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ABSTRACTThe historical centres of many Italian cities are integral parts of the Country's cultural heritage, and guaranteeing their conservation over time is paramount. Many constructions are characterised by building techniques [...]

ABSTRACT The use of fiber reinforced polymers (FRP) represents an interesting option to inhibit the formation of partial collapse mechanisms on macro-blocks, which is a typical failure mode shown by [...]

ABSTRACT 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 [...]

ABSTRACT In the present paper, different full 3D FE numerical models exhibiting increasing levels of complexity are presented, to have both an insight into the causes of collapse of the [...]

ABSTRACT The seismic vulnerability assessment of eight historical masonry towers, located in the North-East region of Italy, is carried out by means of simplified approaches. Three-dimensional finite element models of [...]

Three alternative numerical strategies ready-to-use by a common practitioner and directly implementable in commercial codes are critically compared in the prediction of the non-linear behavior of a small masonry building [...]

ABSTRACT Existing masonry structures often need to be strengthened or repaired. In many cases, the intervention is realized using composite materials bonded to the surface of the structural element. In [...]

ABSTRACT In this paper, three approaches with different levels of accuracy and approximation are proposed and critically discussed with the aim to model the non-linear out-of-plane response of three-leaf masonry [...]

ABSTRACT A simple homogenized equilibrated and admissible model for the limit analysis of masonry walls in- and out-of-plane loaded is presented. A rectangular running bond elementary cell (RVE) is discretized [...]

An experimental investigation aimed to analyze the mechanical behaviour of Carbon Fiber Reinforced Composite (CFRP) anchor spikes inserted in a brick substrate is reported in this paper. As is well known, such devices can improve the structural performance of CFRP sheets externally bonded to masonry elements (as well as others substrate materials). In structural applications, spike anchors can be subjected to both shear and/or normal actions; the first commonly occurs in structural applications, while the latter may occur in specific applications, such as CFRP sheets bonded to curved surfaces. For this reason, the experimental program described in this paper analyzes the mechanical behavior of a typology of anchor spikes loaded (separately) by pure shear or normal actions. Although, obviously, in anchored CFRP sheet reinforcements the contribution to the bearing capacity of the sheet and of the anchors cannot be additively superimposed (the total capacity is of course not equal to the sum of the capacity of the sheet and of the anchor), the results described in this paper can still give useful indications in practical applications.

Numerical modeling of curved masonry structures reinforced with TRM can be particularly demanding. Indeed, several failure typologies can be encountered when a masonry element is reinforced with this strengthening solution. In the case of arches and vaults, the curvature itself complicates furtherly a correct prediction. The paper wants to provide a reasonable way to model numerically curved masonry structures reinforced with TRM and explore the advantages and detriments of advanced simulation and simplified approaches. At first, an advanced micro-modeling is applied to an arch reinforced at the extrados. Then, the same approach is applied to a limited portion of the same arch and numerical lap shear tests are performed. Finally, a simplified model equipped with a set of truss elements is proposed.

Externally bonded composites have become an effective alternative for building strengthening in recent years, such as FRP (Fiber Reinforced Polymer) and FRCM (Fiber Reinforced Cementitious Matrix) can be utilized in this retrofitting strategy. For masonry structure, curved members are very common and tend to be the weakest parts of the system, meanwhile exhibiting bond behavior differently from that of flat surfaces. In this article, a simplified model consisted of an elastic composite strip and inelastic brittle substrate was adopted, based on which a fully analytical approach is developed for describing the debonding mechanism of FRP/FRCM strengthened curved surface under shear force. This approach requires few parameters, and can be realized with limited computational cost in a standard MATLAB environment, while providing a stable solution. This approach was then validated against numerical method and experimental data available in literatures, proving its effectiveness and reliability.

Curved masonry structures externally strengthened by Fiber Reinforced Polymer (FRP) systems exhibits failure mechanisms that emphasize a local bond behavior particularly influenced by the curved geometry of the substrate and the position of the strengthening (i.e. at the intrados or extrados). Indeed, together with tangential stresses, normal stresses in tension or compression also arise by leading to a combined mode I–mode II behavior of strengthening system at the reinforcement/masonry interface level. In recent studies, the Authors proposed different modeling approaches for FRPs applied to curved masonry structures. In particular, both micro-modeling detailed approaches and simplified approaches were generally proposed. The present paper critically analyzes these models by underlining the main differences among them, the assumptions and their ability to reproduce specific phenomena experimentally observed.

