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Textile Reinforced Mortar (TRM) also known as Fabric Reinforced Cementitious Matrix (FRCM) represents a valid alternative to Fiber Reinforced Polymers (FRP) for structural strengthening. The use of inorganic matrix in place of epoxy resin produces a substantial advantage in terms of physical and chemical compatibility with the substrate, especially for application to masonry members (walls or vaults). However, the increasing use of TRM systems for repair and strengthening of masonry structures is carried out in the absence of specific rules for design and assessment. Aiming at filling this lack in regulation, a joint committee between ACI 549 and RILEM TC250 was established. Based on the experimental results and modelling approaches available in the literature, a preliminary database of the significant parameters characterizing the mechanical behaviour of TRM/FRCM systems applied to masonry vaults was collected. More precisely, the load and displacement capacity of masonry vaults strengthened with FRCM composites are put in relationship with the mechanical parameters characterizing the tensile and bond properties of the strengthening systems. In such a framework, the following relevant aspects are considered: i) the contribution of the strengthening system in terms of additional capacity of the vault with respect of the delamination phenomenon; ii) the influence of the curvature on the capacity of the reinforcement and on its bond to the substrate; iii) the comprehensive effect on the overall deformability of the strengthened structure. Based on the collected data, an analytical approach is proposed to draw up simplified design rules that can be used for application to real cases

This paper focuses on the interaction between tunnelling and historical masonry structures. These latter often characterise the centre of many cities and should be preserved from possible tunnelling-induced damage. In recent years the Authors of this contribution have adopted an advanced numerical approach to investigate this issue in the two-dimensional domain, schematising the block masonry structure as a homogenised anisotropic medium [1, 2]. This study extends the approach to three-dimensional conditions. The behaviour of masonry is described by a modified version of the Jointed Rock model, named hereafter as Jointed Masonry model, an anisotropic elastic perfectly plastic constitutive model implemented in the code Plaxis 3D. This model takes into account the directional properties of the medium, identifying the orientation of three planes along which the Mohr-Coulomb yield criterion applies. The paper first briefly describes how the original Jointed Rock model was modified to more realistically account for some specific features of the nonlinear mechanics of masonry. This is followed by the 3D analysis of a tunnelling-structure interaction problem, aimed at highlighting the key features of the proposed masonry model.

In masonry components strengthened with externally bonded composites, good bonding is one of the most important aspects governing structural behavior, since failure usually takes place with detachment between reinforcement and substrate. This type of event is a brittle, sudden and therefore undesirable failure mechanism; nor does it allow the full strength of the reinforcement to be exploited. Many experimental data on bonding have recently become available from a Round Robin Test carried out within the framework of RILEM TC-223. In the present paper, experimental tests were simulated at increasing levels of complexity; bond behavior was first studied with an analytical model based on bi- linear representation of bond law. Two-dimensional and three-dimensional finite element analyses were then performed, according to various bond-slip laws. In particular, a number of bi-linear and non-linear interface laws were used, calibrated according to several strategies but with the same experimental population. Lastly, several commercial codes and types of finite elements were examined. This work may be said to represent a numerical Round Robin Test, with various simulations and modeling approaches. Analytical and numerical results are compared with experimental ones, in terms of both overall behavior (load to displacement curve) and local behavior (strain profiles on reinforcements at increasing load values), showing the importance of both types of information in order to obtain reliable predictions of experimental results.

The paper investigates the effectiveness of two-dimensional Discrete Element Method as a tool for structural analysis of arches provided with buttresses and backfill and strengthened with externally bonded reinforcement. Masonry vault and buttresses are modelled as an assembly of 2D rigid blocks interacting through non-linear contact joints, the backfill is discretized into deformable elastic-plastic triangular elements, while the reinforcement is modelled by means of truss elements bonded to the substrate through non-linear springs. A parametric analysis on the influence of material parameters and the effect of the discretization of the backfill is carried out, and the outcome of different reinforcement systems, consisting of Steel Reinforced Grout applied either at the intrados or at the extrados, are analysed. The comparison with experimental full-scale tests proved the ability of the numerical approach to capture hinges position, load bearing capability, as well as the increase in deflection and load capacity provided by the reinforcement.

