Search

Recent earthquakes showed that most existing structures are characterized by high seismic vulnerability. In particular, the observations of the damages have individuated in masonry arches and barrel vaults the most critical elements in the seismic vulnerability of existing structures. Therefore, the understanding of their seismic performance has become a crucial problem in the field of structural engineering. Their dynamic behavior is generally evaluated according to simplified methods or, as an alternative, to complex FEM analyses. However, a deep knowledge of their dynamic behavior is still lacking from an experimental point of view and, so far, only few experimental researches have been conducted. At this regard, shaking table tests have been performed to investigate the seismic behavior of a full scale masonry vault with abutments. The vault presents a segmental arch with a span of 298 cm, a rise of 114 cm and 116 cm depth. The vault is made of solid facing clay brick and pozzolanic masonry mortar. The use of composite materials has shown to be effective for these structures. In this background the experimental tests can provide an efficient contribution to the interpretation of the reinforcement effects. The present paper presents a comprehensive overview of the main results of the experimental tests. In particular, the experimental results of an innovative reinforced system coupled with other traditional strengthened systems are herein presented. The reinforcement technique is based on TRM system (Textile Reinforced Mortar). The effects have been investigated by using the shaking table tests, both before and after the TRM reinforcement application. The strengthening systems have been applied to a full-scale masonry vault typically used as roofs in religious buildings. After strengthening, the seismic behavior of the vault was significantly improved. Increasing the PGA, the instrumental response of the specimen started to change, however first visible damage occurred at an almost doubled PGA. The seismic capacity of the unreinforced specimen was more than doubled and the vulnerability moved from the curved element to the masonry abutments. Therefore, additional interventions should be eventually made on the lateral abutments. The strengthening strategy (combination of innovative and traditional systems) was effective in preventing failure of the masonry vault.

The safeguard of existing buildings is currently an issue of great interest in particular for existing heritage buildings. Masonry buildings are often characterized by a strong vulnerability. The vulnerability analyses at regional level could provide significant information. The objective is not to identify the behaviour of individual structures, but to define a typical behaviour for some homogeneous building classes. Therefore, to this aim, the analyses are usually conducted on entire urban areas, or on a multitude of buildings. Mechanical-capacitive analyses have been conducted including in-plane and out-of–plane behaviour of masonry structures to remark the impact of each of the behaviours on the global vulnerability assessment. Fragility curves remark that ordinary buildings are usually vulnerable to out-of-plane mechanisms, while heritage buildings usually incorporate seismic measures able to prevent out-of-plane mechanisms, hence improving the structural performance. In such cases the highest vulnerability is given by the in-plane behaviour. The comparative assessment of fragility including each of the two behaviours individually, and both together, shows that it is not possible a priori to select the most vulnerable behaviour, but they must be analysed together. The behaviour of a class of buildings is provided by the behaviour of the buildings included in that class, hence the designation of buildings to classes is a crucial aspect to be evaluated. Usual designation of building classes is made according to typological approach, while in present study, this approach is compared to an approach based on mechanical behaviour. Hence a class is defined by means of all the features that yield to a homogeneous seismic behaviour. Another outcome of this study, not less relevant in the improvement of knowledge of masonry assessment, is the outline of the most important sources of seismic vulnerability in masonry structures.

The theoretical model of elastic beams on springs is of great interest especially for its usage in many technical applications. The closed-form solution is obtained analysing the behaviour of an elastic beam on uniformly distributed springs. Each spring generates a reaction proportional to displacements. These reactions are continuous as commonly considered in the foundation beam models (Winkler's theory), where soil is modeled by a set of infinitely close bilateral springs, elastic and independent (main assumption). To complete the formulation of interaction the beam model is associated to the soil model. The problem has been extensively investigated and many works in the scientific literature can be found on Euler-Bernoulli model. Much less investigated is the interaction that takes into account the shear deformation contribution of the structural elements ("Timoshenko beam model"). The present paper is focused on derivation of a closed-form solution for the interaction problem of a Timoshenko beam model. In a first step usual differential equations have been analysed, while in a second step the stiffness matrix for beams has been developed. The objective has been to provide explicit expressions of stiffness matrix elements. This formulation represents the exact solution for the Timoshenko beam model on elastic soil, to be implemented in numerical analyses, as a single unified formulation even if soil interaction is inactive.

Masonry vaulted structures are diffused all over the world, in many cases in historical and monumental buildings, often characterized by high seismic risk. For this reason their conservation should be investigated. Composite materials are usually used to retrofit different types of masonry and concrete buildings. The behaviour of masonry arches retrofitted at their intrados and/or extrados surfaces by means of externally bonded composite materials (FRP or FRCM) has been investigated. The load capacity estimate due to composite strengthening could be performed through finite element analyses. The numerical simulations provide important information about the mechanical behaviour of the masonry structures and on the composite-masonry interaction. However, such numerical analyses present often some drawbacks. For this reason it is useful to have simplified calculation methods to estimate capacity increase of masonry vaulted structures due to composite retrofit. Such simplified methods are the goal of this work and they consider linear and nonlinear behaviour of masonry. Validation of the proposed method is carried out by comparing predictions of the load capacity and failure mode with those obtained from shaking table experimental tests.

