Antonella Cecchi

Out of plane model for heterogeneous periodic materials: the case of masonry

Abstract The aim of this paper is to propose a 3D model to study masonry walls subject to in plane and out of plane actions through a rigorous homogenization procedure. 2D rigorous models in several perturbative parameters have been already developed – by Cecchi–Di Marco (European J. Mech. A Solids 19 (2000) 535–546), Cecchi–Rizzi (Internat. J. Solids Structures 38/1 (2001) 29–36) and Cecchi–Sab (European J. Mech. A Solids 21 (2002) 249–268) – so as to study the behaviour of masonry walls subject to actions parallel to the middle plane. By comparison with previous models, in this paper the study of masonry takes into account the formulation of a 3D model where masonry is assumed periodic in the middle plane, i.e. in the orthogonal directions to the thickness. The size of the thickness is comparable with the one of the period. The asymptotic model that has been developed allows the identification of the 3D solid with a 2D Love–Kirchoff plate, in which the anisotropy is connected with the arrangement of blocks. The obtained results give the values of homogenized elastic plate constants (Caillerie, Math. Meth. Appl. Sci. 6 (1984) 159–191).

Heterogeneous elastic solids: a mixed homogenization-rigidification technique

A homogenization technique for heterogeneous elastic solids made up by a matrix containing inclusions modelled as rigid in the limit, is proposed. It is shown that the approach can cause considerable simplifications with respect to the use of standard homogenization procedures. The case of a masonry panel set across on an opening is analysed by applying the proposed technique and some numerical results are given. They are compared first with those obtained by considering the panel as a heterogeneous body and, in turn, by using standard homogenization.

FEM-DEM modeling for out-of-plane loaded masonry panels: a limit analysis approach

In this work the performances of the Discrete Element Method (DEM) applied to kinematic limit analyses of the out-of-plane behavior of masonry wall panels (with different textures) are investigated. A discrete model of masonry is proposed, which assumes that rigid blocks are connected by a mortar interface: this is ap- propriate for historical masonry, where mortar is much more deformable than blocks and joints thickness is negligible. Therefore blocks can be modeled as rigid bodies connected by zero thickness Mohr-Coulomb-type interfaces. The applied method is known as FEM/DEM, which combines finite and discrete element models. A comparison with well-known and meaningful examples presented by Giuffre has been carried out in order to validate this method for studying the behavior of masonry. For this purpose, 2D DEM models reproducing walls sections have been considered: they reproduce masonry walls with different staggered blocks, in particular stack bond and running bond patterns, subjected to lateral loads.

Homogenization of masonry walls with a computational oriented procedure. Rigid or elastic block

Abstract The idea behind this paper is to present a numerical procedure for the analysis of masonry walls, based on the application of an asymptotic homogenization method. In this paper, a masonry wall, obtained by the regular repetition of blocks between which mortar is laid, is modelled as a periodic body in the two plane directions. The local problem is formulated for a base cell tied to the geometry of the body and in a position to generate it entirely through some law of its internal composition. Two homogenized models are formulated: the first envisages that both phases, block and mortar, behave in linear elastic fashion; the other envisages that the mortar behaves in linear elastic fashion, while the block is infinitely stiff. The two models are described theoretically and the construction of the model according to the characteristic module is numerically defined. In the case where the infinitely stiff (rigid) block is assumed, not only is the formulation of the model made extremely simple, but any numerical problems tied to great differences in the numerical values characterizing the constitutive modules of the two phases are overcome. In this regard, the domain of applicability of this model is sought both by comparing the homogenized constitutive functions, while varying the ratios of the elastic coefficients of the mortar and the block, with the rigid solution, and by analysing the structural behaviour that derives from the application, or not, of the rigid model, this being done for two sample problems. It should be underlined that the rigid-block model furnishes qualitatively sound structural answers even for very low ratios between the elastic moduli of the two phases composing the wall, and furnishes answers that are quantitatively sound as well for ratios of the order of 30:1, a realistic ratio in the case of ancient walls. The results obtained can be extended to heterogeneous materials in general, that is, to many of the innovatory materials, the composites, where the constituent phases have stiffness characteristics that are rather different and the condition of regularity of alternation of the phases is adequately plausible.

