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This paper presents a new method to model the nonlinear behavior of double-curvature masonry structures, possibly reinforced by composite materials, by means of conventional elasto-plastic analyses. The method is meant to be used in professional design, especially for assessment and retrofitting purposes, based on the exploitation of the simplest nonlinear finite elements available in commercial software, namely, trusses with elasto-fragile and elasto-ductile behavior (Cutoff Bars, according for instance to the definition provided by Strand7 R3.1.3a). Numerical static nonlinear analyses are carried out by considering elastic hexahedral elements for bricks and by lumping nonlinearities on joints. These are assumed, in turn, to be elastic–brittle and elastic–plastic by using 1D elements, namely, Point Contacts, under the No-Tension Material hypothesis, and Cutoff Bars, respectively, assigning a small tensile resistance to the material. The reinforcement, realized with FRP hooping strips, is successfully modeled in a similar fashion, i.e., by applying perfectly bonded elastic–plastic Cutoff Bars at the extrados of the dome, where debonding is accounted for in a conventional way, limiting the tensile strength according to Italian Standards’ indications. The procedure is validated against benchmark models with the same geometry, using experimental data and more refined structural model results for comparison. After an in-depth analysis of the obtained results, in terms of capacity curves, the robustness and accuracy of the proposed approach are assessed.

Seismic isolation of a structure can be achieved by interposing a rubber device between the foundation and superstructure, which increases the period of the superstructure, resulting in a structure relatively transparent to seismic excitation. Alternating layers of rubber pads and steel laminas or Fiber Reinforced Polymer (FRP) dry textiles suitable treated, typically constitute an elastomeric seismic isolator. The rubber should be processed through several stages to be ready for structural application. One of the most critical is vulcanization. During this stage, rubber is heated with sulfur or peroxides, accelerators, and activators at around 130-160°C. This process triggers the formation of cross-links between long rubber molecules, creating the so called polymer network. The chains are prevented from sliding along each other thanks to cross-links, and the rubber becomes elastic. This study proposes a combined numerical and experimental approach to predict the vulcanization degree for a Fiber-Reinforced Elastomeric Isolator (FREI). According to the numerical results, two typologies of vulcanization have been considered: one suboptimal at 145°C for 5400 seconds and one optimal at 145°C for 7200 seconds. Results, in terms of Shore A hardness measurements, have shown a non-homogeneous distribution within the isolator suboptimal vulcanized. Instead, as expected, the hardness distribution is homogeneous for the optimal one.

The rubber material is widely used either for household or industrial needs. Since the prehistoric era, rubber has been involved in human life by exploiting the latex from specific trees. For elastomeric isolators, rubber pads have a central role. Damping performance is a prerequisite for isolation-bearing materials. Besides, the materials must have an excellent overall performance, such as high strength to resist damage. From a chemical point of view, it is paramount that the rubber used for assembling the devices is vulcanized correctly. It is crucial to determine the optimal vulcanization times and temperatures to properly create the polymer network and make the rubber capable of exhibiting good mechanical properties at large strains applied. All rubber mechanical properties are strongly affected by vulcanization. This study proposes a numerical model to predict the degree of vulcanization of a Fiber-Reinforced Elastomeric Isolator (FREI) made of a Natural Rubber (NR) – Ethylene Propylene Diene Monomer (EPDM) blend. The aim is to determine the optimal vulcanization time and temperature, taking the induction time into account, to obtain a homogeneous curing level distribution within the isolator.

A simple numerical approach to predict the efficacy of FRP hooping in historical masonry domes is presented. The dome is modelled with 8-noded elastic hexahedron elements connected by 1D trusses/springs on meridians and on parallels, where all the non-linearity takes place. The aim is to simulate the nonlinear behaviour of domes through every FE commercial software equipped only with non-linear 1D elements, namely point contacts and cutoff bars. The constitutive behaviour of the trusses is assumed to be either perfectly brittle or perfectly ductile. A possible orthotropic behaviour and the no-tension material case can be reproduced. External retrofitting is simulated using trusses with an elastic perfectly ductile behaviour, assuming a perfect bond between the substrate and the reinforcement and imposing an ultimate strength for the trusses, which takes into account the possible debonding/delamination from the substrate in a conventional way. The Italian code CNR DT200 and the existing specialized literature are used as references. The models are benchmarked on a masonry dome reinforced with three hooping FRP strips and experimentally tested at the University Architecture Institute of Venice IUAV, Italy. The procedure is validated through extensive comparisons with available experimental data and numerical results obtained in the literature with a variety of different models. Through the extensive comparisons that were made and discussed, the robustness and simplicity of the procedure are proven.

