Fabio Di Carlo

Force reduction factor for out-of-plane simple mechanisms of masonry structures

The dynamic behaviour of existing masonry buildings mainly depends on the out-of-plane response of the vertical walls. A proper evaluation of their response can be analytically performed considering the dynamic equation of motion of the rigid body, in the framework of rigid in compression no tension material. The above equation is numerically solved with increasing magnitude of the seismic action, until the collapse condition of the wall, due to a lack of equilibrium, is reached. In the paper two local collapse mechanisms are considered, the two sided and the one sided rocking. The influence of considering a simplified trilinear moment-rotation law is also discussed. For each mechanism, the force-reduction factor, defined as the ratio between the seismic acceleration value causing the collapse of the masonry element and the one corresponding to the activation of the rocking motion, is evaluated. The dependence of this factor on the main parameters of the model is deeply investigated by means of numerical analyses, varying the geometrical characteristics of the panel, the energy dissipation model and the features of the seismic input. A power function law between an effective force reduction factor, defined as the ratio of the force reduction factor multiplied for the gravitational acceleration to the peak ground acceleration, and the Housner Spectrum Intensity is identified for both the examined models. These laws allow accounting for the so-called scale effect within a force-based framework. Eventually, novel formulations for evaluating the force reduction factor of two and one sided rocking systems are here proposed. Their effectiveness has been also highlighted considering both spectrum-compatible accelerograms and natural records.

Numerical modelling of corroded RC columns repaired with high performance fiber reinforced concrete jacket

Reinforcement corrosion can lead to a severe damage in reinforced concrete columns with subsequent loss of bearing capacity. This condition can be deleterious in case of a seismic event. The possibility of repairing and strengthening damaged columns with high performance fiber reinforced concrete (HPFRC) jacketing has been experimentally investigated by some of the authors in previous papers, through full-scale tests on specimens under cyclic loads. The main aim of the intervention was not only to restore the original bearing capacity but also to increase the column durability. In the present paper, a numerical model is developed with the FEM software Diana in order to simulate the cyclic behaviour of corroded r.c. columns reinforced with HPFRC. Particular attention is devoted to the simulation of the corrosion phenomenon and to the strain localization due to the jacket presence. The chemical attack is defined in such a way to account for both the geometrical and mechanical variations of the bar properties. The numerical analyses represent a very useful tool for highlighting the main parameters that have to be considered in evaluating the behaviour of the damaged and then repaired elements. Finally, they constitute a support for the design and, as a consequence, for the reinforcement optimization.

Rocking Mechanism of Masonry Portals with Circular Arches

Unreinforced masonry (URM) structures represent most of the world architectural heritage, whose vulnerability has been also highlighted by damages and collapses occurred after recent seismic events. Numerous studies regarding the seismic capacity of masonry walls, arches and portals have been carried out by applying the so-called equivalent static analysis method, neglecting their dynamic behaviour. A proper evaluation of the dynamic response of masonry elements can be done analytically considering the dynamic equation of rigid bodies not resistant to the tensile stresses. Some studies are available in literature regarding the dynamic behaviour of walls and arches. In this framework, the paper aims to develop an analytical model, able to describe the dynamic behaviour of portals with circular arches, subjected to a base motion. Starting point of the analysis is the evaluation of the mechanism (local, semi-global or global) governing the activation of the motion of the structure, performed in the context of Limit Analysis. Subsequently the equation of motion of the system of rigid bodies is derived applying the Lagrange Equation. Finally a numerical application is carried out.

Rocking in presence of cracking of masonry wall piers

The wall pier represents the vertical element of multi-storey walls with openings, the main resistant structural components of a masonry building. Structural systems of wall piers and spandrels are required to sustain the in-plane seismic actions acting on the wall, opposing with their weights to the action of horizontal forces. The behavior of masonry constructions results to be very far from the one characterizing ductile structures, because of the lack of energy dissipation during the deformation. A strength resource of masonry structures, properly reinforced in order to avoid early local failures, consists in exhibiting rocking behavior, until a failure condition is attained. An investigation on the dynamic behavior of masonry wall piers is carried out by following Housner’s studies and properly introducing the effect of diagonal cracks, shown by typical post-earthquake cracking patterns. As a consequence, the system is characterized by the detachment of a lower triangular region that becomes ineffective during the development of the mechanism and does not oppose with its weight to the overturning. Finally, it is shown that the occurrence of diagonal cracks can be prevented by the execution of suitable retrofit interventions.