DEM & FEM/DEM models for laterally loaded masonry walls

The wide amount of historic masonry constructions in Italy and other European countries makes of paramount importance the development of reliable tools for the evaluation of their structural safety. Masonry is a heterogeneous structural material obtained by composition of blocks connected by dry or mortar joints. The use of refined models for investigating the in-plane nonlinear behavior of periodic brickwork is an active field of research. The mechanical properties of joints are usually considerably lower than those of blocks, therefore it can be assumed that damages occur more frequently along joints. Thus, a key aspect is represented by the evaluation of the effective behavior of joints and its reliable description into numerical models. With this purpose, in this contribution, different models are defined to simulate, with an appropriate accuracy, the behavior of masonry: Discrete Element Model (DEM) and a combined Finite Element and Discrete Element Model (FEM/DEM). Models are based on rigid block hypothesis and joints modeled as Mohr-Coulomb interfaces. These assumptions may be suitable for historical masonry, in which block stiffness is larger than joint stiffness, allowing to assume blocks as rigid bodies, moreover joint thickness is negligible if compared with block size. Analysis is performed in the nonlinear field to investigate the behavior of masonry walls subject to lateral loads, in order to simulate their seismic response, with particular attention to the determination of limit load multipliers.

A Procedure to Investigate the Collapse Behavior of Masonry Domes: Some Meaningful Cases

ABSTRACT Masonry domes represent an important part of the architectural heritage. However, the literature about domes analysis seems less consistent than that referred to other masonry structures. The collapses that have happened in recent years as a consequence of seismic actions or lack of maintenance show the need for detailed studies. Here a limit analysis to evaluate the masonry domes behavior is presented. An algorithm based on the kinematic approach has been developed to evaluate the geometric position of the hinges that determine the minimum collapse load multiplier. The proposed procedure is validated by a comparison with some meaningful cases—the collapse of Anime Sante Church in L’Aquila, the collapse of San Nicolò Cathedral in Noto, the crack pattern of San Carlo Alle Quattro Fontane Church in Rome, and the analysis developed on Hagia Sofia in Istanbul. The comparison with real cases shows a good agreement between the model results and the phenomenological crack patterns.

Multi-Leaf Masonry Walls with Full, Damaged and Consolidated Infill: Experimental and Numerical Analyses

Multi-leaf masonry walls constitute the construction typology most widely adopted in historic buildings. This aspect, together with the intrinsic structural complexity, heterogeneity and irregularity, directs the present research towards a topic not yet sufficiently investigated by the research community of architects and civil engineers. In this paper, the case of multi-leaf masonry wall has been investigated, and with the aim of reproducing historical buildings structural elements, three different typologies of multi-leaf masonry walls have been considered: (i) full infill, (ii) damaged infill, (iii) consolidated infill. A comparative analysis has been performed and results of experimental tests have been compared with numerical ones obtained by means of Finite Element (FE) models.

Preliminary Investigation on FRP Profiles for the Structural Retrofit of Masonry Structures

The paper explores the perspectives of pultruded FRP (PFRP) profiles in the field of masonry building preservation, for ancillary structures or strengthening techniques. The available knowledge about interfaces is briefly summarized; recent experimental results about bolted PFRP-to-masonry joints are cited. A numeric predictive analysis, aimed at evaluating the shear interface behaviour of adhesive PFRP-to-masonry joints, is shown in view of foreseen laboratory tests. The numeric results enlighten a clear influence of compressive loading on the peak shear displacement at varying transfer length. The model, which relies on the assumption of frictional joint behaviour, appears to represent the joint sliding in a satisfactory way.

The Influence of Self-Healing Capacity of Lime Mortars on the Behaviour of Brick-Mortar Masonry Subassemblies

In this paper a methodology is proposed to investigate the influence of healing capacity of lime-based mortars in masonry specimens, by means of shear bond test. A first series of “brick-mortar” triplets – after 28 days curing in lab environment – were tested in shear, with and without transverse normal stress, to determine the shear bond strength. Then, on a second series of samples, a damage is induced by loading them to a prescribed fraction (70%) of the shear bond strength, determined as above; samples were subsequently immersed in water for 3 months and re-tested at the end of this curing period. Reference undamaged samples undergoing the same curing history as the damaged ones were tested as well. The effectiveness of the self-healing capacity has been evaluated through the recovery of shear bond strength. The reliability of this approach has been investigated also by comparing the experimental results with a simplified FE model.

Discrete Model for the Collapse Behavior of Unreinforced Random Masonry Walls

A discrete model with rigid blocks and elastic-plastic interfaces is adopted for studying the collapse behavior of in-plane loaded masonry panels with random texture. An existing random discrete model, originally developed in the elastic field, is here extended to the field of material nonlinearity by adopting a Mohr-Coulomb yield criterion for restraining actions at joint level. The resulting model turns out to be simple and effective in determining collapse loads and mechanisms of rectangular masonry panels, also accounting for a further perturbation parameter able to vary the height of each course of blocks into the masonry panel. The collapse loads turn out to be slightly smaller than those typical of regular assemblages, whereas mechanisms turn out to be influenced by local arrangement and size of blocks.