Based on the scientific and technological revolutions that have characterized Structural Engineering during the last two centuries, we can acknowledge how the historical scale doubling of suspension bridges has occurred for at least four times, from the beginning of the XIX to the end of the XX Century. These four revolutions represent the tangible mankind’s challenge against natural forces: gravity, wind, earthquake. In this context, the prospective scale doubling requested by next-generation bridges (e.g., the Messina Straits Bridge) could take place only if significant scientific and/or technological innovations occur. This opportunity is presently offered by Fracture Mechanics, since any appropriate advanced design approach should take into account also brittleness size-scale effects, in addition to loading-capacity size-scale effects, which are well-known since Galileo’s studies. From the technological point of view, the open problem of physical similitude could be effectively solved by using fibre-reinforcement.

Preface to Volume1 Sponsors VOLUME 1 - New Trends in Fracture Mechanics of Concrete Part I Theoretical and numerical Methods in fracture mechanics of concrete Part II Experimental Methods in Fracture Mechanics of Concrete Part III Constitutive damage modelling of concrete Part IV Time effects in the damage and fracture of concrete VOLUME 2 - Design, Assessment and Retrofitting of RC Structures Part V Theoretical and Experimental Investigation on the Mechanical Behavior of RC Structures Part VI Practical Problems in RC Structural Applications Part VII Monitoring and assessment of RC structures Part VIII Maintenance and retrofitting of RC structures VOLUME 3 - High-Performance Concrete, Brick-Masonry and Environmental Aspects Part IX High-Performance Concrete Part X Fibre reinforced concrete Part XI Brick-masonry and other Quasi-brittle materials Part XII Environmental Issues

Preface to Volume3 Sponsors VOLUME 1 - New Trends in Fracture Mechanics of Concrete Part I Theoretical and numerical Methods in fracture mechanics of concrete Part II Experimental Methods in Fracture Mechanics of Concrete Part III Constitutive damage modelling of concrete Part IV Time effects in the damage and fracture of concrete VOLUME 2 - Design, Assessment and Retrofitting of RC Structures Part V Theoretical and Experimental Investigation on the Mechanical Behavior of RC Structures Part VI Practical Problems in RC Structural Applications Part VII Monitoring and assessment of RC structures Part VIII Maintenance and retrofitting of RC structures VOLUME 3 - High-Performance Concrete, Brick-Masonry and Environmental Aspects Part IX High-Performance Concrete Part X Fibre reinforced concrete Part XI Brick-masonry and other Quasi-brittle materials Part XII Environmental Issues

The same material may appear to be brittle or ductile depending on the initial relative notch depth and/or the size-scale of the specimen. This study examines the double transition from ductile to brittle and back to ductile for bending-dominated tests, with a special attention to the second transition that appears when the remaining ligament becomes too short for an asymptotic singular stress field to develop. The fracture condition is formulated using published shape functions, and the fracture curves are derived and compared to the single plastic collapse curve for three configurations: pure bending specimens, three-point bend specimens, and compact tension specimens. The notch depth to specimen depth ratio is varied to draw the fracture curves, to identify the transition points, and to relate them to the brittleness number. All configurations show the same trends, with a plastic collapse for shallow notches, a brittle window at intermediate notch depths, and a return to plastic collapse for very deep notches. The three-point bend beam returns to ductile behavior for the shortest relative notch depth, representing the most ductile response in the deep notch range. The results confirm that the failure mode depends on material properties, geometrical shape, size-scale of specimen, and initial notch depth. The second transition is a finite-size effect governed by ligament insufficiency, a trend that is analogous to that emerging for extremely small specimen size-scales.

Acoustic (AE), electromagnetic (EME), and neutron (NE) emissions were measured during laboratory compression tests on rock specimens loaded up to failure.

