Luca Salvatori

Displacement capacity of masonry piers: parametric numerical analyses versus international building codes

The nonlinear behaviour of masonry piers loaded in their plane is investigated by parametric numerical simulations. Each pier has a cantilever scheme, is loaded by a constant axial load and is subjected to an increasing horizontal displacement at the top. The macro-modelling approach is used to perform numerical analyses, adopting two different constitutive laws: a total strain crack model and a plastic model. The numerical model is calibrated on a block-masonry type for which experimental tests are available in literature. Parametric numerical simulations are performed by varying the aspect-ratio and the compression level, in order to assess the influence of such parameters on both shear strength and displacement capacity. By comparing numerical results with formulas of international codes, a good agreement for the shear strength is obtained, while significant differences are observed for the displacement capacity, which is influenced by both parameters. The authors propose a simple empirical formula for the displacement capacity, obtained by fitting the numerical results. The expression can be useful in the practical design for considering the influence of aspect-ratio and compression level, currently neglected by building codes.

Incremental dynamic and nonlinear static analyses for seismic assessment of medieval masonry towers

AbstractDiscrete rigid blocks interacting through nonlinear elastic damageable interfaces are used to model the global behavior of a medieval masonry tower under seismic actions. The seismic vulner...

Unreinforced masonry walls with irregular opening layouts: reliability of equivalent-frame modelling for seismic vulnerability assessment

Equivalent-frame modelling for the estimate of in-plane seismic vulnerability of masonry wall is endorsed by international codes. However, in presence of irregular layouts of openings, the definition of equivalent-frame becomes non-unique and may lead to epistemic modelling errors. The aim of this paper is to develop a simplified tool to estimate such errors as functions of the level or geometric irregularity. Four types of irregularity are considered and quantified by geometric indexes. Nonlinear static analyses are carried out through an equivalent-frame model and a nonlinear finite-element model. It is assumed that both models are exact for perfectly-regular walls, while in presence of irregularities only the continuum approach is able to correctly predict the vulnerability, so that the difference between the two results can be taken as a measure of the error of the equivalent frame. A regular wall is taken as case study and both numerical models are calibrated on experimental data. The four typologies of irregularity are introduced separately, each in steps of increasing magnitude. The results show that the equivalent frame approach is usually not safety-preserving and may be affected by a significant error. A tentative global measure of irregularity, weighting the average effects of each irregularity type, is proposed. The resulting simplified relationship between irregularity level and expected error can be used to define a confidence factor on the modelling, which penalizes the application of the equivalent frame in case of irregular walls. Eventually, an applicability limit of the equivalent-frame model might be set.

Epistemic Uncertainties in Structural Modeling: A Blind Benchmark for Seismic Assessment of Slender Masonry Towers

AbstractThe paper reports the results of a blind benchmark developed as a part of the preliminary activity of the research project RiSEM (Italian acronym for Seismic Risk on Monumental Buildings). ...

Seismic response of masonry-infilled steel frames via multi-scale finite-element analyses

Effects of masonry infills on the seismic vulnerability of steel frames is studied through multi-scale numerical modelling. First, a micro-modelling approach is utilized to define a homogenized masonry material, calibrated on experimental tests, which is used for modelling the nonlinear response of a one-story, single span, masonry-infilled portal under horizontal loads. Based on results of the micro-model, the constitutive behavior of a diagonal strut macro-element equivalent to the infill panel is calibrated. Then, the diagonal strut is used to model infill panels in the macro-scale analysis of a multi-span multi-story infilled moment-resisting (MR) steel frame. The seismic vulnerability of the MR frame is evaluated through a nonlinear static procedure. Numerical analyses highlight that infills may radically modify the seismic response and the failure mechanism of the frame, hence the importance of the infill correct modelling.

A Continuum-Discrete Multiscale Model for In-Plane Mechanical Modeling of Masonry Panels

A multiscale numerical model for the in-plane mechanical behavior of masonry panels is presented. At the microscale, masonry is modeled by rigid blocks interacting through plane, deformable interfaces. These may represent actual mortar joints or virtual preferential fracture surfaces of the blocks (e.g., vertical surfaces crossing a block and connecting vertical joints in the brick rows above and below the considered one). Damage parameters control the interface transitions from a cohesive linear-elastic phase to an elastic-plastic one (modeling frictional sliding and contact) and, eventually, to a completely damaged one. At the panel scale, the material is treated as a finite-element discretized Cauchy continuum, homogenizing the periodic microstructure. The model allows reproducing the main anisotropic nonlinear behaviors of masonry by finite element simulations at a reasonable computational cost. With respect to more traditional phenomenological continuum nonlinear models, a more direct use of experime...

Interdependence of mechanical parameters on probabilistic seismic performance of masonry towers

The assessment of seismic performance of historical masonry towers is complicated by the lack of experimental data on the material properties. The peculiarity of these structures and their historical value render difficult performing experimental tests, particularly destructive ones. For each mechanical parameter, only reasonable intervals can be defined, mostly on the base of expert judgement. In the absence of a correlation structure among them, they are usually treated as independent variables. However, the selection of material parameters in itself is non-unique. For example, considering compressive strength, elastic modulus, and strain at elastic limit, there is no obvious choice of which two should be considered as input parameters, leaving the third as a derived quantity. In the paper, the effects of different choices on the probabilistic seismic performance are investigated. A significant role of the parameter interdependence is highlighted. The most safety preserving choice of independent parameters, in the absence of a desirable correlation structure, is the one in which compressive strength, elastic modulus, and strain ductility factor are treated as independent variables while the strain at elastic limit and the ultimate strain are considered as derived quantities.