The Ph.D. thesis starts from a vulnerability study at regional level. This analysis on a typical historical centre located in the Italian region has been performed. This is a preliminary study in order to assess the main parameters which cause vulnerabilities. The result remarks the influence of local mechanisms in the existing masonry buildings, when there are thrusting elements. For this reason, a structural assessment of masonry vaults, by using a detailed modelling, has been performed. The work focuses on a particular typology of barrel vaults typically used as roofs in religious buildings. These vaults typically do not include any backfill and are slender. These barrel vaults cannot be analysed through the classical approaches where no-tensile strength is assumed. The tensile strength must be included to assess the seismic capacity. Therefore a simplified analytical model, in the framework of limit analysis, is proposed which includes the tensile strength. Tensile strength in these analyses is not only affected by the strength of basic materials, but also by the bond at the unit-to-joint interfaces, which could be rather difficult to assess reliably. The proposed model is useful to have simplified calculations to estimate the increase in capacity of vaulted masonry due to the strengthening interventions. The validation of the analytical model was provided by comparing predictions of the load capacity and the failure mode with those obtained from shaking table tests. The dynamic test used to validate the analytical model has been performed on a full scale masonry vault, previously tested. Starting from the validation of the proposed analytical model, sensitivity analyses have been performed in order to assess the impact of some mechanical and geometrical parameters on the seismic capacity. These analyses were performed using the proposed analytical model. Furthermore, the model, previously validated, has been used in order to design dynamic tests on another masonry vault. The proposed method represents a useful modelling tool to design dynamic tests on masonry vaults and to assess their vulnerability. The dynamic response of the specimen has been investigated by using the shaking table system, before and after application of strengthening systems. In particular, after suffering damage, the vault was repaired and strengthened. Then the strengthened specimen was tested again. The strengthening techniques are based on TRM system (Textile Reinforced Mortar) in addition to traditional strengthening techniques (steel ties and masonry ribs). The performance of the strengthening vault was assessed comparing the behaviour of two specimens (unreinforced and strengthening) during the several tests. In order to support the experimental studies, several FEM analyses have been performed additionally to the simplified modelling. The results are intended as a contribution to the understanding of dynamic behaviour and towards the development of simplified models to estimate seismic capacity of vaulted structures. The experimental results remark the effectiveness of the TRM system coupled with traditional interventions (masonry rib and unidirectional steel tie). In particular, the strengthening system is particularly advisable to safeguard of heritage buildings. In fact, given the high efficiency and compatibility of the strengthening techniques experimentally used, they have been implemented in a real heritage building (Monastery of Santo Spirito, Ocre (Italy)).

Gli edifici in muratura sono generalmente caratterizzati da un'ampia variabilità di parametri che ne condizionano il comportamento strutturale (tipologia muraria, tipologia di solaio, presenza di cordoli, catene, ecc.). Tuttavia, alcuni centri storici italiani, realizzati in periodi coevi e con tecniche costruttive e materiali similari, presentano spesso caratteristiche comparabili. Sulla base di questa considerazione, il centro storico di Benevento è stato scelto al fine di individuare delle tipologie edilizie ricorrenti e degli intervalli di variabilità dei principali parametri geometrici e meccanici che le connotano, attraverso rilievi su più di duecento edifici. Sono stati definiti edifici “prototipo” rappresentativi di un comportamento strutturale significativo anche di altri centri storici aventi caratteristiche similari, ai quali estendere la procedura di valutazione della vulnerabilità sviluppata successivamente. Per tali modelli sono state eseguite analisi statiche non lineari finalizzate ad individuare classi strutturali aventi prestazioni sismiche analoghe. Sono state successivamente elaborate stime di danno mediante la definizione di curve di fragilità per ciascuna classe di edifici e per diversi livelli di danno. Gli edifici rilevati nel centro storico di Benevento sono stati quindi assegnati alle singole classi e, mediante le curve di fragilità, per ogni classe individuata, è stata valutata la vulnerabilità sismica per diversi livelli di danno

Nowadays retrofitting and strengthening of masonry buildings are important challenges for structural engineering to ensure the structural safety under seismic or exceptional loads. This paper aims to clarify the effects of strengthening systems on out-of-plane mechanisms activation, such as horizontal and vertical bending mechanisms, by analyzing P-M interaction diagrams according to available international design guidelines. They enable the assessment of structural behavior of strengthened masonry walls under different external loads. Dimensionless equations of maximum bending moment capacity of masonry cross sections retrofitted with composite strengthening systems are derived, assuming different failure modes such as crushing of masonry and rupture of the strengthening system. Parametric analyses are performed to assess the impact of the mechanical parameters of the strengthening systems in terms of strength. The results show that the strengthening systems play a fundamental role in terms of cross section capacity and, if not well designed, the strengthening systems may be ineffective or deleterious in cultural heritage.

