F. Cannizzaro

A Discrete Element for Modeling Masonry Vaults

The assessment of the seismic response of historical masonry buildings represents a subject of considerable importance but, at the same time, of very difficult task. Refined finite element numerical models, able to predict the non-linear dynamic mechanical behavior and the degradation of the masonry media, require sophisticated constitutive law and a huge computational cost that makes these methods nowadays not suitable for practical application. In the past many authors developed simplified or alternative methodologies that, with a reduced computational effort, should be able to provide numerical results that can be considered sufficiently accurate for engineering practice purposes. However most of these methods are based on simplified hypotheses that make these approaches inappropriate for monumental buildings. In this paper a three dimensional discrete element model, able to predict the nonlinear behaviour of masonry shell elements, is presented as an extension of a previously introduced spatial discrete-element conceived for the simulation of both the in-plane and the out-of-plane behavior of masonry plane elements. The new macro-element enriches a larger computational framework, based on macro-element approach, devoted to the numerical simulation of the seismic behaviour of historical masonry structures.

Numerical and Experimental Validation of a 3D Macro-Model for the In-Plane and Out-Of-Plane Behavior of Unreinforced Masonry Walls

ABSTRACT The behavior of historical UnReinforced Masonry (URM) buildings subjected to earthquake loading is usually governed by a complex interaction between the in-plane and out-of-plane response of masonry walls. In modern masonry building, the in-plane behavior of masonry walls is generally guaranteed in the structural design, but thin non-structural masonry infills are often vulnerable to out-of-plane actions. A reliable prediction of the combined in-plane and out-of-plane behavior of URM walls requires rigorous nonlinear finite element models, whose complexity and computational cost are generally unsuitable for current engineering applications, motivating the research of alternative numerical approaches. This article presents a study for validation of a 3D macro-model intended to simulate the combined in-plane and out-of-plane behavior of unreinforced masonry walls, against experimental results available in the literature and FEM simulations. The model is based on a three-dimensional macro-element whose kinematics is governed by seven degrees of freedom only. The mechanical behavior of the element is based on a fiber discretization approach that adopts basic material parameters. The performance of the proposed macro-element strategy is assessed by means of nonlinear static analyses performed on masonry walls, for which both numerical and experimental results are available in the literature.

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (VI): Discrete Element Approach

ABSTRACT Although many experimental tests and numerical models are available in the literature, the numerical simulation of the seismic response of existing masonry buildings is still a challenging problem. While the nonlinear behavior of masonry structures is reasonably predictable when the out-of-plane behavior can be considered inhibited, when the in-plane and out-of-plane responses coexist and interact, simplified models seem unable to provide reliable numerical predictions. In this article, taking advantage of the experimental tests carried out in a shaking table on two masonry prototypes at LNEC, a macro-element approach is applied for the numerical simulations of their nonlinear response. The adopted approach allows simulating the nonlinear behavior of masonry structures considering the in-plane and out-of-plane responses. Since it is based on a simple mechanical scheme, explicitly oriented to representing the main failure mechanisms of masonry, its computational cost is greatly reduced with respect to rigorous solutions, namely nonlinear FEM approaches. Two modeling strategies are adopted, namely a regular mesh independent from the real texture of the prototypes and a detailed one coherent with the units disposal. The numerical results are discussed and the correlation between the nonlinear static analyses and the dynamic response is provided.

A new discrete‐element approach for the assessment of the seismic resistance of composite reinforced concrete‐masonry buildings

In the present study a new discrete‐element approach for the evaluation of the seismic resistance of composite reinforced concrete‐masonry structures is presented. In the proposed model, unreinforced masonry panels are modelled by means of two‐dimensional discrete‐elements, conceived by the authors for modelling masonry structures, whereas the reinforced concrete elements are modelled by lumped plasticity elements interacting with the masonry panels through nonlinear interface elements. The proposed procedure was adopted for the assessment of the seismic response of a case study confined‐masonry building which was conceived to be a typical representative of a wide class of residential buildings designed to the requirements of the 1909 issue of the Italian seismic code and widely adopted in the aftermath of the 1908 earthquake for the reconstruction of the cities of Messina and Reggio Calabria.

Closed-form solution based genetic algorithm software: Application to multiple cracks detection on beam structures by static tests

Abstract In this paper a procedure for the static identification and reconstruction of concentrated damage distribution in beam-like structures, implemented in a dedicated software, is presented. The proposed damage identification strategy relies on the solution of an optimisation problem, by means of a genetic algorithm, which exploits the closed form solution based on the distribution theory of multi-cracked beams subjected to static loads. Precisely, the adoption of the closed-form solution allows a straightforward evolution of an initial random population of chromosomes, representing different damage distributions along the beam axis, towards the fittest and selected as the sought solution. This method allows the identification of the position and intensity of an arbitrary number of cracks and is limited only by the amount of data experimentally measured. The proposed procedure, which has the great advantage of being robust and very fast, has been implemented in the powerful agent based software environment NetLogo, and is here presented and validated with reference to several benchmark cases of single and multi-cracked beams considering different load scenarios and boundary conditions. Sensitivity analyses to assess the influence of instrumental errors are also included in the study.

