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[EN] This study aimed to experimentally analyse the robustness of riveted steel bridges based on truss-type structures and to define practical recommendations for early detection of local failures before they cause progressive structural collapse. Although there are many experimental studies on robustness and progressive collapse on buildings, those on bridges are either theoretical or deal with actual collapses. This paper describes a unique case of a 21m full-scale bridge span tested under laboratory conditions with an extensive monitoring system, together with an experimental study to evaluate structural behaviour and robustness as damage or failure progressed in its elements. A linear-static finite-element analysis was also included to examine other possible causes not included in the experiment. The results proved the structural redundancy of this type of truss structure based on the joints¿ resistance to bending moments and gave rise to a series of practical structural health recommendations to identify early failures and avoid progressive or sudden bridge collapse. The study carried out and the recommendations it produced are now being applied in three similar bridge case studies., We would like to express our gratitude to the FGV (Ferrocarrils de la Generalitat Valenciana) and FCC Construcción S.A., CHM Obras e Infraestructuras S.A., Contratas y Ventas S.A. and CALSENS S.L. for giving us the opportunity to test a bridge at the ICITECH facilities, also to Juan Antonio García Cerezo, of FGV, for his invaluable cooperation and recommendations. We also wish to show our gratitude for the magnificent work on the bridge by Jesús Martínez, Eduardo Luengo and Daniel Tasquer. The tests on the bridge meant that much of the Structures Laboratory was out of service for other work, for which we owe a debt of gratitude to our ICITECH colleagues for their infinite patience and understanding.

[EN] This paper contains a numerical study based on tests carried out at the Universitat Politècnica de València (Spain) on a U-shaped unreinforced and TRM-reinforced masonry building structure subjected to horizontal loads. The masonry was composed of clay bricks with 10 mm thick mortar joints arranged in an English bond manner. The prototype was tested by applying pseudo-dynamic displacement-driven cycles and varying cyclic amplitudes and frequencies in two different stages: (i) on the as-built structure and (ii) after the repair and the application of Textile Reinforced Mortar (TRM) material. A series of non-linear numerical simulations were performed adopting the ABAQUS/Explicit FE software. The FE calibration was carried out using the results obtained during ambient vibration tests. Simulations were then used to evaluate the effectiveness of the proposed TRM technique to increasing the strength of low-rise old masonry building structures., The authors would like to express their gratitude to the Spanish Ministry of Economy, Industry and Competitiveness for the funding provided (BIA 2014-59036-R-AR), and also to the Grupo Mapei and Grupo Puma for their invaluable assistance during the experimental tests.

This paper describes a double experimental and analytical study of the fatigue behaviour of the Quisi and Ferrandet Bridges, twin 170 m long steel railway bridges constructed between 1913 and 1915 with typical Pratt truss structures and riveted connections. These bridges are part of the Spanish national railway network connecting the towns of Alicante and Denia, one of the key networks in the Valencia Region (Spain). The experimental laboratory investigation involved fatigue testing in one of the ICITECH laboratories at the Universitat Politecnica de Valencia of: (i) a full-scale bridge span and (ii) an upper cross beam from the Ferrandet Bridge. During the tests, Linear Variable Displacement Transducers (LVDTs) and Strain Gauge (SG) sensors were used to capture the possible nucleation and propagation of fatigue cracks. Fatigue test carried out on the cross beam identified: (i) fatigue life of the critical detail, (ii) fatigue hot-spots along the cross beam and (iii) strain redistribution along the riveted element during crack growth. The experimental results from the full-scale bridge were adopted to calibrate an elastic numerical model of the whole structure, which was in turn used to estimate the Quisi Bridge's remaining fatigue life. The definition of the class of detail and remaining fatigue life were calculated by the S–N curves method, according to Eurocode 3, considering the available information on the bridges' loading histories.

The main results of an experimental program concerning masonry pillars reinforced by CFRP strips (also provided by spike anchors) subjected to single lap shear tests are described in this paper. The experimental results, also compared with a previous experimental program, allowed to analyze the increment of bearing capacity produced by spike anchors to CFRP sheets having different bonding length.

Aim of the present paper is the proposal of a simple modeling approach for the numerical simulation of the bond behavior of masonry specimens externally strengthened by FRP strips equipped with anchor spikes. The model is based on a simple 1D-schematization of specimens, previously proposed by the authors and based on the use of linear and nonlinear spring elements schematizing the support, the FRP, the masonry/FRP interface. The approach here proposed specifically considers the coupled behavior between shear and normal stresses arising at the masonry/FRP interface level and, moreover, it introduces constitutive laws for modeling local failure mechanisms involving the anchor. The parameter setting procedure presented in the paper is indeed devoted to implicitly consider the contribution of the anchor and its interaction with the masonry support, directly at the FRP/masonry interface level. This allows to reduce computational efforts while preserving a good reliability level of the model. The validation of the proposed modeling approach is here carried out by considering experimental tests performed by the authors and available in the current literature. The results obtained from the numerical analyses reported in the paper show both the reliability of the proposed approach to capture the experimental behavior and, moreover, its efficacy for investigating the role of the anchor on the bond behavior of the strengthening system.