The utilization of fiber-reinforced polymer (FRP) composites for building reinforcement has gained widespread acceptance. However, the bond behavior between externally applied composites and strengthened substrates, which are crucial for system efficacy, has primarily focused on flat surfaces. Yet, the challenge of curved substrates, common in masonry arches and vaults, remains less explored. This study introduces a classical analytical model addressing the bond behavior between FRP plates and curved substrates. This classical approach is structured upon a simplified model that concentrates all the non-linearities of the FRP–substrate interface. The interface is described through a universal multi-linear stress–slip relationship, with the influence of the curved substrate being considered by the normal stress that impacts the interface law. Closed-form solutions for distinct bond-slip law stages are derived and verified against the previous study. Through comparisons with existing experimental data and simulations, this approach is able to predict the maximum load, the trends of the global load-slip curves, and give insights into detailed local behavior. Additionally, the exploration of employing neural networks for determining the interface law exhibits promising outcomes.

Masonry-Infilled Reinforced Concrete Frames are a very widespread structural typology all over the world for civil, strategic or productive uses. The damages due to these masonry panels can be life threatening to humans and can severely impact economic losses, as shown during past earthquakes. In fact, during a seismic event, most victims are caused by the collapse of buildings or due to nonstructural elements. The damage caused by an earthquake on nonstructural elements, i.e., those not belonging to the actual structural body of the building, is important for the purposes of a more general description of the effects and, of course, for economic estimates. In fact, after an earthquake, albeit of a low entity, it is very frequent to find even widespread damages of nonstructural elements causing major inconveniences even if the primary structure has reported minor damages. In recent years, many territories have been hit worldwide by strong seismic sequences, which caused widespread damages to the nonstructural elements and in particular to the masonry internal partitions and the masonry infill panels of the buildings in reinforced concrete, with damage to the floor and out-of-plane expulsions/collapses of single layers. Unfortunately, these critical issues have arisen not only in historic, but also in recent buildings with reinforced concrete, in many cases exhibiting inadequate seismic behavior, only partly attributable to the intrinsic vulnerability of the masonry panels against seismic actions. Such problems are due to the following aspects: lack of attention to construction details in the realization of the construction, use of poor-quality materials, and above all lack of design tools for the infill masonry walls. In 2018, regarding the design of nonstructural elements, the formulation of floor spectra has been recently introduced in Italy. This entry article wants to focus on all these aspects, describing the state of the art, the literature studies and the design problems to be solved.

The goal of this paper is to analyze the aging behavior and the mechanism evolution of nano-Al2O3 (NA)-reinforced styrene-butadiene-styrene (SBS) asphalt under different thermal-oxidative aging conditions. First, NA/SBS-modified asphalt and SBS-modified asphalt with different aging levels were prepared. Second, the viscosity and high temperature rheological performance of the specimens were tested and the property-related aging indexes were calculated and compared. Third, a Fourier transform infrared (FTIR) test of the specimen was conducted and the chemical group-related aging indexes were calculated and analyzed. Fourth, gel permeation chromatography (GPC) was used to analyze the molecular weight of the specimens under different aging levels. Then, an atomic force microscope (AFM) was adopted to analyze the microsurface morphology of different specimens. Finally, correlation analysis between property-related indexes and chemical group indexes was conducted. The results show that NA can enhance the thermal-oxidative aging resistance of SBS asphalt. NA can inhibit the increase in sulfoxide groups and the degradation of the SBS polymer with the increase in aging. NA can slow down the formation of large molecule during the aging process. The degree of change in both the bee structures and micromorphological roughness of NA/SBS asphalt is lower than that of SBS asphalt under different aging levels.

