Michele Betti

Assessment of seismic resistance of a basilica-type church under earthquake loading: Modelling and analysis

In this paper a finite element methodology for the static and dynamic non-linear analysis of historical masonry structures is described and applied to a case study. A basilica-type masonry church is analysed in order to assess its structural behaviour and its seismic vulnerability with respect to the actual state of conservation. Moreover the actual efficiency of current techniques for repairing and strengthening are analyzed in order to evaluated their benefits. A quasi-static approach (the seismic coefficient method) for the evaluation of the seismic loads have been used (as indeed common in many analyses of the seismic behaviour of masonry structures). This paper addresses the concern of seismic analysis and vulnerability of a basilica-type church with a specific case study: the Farneta abbey. The comparison demand vs. capacity confirms the susceptibility of this type of buildings to extensive damage and possibly to collapse, as frequently observed. The analysis of repairing and strengthening techniques show the effectiveness of the usual structural reinforcement in term of increased seismic capacity. It is believed that the conclusions obtained with respect to the seismic assessment of masonry church can be extrapolated for the wide variety of historical basilica-type church.

A numerical study on seismic risk assessment of historic masonry towers: a case study in San Gimignano

After a brief introduction on the research project RiSEM (Seismic Risk of Monumental Buildings), the paper discusses on the seismic assessment of historic masonry towers according to the Italian “Guidelines for the assessment and mitigation of the seismic risk of the cultural heritage” that identifies an analysis methodology based on three different levels of evaluation, according to an increased knowledge of the structure. The RiSEM project aimed at developing and testing innovative and expeditious methodologies (i.e. either without or with a minimal direct contact with the masonry building) to evaluate all the main structural features of the monumental buildings required for the assessment of their seismic safety. As a relevant case study the “Town of Fine Towers”, San Gimignano (Italy), listed under the UNESCO World Cultural Heritage Sites, was selected. The paper summarizes the analyses performed on one of the San Gimignano towers: the Coppi-Campatelli one. The seismic vulnerability of the tower was evaluated with reference to the above guidelines, and the paper reports and critically compares the results obtained for the three levels of evaluation there defined: LV1 (analysis at territorial level), LV2 (local analysis) and LV3 (global analysis).

Cappella dei Principi in Firenze, Italy: Experimental Analyses and Numerical Modeling for the Investigation of a Local Failure

AbstractThe paper reports the results of a research aimed at analyzing and interpreting the cracking pattern on the Cappella dei Principi (Prince’s Chapel, the Medici’s mausoleum) in the Basilica of San Lorenzo (Florence, Italy). The research was motivated by the sudden collapse of a keystone of an internal barrel vault sustaining one of the lateral apses. After a brief description of the geometry of the structure, the principal results obtained from in situ surveys (flat-jack tests and cored samples) are described; then the numerical analyses developed both to obtain the static identification of the monument and to assess the possible causes leading to the observed failure are illustrated. The numerical modeling operation has been performed step by step, from linear and quite simple models built with plane elements up to a nonlinear model with three-dimensional elements. The nonlinear FEM, which has been tuned by utilizing the results of the in situ measures, is allowed to both qualitatively and quantita...

Simplified Seismic Analysis of Disordered Masonry Towers

AbstractThe structural assessment of existing masonry towers under exceptional loads, such as earthquake loads, requires reliable and expedite methods of analysis. These approaches should take into account both the specific nonlinear behavior of the material (for instance, the small tensile strength) and the randomness that affect the masonry material’s properties (in some cases the distribution of the elastic parameters too). Considering the need of simplified but effective methods to assess the seismic response of such a class of structures, the paper proposes an expeditious approach based on an equivalent Bouc and Wen model. As a prototype of masonry towers, a cantilever masonry beam is analyzed assuming that the first mode shape governs the dynamic behavior. With this hypothesis, the nonlinear Bouc and Wen model is employed to reproduce the system hysteretic response. Subsequently, assuming the material properties as random variables, stochastic linearization and the perturbative approach are employed...