[EN] Up-and-down cyclical displacement of supports-foundations, due for example to the presence of expansive soils, can affect the integrity of a structure and may even lead to its collapse. A recent study carried out at the ICITECH laboratories of the Universitat Politècnica de València analysed the effects of earth settlements on the behaviour of masonry cross vaults. One of the tests involved the construction and testing of a full-scale timbrel cross vault, one of whose supports was subjected to up-and-down vertical displacement cycles. The 4×4 m2 vault was composed of four 3.6 m diameter arches supporting a masonry web. Vertical displacements were applied to one of the supports by means of two synchronised mechanical jacks. The results of the tests provide valuable information to the scientific community, architects and engineers on the behaviour of timbrel cross vaults when one of their supports is subjected to cyclical movements., The authors wish to express their gratitude to the Spanish Ministry of Economy, Industry and Competitiveness for the funding provided through Project BIA 2014-59036-R, and also to LIC-Levantina Ingenieria y Construction and the Grupo Puma for their invaluable assistance. The second author (Elisa Bertolesi) would like to thank the Universitat Politecnica de Valencia for funding received for her postdoctoral grant (PAID-10-17).

[EN] Structural robustness is a significant property towards improving resilience of buildings, i.e. enhance their ability to withstand and recover from extreme events which often can cause local damage and progressive collapse. It is widely accepted that robustness depends on the capacity of the structure to activate alternative load paths (ALPs) after the failure of load-bearing elements, e.g. columns. Early evidence during World War II showed that progressive collapse of some buildings was avoided by the presence of masonry infill walls. Subsequent studies focused on this effect for cases of sudden column removal although most of these studies were analytical, numerical and only looked at internal columns which are generally less vulnerable to accidental events compared to corner and edge columns. The aim of this study was to analyse how infill walls can improve the robustness of reinforced concrete (RC) buildings in corner columns failure scenarios. A purpose-built 3D two-storey full-scale RC building structure with infill masonry walls was tested. The contribution of masonry infill walls was analysed in terms of: i) load redistribution, ii) ALPs, and iii) Dynamic Amplification Factors (DAFs) to be applied in linear-static analyses. The test was highly monitored by 38 strain gauges, 38 LVDTs and 2 accelerometers to register the vertical and lateral response. The results showed that masonry infill walls had a significant influence on the structural response and activated the predominant ALPs at very small deflections., This work was carried out with the support of a 2017 Leonardo Grant for Researchers and Cultural Creators from the BBVA Foundation. The authors would also like to express their gratitude to the Levantina, Ingenieria y Construccion S.L. (LIC) company for funding the construction of the building, and to the Generalitat Valenciana/Fons Social Europeu [APOSTD/2019/101] and Universitat Politecnica de Valencia [PAID-10-17] for funding received under different postdoctoral programs.

[EN] Building progressive collapse is currently one of the hottest topics in the structural engineering field. Most of the research carried out to date on this topic has been focused on the structural analysis of the failure of one or more columns in a building to determine the Alternative Load Paths (ALPs) the structure can activate. Past research was mainly focused on extreme situations with high loads and large structural deformations and, to a lesser extent, research looked at lower loads used in design accidental situations, which requires a different set of assumptions in the analysis. This paper describes a study aimed at analysing accidental design situations in corner-column removal scenarios in reinforced concrete (RC) building structures and evaluating the available real ALPs in order to establish practical recommendations for design situations that could be taken into account in future design codes. A wide parametric computational analysis was carried out with advanced Finite Element (FE) models which the authors validated by full¿scale tests on a purpose¿built building structure. The findings allowed us to: (i) establish design recommendations, (ii) demonstrate the importance of Vierendeel action and (iii) recommend Dynamic Amplification Factors (DAFs) for design situations., This research was funded by Fundacion BBVA-Becas Leonardo a Investigadores y Creadores Culturales 2017; the Spanish Ministry of Economy, Industry and Competitiveness, grant number BIA2017-88322-R-AR; Generalitat Valenciana/Fons Social Europeu, grant number APOSTD/2019/101 and Universitat Politecnica de Valencia, grant number PAID-10-17. This work is also part of the project "Extension of theoretical models against progressive collapse for tall and supertall concrete buildings", funded by the Engineering Physical Science Research Council (EPSRC) of the UK as part of an Impact Acceleration Account (IAA) held at the University of Surrey (grant number EP/K008153/1), and a continuation of two research projects also funded by EPSRC of the UK (grant ref: EP/K503939 and grant ref: EP/K008153/1).

This paper presents the experimental results obtained from tests on a 2/3 scale U-shaped masonry building constructed in one of the ICITECH laboratories at the Universitat Politecnica de Valencia (Spain). The prototype measured 3.31 × 4.19 m2 by 2.15 m high and had a wall thickness of 230 mm. The masonry was composed of 230 × 110 × 50 mm3 solid clay bricks with approximately 10 mm-thick mortar joints arranged in English bond. The tests were aimed at evaluating the effectiveness of cement-based reinforcing materials (Textile Reinforced Mortar) applied to weak masonry substrates severely damaged by horizontal loads such as those induced by a seismic event. The tests were carried out in three phases: (i) testing of the as-built structure, (ii) application of one external layer of TRM to restore the masonry’s original load-bearing capacity and then (iii) testing the TRM-strengthened structure. Dynamic behaviour was monitored by both traditional and fibre optic sensors (FO), including 28 Linear Variable Displacement Transducers (LVDTs) and 3 long-gauge optical sensors. Strengthening effectiveness was evaluated by several parameters: hysteretic curves, strength degradation, computed cumulative energy dissipation and cracking mechanisms. TRM reinforcement was shown to significantly extend the load-bearing and displacement capacity of the masonry prototype, reducing seismic-induced damage applied by pseudo-dynamic excitation, although it had a limited effect on cumulative energy dissipation.