Arches are an important part of the masonry architectural heritage and also serve as infrastructure for bridges and culverts. The behavior testing and structural health monitoring of masonry arches require effective measurement methods. There have been a lot of testing methods applied regarding this subject, among which the vision-based non-destructive methods are very appealing. However, as the demands of measuring accuracy and range increase, the labor and economic costs expand to uneconomical levels. A novel, cheap, and fast measurement strategy which focuses directly on the mechanical failure of masonry arches has been developed. This strategy termed Behavior Mapping (BM) is based on homography and does not require a high-precision camera or extensive experimental setup. A scale dry-stack arch was subjected to repeated collapses through springing displacements during the proof-of-concept development of BM. This generated a huge amount of data and required the development of a MATLAB® based graphical user interface (GUI). The objective of this article is to introduce the GUI and the accompanying data for the purpose of providing educational insight into the behavior of masonry arches. These educational experimental cases integrated in the GUI provide the possibility to better understand the failure mechanism of dry-stone arch under foot displacement, as well to easily identify the occurrence of mechanical joints and determine the value of deformations. This GUI can also be adapted for different arch configurations, as well for further real-time monitoring.

Unreinforced masonry (UM) is well known as a vulnerable structure against earthquakes. However, it remains a popular structural system for low-rise residential housing in many high-seismicity areas, particularly in developing regions due to its low cost and easy construction. In the present study, a retrofitting strategy using locally available material, bamboo strips, was proposed. In addition to its fast-growing rate, the tensile strength of bamboo is considered high, nearly comparable to its steel counterpart. A series of experimental tests were performed in this study, including the bamboo tensile test, the mortar flexural test, the diagonal compressive shear test on the masonry assemblages, and the in-plane pushover test on masonry wall specimens without and with bamboo reinforcement. The retrofitted specimens with different volumes of bamboo reinforcement were also considered. The results show that the application of bamboo reinforcement, at a proper volume, significantly increases the ultimate strength and the ductility of the masonry wall. Such results indicate that the brittle failure of UM structures can be avoided by means of bamboo retrofitting.

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

The dynamic behaviour and the seismic vulnerability of the ancient civic tower of Amatrice, dramatically damaged by the last shocks sequence of 2016 that occurred in Central Italy, have been studied in this paper by means of advanced 3D numerical analyses with the Discrete Element Method (DEM). Thus, a discontinuous approach has been used to assess the dynamic properties and the vulnerability of the masonry structure, through large deformations regulated by the Signorini’s law, concerning the impenetrability between the rigid bodies, and by the Coulomb’s law, regarding the dry-friction model. Afterward, different values have been assigned to the friction coefficient of the models and real seismic shocks have been applied in the nonlinear analyses. The major purpose of this study is to highlight that relevant data on the real structural behaviour of historical masonry can be provided through advanced numerical analyses. The comparison between the results of the numerical simulation and the survey of the existing crack pattern of the bell tower permitted to validate the approach used. Finally, from the results and conclusions of this case study, it is possible to affirm that the used methodology can be applied to a wide variety of historical masonry structure in Europe.

Elastomeric seismic isolation is a technique diffused in civil engineering to protect existing and new structures against earthquakes. It consists in introducing between the superstructure and the foundation several devices (called seismic isolators) having the property to carry vertical loads maintaining at the same time the shear modulus small, increasing considerably the natural period of the structure, where the spectral acceleration drops down (Habieb et al., 2020 and 2019a, 2019b, 2019c, 2019d, 2018). This study investigates the possibility of using recycled rubber in the form of reactivated EPDM (made by 2/3 of regenerated rubber and 1/3 of virgin rubber) for the production of low cost rubber isolators (Habieb et al., 2020). A Fiber Reinforced Elastomeric Isolator FREI prototype constituted by five EPDM pads and four GFRP laminas interposed between contiguous pads is cured in the lab at 130°C and the level of vulcanization is experimentally provided measuring Shore A hardness on several points. A 3D numerical model based on both finite differences and FEM is proposed to predict the degree of vulcanization of the FREI numerically. It is found that the crosslinking density obtained is suboptimal (but still acceptable for an engineering point of view) and that it is required to increase the vulcanization temperature to obtain a full and homogeneous curing.