In recent years, strengthening with Fiber Reinforced Polymers (FRPs) has emerged as an effective way for the structural upgrading of masonry elements. In such typology of external reinforcement, the bond quality is crucial for the increase of the load bearing capacity. The bond efficacy beyond the elastic limit can be studied analytically or numerically via several different models, where the most important issue to tackle is the reproduction of the typical brittle behavior of the substrate. In this paper, a simple numerical approach which models FRP as elastic and lumps all non-linearity on the FRP/masonry interface is proposed. The non-linear behavior of such interface is modeled in a simplified but effective way integrating numerically the differential equations deduced from equilibrium and compatibility (once that a non-linear constitutive relationship between tangential stress and slip is assumed at the interface). Such integration is carried out by means of a particularly simple forward scheme that requires the estimation of the slip value and its derivatives on specific knot points. A comparison against existing literature indicated that the proposed numerical procedure can adequately reproduce global load-displacement curves in standard single lap shear tests, as well predict the local slip behavior.

In the framework of the Mediterranean cultural heritage, the term “fictile tubule” identifies a peculiar type of brick, characterized by a cylindrical shape and a hollow core. Its unique geometry and characteristics rank it among the first hollow clay bricks in history. The large-scale production of fictile tubules allegedly began in the Roman provinces of Northern Africa during the 2nd Century A.D., where they were employed for building vaulted and domed structures without the need of centrings. Over the following Centuries, the construction technique of fictile tubules embedded in mortar was constantly refined and improved. This led to an extensive use of such technique in several buildings - as part of different structural elements (vaults, domes, floors, walls) - all over the Mediterranean area, and especially in Southern Italy. In 1909, after the disastrous earthquake in Messina and Reggio Calabria, Calabrian engineer Pasquale Frezza devised and patented an anti-seismic construction system which evolved the technology of casa baraccata. Frezza’s take on this traditional Calabrian way of erecting buildings involved the use of a specific type of fictile tubule, named carosello, alternated with common bricks in masonry walls, which are then encased in a timber frame. This paper presents an investigation on the structural behavior of Frezza’s evolution of casa baraccata, aimed at its possible revival as a relevant anti-seismic construction technique. Two specimen walls with dimensions equal to 60×60×15 cm3 are built according to Frezza’s patent and experimentally examined through a diagonal compressive test at the Civil Engineering Laboratory of University of Calabria. For the first specimen wall the test is carried out until failure to identify the collapse load. Conversely, for the second specimen wall the test is halted immediately after the formation of the first vertical cracks. The specimen is subsequently repaired using B-FRCM (Basalt Fiber-Reinforced Cementitious Matrix) as reinforcement, and the diagonal compressive test is repeated, this time until failure. The results in terms of collapse load and shear strength for both specimens are then compared and critically discussed, highlighting the increased load-bearing capacity of the wall built according to Frezza’s patent and reinforced with B-FRCM.

The problem of the dynamic behavior of masonry arches and vaults has gained increasing interest in recent years, since the key role of these structural elements in the masonry constructions, especially of historic interest. Despite this, the literature still lacks a sufficiently large number of contributions on this important subject, and this deficiency is even more marked for the case of reinforced masonry. In this context, the present paper shows and discusses some preliminary experimental results on full-scale dynamic tests on unreinforced and GFRCM-reinforced Apulian tuff masonry arches. The experiments have been performed by using a test bench appositely designed and built; the dynamic excitation consisted of a harmonic base motion with fixed amplitude and increasing frequency. The acceleration in suitable points of the arches, the base shear and the base motion have been continuously monitored during the tests.