Fiber Reinforced Cementitious Matrix (FRCM) systems have been recently introduced as an alternative solution for strengthening interventions of existing masonry and concrete constructions. The current literature provides interesting experimental and numerical studies which underline the potentialities of FRCMs together and their specific features. Direct tensile tests are generally used for characterizing the behavior of FRCM. Indeed, these tests underline the occurrence of important phenomena influencing the behavior of FRCM, such as the cracking of the matrix and the debonding of the reinforcement from the matrix. The present paper aims at numerically analyzing the response of FRCM systems during tensile tests carried out throughout different setup configurations. To this end, a simple model carried out from literature and opportunely modified is presented in the paper and validated with reference to experimental case studies. Moreover, the obtained results are critically analyzed in order to emphasize the role of the proposed model for the interpretation of the results carried out from standard tensile tests.

[EN] The topic of robustness and progressive collapse of structures has attracted significant attention within the field of structural engineering recently. This is reflected by the rise in the number of scientific papers published in recent years as well as efforts in reviewing and developing codes for design. Although important numerical and experimental studies have been carried out to date simulating the sudden removal of columns to reproduce the possible consequences of an extreme event, most of these studies focus on subassembly systems and internal columns. Edge and corner columns are most vulnerable to accidental events. This paper gives the results of a test carried out on a purpose-built full-scale reinforced concrete building with a specially designed corner steel column used for the sudden column removal. The test was highly instrumented, involving 38 strain gauges, 38 displacement transducers and 2 accelerometers to monitor the vertical and lateral response. The results were used to analyse the dynamic performance of the structure after the sudden column removal as well as the alternative load paths (ALPs) mobilised during the test (i.e. flexural and Vierendeel action). The test showed a clear dynamic amplification of the strains and displacements (with high peaks); dynamic amplification factors (DAFs) were obtained accordingly. The load initially carried by the removed column was redistributed through the entire building system (not just the neighbouring columns). Tests on full-scale buildings, including the one described here, can be used to compile a database to validate codes and future numerical studies., This work was carried out with the support of a 2017 Leonardo Grant for Researchers and Cultural Creators from the BBVA Foundation. The authors would also like to express their gratitude to the Levantina, Ingenieria y Construccion S.L. (LIC) company for funding the construction of the building.

The paper synthetizes the main results of an experimental program devoted to the analysis of the structural behavior of both flat and curved masonry pillars reinforced with anchored and not anchored Carbon Fiber Reinforced Polymer (CFRP) sheets. A single lap shear test scheme has been selected: the specimens were constrained at the upper and lower faces and were loaded by a force tangent to an end of the reinforcement. The experimental outcomes allowed to analyze the effects of the position (intrados/extrados), of the curvature and of the anchor on the performance of the reinforcement.

The paper presents two different modeling strategies for the study of the debonding of anchored Fiber Reinforced Polymers (FRP) externally applied to curved masonry substrates. The first one is based on a fast and computationally effective simple 1D-schematization of specimens based on the use of linear and nonlinear spring elements schematizing the support, the FRP strengthening and the masonry/FRP interface. The second one consists of a tri-dimensional micro-modelling FE approach comprising a damaging behavior of the constituent materials and elastic zero-thickness cohesive masonry-to-FRP interfaces. Both the approaches are presented in detail in the paper and they are validated by considering experimental tests performed by the authors.

[EN] This paper presents the experimental results obtained from tests on two masonry vaults reinforced by Textile Reinforced Mortar (TRM) materials subjected to monotonic and cyclic vertical settlements in one of their sup-ports. Two full-scale square masonry timbrel vaults were built in one of ICITECH's laboratories at the Universitat Politecnica de Valencia (Valencia, Spain) using the traditional Catalan layered-construction technique, with various layers of clay tiles arranged in two perpendicular masonry textures joined by lime and cement mortar joints. Due to their peculiar geometric and mechanical features, i.e. their high slenderness ratio, low tensile strength and high material heterogeneity, these structures are especially prone to damage from high-risk events such as soil settlement or seismic excitation. To evaluate their response to vertical support displacements, both vaults were pre-damaged by either vertical monotonic or cyclic settlements. They were then strengthened by a radial TRM strengthening configuration and re-tested until failure. A complex network of traditional and optical sensors was used to monitor displacements, deformation and the development of the cracking mechanism under both settlement conditions. The results obtained show that TRM materials can be used to effectively repair severely damaged masonry timbrel vaults, helping to partially restore the initial elastic stiffness, as well as doubling the vaults' elastic phase and ultimate displacements. In addition, TRM materials did not alter the stiffness degradation trend, although they had a strong effect on peak reaction degradation and failure modes. This investigation represents a valuable and unique source of information about the efficacy of TRM materials to repair full-scale pre-damaged masonry timbrel vaults., The authors wish to express their gratitude to the Spanish Ministry of Economy, Industry and Competitiveness for the funding provided through Project BIA 2014-59036-R, and also to LIC-Levantina Ingenieria y Construccion and the Grupo Mapei for their invaluable assistance. The first author (Elisa Bertolesi) would like to thank the Universitat Politecnica de Valencia for funding received for her postdoctoral grant (PAID-10-17).

Fiber Reinforced Polymer (FRP) composites represent an effective retrofitting strategy for the rehabilitation of masonry and concrete structures. The importance of adhesion between support and strengthening material is crucial and great research effort has been aimed at understanding this phenomenon from an analytical perspective. According to interfacial stress analysis, the debonding mechanism may be idealized and studied as an FRP–interface-support system with elastic FRP bonded to a brittle inelastic interface. In the present work, a fully analytical approach is developed to analyse the debonding mechanism of FRP strips applied to flat masonries providing a closed form solution characterized by few parameters governing the mathematical problem. Compared with other analytical methods, the present approach is advantageous in its closed form formulation, which allows the problem to be solved with a limited computational effort in a standard Matlab environment. The approach is benchmarked with two different sets of experimental results taken from the technical literature and from an ongoing investigation carried out by the authors. The results demonstrate the reliability of the method in analysing the debonding of FRP applied on flat masonry prisms.

