Domenico Liberatore

The performance of churches in the 2012 Emilia earthquakes

In this study the damage suffered by churches during the 2012 Emilia seismic sequence in Italy is analysed, based on surveys and inspections carried out in the area. Similarly to what was observed after other Italian earthquakes, the damage to churches was severe. However, the Emilia churches present some characteristic features such as the use of unreinforced clay brick masonry. In order to appropriately address the performance of this class of buildings, typical architectural layouts and construction techniques are described. Such techniques are interpreted also in the light of the local seismic catalogue. Fifty churches are then selected and their damage is studied, with reference to typical local-collapse mechanisms of different macro-elements. The study highlights that the damage is often concentrated at the top section of the façade, in the clerestory walls, in the vaults and in the bell towers. Structural analyses are performed to explain some of the observations. The overturning of the top section of the façade is analytically addressed, modelling the friction interlocking. With reference to the case study of San Francesco in Mirandola, non-linear static and dynamic analyses allow us to correlate the directionality of damage to the higher seismic demand along the NS direction, to point out the negligible role of the large vertical component of ground motion and to emphasise the relevance of the buttresses for the seismic response of the façade.

The behaviour of vernacular buildings in the 2012 Emilia earthquakes

Vernacular buildings are a relevant part of the building stock affected by the Emilia, 2012, earthquakes and they contribute to shape the rural landscape of the Po valley. Unfortunately, due to overall layout, constructive details and poor maintenance, they have shown a very poor seismic performance. Because most of these buildings are lightly used or abandoned, the risk that they will be demolished is rather high; this could be the most long-lasting outcome of the seismic sequence, deeply affecting the traditional landscape of this portion of the Po valley. In this paper a brief description of the architectural features of these buildings is given and their typical seismic performances are analysed. Because damage is usually related to local-collapse mechanisms, rocking spectra are computed for the near field accelerograms and they are compared with observed behaviours. Finally, suggestions are given to improve the earthquake response of these structures, with the aim of preserving important testimonies of the civilisation of the area.

Force-Based Beam Finite Element (FE) for the Pushover Analysis of Masonry Buildings

A simplified approach for analyzing the nonlinear response of masonry buildings, based on the equivalent frame modeling procedure and on the nonlinear equivalent static analyses, is presented. A nonlinear beam finite element (FE) is formulated in the framework of a force-based approach, where the stress fields are expanded along the beam local axis, and introduced in a global displacement-based FE code. In order to model the nonlinear constitutive response of the masonry material, the lumped hinge approach is adopted and both flexural and shear plastic hinges are located at the two end nodes of the beam. A classical elastic-plastic constitutive relationship describes the nonlinear response of the hinges, the evolution of the plastic variables being governed by the Kuhn-Tucker and consistency conditions. An efficient element state determination procedure is implemented, which condenses the local deformation residual into the global residual vector, thus avoiding the need to perform the inner loops for computing the element nonlinear response. The comparison with some relevant experimental and real full-scale masonry walls is presented, obtaining a very good agreement with the available results, both in terms of global pushover curves and damage distributions.

Methods and Approaches for Blind Test Predictions of Out-of-Plane Behavior of Masonry Walls: A Numerical Comparative Study

ABSTRACT Earthquakes cause severe damage to masonry structures due to inertial forces acting in the normal direction to the plane of the walls. The out-of-plane behavior of masonry walls is complex and depends on several parameters, such as material and geometric properties of walls, connections between structural elements, the characteristics of the input motions, among others. Different analytical methods and advanced numerical modeling are usually used for evaluating the out-of-plane behavior of masonry structures. Furthermore, different types of structural analysis can be adopted for this complex behavior, such as limit analysis, pushover, or nonlinear dynamic analysis. Aiming to evaluate the capabilities of different approaches to similar problems, blind predictions were made using different approaches. For this purpose, two idealized structures were tested on a shaking table and several experts on masonry structures were invited to present blind predictions on the response of the structures, aiming at evaluating the available tools for the out-of-plane assessment of masonry structures. This article presents the results of the blind test predictions and the comparison with the experimental results, namely in terms of formed collapsed mechanisms and control outputs (PGA or maximum displacements), taking into account the selected tools to perform the analysis.