Modeling of masonry confinement has been usually derived from concrete confinement, which was deeply tested in the last decades. However concrete and masonry have some crucial differences, e.g., ordinary concrete performance can be usually fully defined by the cylindrical compressive strength, while masonry does not. In the present work, a failure criterion is considered on a solid mechanics base. Such criteria are useful not only to introduce non-uniform stress states, as those developed in non-axisymmetric confined elements, but also to be implemented in FEM. The validity of the adopted failure criterion has been checked against actively confined clay brick masonry and a database of passive confinement tests available in the scientific literature.

Recent seismic events revealed the vulnerability of heritage buildings, and curved elements (arches, vaults and domes) add further vulnerability to those buildings. The internal thrust increases yielding to the out-of-plane mechanisms of the supporting masonry walls when curved elements are subjected to dynamic actions. This effect is strongly influenced by the shape and type of elements. For single curvature elements (arch, barrel vault), a kinematic failure mode can occur not involving the supporting structure. The collapse of more complex structures (e.g. domes) is generally related to out-of-plane mechanisms of the supports. Simplified approaches for dome assessment provide barely the cracking conditions. Key aspects on structural behavior of domes and effects of recent Casamicciola earthquake in 2017 (Ischia, Italy), confirming them, are discussed by means of a case study.

Significant part of the world cultural heritage is represented by masonry buildings. Many of them are characterised by a complex architecture like as the religious buildings and need to be preserved, from a structural point of view, especially in high seismic risk areas. The recent earthquakes showed that the Historical and Monumental buildings are often characterised by high seismic vulnerability. The lowest seismic performances are associated with the presence of thrusting elements like as arches and vaults. In this background, the numerical analyses and experimental simulations provide important information about the structural behaviour of such elements. The structural behaviour of curved elements can be complex to simulate and to predict exclusively by numerical analyses. Indeed, the experimental tests can provide an efficient contribution to the calibration and interpretation of the numerical models. The present work focuses on a particular typology of vaults generally used as roofs in religious buildings. These vaults typically do not include any backfill and are slender. These typologies of masonry vaults cannot be analysed with classical approaches where no-tension is assumed. In fact, the tensile strength must be included in order to assess the seismic capacity of these masonry elements. A simplified analytical model, which includes the tensile strength, was proposed. Validation of the analytical model is provided by comparing predictions of the load capacity and the failure mode with those obtained from previous shaking table test series on two full scale masonry vaults. The proposed method represents a useful modelling tool in order to design dynamic tests on masonry vaults and to assess their vulnerability.

Models able to assess the effects of composite strengthening on masonry structures are worthy of further developments. This is also evident in modern design codes and guidelines where, for the masonry, there is lack of well-established approaches. In fact, most of the strengthening applications on masonry structures are designed based on suggestions by the manufacturers, missing strict and clear calculations. Such an approach leads, very often, to the execution of large and therefore economically demanding strengthening systems, also not encouraging their diffusion. Furthermore, the use of excessive strengthening often involves an excessive, and above all involuntary, reduction of ductility capacity. It needs also further investigation the impact of peculiar behaviors of composites (e.g. up to trilinear stress strain behavior for FRCM) on the flexural response of masonry. In this paper the behavior of strengthened masonry members is analyzed accounting for the variability of mechanical characteristics of both masonry and the strengthening systems. The behavior of the members is analyzed in terms of the moment-curvature relationships. This approach allows to evaluate both the flexural capacity and the ductility capacity of the strengthened masonry sections. In fact, the ductility is a key aspect in the retrofit of masonry structures. Finally, the process of adimensionalization, allows to extend the results to any case, providing a useful tool not only for verification but also for the design of interventions.

In this work, two main fiber strengthening systems typically applied in masonry structures have been investigated: composites made of basalt and hemp fibers, coupled with inorganic matrix. Starting from the experimental results on composites, the out-of-plane behavior of the strengthened masonry was assessed according to several numerical analyses. In a first step, the ultimate behavior was assessed in terms of P (axial load)-M (bending moment) domain (i.e., failure surface), changing several mechanical parameters. In order to assess the ductility capacity of the strengthened masonry elements, the P-M domain was estimated starting from the bending moment-curvature diagrams. Key information about the impact of several mechanical parameters on both the capacity and the ductility was considered. Furthermore, the numerical analyses allow the assessment of the efficiency of the strengthening system, changing the main mechanical properties. Basalt fibers had lower efficiency when applied to weak masonry. In this case, the elastic properties of the masonry did not influence the structural behavior under a no tension assumption for the masonry. Conversely, their impact became non-negligible, especially for higher values of the compressive strength of the masonry. The stress-strain curve used to model the composite impacted the flexural strength. Natural fibers provided similar outcomes, but a first difference regards the higher mechanical compatibility of the strengthening system with the substrate. In this case, the ultimate condition is due to the failure mode of the composite. The stress-strain curves used to model the strengthening system are crucial in the ductility estimation of the strengthened masonry. However, the behavior of the composite strongly influences the curvature ductility in the case of higher compressive strength for masonry. The numerical results discussed in this paper provide the base to develop normalized capacity models able to provide important information on the out-of-plane behavior of masonry elements strengthened with inorganic matrix and several kinds of fibers, both synthetic and natural.