The use of fiber reinforced polymer (FRP) materials for strengthening interventions of existing constructions is a consolidated and widespread technique. In this context, although strengthening interventions generally involve curved masonry elements (arches, vaults, domes, etc.), only a few studies specifically concern the influence of the geometry curvature, or the effect of mechanical anchors (widely used in current practice for preventing premature failures), on the bond behavior of FRPs. The present paper proposes an interface exponential model for simulating the bond behavior of curved masonry pillars reinforced with FRP strips applied at the intrados or extrados by both epoxy adhesive and anchor spikes. The proposed model is based on a relatively simple boundary value problem (BVP) obtained by assuming for the spike a constitutive behavior under shear forces quantitatively deduced by post-processing the numerical data from a finite element micro-modeling approach previously proposed by the authors. The application of the proposed model to experimental cases carried out by the authors underlines the stability of solution and the reliability of the proposed approach to account for the effect of both the curvature of the substrate and the presence of the spike anchor on the bond behavior of FRPs.

The paper presents the results of a series of In Situ tests carried out on two masonry arches, one unreinforced and the other reinforced with SRG (Steel Reinforced Grout). An advanced numerical modelling based on a heterogeneous discretization is also reported. The arches have a span equal to 3.30 m and height 0.83 m, and are built with common Italian bricks with dimensions 250x120x55 mm3 and 10 mm thick mortar joints. The arches are built regularly spacing out two bricks laid edge on (thickness of the arch 12 cm) with two bricks (one over the other) disposed in single leaf. One of the two arches is tested unreinforced, whereas the second is reinforced with an SRG constituted by an inox grid embedded into a layer of lime mortar. For all samples, an eccentric vertical load placed at 1⁄4 of the span is increased up to failure. An advanced numerical technique is adopted to reproduce experimental results, namely a heterogeneous micro-modelling where bricks, mortar and strengthening are meshed separately. The numerical outcomes are comparatively assessed with respect to the experimental global behavior and crack patterns obtained at the end of the tests.

The paper deals with the analysis of FRCM reinforced masonry panels in simple bending by means of a two-step homogenization approach. In the first step, homogenization is performed on unreinforced masonry through a straightforward procedure already validated for in-plane loaded FRCM reinforced panels, where the elementary cell is discretized by means of 24 CST elastic elements (bricks) and joints are reduced to interfaces with holonomic softening behavior. Out-of-plane homogenized quantities (moment-curvature relationships) are then obtained by simple on-thickness integration. At a structural level (step two), masonry is modeled with rigid elements and homogenized torsional and bending springs, whereas FRCM by two noded trusses with equivalent mechanical properties evaluated on the base of experimental data available. The implementation is handled within the commercial FE software Abaqus. As a matter of fact, the Concrete Damage Plasticity Model (CDP) already implemented into the code allows taking into account the progressive change of stiffness of brittle supports when subjected to alternate cracking-crushing mechanisms, as well as to properly deal with the cyclic behavior. The validation of the procedure is conducted against a series of full scale masonry walls tested by Nanni and co-workers at the University of Miami. A tri-dimensional heterogeneous micro-modeling technique is also used for both unreinforced and FRCM strengthened panels to further validate the homogenization model proposed. The discretization adopted is adjusted in order to allow the presence of two eight-noded FEs along the mortar joint thickness. FRCM is modeled by means of truss elements whose mechanical properties are calibrated to reproduce the behavior of the textile net embedded into the cementitious matrix. The elastic and inelastic mechanical parameters of all the materials involved into the numerical analyses have been calibrated in agreement with laboratory tests, when available. Pros and cons of the two numerical strategies are discussed mostly with respect to the accuracy of the outcomes in terms of global behavior of the panels and damage mechanisms, as well as with respect to the computational effort required by the two approaches to complete the analyses.

[EN] 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.

The paper presents a study concerning the numerical modeling of the bond behavior of fabric reinforced cementitious matrix (FRCM) strengthening systems externally applied on masonry supports. In particular, the authors analyze the efficacy of different modeling strategies which specifically account for the interaction between the reinforcement and the matrix. For this aim, numerical analyses are developed with reference to some case studies deduced from the recent literature by considering shear stress-slip laws both derived from experimental measurements and obtained through calibration procedures. Different numerical modeling approaches are used in order to investigate the local bond behavior of the accounted cases.

The paper presents the numerical results obtained testing a series of masonry panels. The experimental campaign is characterized by some in-situ diagonal compressive tests performed on both unreinforced and reinforced walls with overall dimensions equal to 1000 × 1000 × 300 mm3. The present study is intended to analyze from a numerical point of view, the behavior of ancient double wythe brick masonry panels subjected to in-plane diagonal compressive loads. To this scope, two different types of strengthening have been applied on the tested walls: (i) TRM (Textile Reinforced Mortar) materials symmetrically applied on the panel and (ii) an asymmetric reinforcement made with a layer of TRM materials and with a NSM (Near Surface Mounted) technique on the other. A series of numerical analyses have been carried out by means of a sophisticated heterogeneous micro-modeling technique, by means of which bricks, mortar joints and the strengthening systems have been modeled separately. In detail, a Concrete Damage Plasticity model, already implemented into the FE software Abaqus, has been used to describe the possible crushing and cracking failures of the constituent materials. Finally, the numerical outcomes have been comparatively assessed with respect to the experimental results and the damage patterns obtained at the end of the tests, showing a promising agreement.