Fiber Reinforced Cementitious Matrix (FRCM) systems are an innovative 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 and their specific features. Direct tensile tests are generally used for characterizing the behavior of FRCM strengthening systems. These tests particularly underline the occurrence of both matrix cracking and debonding of the reinforcement from the matrix, phenomena which particularly influence the performance of FRCM systems. The present paper aims at numerically analyzing the response of FRCM strengthening 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 examined to emphasize the role of the proposed model for the interpretation of the results carried out from standard tensile tests.

Heritage masonry structures are often modelled as dry-jointed structures. On the one hand, it may correspond to the reality where the initial mortar was weak, missing, or has disappeared through time because of erosion and lixiviation. On the other hand, this modelling approach reduces complexity to the studied problem, both from an experimental and theoretical/numerical point of views, while being conservative. Still, for modelling purposes, in addition to the joint friction, numerical approaches require a specific elastic parameter, the dry-joint stiffness, which is often hard to estimate experimentally. This work numerically investigates the effect of the joint stiffness on the collapse of scaled-down tilting test experiments carried out on perforated dry-joint masonry shear walls. It is found that geometrical imperfections of bricks and the absence of vertical precompression load can lead to very low equivalent dry-joint stiffness, which strongly affects the results, both in terms of collapse and damage limit state (DLS) loads, with practical implications for the engineering practice.

A Finite Element (FE) based macro–element is described for the mechanical response of masonry structures within different ranges of analysis. The macro–element is composed of discrete rigid quadrilateral FE plates whose adjoining interfaces are connected through FE trusses. It allows representing both elasticity and strength orthotropy, full material nonlinearity and damage through a scalar–based model. The possibility of coupling with a so–called FE2 (multi–scale) strategy is also addressed. Validation of the macro–element is conducted within linear static, vibration, and cyclic (nonlinear) problems, in which both static and dynamic ranges are explored. Results are compared with those retrieved from traditional FE continuous models. Advantages are highlighted, as well as its robustness to cope with convergence issues and suitability to be applied within more general and larger–scale scenarios, such as the analysis of anisotropic materials subjected to static and dynamic loading. Formal details are given for its reproducibility by academics and practitioners—eventually within other FE platforms—as the improved running times may be of utmost importance in dynamic problems or highly nonlinear (material) quasi–static analysis.

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

Physical and mechanical properties of timber components are the basis of developing the technical measures for the conservation and restoration of historical timber structural buildings. By means of integrating on-site investigation (such as a visual survey, moisture content test, micro-drilling resistance test, and material samples collection of historical timber components) and laboratory tests, this study proposed a series of methodologies for comprehensively evaluating the physical and mechanical properties of timber. This method can be quickly mastered by various non-professionals and can help the cross-learning of various disciplines engaged in the research of architectural heritage protection. As a trial, the methodologies were applied to survey and assess a typical historical Chinese timber structural building named the Fujiu Zhou house (the house is located in No. 19, Qinglian lane, Yangzhou city, Jiangsu province, China). The paper studies the 224 components of the main structure of the building, including 128 columns and 96 beams. With the help of the components’ defects and damage status, GB/T13942.2-1992 and the National Lumber Grades Authority (NLGA), the grade of timber components was distinguished. The modulus of elasticity (MOE), modulus of rupture (MOR), and other related material properties parameters of timber components were also obtained. The trial results verify that the proposed methodologies are reasonable, and they can be helpful for the conservation of a historical timber structural building.

