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Considering the high vulnerability of existing masonry buildings, which often have strategic or cultural value, professionals and specialized engineers are frequently required to model complex historical buildings. The approaches proposed by National Building Codes may not always be suitable for such cases, but more detailed approaches are necessary, relying on FEM continuum modeling and inelastic constitutive law. There are many constitutive laws proposed in the literature that allow us to accurately reproduce the mechanical behavior of masonry. However, they require the identification of several parameters that are not easy to determine. In this study, a sensitivity analysis of the parameters of a nonlinear constitutive law very popular for masonry modeling (the "Concrete Damage Plasticity—CDP" model) is conducted, considering literature tests of masonry panels under shear stress as the benchmark. The aim is to assess the influence of the main parameters of the model and compare them to one of the more commonly used Mohr–Coulomb failure criteria. [ABSTRACT FROM AUTHOR]

A static meshfree implementation of the bond-based peridynamics formulation for linearly elastic solids is applied to the study of the transition from local to nonlocal behavior of the stress and displacement fields in the vicinity of a crack front and other sources of stress concentration. The long-range nature of the interactions between material points that is intrinsic to and can be modulated within peridynamics enables the smooth transition from the square-root singular stress fields predicted by the classical (local) linear theory of elasticity, to the nonsingular fields associated with nonlocal theories. The accuracy of the peridynamics scheme and the transition from local to nonlocal behavior, which are dictated by the lattice spacing and micromodulus function, are assessed by performing an analysis of the boundary layer that surrounds the front of a two dimensional crack subjected to mode-I loading and of a cracked plate subjected to far-field tension. [ABSTRACT FROM AUTHOR]

A mechanistic model with rigid elements and interfaces suitable for the non-linear dynamic analysis of full scale 3D masonry buildings is presented. The model relies into two steps: in the first step, a simplified homogenization is performed at the meso-scale to deduce the mechanical properties of a macroscopic material, to be used in structural applications; the second step relies into the implementation of a Rigid Body and Spring Model (RBSM) constituted by rigid elements linked with homogenized interfaces. In the homogenization step, a running bond elementary cell is discretized with 24 three-node plane-stress elastic triangular elements and non-linear interfaces representing mortar joints. It is shown how the mechanical problem in the unit cell is characterized by few displacement variables and how homogenized stress-strain curves can be evaluated by means of a semi-analytical approach. The second step relies on the implementation of the homogenized curves into a RBSM, where an entire masonry structure can be analyzed in the non-linear dynamic range through a discretization with rigid elements and inelastic interfaces. Non-linear structural analyses are conducted on a church façade interconnected with a portion of the perpendicular walls and on a small masonry building, for which experimental and numerical data are available in the literature, in order to show how quite reliable results may be obtained with a limited computational effort. [ABSTRACT FROM AUTHOR]

Seismic shocks occur sometimes as a sequence, close in space and time, of destructive events of comparable intensity. In these cases, a significant portion of the damage to historical buildings can be related with the cumulated damage on structures that become progressively more vulnerable. This research investigates the specific increase of damage determined by a sequence of strong ground motions, focusing the interest on the out-of-plane response of 2 church masonry façades. The dynamic analyses were performed by a specific rigid body and spring model RBSM, which only accounts for out-of-plane damage mechanisms. Two idealized models of façade, each made of 2 different masonry bonds, have been studied by applying various sequences of recorded accelerograms. The results highlighted a complex relationship between the spectral content of the seismic shocks and the characteristics of the structures that change in the course of the loading sequence due to the development of damage. The Housner spectral intensity proved to be a reliable scalar measure of the ground motion destructiveness for these façades. Moreover, when considering a design-consistent accelerogram that causes a relevant damage pattern, ie, with a significant elongation of the effective first period of vibration, the numerical results indicated a possible spectral intensity threshold below which the occurrence of repeated seismic shocks, both before and after the reference design shock, can be considered as irrelevant. On the other hand, a catastrophic increase of damage should be expected when this threshold is overcome. [ABSTRACT FROM AUTHOR]