Fabric-reinforced cementitious matrix (FRCM) strengthening is an innovative technology for effective reduction of seismic vulnerability of existing masonry and historical structures. At present, numerical modeling strategies for evaluation of the in- and out-of-plane performance of masonry structures strengthened with these composites are in their embryonic stage. The present chapter is aimed at presenting two alternative approaches to such strategies. In particular, a detailed 3D heterogeneous and an inexpensive homogenization approach are reviewed. In the first model, brick and mortar joints are meshed separately with 3D eight-noded elements, whereas FRCM is discretized using trusses (fiber grid) and 3D eight-noded elements (cementitious matrix). These 3D elements are made in all cases with a softening and damage behavior with plasticization, both in tension and compression, using the concrete damage plasticity model. In the homogenization approach, masonry is substituted with an equivalent nonlinear orthotropic material exhibiting softening. The elementary cell is discretized using a few triangular elastic elements (bricks) and holonomic interfaces (joints) in which all the nonlinearities are lumped. The FRCM reinforcement is applied to the homogenized masonry using equivalent trusses with limited tensile strength and fragile behavior, connecting adjoining rigid elements. Equivalent mechanical properties of the trusses can be eventually tuned accounting for FRCM debonding or rupture of the fibers. The pros and cons of the two numerical procedures are discussed with respect to their reliability in fitting experimental force–displacement curves and crack patterns, as well as to the rather different computational effort required by the two strategies.

The creation of an effective, accurate finite element mesh is crucial for running whatsoever numerical analysis on structural models. This is especially true when micro-scale, mesoscale, and homogenization-based approaches are used, since they involve a precise and distinct representation of the constitutive materials. One fitting example is embodied by masonry with irregular bond, where blocks are randomly assembled and often present different shapes and dimensions. This work presents a Matlab script for the generation of a full 3D finite element mesh, which is created directly from a simple rasterized picture of the masonry element under investigation. A voxel approach is here used, where one pixel of the image is turned into one solid finite element. The resulting 3D mesh is employed into a broader Matlab script which derives homogenized failure surfaces for masonry test-windows. In particular, the effectiveness of the 3D mesh is validated by comparing the homogenized failure surfaces obtained for an in-plane loaded masonry panel to those retrieved from the 2D version of the script with a 2D mesh, whose reliability has already been established.

Two distinct non-linear FE modeling techniques are compared to have an insight into the efficacy of FRCM reinforcement for masonry subjected to out-of-plane loads. In particular, both a micro-modeling technique and a homogenization approach are compared. The first approach is a tridimensional heterogeneous procedure where constituent materials (bricks, joints, reinforcing mortar and reinforcing grid) are modeled separately. The second technique is a consolidated two-step homogenization where the meso-scale homogenization problem is solved discretizing the elementary cell with few elastic constant stress triangles (bricks) and non-linear interfaces (joints). The non-linear structural analyses are performed replacing masonry at the macro-scale with an assemblage of rigid elements interconnected by non-linear homogenized springs (HRBSM modelling). Both models are directly implemented in the commercial software Abaqus. Advantages and limitations of the two approaches are discussed in detail –especially as far as the rather different computational effort required by the two strategies is concerned-with reference to their ability in reproducing global force-displacement curves and crack patterns of some reinforced wallettes in simple bending.

A 3D-FE heterogeneous approach is proposed to reproduce experimental single lap shear tests performed on curved masonry prisms reinforced either at the intrados or extrados with FRP strips fixed to the masonry surface by both epoxy resin and an anchor device placed in the middle of the strip. Bricks and mortar are modeled with a concrete damage plasticity material exhibiting softening, whilst for both the FRP and spike a linear-elastic behavior is assumed. An elastic uncoupled cohesive interface between FRP/substrate and anchorage/substrate is also introduced in the model to properly reproduce experimental stiffness and damage diffusion inside masonry. The model is benchmarked against four sets of single lap shear tests performed by the authors at the University of Florence, Italy. A good match between experimental evidences and numerical predictions is obtained. Sensitivity analyses are finally performed in order to furnish a prediction of the delamination strength also in cases not studied experimentally.

A novel interface numerical model for the incremental analysis of the debonding phenomenon of Carbon Fiber Reinforced Polymer (C-FRP) reinforcements externally applied on flat and curved masonry pillars is presented. The interface tangential stress-slip behavior is suitably described by a C ∞ exponential function, that accounts for the ductility and residual strength variation due to the presence of interfacial normal stresses, according to a frictional-cohesive relationship. Such dependence is particularly important when dealing with C-FRP reinforcements applied to masonry curved structures (i.e. arches and vaults). The smooth interface relationship here adopted allows to deal with a boundary value problem for a system of second order differential equations, representing a standard delamination problem, without singularities. Consequently, an easy and robust numerical solution algorithm based on a standard finite differences approach can be adopted. The model is validated against some experimental and numerical results obtained previously by the authors and concerning shear-lap bond tests of flat and curved masonry pillars reinforced by C-FRP sheets. The obtained results underline an excellent robustness and reliability of the experimental global and local behavior.