With each new earthquake the damages to vaulted masonry and their vulnerability are continuously observed. Understanding the behaviour of these systems continues to increase, and reinforcement strategies and techniques are continually advancing. The application of reinforcement is often done such that the failure of the system is transformed directly from one of stability to strength. This direct transformation overlooks the intermittent stages that exist, and thus provides a partial picture of the system. An experimental campaign was carried out to test the capacity of a dry-stack masonry arch subjected to hinge control and failed through a tilting test. From the experimentation, it was observed that controlling the hinge locations can increase the resistance of the arch while also providing a defined failure mechanism, but the capacity of the system was greatly reduced when compared to numerical results. Investigation into the capacity reduction revealed stable mechanical deformations resulting from a non-rigid reinforced base joint. This work focuses on the relationship between capacity and stable deformations to calculate a rotational stiffness value for the non-rigid reinforced base joint.

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.

This work focuses on an experimental and numerical study of a tuff barrel vault first damaged by differential vertical settlements of the abutments without rotations, then reinforced with a FRCM system composed by a fiber-reinforced mortar embedding a basalt fiber net, and finally subjected to a concentrated load on a generatrix (still ongoing). The geometry of the vault (polycentric near parabolic shape) and the masonry material (Apulian tuff) have been chosen in order to be representative of some masonry vaults common in rural constructions of Apulia region; also, a load representative of the infill weight has been applied during all the experimental tests. In parallel to the experiments, numerical simulations by a heterogeneous FE Abaqus model calibrated on the experimentally determined mechanical properties of materials have been performed. This model aims at reproducing the settlement phase and to accurately predict the load bearing capacity of the reinforced structure. To this aim, Concrete Damage Plasticity model has been used for modeling mortar joints and cementitious matrix, whereas tuff bricks have been assumed linearly elastic; finally, the basalt fiber net used in the FRCM reinforced has been described by suitable equivalent elasto-damaging trusses.

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.

The seismic vulnerability and resulting damages to vaulted masonry is continuously observed with each new earthquake. The understanding of these systems is quite strong, and reinforcement strategies and techniques are continually advancing. Unfortunately, the application of reinforcement is typically applied in a way that the failure transforms directly from one of stability to strength. This direct transformation overlooks the potential behaviors of the system that exist between the two limits. To investigate and better understand the intermittent behavior of masonry arches, an in-scale dry joint masonry arch subjected to hinge control and a tilting plane loading condition was experimentally tested. The result of that experimentation revealed that the capacity can be increased and the failure defined, but the non-ideal conditions of slip and base deformations were observed as well. This work presents the second experimental campaign of a full-scale dry stack masonry arch subjected to hinge control and a tilting plane loading condition. In this campaign, the issue of slip is addressed in the arch construction, and the results show that the capacity of the full-scale arch can be increased and the failure defined.

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.

The studies contained in the current literature particularly emphasize the importance of the role of the local bond mechanism on the global performance of fiber reinforced polymer systems (FRPs) employed for the strengthening and the rehabilitation of structures. Nevertheless, although several applications of FRPs involve curved masonry structures (arches, vaults, domes, etc.), the bond mechanism of FRPs applied on masonry samples with curved substrates is a topic still scarcely investigated and the actual guidelines do not provide specific design formulas. The aim of the present paper is to analyze the main features characterizing the bond behavior of FRPs externally applied to masonry specimens with a curved substrate configuration throughout a simple modeling approach based on the interface concept. Particular consideration is devoted to the development of suitable constitutive laws for the FRP/masonry interface. Considering 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, numerical analyses are carried out in order to emphasize the ability of the model to capture the bond behavior of FRP applied on curved masonry substrates.

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.

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.

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.

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 use of hollow clay elements (fictile tubules, amphorae and caroselli) for erecting arches, vaults and domes was a building technique very popular in the Mediterranean area from the Roman Empire on. It was devised to ensure lightness and thermal insulation of structural elements. This paper presents experimental investigations and some preliminary numerical analyses regarding an arch consisting of caroselli embedded in mortar. A full-scale laboratory model was constructed and subject to vertical loads. After the development of hinges, the arch was repaired and strengthened with FRCM strips and further loads were applied to investigate the post-strengthening mechanical behavior. Also, numerical models of caroselli and mortar are created in Abaqus. Then, an elementary cell comprised of caroselli and mortar is created. The mechanical properties of the cell are evaluated by studying its behavior under uniaxial tensile and compressive loads. These properties set the basis for a possible homogenized material which can be used for numerical analyses of the arch.