A new orthotropic limit function is developed to describe the failure of masonry under in-plane loads. The formulation starts from the isotropic smooth 3D yield function proposed by Bigoni and Piccolroaz (2004) to provide a strength condition for masonry through a single analytical function including orthotropy and different tensile and compressive strengths. The material parameters are calibrated by means of a simple optimization procedure based on available experimental and numerical data. Finally, the limit function is implemented in a finite element code in the framework of a perfect plasticity, through a numerical procedure based on a predictor–corrector algorithm. The effectiveness of proposed model is verified through the comparison of numerical simulations with experimental data available in the literature.

The paper is related to the assessment of collapse mechanisms of historic masonry structures suffering settlements induced by ground movements. Two numerical strategies are adopted in order to study the influence of the settled zone on the cracking of masonry buildings: a discrete rigid block model and a continuous homogenized model. The first approach provides an estimate of the collapse load and failure pattern of masonry based on the lower bound theorem of limit analysis. The second approach is formulated in the framework of multi-surface plasticity and implemented in a FE code for the path-following non-linear analysis of masonry wall described as continuous anisotropic plate. Several settlement configurations, of masonry walls under moving ground support are investigated and the corresponding failure patterns resulting from the analysis are obtained resulting in local or global failure modes. The results of the two modeling formulations are compared and discussed in order to highlight the features of the two different approaches in the prediction of settlement-induced damage.

The structural assessment of masonry remains an open challenge due to its intrinsic nonhomogenous nonisotropic and nonlinear behavior. Aiming at providing a tool for structural applications, this paper presents the formulation and implementation in a FE code of a simple constitutive model to describe the behavior of masonry walls regarded as elastoplastic homogenized anisotropic plates. The model is based on few geometrical and mechanical parameters that can be easily detected from masonry typology. Nonetheless, it can capture the essential features of the structural behavior of ancient masonry, i.e., the failure in traction and the anisotropic behavior deriving from the joints layout. The model succeed in predicting the failure mechanism and load carrying capacity under different boundary and loading conditions, including soil settlement and seismic loading. Its validation is finally carried out for some selected case studies.

Masonry walls are particularly vulnerable against out-of-plane seismic actions. Steel tie-bars and crowing beams in reinforced masonry can prevent their overturning, but collapse may take place also by bending, leaf separation or disaggregation. Textile Reinforced Mortar (TRM) composites, comprising high strength fabrics and inorganic matrices, can be effectively applied to improve the seismic capacity of masonry load-bearing walls and infill panels. Nevertheless, a deeper knowledge on the dynamic response and ultimate capacity of retrofitted walls still needs to be gained before TRM systems can be confidently used in engineering practice. This work describes a shake table test carried out on two full-scale wall specimens, one made of regular tuff blocks and one of two leaves of rubble stones, subjected to seismic out-of-plane vertical bending. The walls were tested unreinforced, repaired and strengthened with TRMs and tested again. A unidirectional textile of ultra high tensile strength steel was used on the tuff wall, whereas a bidirectional basalt mesh was applied over the entire surface of the stone wall, with the addition of transversal steel connectors. The responses of the specimens before and after retrofitting are compared to show the improvement in terms of acceleration and displacement capacity entailed by TRM retrofitting and the modification of, deflection profiles, failure modes, damage development and dynamic properties. Test outcomes prove the effectiveness of TRM composites for the protection of existing masonry structures, including architectural heritage, in earthquake prone areas and provide information on the reliability of analytical predictions for seismic assessment.

Detecting the onset of structural damage and its progressive evolution is crucial for the assessment and maintenance of the built environment. This paper describes the application of a computer-vision-based methodology for structural health monitoring to a shake table investigation. Three rubble stone masonry walls, one unreinforced and two reinforced, were tested under natural earthquake base inputs, progressively scaled up to collapse. White noise signals were also applied for dynamic identification purposes. Throughout the experiments, videos were recorded, under both white noise excitation and environmental vibrations, with the table at rest. The videos were preprocessed with motion magnification algorithms and analyzed through a principal component analysis. The natural frequencies of the walls were detected and their progressive decay was associated with damage accumulation. Results agreed with those obtained from another measurement system available in the laboratory and were consistent with the crack pattern development surveyed during the tests. The proposed approach proved useful to derive information on the progressive deterioration of the structural properties, showing the feasibility of this methodology for real field applications.