[EN] The paper presents an experimental study concerning the bond behaviour of Carbon Fiber Reinforced Polymers (CFRP) sheet reinforcements applied to curved masonry surfaces. Such strengthening technique is more and more used in structural rehabilitation and retrofitting of existing buildings. Its effectiveness has been demonstrated by several studies published in the literature, mostly devoted to flat bonded surfaces. Observing that CFRPs are extensively applied on arches and vaults but only few research activities concern curved bonded surfaces, the experimental study described in this paper is aimed to contribute to fill this gap. The experimental program was carried out on portions of masonry arches, reinforced by CFRP sheets bonded at extrados or intrados, tested by a single lap shear test. The experimental results allowed to analyse the effectiveness of such reinforcements, loaded by actions tangent to an end of the reinforcement itself, with respect to its position (intrados or extrados) and to the curvature of the bonding surface. As expected, the results highlight that the bond behaviour strongly depend on the position of the reinforcement. In particular, the capacity of reinforcements bonded at the extrados increases with the curvature, while decreases with the curvature for those bonded at intrados., The Authors gratefully acknowledge the financial support provided by the Italian Department of Civil Protection and ReLUIS (Rete dei Laboratori Universitari di Ingegneria Sismica), 2014-2016 Grant - Innovative Materials.

[EN] The two arches and the three vaults experimentally described in Carozzi et al. (2017) are here analyzed with a novel robust FE lower bound limit analysis code, suitable to predict active failure mechanisms, lines of thrust and collapse loads in absence and presence of TRM, SRG and FRP reinforcement. The approach relies into a discretization into rigid-infinitely resistant quadrilateral elements for masonry, interfaces between contiguous elements exhibiting limited strength and perfectly bonded rigid-plastic trusses representing the reinforcement. For masonry, a No Tension Material NTM model can be adopted to compare with classic Heyman¿s results, but also a limited compressive and tensile strength with a cohesive frictional behavior in shear may be accounted for in a relatively simple fashion, i.e. in principle with the possibility to model shear sliding and compression crushing. Debonding and delamination of the reinforcement are considered in a conventional way, assuming trusses with a limited tensile strength derived from either experimental data available or consolidated formulas from the literature. With the knowledge of the exact position of the hinges provided by limit analysis, 2D FE static analyses with non-linearity and softening concentrated exclusively on hinges are carried out, to simply extend the knowledge beyond collapse loads estimation towards a prediction of initial stiffness and ultimate displacements. In all cases, promising agreement with experiments is observed., Part of the analyses were developed within the activities of Rete dei Laboratori Universitari di Ingegneria Sismica - ReLUIS for the research program funded by the Dipartimento di Protezione Civile.

The present paper discusses the results obtained by using a micro-mechanical FE numerical model for the study the bond behavior of some curved specimens strengthened by Fiber Reinforced Polymer (FRP) composite materials. The numerical model, implemented into the FE code Abaqus , is a sophisticated micro-modelling (heterogeneous) approach, where bricks and mortar are meshed separately by means of 4-noded plane strain elements exhibiting distinct damage in tension and compression, FRP is assumed elastic and an elastic uncoupled cohesive layer is interposed between FRP reinforcement and masonry pillar. The experimental investigation considered to benchmark the numerical approach is aimed at characterizing the influence of normal stresses induced by curved supports on the stress-transfer mechanism of FRP materials. To this scope some single lap shear tests performed at the University of Florence on FRP reinforced curved pillars with two different curvature radii (1500 and 3000 mm) are here considered. The obtained numerical results show a promising match with experimental evidences, in terms of elastic stiffness , peak loads and post-peak behavior. Indeed, the proposed approach allows to correctly account for important local effects, such as the effect of FRP-masonry interfacial normal stresses on the global delamination strength and the distribution of damage in the pillar volume. By using the proposed modelling approach, comprehensive numerical sensitivity analyses to investigate the role played by the curvature on the ultimate delamination strength, are also presented in the paper.

The effectiveness of Carbon Fiber Reinforced Polymers (CFRP) reinforcements bonded to masonry structures is demonstrated by the several interventions made on existing buildings as well as by the numerous studies presented in the scientific literature. In practical strengthening interventions, CFRP sheets are being used to reinforce both plane and curved structural elements. Contrariwise, research in the scientific literature are mainly devoted to the analysis of the effectiveness of such reinforcements bonded on plane surfaces. For this reason, the experimental program described in this paper concerns the analysis of the mechanical behavior of portion of masonry arches reinforced by CFRP sheets. The experimental results allowed to analyze the effectiveness of such reinforcements applied at intrados or extrados, loaded by actions tangent to an end of the reinforcement itself. The influence of the mortar joints thickness on the performance of such reinforcements has been also analyzed in the experimental program.

The present paper discusses the experimental results obtained testing some curved specimens strengthened using Fiber Reinforced Polymer (FRP) composite materials. The experimental investigation has been aimed at characterizing the influence of normal stresses induced by curved supports on the stress-transfer mechanism of FRP composites. To this scope some single lap shear tests performed at the University of Florence on FRP strengthened curved prisms with two different curvature radii (1500 and 3000 mm) have been analyzed. The numerical model, implemented in the FE code Abaqus, is a sophisticated micro-modeling (heterogeneous) approach, where bricks and mortar are simulated separately with 4-noded plane strain elements with damage in tension and compression, FRP is assumed elastic and an elastic uncoupled cohesive layer is placed between FRP reinforcement and the masonry support. Numerical results obtained are in satisfactory agreement with the experimental ones in terms of peak loads, collapse mechanisms and damage patterns at collapse. A detailed investigation of the effect of FRP-masonry normal stresses is also present in the proposed paper.