SUMMARY The paper proposes a systematic comparison between two methods of analysis that are well established in the field of earthquake engineering: nonlinear dynamic analysis and nonlinear static procedure (NSP), applied to the out-of-plane seismic response of two masonry façades representative of many ancient Italian churches. The comparison is based on extensive numerical analyses, which focus on the flexural and torsional mechanisms, while the in-plane damage mechanisms and the possible detachment between the façade and the lateral walls because of a poor connection have been presently disregarded. The computations, both in the static and in the dynamic field, are based on a rigid body and spring model specifically implemented for this issue, computationally efficient and equipped with a realistic model of damage and hysteresis at the mesoscale. An innovative aspect of this study is the heuristic modelling of three-wythe masonry, to include some typical texture effects on the macroscale nonlinear response. For each façade, two different masonry textures were considered, performing extensive dynamic analyses that offered a detailed overview about the performance under earthquakes of different intensities. In parallel, NSP and the classical N2-based seismic assessment were applied. A critical discussion and comparison of the results of the two methods is presented to rationally appraise limits and opportunities. In particular, flexural and twisting out-of-plane mechanisms were clearly appraised in the dynamic field, whereas NSPs were not always able to describe the collapse, because they missed the partial failures determined by higher vibration modes, as could be expected. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A comparative numerical study on a 12th-century masonry tower located in northern Italy is described. To assess the safety of the tower under seismic loads, different numerical analyses have been performed: nonlinear static, limit, and nonlinear full dynamic analyses. In the first two cases, a full three-dimensional (3D) detailed finite element model (FEM) is adopted, changing the seismic load direction and assuming different hypotheses for the interconnection between the core and the external walls. When dealing with the FEM incremental analysis, a commercial code is utilized assuming for masonry a smeared crack isotropic model. For limit analysis, a noncommercial full 3D code developed by the authors is utilized. It provides good estimates of limit loads and failure mechanisms to compare with standard FEM results. The dynamical analyses have been performed by a specific two-dimensional (2D) rigid body and spring model (RBSM), accounting for the asymmetries along the thickness and the irregularities of thickness of both the external and internal walls in an approximate but realistic way. Four different accelerograms are utilized—passing from low to high seismicity zones—to evaluate the performance of the tower under dynamic loads. From numerical results, the role played by the actual geometry of the tower is envisaged, as well as a detailed comparison of failure mechanisms provided by the incremental FEM and limit analysis is provided. In all cases, the numerical analysis has given a valuable picture of possible damage mechanisms providing useful hints for the introduction of structural monitoring. [ABSTRACT FROM PUBLISHER]

Abstract: The seismic analysis of a large monument subjected to strong earthquakes is the object of the present paper. As a case study, the response of the “Maniace Castle” of Syracuse has been investigated by a multi-level approach which adopts traditional finite element modelling as well as a specific mechanistic computational model for the final non-linear seismic analyses. At first, the linear behaviour of the monument was studied by means of two 3D FE models in order to understand the global response of the building, its points of weakness, and the kinematics of the corresponding collapse mechanisms. Then, these results were used to calibrate a mechanistic 2D plane rigid body and spring model, RBSM, specifically formulated with the aim of approximating the macroscopic behaviour of masonry walls with reduced degrees of freedom, and taking into account the influence of the masonry texture and energy dissipation capacity of the material. Given the uncertainties and the variability of the material characteristics, an extensive parametric non-linear static analysis and the dynamic analyses, with artificial and natural accelerograms, were made in accord with the EC8 seismic code, and compared together. These results were then used to formulate and verify a simple proposal for the restoration design. [Copyright &y& Elsevier]