Collapse state of multi-storey masonry walls reinforced by steel ties subjected to in-plane horizontal loads

The determination of the seismic strength of masonry building is strictly connected to the in-plane strength of masonry walls under the action of horizontal forces. Simplified criteria are currently available in literature, based on modelling of the structure as loaded by dead loads and by a gradually increasing distribution of horizontal forces, proportional to the mass of the building. According to this approach, called push-over method, the seismic strength of the building corresponds to the intensity of these gradually increasing horizontal loads, leading the building to the failure condition. This paper moves in the framework of the Limit Analysis, based on the Heyman’s masonry model (1966), rigid in compression with no tensile strength. The resistant model refers to a multi-storey wall with openings arranged in regular patterns, along both vertical and horizontal directions, reinforced at floor levels by steel ties. The in-plane failure of the regular multi-storey walls can occur with the development of various kinematically admissible mechanisms, characterized by the attainment of the yielding state in the steel ties. The proposed methodology consists in the definition of the mechanism along which the failure effectively occurs and in a subsequent check of the statical admissibility of the internal stress state at the limit load. Only in this case, the corresponding kinematical multiplier is the effective collapse multiplier. The presence of the panels situated above the openings strongly conditions the in-plane failure of the wall, acting as diagonal struts, causing different horizontal displacements between the piers at the floor levels and consequently engaging the horizontal ties in the mechanism. In order to ensure the development of the global failure, avoiding local brittle failures, steel strengths of the ties have thus to be suitably defined. Finally, a parametric investigation is carried out considering different geometries of masonry walls and varying the position of the piers self-weights and the horizontal forces distribution, constant or proportional to the height of the masses from the foundation level.

Dynamics of masonry pointed arches under base motion

The paper deals with the topic of the seismic assessment of masonry pointed arches, one of the typical resistant systems of unreinforced masonry structures, whose vulnerability has been further highlighted by damages and collapses occurred with recent seismic events. According to the hypotheses of limit analysis and following the Oppenheims approach, a single-degree-of-freedom analytical model is proposed to study their dynamic behaviour. The structure is represented as an assembly of rigid bodies, connected through hinges with each other and subjected to a horizontal ground acceleration. An ad hoc energy dissipation model is specifically implemented for the studied case, according to the classical Housners approach. A comparison with the circular arch case is shown with reference to the arch geometry studied by Oppenheim, tracing the main features and differences. Finally, a numerical survey is carried out by varying the main geometrical parameters of the pointed arch, in order to evaluate their influence on the dynamic response.

Seismic Behaviour of Rocking Elements Reinforced with Composite Materials

Seismic behaviour and vulnerability of existing masonry structures are typically characterized by out-of-plane response of vertical walls. The dynamic response of such elements can be analytically assessed considering the dynamic equation of rigid bodies not resistant to tensile stresses. Many studies available in literature have highlighted the vulnerability of this type of structures against out-of-plane movements. In order to withstand horizontal seismic actions, appropriate and effective retrofitting interventions have to be properly designed. In this paper, the rocking response of a masonry wall retrofitted with elastic GFRP bars is investigated. A parametric survey is also carried out, to evaluate the increase in strength of the masonry wall, due to the presence of the composite material.

A Reformulation of a Multi-Axial Failure Criterion for the Concrete

The research of a failure criterion for concrete under multi-axial stresses is a very important task because of the numerous civil engineering applications. Nowadays several concrete failure tests are available in literature and various criteria have been proposed. A multi-axial failure criterion for the concrete founded on a simple physical basis, has been proposed by one of the authors. In this paper a sharper foundation of this criterion is given. The hardened cement paste (hcp), the binder of all the aggregate particles, is responsible of the concrete strength. Consequently, a preliminary average evaluation of the stresses, occurring, when the concrete is loaded, into the various phases components, and particularly in the hcp, is necessary to analyse the failure. To that end, the paper revolves around the analysis of the thermal behaviour of the concrete at its early stage of setting. It is shown that the heat production during the cement hydration process, is responsible to produce clearances among the various particles and the surrounding hcp that, in turn, the consequent statically determined structure of the concrete. Validation of this result comes out by analysing the elastic moduli and the thermal expansion coefficients. The micro-macro failure condition of Como & Luciano thus receives a sounder physical basis.