Advances in dynamic instability: can a beam-column undergo tensile flutter?:

Tensile instability in beam-like structures has been highlighted in very few papers; the studies reported in the specific literature are limited to beam-columns characterised either by high shear deformation or by the presence of a single structural junction allowing a transversal displacement discontinuity. Moreover, to the authors’ knowledge, the flutter instability associated to tensile axial load has not yet been disclosed. This work aims to offer further contribution to the knowledge of tensile instability of beam-columns by considering the dynamic instability of an Euler Bernoulli beam in presence of an arbitrary number of internal sliders endowed with translational elastic springs. The use of the generalised functions allows an exact evaluation of the eigensolution, provided in closed form, both for conservative and nonconservative axial load. In particular, the following relevant question is posed: Can a beam-column undergo tensile flutter instability? A comprehensive parametric analysis conducted in this work gives an affirmative answer to the asked question.

Damage identification on spatial Timoshenko arches by means of genetic algorithms

In this paper a procedure for the dynamic identification of damage in spatial Timoshenko arches is presented. The proposed approach is based on the calculation of an arbitrary number of exact eigen-properties of a damaged spatial arch by means of the Wittrick and Williams algorithm. The proposed damage model considers a reduction of the volume in a part of the arch, and is therefore suitable, differently than what is commonly proposed in the main part of the dedicated literature, not only for concentrated cracks but also for diffused damaged zones which may involve a loss of mass. Different damage scenarios can be taken into account with variable location, intensity and extension of the damage as well as number of damaged segments. An optimization procedure, aiming at identifying which damage configuration minimizes the difference between its eigen-properties and a set of measured modal quantities for the structure, is implemented making use of genetic algorithms. In this context, an initial random population of chromosomes, representing different damage distributions along the arch, is forced to evolve towards the fittest solution. Several applications with different, single or multiple, damaged zones and boundary conditions confirm the validity and the applicability of the proposed procedure even in presence of instrumental errors on the measured data.

Automatic evaluation of plastic collapse conditions for planar frames with vertical irregularities

The plastic load and failure modes of vertically irregular planar frames are studied by means of an original software code developed in the agent-based programming environment NetLogo with a user-friendly interface. The proposed method lies in the limit analysis framework and is based on the generation of elementary collapse mechanisms and on their linear combination aimed at minimizing the collapse load factor. The considered irregularities consist in the absence of an arbitrary column in a regular grid of the frame and require considering additional elementary mechanisms, here presented for the first time, with respect to those associated to the corresponding regular frame. A further novelty of the method is the adoption, in the linear combination of elementary mechanisms, of negative coefficients, which, as better shown in the applicative section, is fundamental to grasp the actual collapse mechanism in irregular frames. The minimization procedure is efficiently performed by means of genetic algorithms, which allow computing both the collapse load factor and the correspondent failure mode with great accuracy and in a very short computing time. Many applications have been performed considering seismic load scenarios. Finally, by means of a parametric study, some general considerations on the weakest configurations of this typology of vertically irregular frames are provided.

New Frontiers on Seismic Modeling of Masonry Structures

An accurate evaluation of the nonlinear behaviour of masonry structural elements in existing buildings still represents a complex issue that rigorously requires nonlinear finite element strategies difficult to apply to real large structures. Nevertheless, for the static and seismic assessment of existing structures, involving the contribution of masonry materials, engineers need reliable and efficient numerical tools, whose complexity and computational demand should be suitable for practical purposes. For these reasons the formulation and the validation of simplified numerical strategies represents a very important issue in masonry computational research. In this paper an innovative macro-element approach, developed by the authors in the last decade, is presented. The proposed macro-element formulation is based on different, plane and spatial, macro-elements for the simulation of both the in-plane and out-of-plane behaviour of masonry structures also in presence of masonry elements with curved geometry. The mechanical response of the adopted macro-element is governed by nonlinear zero-thickness interfaces, whose calibration follows a straightforward fibre discretization, and the nonlinear internal shear deformability is ruled by equivalence with a corresponding geometrically consistent homogenized medium. The approach can be considered as ‘parsimonious’ since the kinematics of the adopted elements is controlled by very few degrees of freedom, if compared to a corresponding discretization performed by using nonlinear FEM strategies. This innovative discrete-element strategy has been implemented in two user-oriented software codes 3DMacro and HiStrA (Historical Structures Analysis), which simplifies the modelling of buildings and historical structures by means of several wizard generation tools and input/output facilities. The proposed approach, that represents a powerful tool for the structural assessment of structures in which the masonry plays a key role, is here validated against experimental results involving typical masonry monumental sub-structural elements and numerical results involving real-scale structures.

Assessment of the Seismic Vulnerability of an Unreinforced Masonry Structure Based on Discrete-Macro Dynamic Analyses

UnReinforced Masonry (URM) structures experience severe damage due to in-plane and out-of-plane mechanisms when subjected to seismic actions. The assessment of the seismic vulnerability of URM generally requires complex analytical procedures consisting of the application of sophisticated numerical models. However, these models may request a high computational effort or may present an over-simplified scheme, mainly when the out-of-plane mechanisms are neglected. In this sense, a 3-dimensional macro-element model is here used for a preliminary assessment of the seismic vulnerability of a URM prototype characterized by an out-of-plane collapse mechanism. In this paper, the seismic vulnerability of this type of constructions is investigated by means of fragility functions in accordance with specific damage states and a given seismic input. The structural safety assessment was conducted by means of time history analyses with a limited computational effort. In addition, the evaluation of the limit states is here performed by means of an alternative approach named as Capacity Dominium based on the application of nonlinear static analyses.