Aim of the present paper is to numerically study the bond behavior of curved masonry specimens externally strengthened by Carbon Fiber Reinforced Polymer systems (CFRP). A simple 1D-modeling approach is presented to this aim, where the coupled behavior between shear and normal stresses developing at the reinforcement/masonry interface level is specifically introduced to properly account for the role played by the curvature radius. The model is indeed enriched by the introduction of shear stress-slip laws able to account for the beneficial friction effect, when compression normal stresses develop at the interface level and the reduction of the slip strength corresponding to the de-cohesion in presence of normal stresses in tension. Considering some case studies derived from the current literature, consisting of shear-lap bond tests of curved masonry specimens characterized by different curvatures of the bonded surface and different strengthening configurations, the validation of the proposed approach is carried out. In particular, two modeling strategies are considered and critically compared: the first one, denoted as approach (A), where the presence of the mortar joints is neglected, and the second one, denoted as approach (B), where mortar joints are specifically introduced in the model. Finally, the results obtained by using the proposed simple approach are compared with those obtained from both sophisticated FE numerical models and theoretical formulas deduced from the current literature.

Masonry arches and their typical failure do not fall elegantly into standard design and analysis methods. The system is highly dependent on geometry and failure is dominated by mechanization, not material strength. Focusing directly on the mechanized failure, this work presents the kinematic collapse load calculator (KCLC) for circular arches. The KCLC, a MATLAB® based graphical user interface, provides a simple interactive limit analysis of any ideal semi-circular masonry arch subjected to either an asymmetric point load or constant horizontal acceleration. After defining key geometric factors, the KCLC analyses the arch for any selected and kinematically admissible hinge configuration. For a selected configuration, an equilibrium approach to the upper bound theorem of limit analysis is used to calculate the collapse load multiplier and hinge reactions. The resulting collapse condition values are displayed and used to plot the thrust line that maintains a zero moment at the hinges. Designed primarily as an educational tool, the KCLC also provides a simple and efficient foundation for adapting to different arch geometries and loading conditions. Keywords: Masonry arch, Limit analysis, Kinematic approach, MATLAB®, Interactive analysis

The present paper is devoted to the discussion of a series of unreinforced and FRP retrofitted panels analyzed adopting the Rigid Body and Spring-Mass (HRBSM) model developed by the authors. To this scope, a total of four out of plane loaded masonry walls tested up to failure are considered. At a structural level, the non-linear analyses are conducted replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage by means of which out of plane mechanisms are allowed. FRP retrofitting is modeled adopting two noded truss elements whose mechanical properties are selected in order to describe possible debonding phenomenon or tensile rupture of the strengthening. The outcome provided numerically are compared to the experimental results showing a satisfactory agreement in terms of global pressure-deflection curves and failure mechanisms.

The aim of the paper is to propose and assess the reliability of a modeling strategy which combines the homogenization of the masonry material and the use of zero-thickness interface elements. This strategy is specifically proposed for numerically investigating the structural response of FRP-reinforced curved masonry structures. Indeed, in order to consider the influence of the geometry curvature of the masonry substrate on the local bond behavior of the FRP-strengthening system, bond-slip laws which specifically account for the geometric curvature of the substrate are introduced at the FRP/substrate interface layer. Numerical analyses concerning masonry arches selected from the current literature are presented in the paper in order to assess the reliability of the proposed modelling approach.

The paper presents the results of a series of in-situ tests carried out on two masonry arches, one unreinforced and the other reinforced with SRG (Steel Reinforced Grout). The arches are built adopting a peculiar construction technique using common Italian bricks with dimensions 250 × 120 × 55 mm3 and 10 mm thick mortar joints. One of the two arches has been reinforced with an SRG material constituted by an inox grid embedded into a layer of lime mortar, whereas the second one is maintained unreinforced for comparison purposes. The experimental set-up is designed to apply an eccentric vertical load placed at ¼ of the span in a series of loading and unloading cycles up to the failure. The numerical analyses have been performed using a sophisticated heterogeneous micro-modeling technique, where bricks, mortar joints and the strengthening have been modeled separately. Finally, the numerical outcomes have been comparatively assessed with respect to the experimental results and the crack patterns obtained at t...

[EN] A simple holonomic compatible homogenization approach for the non-linear analysis of masonry walls in-plane loaded is presented. The elementary cell (REV) is discretized with 24 triangular elastic constant stress elements (bricks) and non-linear interfaces (mortar). A holonomic behavior with softening is assumed for mortar joints. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how the homogenized stress-strain behaviour can be evaluated semi-analytically. At a structural level, it is therefore not necessary to solve a FE homogenization problem at each load step in each Gauss point. Non-linear structural analyses are carried out on a windowed shear wall, for which experimental and numerical data are available in the literature, with the aim of showing how quite reliable results may be obtained with a limited computational effort.

A simple quasi analytical holonomic homogenization approach for the non-linear analysis of masonry walls in-plane loaded is presented. The elementary cell (REV) is discretized with 24 triangular elastic constant stress elements (bricks) and non-linear interfaces (mortar). A holonomic behavior with softening is assumed for mortar. It is shown how the mechanical problem in the unit cell is characterized by very few displacement variables and how homogenized stress-strain behavior can be evaluated semi-analytically.

The simple quasi analytical holonomic homogenization approach for the non-linear analysis of in-plane loaded masonry presented in Part 1 is here implemented at a structural leveland validated. For such implementation, a Rigid Body and Spring Mass model (RBSM) is adopted, relying into a numerical modelling constituted by rigid elements interconnected by homogenized inelastic normal and shear springs placed at the interfaces between adjoining elements. Such approach is also known as HRBSM. The inherit advantage is that it is not necessary to solve a homogenization problem at each load step in each Gauss point, and a direct implementation into a commercial software by means of an external user supplied subroutine is straightforward. In order to have an insight into the capabilities of the present approach to reasonably reproduce masonry behavior at a structural level, non-linear static analyses are conducted on a shear wall, for which experimental and numerical data are available in the technical literature....