An integrated three-step approach for the optimization of tires mechanical properties based on experimental characterization, kinetic steady-state model and Finite Element FE heat transmission modelling is presented. The first experimental characterization is needed to calibrate a kinetic numerical model (second step), directly nested in the last step into a FE software for the simulation of 3D heat transmission problems. The kinetic model is a phenomenological approach based on 3 kinetic constants, which allows predicting the initial curing rate, maximum crosslinking and reversion. Kinetic constants are deduced fitting normalized experimental rheometer curves. FE transient curing computations are carried out on a real car tire, discretizing the geometry through a refined mesh. All element of the tire (e.g. belts, carcass, core etc.) can be separately meshed, so the exact vulcanization process in different phases can be eventually accounted for.

The Italian territory is rich of constructions belonging to the architectural heritage which deserve to be protected against earthquakes. In seismic prone areas ecclesiastic complexes, including churches, bell towers, monasteries, basilicas, synagogues, cathedrals and so on, have shown to be very susceptible at damage, even with partial or total collapses, when undergoing earthquakes. Indeed, these constructions, which are usually designed to withstand gravity loads only, are characterized by slender walls, lack of horizontal floors, bad quality of the masonry apparatus, ineffective connections among walls and between roofs and walls and absence of tie-beams absorbing the thrusts of arches and vaults. All these issues are responsible of the damages suffered by these structures, as detected after the last Italian earthquakes, such as those occurred in L'Aquila (2009), Emilia-Romagna (2012), Central Italy (2016), and Ischia (2017). In the current paper the seismic vulnerability assessment of the bell tower of the SS. Rosario ecclesiastic complex in Finale Emilia (district of Modena, Italy) is presented and discussed. After the geometrical and structural surveys of the whole masonry structure have been performed, the global seismic analysis of the bell tower by the 3Muri analysis software has been done. In particular, the behavioral differences between the isolate condition of the tower and the case within the ecclesiastic complex have been highlighted, showing the aggregate beneficial effect. Finally, proper retrofitting interventions have been designed and applied to the masonry bell tower, considered both as isolate construction and aggregate one, and the different benefits deriving from these interventions in the two inspected cases have been emphasized.

The renaissance bell tower of San Benedetto in Ferrara (Italy) has been investigated to understand its nonlinear dynamics correctly with the Non-Smooth Contact Dynamic (NSCD) method. The masonry structure has been modeled with the Discrete Element Methods (DEM), assuming rigid blocks and frictional joints, with the aim to recreate the tower in the actual configuration with the inclination and in a fictitious perfect vertical shape in order to assess the influence of the initial slope on its dynamics. The contacts between blocks are governed by the Signorini's impenetrability condition and by dry-friction Coulomb's law. Both configurations have been analyzed inducing real seismic excitations of various types and intensities, corresponding to the six main seismic events of the last few decades in Italy. Thus, the seismic vulnerability of the examined tower is clearly expressed in the numerical results, proving the effects due to the inclination on the amplification of the vulnerability and the several possible collapse mechanisms. Moreover, the NSCD has demonstrated to be a powerful numerical technique to obtain highly accurate results in the structural analyses of masonry structures in the nonlinear range.

The present research paper properly focuses on the dynamics and failure mechanisms of the masonry “Apennine Church” of Santissimo Crocifisso in Pretare, municipality of Arquata del Tronto in the province of Ascoli Piceno (Marche region, Central Italy). Such a peculiar structural type traditionally characterizes the intense seismic area of Central Italy, unfortunately almost totally damaged by the recent shock sequence of 2016. Advanced numerical modeling through discontinuous and continuous approaches were here utilized to have an insight into the dynamic properties and behavior of the structure under strong nonlinear dynamic excitations. In the discrete element approach, the non-smooth contact dynamics method, implemented in LMGC90©, was applied, adopting a full 3D detailed discretization. The church was schematized as an arrangement of rigid blocks, subjected to sliding by friction and perfect plastic collisions, with a null restitution coefficient. In the finite element approach, the concrete damaged plasticity model available in Midas FEA NX© was involved. This model allows reproducing the tensile cracking, the compressive crushing, and the degradation of the material under cyclic loads. Finally, the numerical analyses provided a valuable picture of the actual behavior of the church, thus giving useful hints for future strengthening interventions.