Settlements severely affect historic masonry arch bridges worldwide. There are countless examples of structural dislocations and ruins in recent years due to severe settlements at the base of pier foundations, often caused by shipworm infestation of wooden foundations or scouring and riverbed erosion phenomena. The present paper proposes an original way to approach the failure analysis of settled masonry arch bridges. The proposed method combines two different 2D numerical models for the prediction of masonry arch bridge capacity against settlements and for safety assessment. The first one is the Piecewise Rigid Displacement method, i.e. a block-based limit analysis approach using the well known Heyman's hypotheses; the second one is a continuous Finite Element approach. The case study of the four-span Deba Bridge (Spain, 2018) failure is presented with the aim to illustrate how the methods work. The failure analysis produced satisfactory results by applying both methods separately, in confirmation of their reliability. Their combination also allowed to obtain a significantly reduction in computational cost and an improvement of prediction accuracy. A sensitivity and a path-following analysis were also performed with the aim to demonstrate the robustness of the presented method. The obtained simulations highlighted that the results do not depend on the friction angle and that a proper prediction of the evolution of the structural behavior can be obtained only taking into account geometric nonlinearities. Such results demonstrate once again that in settled masonry arches geometry prevails over the mechanical parameters. The current study paves the way for the fruitful use of the proposed approaches for a wider range of applications, as, for example, the mechanism identification or the displacement capacity assessment of masonry structures under overloading as seismic loads.

Two techniques for the seismic strengthening of fair faced rubble masonry walls are proposed and tested on a shake table. The first solution entails the use of carbon fibre reinforced polymer connectors installed from outside through the natural stone units, without perforating the entire wall thickness, thus leaving the internal wall surface undisturbed. In the second solution, stainless-steel cords are embedded in repointed mortar joints of the fair face and connected, by means of stainless-steel bars, to a thermo-insulating composite reinforced mortar applied to the internal side. Shake table tests were performed under natural accelerograms on real scale multi-leaf rubble masonry walls, built with the stone units retrieved from the debris of a hamlet heavily damaged in the 2016 Central Italy earthquakes. Both strengthening solutions proved effective in enhancing the seismic capacity by preventing leaf separation and masonry disintegration, and in limiting damage development under earthquake excitation. Thanks to the compatibility with original materials and the preservation of the fair face, they are suitable for mitigating the seismic vulnerability of architectural heritage.

Failure mechanisms and crack patterns characterizing the nonlinear response of masonry under both vertical and horizontal load conditions are strongly affected by its intrinsic anisotropic behaviour. Moreover, in case of ancient masonry walls, typically constituted by high strength units (stone blocks or bricks) and weak mortar, texture is one of the key elements that determine failure morphological features. Some analogies between this material and fissured rocks can therefore be envisaged: the discontinuities of a rock mass and their orientation drive failure similarly to mortar joints in masonry walls and in both cases cohesion and friction characterize the response along these weakness planes. However, peculiar features such as interlocking due to staggered head joints and the periodic nature of masonry need to be considered and make its constitutive response more complex. In this research work the in-plane and the out-of-plane behaviour of masonry walls are analysed. The adopted constitutive model has been formulated stemming from a pre-existing one, originally conceived to simulate the behaviour of jointed rock layers, and has been implemented in the commercial code PLAXIS 3D. It is a three-dimensional model based on the identification of preferential orientation of failure planes, on which a Mohr Coulomb failure criterion holds in conjunction with a tensile stress cut-off. Elastic properties are derived from a relatively simple homogenization procedure and geometrical characteristics of blocks as well as the effect of staggered arrangement of head joints are accounted for. Some case-studies for different geometrical configurations are analysed. Results are compared with both experimental evidences and the numerical outcomes obtained resorting to a different constitutive model in which masonry is described as a homogenized anisotropic medium. The proposed model is also adopted for the simulation of a real-scale static soil-structure interaction problem, aiming at highlighting the capability of the model to describe the macroscopic behaviour in terms of collapse mechanism and collapse multiplier. In spite of its simplicity, the proposed approach is able to account for the role of texture with low computational cost and a relatively limited number of mechanical parameters.