A two-step homogenisation model, formulated by the authors for the in-plane case, is herein extended for the nonlinear out-of-plane analysis of masonry structures. A rectangular running bond elementary cell is discretised by 24 elastic CST elements and inelastic zero-thickness interfaces. The mechanical meso-scale problem is briefly recalled, whereas the out-of-plane homogenised behaviour is evaluated by means of a simple on-thickness integration of the in-plane homogenised curves. At a macro-scale, the rigid body and spring model is slightly modified to allow both flexural and torsional failure mechanisms. The validation of the numerical approach is achieved comparing with some full-scale masonry panels tested in two-way bending up to failure. A series of nonlinear structural analyses are conducted considering different parameters, which have been varied during the experimental campaign. The numerical results are promising and demonstrate the capability to deal with different failure mechanisms as result of a combination of various experimental aspects.

The 50 m high masonry chimney located in the old industrial facility that houses the School of Engineering of the University of Ferrara, Italy, suffered severe damages during the 2012 Emilia seismic sequence. Afterward, for security reasons, the upper damaged 12.40 m were disassembled. Both before and after shortening, the ratio between the effective mass of the fundamental mode and the total mass is approximately 20%, leading standard pushover analysis methods not to be appropriate for estimating the seismic demand. Using a single, consistent 3D FE formulation, the results of a Modal Pushover Analysis (MPA) and four nonlinear Response History Analyses (RHA) for the shortened and the original chimney were presented in the paper. The ground motions considered in the simulations are accelerograms recorded during recent and less recent devastating seismic events in Italy, New Zealand, and Japan. For both chimneys, a very good agreement between MPA and RHA was observed in terms of lateral displacements. Moreover, for the 50 m high chimney, a strong similarity was observed between the damage maps deriving from the MPA and those obtained with the RHA. All analyses confirmed a significant contribution of the higher modes. For the shortened chimney, the MPA revealed damages in the lower part of the stack (8–21 m), because of a prevailing influence of the fundamental mode. In the RHA, a more evident contribution of the higher modes was observed, probably because of the effect of the vertical component of the ground motion, not accounted for in the MPA.

A simple homogenized rigid body and spring model (HRBSM) is presented and applied for the non-linear dynamic analysis of 3D masonry structures. The approach, previously developed by the authors for the modeling of in-plane loaded walls is herein extended to real 3D buildings subjected to in- and out-of-plane deformation modes. The elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. At a structural level, the non-linear analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM) by means of which both in and out of plane mechanisms are allowed. All the simulations here presented are performed using the commercial software Abaqus. In order to validate the proposed model for the analyses of full scale structures subjected to seismic actions, two different examples are critically discussed, namely a church facade and an in-scale masonry building, both subjected to dynamic excitation. The...

Two simple homogenization models in the inelastic range for running bond masonry.Subdivision of the RVE into few triangular elastic elements for bricks and non-linear joint interfaces.Closed form or semi-analytical solution of the discretized non linear homogenization model.Utilization at a structural level of a homogenized rigid body and spring model (HRBSM).Comprehensive validation at a structural level on shear walls and a deep beam. Two simple homogenization models suitable for the non-linear analysis of masonry walls in-plane loaded are presented. A rectangular running bond elementary cell is discretized by means of twenty-four constant stress three-noded plane-stress triangular elements and linear two-noded interfaces. Non-linearity is concentrated on mortar reduced to interface, exhibiting a holonomic behavior with softening. The paper shows how the mechanical problem in the unit cell can be characterized by very few displacement/stress variables and how homogenized stress-strain behavior can be evaluated by means of a small-scale system of non-linear equations. At a structural level, it is therefore not necessary to solve a homogenization problem at each load step in each Gauss point and a direct implementation into commercial software as an external user supplied subroutine is straightforward. Non-linear structural analyses are conducted on a variety of different problems, for which experimental and numerical data are available in the literature, in order to show that accurate results can be obtained with a limited computational effort.

Two FE modeling techniques are presented and critically discussed for the non-linear analysis of tuff masonry panels reinforced with FRCM and subjected to standard diagonal compression tests. The specimens, tested at the University of Naples (Italy), are unreinforced and FRCM retrofitted walls. The extensive characterization of the constituent materials allowed adopting here very sophisticated numerical modeling techniques. In particular, here the results obtained by means of a micro-modeling strategy and homogenization approach are compared. The first modeling technique is a tridimensional heterogeneous micro-modeling where constituent materials (bricks, joints, reinforcing mortar and reinforcing grid) are modeled separately. The second approach is based on a two-step homogenization procedure, previously developed by the authors, where the elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. The non-linear structural analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM). All the simulations here presented are performed using the commercial software Abaqus. Pros and cons of the two approaches are herein discussed with reference to their reliability in reproducing global force-displacement curves and crack patterns, as well as to the rather different computational effort required by the two strategies.

A fast and reliable non-linear heterogeneous FE approach specifically conceived for the analysis of FRP-reinforced masonry arches is presented. The approach proposed relies into the reduction of mortar joints to interfaces exhibiting a non-linear holonomic behavior, with a discretization of bricks by means of four-noded elastic elements. The FRP reinforcement is modeled by means of truss elements with elastic-brittle behavior, where the peak tensile strength is estimated by means of a consolidated approach provided by the Italian guidelines CNR-DT200 on masonry strengthening with fiber materials, where the delamination of the strip from the support is taken into account. The model is validated against some recent experimental results relying into circular masonry arches reinforced at both the intrados and the extrados. Some sensitivity analyses are conducted varying the peak tensile strength of the trusses representing the FRP reinforcement.