The adhesion failure between the bitumen and aggregates is the main reason leading to the cracking of asphalt mixtures and moisture damage of asphalt pavements, greatly compromising the resilience of the world's transportation network. Due to the complexity resulting from the multivariable and multiscale characteristics of the behavior at the bitumen-aggregate interface, the origin and evolution mechanisms of failure at this interface are still unclear. Six types of rock-forming minerals were selected as representatives to construct the bitumen-aggregate interface models in this study, and the interface model was subjected to tensile simulation using the molecular dynamics (MD) method. The failure modes of bitumen-aggregate interface models under different loading rates and the impact of aggregate mineralogy on the behavior of interface cracking were investigated. The research results indicate that several debonding modes are displayed by the bitumen-aggregate interface model at varying loading rates. As the loading rate slows down, the failure mode of the interface model gradually transitions from adhesive failure to cohesive failure, with a decrease in interfacial strength at failure and an increase in critical deformation and fracture energy. The exponential cohesive zone model (CZM) provides a relatively accurate fitting for the bitumen-aggregate interface debonding behavior. However, due to the appearance of a clear plateau in the traction-deformation curve of the interfacial model at the intermediate loading rate range (0.0001-0.01 & Aring;/fs), the applicability of the exponential CZM will decrease to a certain extent. Among the six rock-forming minerals aggregate models constructed in this study, two interface models of bitumen-quartz and bitumen-anorthite exhibit weaker adhesion performance than that of other interface models, manifested as lower interfacial strength, critical normal separation, and fracture energy. This study reveals the mechanism of bitumen-aggregate interfacial cracking at the atomic scale and is expected to provide a basis for multiscale forecasting of failure patterns of the bitumen-aggregate interface.

One of the most important medieval remnants and a municipal icon in Bologna (Italy) is the Garisenda Tower. It was built in the early-twelfth century at the same time as the Asinelli Tower. The towers, known as the "Due Torri" of Bologna, were initially intended to be the same height, but in 1351, the Garisenda started to tilt because of foundation subsidence. As a result, it was reduced in height from 61 m to around 13 m for safety, today sitting at 48 m (about half of the 97 m of the Asinelli). The Garisenda Tower is wide 7.5 m on its sides, with walls up to 2 m thick, and it leans about 3.22 m to the East side. Since the beginning of the last century, the structural behavior of the tower has been studied and, in more recent years, the topic of the tower's stability started to gain traction. This sparked the interest of assessing structural damage and cracking evolution by means of different non-destructive testing (NDT) techniques. There is currently a multitude of sensors installed in the Garisenda Tower. More precisely, 16 Acoustic Emission (AE) sensors, six thermometers, five Fiber Optic Sensors (FOSs), four extensometers, two accelerometers, one seismometer, and (impressively) a 30mlong pendulum are located inside the tower. The accelerometers and the thermometers are present in the Garisenda since 2009. The optical strands were installed on March 2019 and were followed by the AE sensors on May 2019. The pendulum was installed on March 2021 and, lastly, the extensometers on June 2021. Together, these instruments compose a database capable of analyzing and relating various aspects of the mechanical behavior of the tower: with the aid of the FOS, the extensometers, and the pendulum, the steady-state displacement regime of the tower can be described by means of displacements and strains. This data can be confronted with AE and temperature data to quantify damage, for example. Short-term events, such as seismic activity, can also be analyzed via AE and the seismometers. In these regards, the present work intends to showcase a methodology for the damage assessment of the Garisenda Tower in Bologna by the combined analysis of some of these sensors. In particular, the pendulum displacements, the FOS strains, and AE data will be analyzed. These highlight how the correlation of different SHM equipment datasets can provide valuable insights about the damage state of the tower (particularly by means of the b-value parameter), and the mechanical behavior-in particular, its in-plane movements.

Advanced structural design approaches should consider the economic and technological benefits offered by the structural applications of fibre-reinforced concrete. In this framework, it is important to highlight how the ductility of fibre-reinforced concrete structures is strongly dependent on the fibre volume fraction together with the structural size. This crucial coupling induces two reverse ductile-to-brittle transitions in the mechanical response of fibre-reinforced and hybrid-reinforced concrete elements: by increasing the characteristic size of the structure, an increase in its load-bearing capacity can be observed together with a decrease in its plastic rotation capacity. These size-scale effects can be taken into account by an effective fracture mechanics approach represented by the Updated Bridged Crack Model (UBCM), which can provide significant improvements in current Standards and regulations on fibre-reinforced concrete structures.

In this paper, we commemorate the centenary since death of the Swedish mathematician Niels von Koch (and the 120th anniversary of the birth of its famous fractal set). The buckling analysis of a von Koch beam is investigated, which can effectively define the elastic stability problem for fractal-shaped antennas or more general and random natural forms. Results depending on the fractal dimension of the structure suggest peculiar scaling laws for the buckling load of fractal-shaped beams. It is found that the buckling load tends to zero when the iteration n -> infinity, proving the high sensitivity to buckling of fractal antennas and trees. As in the case of free vibration, the eigenvalue tends to zero: the buckling load in the present case as well as the resonance frequency in dynamics. In the case of vibration, the fractal effect is extremely beneficial, whereas it is extremely dangerous in the case of buckling instability. The sudden collapse of a natural tree after a wind gust can be produced by elastic buckling much more likely than by dynamic resonance.