Seismic Response Of Masonry Plane Walls: A Numerical Study On Spandrel Strength

The paper reports the results of a numerical investigation on masonry walls subjected to in‐plane seismic loads. This research aims to verify the formulae of shear and flexural strength of masonry spandrels which are given in the recent Italian Standards [1]. Seismic pushover analyses have been carried out using finite element models of unreinforced walls and strengthened walls introducing reinforced concrete (RC) beams at the floor levels. Two typologies of walls have been considered distinguished for the height to length ratio h/l of the spandrels: a) short beams (h/l = 1.33) and b) slender beams (h/l = 0.5). Results obtained for the unreinforced and the strengthened walls are compared with equations for shear and flexural strength provided in Standards [1]. The numerical analyses show that the reliability of these equations is at least questionable especially for the prediction of the flexural strength. In the cases in which the axial force has not been determined by the structural analysis, Standards ...

Finite Element Modelling for Seismic Assessment of Historic Masonry Buildings

The chapter discusses on the use of the finite element modelling technique for the seismic assessment of historic masonry buildings, outlining that advanced numerical analyses can provide significant information to understand their actual structural behaviour. A finite element methodology for the static and dynamic nonlinear analysis of historic masonry structures is described and exemplified through the discussion of two representative case studies: a masonry church and an old residential building.

Numerical Modeling of the Structural Behavior of Brunelleschi’s Dome of Santa Maria del Fiore

The study discusses some recent results regarding the identification of the static and dynamic behavior of the Brunelleschi’s Dome of Santa Maria del Fiore in Florence, which was declared part of the UNESCO World Heritage sites in 1982 together with the city center. First, a brief sketch of the main geometric characteristics and the relevant constructive aspects conceived by Brunelleschi are outlined with a description of the present crack pattern. Then a finite element model was built to assess the static and dynamic behavior of the monument and identified taking into account the results of an in situ investigation developed in the 1980s. The numerical model was used with an ad hoc nonlinear procedure to replicate the mechanical behavior of masonry. Obtained results allowed to assess and to discuss both the Dome’s internal stress and cracking pattern. The identified numerical model was subsequently employed to provide a first evaluation of the seismic behavior of the Dome. While showing how advanced numerical analyses can provide useful hints to evaluate the existing damage on monumental heritage, this study aims at contributing to the assessment of the safety and vulnerability of one of the most emblematic masonry domes all over the world.

Semiempirical Formulations for Estimating the Main Frequency of Slender Masonry Towers

AbstractThe paper focuses on the analysis of the outcomes of some experimental tests carried out in San Gimignano (Siena, Italy), aimed at measuring the natural frequencies of the medieval masonry ...

Diagonal cracking shear strength of unreinforced masonry panels: a correction proposal of the b shape factor

Abstract After summarising the failure criteria adopted by the new Italian Seismic Code (NTC 2008) for the seismic assessment of unreinforced masonry panels (URM), the paper presents a numerical study aimed at investigating the b shape factor. This factor is a coefficient, function of the panels’ slenderness, employed to evaluate the ultimate shear strength of URM for the failure mechanism with diagonal cracking. The results herein presented show that the actual values of the coefficient b are higher than those proposed by the NTC (2008); consequently, the shear strength obtained by applying the Italian Seismic Code is not conservative. An amendment is proposed for the b shape factor, and its effects are evaluated through the analysis of three plane-URM walls with regular openings and different slenderness of the masonry beams. Pushover analyses were performed to estimate their seismic capacity and their collapse modes. The walls were modelled by both the finite element method (FEM) and the equivalent frame approach (EFM). In the EFM approach the b shape factor was selected both according to the NTC (2008) and as proposed in the paper. The seismic capacity curves show that the EFM approach significantly overestimate the ultimate shear strength of the walls with respect to the results obtained by the FEM, and this effect is amplified when the b shape factor is evaluated as recommended by the NTC (2008).

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). ...