Every year landslides occur all over the world as a consequence of specific ground conditions, geomorphological, physical or man-made processes. Such phenomena, often triggered by heavy rainfalls or earthquakes, can affect buildings and infrastructures, causing economic and life losses. This work investigates the effects of a landslide, occurred on the 26th of November 2018, on the Monastry of Santa Scolastica in Subiaco (Rome), one of the most ancient and well-preserved examples of medieval architecture in Central Italy. The evolution of the damage pattern observed on the structure is discussed and related to its different causes, aiming at evaluating if possible worsening effects should or not be ascribed to the occurred landslide or to possible future similar events. The study relies on an accurate geometrical description of both the slope and the building, made possible by advanced survey tools. Most of the analyses used to simulate the history of the events occurred to the Monastry were performed by a three-dimensional non-linear finite element model. Elastic-perfectly plastic constitutive assumptions were adopted for the soil, while the structure was modelled by a three-dimensional anisotropic elastic-perfectly plastic constitutive model, specifically conceived for masonry, accounting for block dimensions and staggering joints effects. Finite element approach has proven to be very effective in the analysis of such a coupled interaction problem, leading to a realistic representation of the interplay between the soil displacements and their effects within the structure. The safety conditions of the structure could then be assessed, and the causes of the damage pattern identified, showing that the slope movement did not worsen the pre-existing damage conditions, which should instead be ascribed to the original soil-structure interaction phenomena occurred when an extension of the original structure had been built.

Numerical modeling of masonry structures is nowadays still an active research field, and this is partly due to a number of open issues related to preservation and restoration of historical constructions and the availability of computational tools that have become more and more refined. This work focuses on the analysis of settlement-induced failure patterns characterizing the in-plane response of two-dimensional dry-joints masonry panels, which differ in terms of texture, geometry, and settlement configuration. Brick-block masonry, interpreted as a jointed assembly of prismatic particles in dry contact, can be modeled as a discrete system of rigid blocks interacting through contact surfaces with no tensile strength and finite friction, modeled as zero thickness elasto-plastic Mohr-Coulomb interfaces. Different approaches and numerical models have been adopted herein: Limit Analysis (LA), a discrete model DEM, and a continuous Finite Element Model (FEM). Limit Analysis is able to provide fast and reliable results in terms of collapse multiplier and relative kinematics. In this work, a standard LA procedure was coded through Linearized Mathematical Programming to take into account sliding mechanisms through dilatant joints. Discrete models are particularly suitable to study historical masonry materials, where rigid bodies interact between contact and friction. Here, a combined Finite/Discrete Element approach (FEM/DEM) is adopted. Finally, analyses are conducted through the Finite Element approach, resorting to a continuum anisotropic elastic perfectly plastic constitutive model. Some selected case studies have been investigated and found to have adopted the above mentioned models, and numerical results have been interpreted to highlight the capability of the approaches to predict failure patterns for various geometrical features of the structure and settlement configurations.

Masonry walls are particularly vulnerable against out-of-plane seismic actions. Fabric Reinforced Mortars (FRM) composites, comprising high strength fabrics applied with inorganic matrices, may be used to prevent or delay the onset of collapse mechanisms, and integrated with traditional techniques in compliance with the preservation criteria required for applications to historic structures. This work describes a shake table test carried out on two full-scale wall specimens, one made of two leaves of rubble stones and one of regular tuff blocks. The walls were subjected to out-of-plane vertical bending under seismic base motion. Natural accelerograms were applied in both horizontal and vertical direction with increasing scale factor to collapse. The walls were tested unreinforced, then repaired and strengthened with FRMs, and tested again.

The aim of this paper is to show to what extent a simple constitutive model can adequately describe the collapse mechanisms of historic masonry structures under horizontal seismic loads. Referring to block masonry, the paper presents the formulation and the numerical implementation of a constitutive relationship for modeling masonry structures regarded at a macroscopic scale as homogenized anisotropic continuum. The macroscopic model is shown to retain memory of the mechanical characteristics of the joints and of the shape of the blocks. The overall mechanical properties display anisotropy and singularities in the yield surface, arising from the discrete nature of the block structure and the geometrical arrangement of the units. The model is formulated in the framework of multi-surface plasticity. It is implemented in a FE code by means of a minimization algorithm directly derived from the Haar-Karman principle. A sensitivity analysis to mechanical and geometrical parameters was carried out to show the influence on the predicted response of small-scale wall components from the literature. The model is then used for the analysis of a numerical case study which is representative of a masonry church subjected to horizontal seismic action. The result of the model will be compared with those obtained by a rigid block model (RBM) of the same small-scale masonry prototypes and of the church building. In the paper, the results of the two models are discussed and analyzed in the way to highlight the weakness and the potentiality of the two different approaches.