The development of artillery in Europe at the end of the Middle Ages brought a necessary change in military architecture. This change was a radical rethinking of the entire geometry and architectural design of city walls which required an increase in thickness to resist repeated artillery strikes. The damage due to the impact loads on Middle Age fortification walls is analyzed herein with explicit dynamic analyses. This study was developed both with finite element models and an innovative rigid body-spring model with diagonal springs (RBSM), showing the different peculiarities of these two different approaches and how their results can be integrated. The numerical models clearly showed that the presence of an inner core of softer material tends to modify the impact effects by reducing the degree of damage at the expense of an extension of the damaged area. [ABSTRACT FROM AUTHOR]

A specific rigid element approach is proposed for the in-plane dynamical analysis of masonry walls, whose seismic performance is strongly related to mechanical deterioration and hysteretic energy dissipation. Since the execution of effective time-history analysis necessitates the use of discrete models with reduced number of degrees of freedom, the tricky issue lies in achieving a balance between accuracy in the geometrical description and the need for a realistic damage material model. For this reason, a mechanistic 'rigid body spring model' (RBSM) was adopted, which consists of a collection of plane quadrilateral rigid elements connected to each other by two normal springs and one shear spring at each side. The material model was based on a phenomenological description of the cyclic response of masonry, and specific separate hysteretic laws were assigned for the axial and shear deformation between the elements. This separation led to a large reduction in computational effort, though a Coulomb-like law was adopted in order to relate the strength of the shear springs to the vertical axial loading. The effective performance of the present approach is demonstrated by the numerical validation and by comparisons with some well-known experimental and numerical tests presented in the literature. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The evaluation of seismic risk of masonry monuments requires to study the combination of vulnerability and hazard. In the present work, the global seismic response of slender masonry towers has been studied by means of a specific 3-D fibre model. Accounting for the particular behaviour of such structures, the hazard should also be described by a suitable measure of intensity of the seismic action. A variety of different parameters relating with the ground acceleration recordings have been investigated for what regards their correlation with the damage indicators of the model. The combination of the peak ground velocity of the horizontal component and of the significant duration is an effective measure of intensity. This measure can be improved by considering the accord of the frequency content of the ground motion with the dynamical characteristics of the tower. Since in some cases the effect of the vertical component proved to be important, a further improvement can be obtained by taking into account also the vertical ground motion intensity. [ABSTRACT FROM AUTHOR]

A discrete Lagrangian approach is the basis for modelling the macroscale elastic response of a solid material, which can be homogeneous as well as a periodic composite. The basic topology is a square "heuristic molecule" that is an assemblage of four rigid bodies with a definite shape bonded by elastic springs. This is the minimum unit cell, UC, that contains all the macroscopic mechanical properties of the solid material, object of study. The paper presents 4 unit cells, in progression from a basic molecule bonded by 2 types of central forces, to a refined "Cosserat-auxetic" molecule that is connected by 4 types of shear and central bond-springs. The emphasis is given to the isotropic response in relation to the value of the macroscopic Poisson ratio, and the four examples of UC topologies are presented showing their relationship to different materials at the macro-scale: from a "rari-constant" continuum, through a standard isotropic Cauchy continuum, up to an isotropic centre-symmetric auxetic Cosserat solid. [ABSTRACT FROM AUTHOR]

A simplified method for investigating the out-of-plane behaviour of masonry walls subjected to seismic loading is presented. A survey of the large walls of monuments hit by earthquakes reveals that in many cases the damage is mainly due to lateral actions, and the crack patterns often tend to subdivide the walls into a number of rigid blocks. In the present study such walls are modelled as a series of plane rigid elements in which only the out-of-plane displacements are considered. The elements are quadrilateral and are connected to each other in the middle of their adjoining sides by hinges that can be regarded as spherical joints at which all the deformation takes place. The mechanical characteristics of these connections are defined so as to approximate the brittle behaviour of masonry material. The results obtained using a limited number of elements are in accord with the observed out-of-plane response of masonry panels. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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