The load-displacement softening response of quasi-brittle solids exhibits an unstable structural behavior, which is characterised by a negative slope in the post-peak regime. In severely brittle situations, the post-peak behaviour can show a virtual positive slope, the fracture propagation occurring unexpectedly with a catastrophic loss in the load-carrying capacity. In this case, if the displacement controls the loading process, the curve exhibits a discontinuity and the representative point drops to the lower branch with a negative slope. On the other hand, in order to obtain a stable crack growth, a decrease both in load and in displacement is required. In the last forty years, in-depth study of the so-called snap-back instability was conducted in relation to crack propagation phenomena in quasi-brittle materials. In the present work, the structural response of two brittle-matrix specimens is analysed: the first contains a distribution of collinear micro-cracks, whereas the second presents multiple parallel reinforcing fibres embedded in the matrix. In both cases, it is shown that the structural response presents a discrete number of snap-back instabilities with related peaks and valleys, the crack propagation occurring alternately within the matrix and through the heterogeneities. Thus, the strong analogy between weakened and strengthened zones consists in a multiple snap-back mechanical response, where descending branches of propagating cracks alternate with ascending (linear) branches of arrested cracks.

Current design Standards for reinforced concrete beams prescribe to respect a minimum, ρ min , and a maximum, ρ max , reinforcement ratio in the design of structures. Below ρ min a brittle failure due to unstable crack propagation is expected. On the other hand, for ρ > ρ max a brittle failure due to concrete crushing is obtained. In this framework, a reinforced concrete element with ρ min < ρ < ρ max presents yielded steel at Ultimate Limite State (ULS) with a stable behaviour and no catastrophic loss of bearing capacity. Design Standards define ρ min and ρ max limits on the basis of the Bernoulli’s hypothesis of plane sections, and completely disregard size-scale effects. Within the present paper, Dimensional Analysis is used to determine the Brittleness Numbers that govern the behaviour of reinforced concrete (RC) as well as of prestressed reinforced concrete (PC) beams. Therefore, parametric analyses carried out by means of the Cohesive/Overlapping Crack Model (COCM) are used to study the ductile-to-brittle transitions in RC and PC beams, and to highlight the size-scale dependency of the two above-mentioned reinforcement limits.

Structural Health Monitoring (SHM) of historic masonry structures, a topic of notable economic and cultural importance, has been gaining momentum, made possible by the rapid development of monitoring technology and methodology, and motivated by factors such as seismic events and the ever-increasing number of extreme weather situations experienced all over the world. In this scenario, this work intends to contribute to the state-of-the-art by showcasing a combined numerical and experimental methodology to the structural assessment of historical masonry structures. Specifically, this work presents thermal, permanent strain, dynamic response spectrum and operational modal analyses performed to evaluate the damage evolution in the Garisenda tower of Bologna. The analyses were performed with the use of a commercial FEA software, moreover in situ Acoustic Emission (AE), Fiber Optic Sensor (FOS), were also investigated. The proposed methodology could be a tool of choice for the SHM of historical masonry structures alike-such as towers-or it could even be extended to other types of constructions.

In the Garisenda Tower of Bologna, several non-destructive (NDT) techniques are being used to examine structural damage and cracking evolution. The acoustic emission (AE) activity emerging from the masonry structures is analysed and related to surrounding temperature and strain measurements by distributed fibre optic sensors (FOSs). A seismometer was used to monitor low-frequency vibrations propagating across the ground-building foundation interface in order to examine the impact of local seismic activity or heavy vehicle traffic on tower vibration. The obtained data has led to the identification of several sources of AE activity, which apparently indicates the existence of an evolving cracking pattern. A consistent increase in the cumulated function of AE signals suggests that tower damage is caused by more than temperature changes. As a result, the origin of damage can be identified as the material's time-dependent creep behaviour under dead load and its interaction with fatigue generated by thermal fluctuations.

The Garisenda Tower in Bologna is a city symbol and one of the most valuable medieval heritages. The tower was built on compressible soils and suffered from the very beginning for increasing tilting. For this reason, Dante Alighieri refers to the tower to describe the fear caused by the giant Antaeus bending over him when he tries to descend from the eighth to the ninth circle of hell, in the Divina Commedia. Consequently, the tower has always deserved special attentions to preserve its structural safety. The paper describes some of the most recent results obtained from non-destructive monitoring techniques and presents a finite element model suitable to represent the structural behaviour of the tower, included the effect of thermal deformation.