by means of a simple semi-analytical approach. The reliability of the procedure proposed is benchmarked on some 70% NR- 30% PB blends with two different accelerants (N-terbutyl, 2-benzothiazylsulfenamide TBBS and N,N-diphenylguanidine DPG) in different concentrations tested experimentally on a standard rheometer chamber at 170 and 180 °C. Quite good match is found between numerical predictions and normalized rheometer curves, with a clear practical impact into the Finite Element FE modelling of vulcanization of real items. [ABSTRACT FROM AUTHOR]

A series of simplified approaches are evaluated for their effectiveness to estimate the seismic vulnerability of historical masonry towers. First, collapse loads are evaluated on sixteen “idealized” benchmark cases with different slenderness and shear area. Both analytical and computational approaches are used, namely the analytical procedure proposed by the Italian Guidelines on the Built Heritage and pushover analyses conducted using the commercial codes UDEC and 3Muri. The sixteen towers are representative cases which can be encountered in practice. Their geometry is idealized into parallelepiped blocks with hollow square cross-sections, thus favoring the utilization of 2D approaches, beneficial to drastically reduce the effort required for repeated computations. In addition, a Monte Carlo MC upper bound limit analysis strategy is proposed, in order to have an insight into the possible failure mechanisms for the different cases investigated. Deliberately is avoided the introduction of any form of irregularity and they are supposed isolated from the neighboring buildings, to obtain results exclusively dependent from geometric features. Among all the possible collapse mechanisms, five of them are selected according to the probability of occurrence based on past earthquake experiences. Five million cloud points of collapse accelerations are obtained by carrying the height, slenderness and shear area of the idealized towers. The approach is very fast and allows identifying different regions where single mechanisms are active. The results are confirmed repeating MC simulations with a triangular FE upper bound limit analysis discretization of the idealized towers. A series of equations are provided in order to assist engineers and practitioners to obtain a preliminary estimation of their expected collapse acceleration. For validation purposes, the results obtained previously with refined full 3D FE models of 25 towers located in the Northern Italy are reported. Satisfactory agreement between the predictions provided by simplified methods and sophisticated analyses are obtained. [ABSTRACT FROM AUTHOR]

The role played by inclination in both the load carrying capacity and seismic assessment of masonry bell towers is investigated through the results obtained from different analyses on three case studies. The Italian Code for the built heritage is not explicit about the influence of inclination on the seismic assessment of towers, leaving to practitioners the task to properly consider it, potentially leading to both an overestimation of the capacity and an underestimation of the horizontal actions. The case studies investigated in this paper are three leaning masonry bell towers, all exhibiting a quite meaningful inclination and all located in Emilia-Romagna region (Italy), recently (2012) stricken by a moderate/high intensity seismic sequence. This study compares the procedure provided by the Italian Code with the finite element (FE) results obtained through non-linear static analyses and proposes a modification of the Italian code simplified mechanical model (SMM), which explicitly accounts for the actual inclination of the towers within a cantilever beam approach. The FE results show that inclination may considerably reduce the load carrying capacity, increasing the seismic vulnerability of the structures. The SMM approach proposed properly takes into account the role played by inclination, always providing results on the safe side with respect to FEM. [ABSTRACT FROM AUTHOR]

simple rigid-plastic homogenization model for the limit analysis of masonry walls in-plane loaded and constituted by the random assemblage of blocks with variable dimensions is proposed. In the model, blocks constituting a masonry wall are supposed infinitely resistant with a Gaussian distribution of height and length, whereas joints are reduced to interfaces with frictional behavior and limited tensile and compressive strength. Block by block, a representative element of volume (REV) is considered, constituted by a central block interconnected with its neighbors by means of rigid-plastic interfaces. The model is characterized by a few material parameters, is numerically inexpensive and very stable. A sub-class of elementary deformation modes is a-priori chosen in the REV, mimicking typical failures due to joints cracking and crushing. Masonry strength domains are obtained equating the power dissipated in the heterogeneous model with the power dissipated by a fictitious homogeneous macroscopic plate. Due to the inexpensiveness of the approach proposed, Monte Carlo simulations can be repeated on the REV in order to have a stochastic estimation of in-plane masonry strength at different orientations of the bed joints with respect to external loads accounting for the geometrical statistical variability of blocks dimensions. Two cases are discussed, the former consisting on full stochastic REV assemblages (obtained considering a random variability of both blocks height an length) and the latter assuming the presence of a horizontal alignment along bed joints, i.e. allowing blocks height variability only row by row. The case of deterministic blocks height (quasi-periodic texture) can be obtained as a subclass of this latter case. Masonry homogenized failure surfaces are finally implemented in an upper bound FE limit analysis code for the analysis at collapse of entire walls in-plane loaded. Two cases of engineering practice, consisting on the prediction of the failure load of a deep beam and a shear wall arranged with random texture are critically discussed. In particular, homogenization results are compared with those provided by a heterogeneous approach. Good agreement is found both on the failure mechanism and on the distribution of the collapse load. [ABSTRACT FROM AUTHOR]

A three-dimensional (3D) homogenized limit analysis model for the determination of collapse loads of out-of-plane loaded FRP reinforced masonry walls is presented. Homogenization is performed on unreinforced masonry, whereas strips are applied at a structural level on the already homogenized material. Unreinforced masonry strength domain is obtained by means of a compatible approach in which bricks are supposed infinitely resistant and joints are reduced to interfaces with frictional-cohesive behavior and associated flow rule. A sub-class of elementary deformation modes is a-priori chosen in the representative volume element (RVE), mimicking typical failures due to joints cracking and crushing. Masonry strength domains are obtained equating power dissipated in the heterogeneous model with power dissipated in a fictitious homogeneous macroscopic plate. Afterwards, an upper bound FE limit analysis code is implemented to study entire unreinforced and FRP reinforced walls out-of-plane loaded. For unreinforced masonry, rigid infinitely resistant wedge-shaped 3D elements are used. The utilization of 3D elements is necessary to simulate the flexural strength increase induced by the introduction of FRP strips with negligible thickness, which are modeled by means of triangular rigid elements. FRP strips contribution is taken into account assuming that masonry and FRP layers interact by means of interfacial tangential actions. Internal power dissipation is possible at the interfaces between wedge adjoining elements (masonry failure), at the interfaces between triangular FRP and wedge masonry elements (delamination) and between triangular FRP adjoining elements (FRP failure). Two different structural examples are presented to validate the numerical model, namely a FRP reinforced masonry wall in cylindrical flexion and a set of masonry walls with openings in two-way bending. Results obtained with the model proposed fit well both experimental and numerical data available for all the cases analyzed, meaning that the procedure proposed can be used in building practice. [ABSTRACT FROM AUTHOR]