The use of composite materials as structural retrofitting tools has been strongly encouraged by their capability of improving structural performance causing minimum invasiveness and reduced weight increment. For decades, Fiber Reinforced Polymers were considered the most suitable composites for retrofitting purposes but, more recently, technological issues have revealed some drawbacks, mainly related to their applications on masonry substrates. A viable alternative is represented by Fabric Reinforced Cementitious Matrix (FRCM), a class of composites made of high-strength textiles with inorganic matrix. Among them, Steel Reinforced Grout (SRG) systems, made of Ultra High Tensile Strength Steel cords embedded in cement or lime-based mortar, are widely used, particularly for repairing or strengthening masonry constructions. Qualification tests and acceptance criteria of these composites have been recently proposed. Numerical simulations of current available experimental test procedures need to be performed to provide a more rigorous insight into the mechanisms that control the composite response up to failure, namely the brittle cracking of the matrix, the ductile response of the steel and the debonding at the mortar-fabric interface. These aspects not only affect the microscale, but are indeed responsible for the macroscopic response of the composite. In this work a finite element simulation of direct tensile tests on SRG systems is presented. Two different gripping methods have been considered, the clamping-grip and the clevis-grip, which identify two standardized test procedures according to RILEM and ACI respectively. Numerical results are first compared with the experimental outcomes to assess the accuracy of the model in reproducing the quantitative and qualitative aspects of composite tensile response. Then, the effects of different boundary conditions on failure mechanisms are investigated, analysing damage and stress patterns in the constituents.

Mortar-based reinforcements are an innovative solution for retrofitting existing structures that combine effectiveness, compatibility, and sustainability. Despite the recent spreading of field applications, there is still insufficient knowledge on their fundamental mechanical properties, and a regulatory gap for experimental procedures and design criteria. A Round Robin Test initiative was organized by the Rilem TC 250-CSM (Composites for the Sustainable strengthening of Masonry) to investigate the tensile and bond behaviour of mortar-based composites with basalt, carbon, glass, polyparaphenylene benzobisoxazole (PBO), aramid and steel textiles. This paper presents the tests carried out on Steel Reinforced Grout (SRG) systems, comprising three textile and four mortar types, supplied by three producers. Ten laboratories from Italy, Poland and Portugal were involved for a total of 150 tests, including direct tensile tests on textiles and composites, and single-lap bond tests on masonry substrate. The influence of the layout of the textile, the mechanical properties of the mortar matrix, the manufacturing and curing conditions, as well as the testing setup and instrumentation, is discussed to contribute to the optimization of the reinforcement systems and to the development of recommendations for laboratory testing. Finally, results are combined to derive engineering parameters for qualification and design purposes.

Following the work by Psycharis [1], in this paper we study the dynamic behavior of a rocking block resting on an elastic Winkler-type foundation for the out-of-plane seismic assessment of masonry walls. The equations of motion are derived and implemented for the simple smooth-rocking block and the calibration of the Winkler-type foundation stiffness is carried out according to the experimental results available in the literature. The dynamic response under natural seismic records is evaluated and the effect of the stiffness on the overall response is analyzed for different natural accelerograms. Both demand and capacity are calculated with reference to the kinetic and potential energies of the system and different intensity measures are considered with the aim of identifying the most representative one for the rocking motion. Finally, a comparison between non-linear time history analyses and a possible energy-based approach is discussed.

The paper presents the experience of a working group within the Rilem Technical Committee 223-MSC ‘Masonry Strengthening with Composite materials’, aimed at developing a standardized, reliable procedure for characterizing the bonding mechanism of masonry elements strengthened with composite materials under shear actions. Twelve laboratories from European universities and research centers were involved. Two different set-ups were compared, for single-lap and double-lap shear tests (the latter in two versions). Four kinds of fiber fabrics, i.e., glass, carbon, basalt and steel, were applied with epoxy resins (wet lay-up system) to clay brick units, for a total of 280 monotonic tests. The results provided information regarding the response of externally bonded-to-brick composites in terms of observed failure mechanisms, load capacity, effective transfer length, and bond shear stress-slip behavior. The test results of the twelve laboratories constitute a set of statistically representative data which may conveniently be used for setting appropriate design provisions and guidelines.