Identifying Seismic Local Collapse Mechanisms in Unreinforced Masonry Buildings through 3D Laser Scanning

The surveys following severe earthquakes show that existing unreinforced masonry buildings are highly vulnerable to local collapse mechanisms. However, their assessment is strongly sensitive to the choice of the mechanism, whose boundary conditions are largely unknown. In the past the mechanism has been selected based on the crack survey alone, because the survey of the deformations is very difficult if traditional tools are used. In the last years advanced survey techniques have been developed, the most powerful of whom resorts to laser scanning. A laser scanner allows the acquisitions of a very large amount of information: building overall dimensions and single elements detailed survey, detection of anomalies, and identification of very limited deformations undetectable with the naked eye. Moreover, contrary to traditional procedures, it allows the survey of the façades without any direct contact with the building, which could be damaged after an earthquake. A laser-scanner survey has been performed in the whole historical centre of Rovere, in the municipality of Rocca di Mezzo, affected by the 2009 L’Aquila earthquake. This survey has been used to study the façades of three different building units, recognising the collapse mechanism triggered by the earthquake ground motion. The mechanisms are fairly different from what suggested by the crack pattern alone and pertain to deformations that cannot be recognised in the photos. Moreover, the faithful geometric models that can be generated from laser scanning allow accounting for deformations and out-of-plumb. Thus, the acceleration activating the mechanism can be estimated much more accurately compared to a perfectly vertical and parallelepiped wall.

Vulnerability Assessment of Unreinforced Masonry Churches Following the 2010–2011 Canterbury Earthquake Sequence

The 2010–2011 Canterbury, New Zealand earthquake sequence caused extensive damage to unreinforced masonry churches. A sample of 80 affected buildings was analysed and their performance statistically interpreted. Structural behaviour is described in terms of mechanisms affecting the so-called macro-elements, and damage probability matrices are computed. Regression models correlating mean damage level against macroseismic intensity are also developed for all observed mechanisms, improving the initial simple-linear formulations through use of multiple-linear regressions accounting for vulnerability modifiers, whose influence is evaluated via statistical procedures. Results presented herein will support the future development of predictive tools for decision-makers, also contributing to seismic vulnerability mitigation at a territorial scale.

Guest editorial: The Emilia 2012 earthquakes, Italy

On May 20th, 2012, at 02:03 UTC (04:03 local time), Emilia region of Northern Italy was struck by an earthquake of local magnitude ML 5.9. The focal mechanism was reverse,withmaximumcompression along theN–Sdirection (dip = 46.45◦, strike = 103.28◦, rake = 93.87◦). The municipalities that suffered the highest damage were San Felice sul Panaro and Finale Emilia. Many other damaged municipalities were located in the districts of Modena and Ferrara. The main shock was preceded by foreshocks, begun on May 18th, the strongest of which, with local magnitude 4.1, occurred on May 19th at 23:13 UTC. After the main shock, several aftershocks occurred. At 23:00 of May 25th, more than 500 events took place, two of which with ML ≥ 5.0 (event of May 20th, 13:18 UTC, ML 5.1; event of May 25th, 02:07 UTC, ML 5.1), and 15 with magnitude ranging between 4.0 and 4.9 (INGV 2012). On May 29th, at 07:00 UTC, another significant event of magnitude ML 5.8 occurred, located nearly 12 km W of the May 20th main event and close to San Felice sul Panaro. This event was followed by two aftershocks of ML ≥ 5.0. The aftershocks of the May 29th events affected an area elongated according to the E–W direction, between the municipalities of Novi di Modena and San Felice sul Panaro, nearly 20 km long. On June 3rd, a new event of magnitude ML 5.1, located to the W of the previous ones struck the same area (INGV 2012). Themaximummacroseismic intensity,measured according to theEuropeanMacroseismic Scale (IE M S),wasVIII in themunicipality ofCavezzo as the cumulative effect of the sequence (Tertulliani et al. 2012). In the most damaged municipalities (IE M S > VII), a few total collapseswere observed.Collapses of individual reinforced-concrete (RC) buildings occurred

Seismic Risk Assessment of New Zealand Unreinforced Masonry Churches using Statistical Procedures

ABSTRACT The 2010–2011 Canterbury earthquake sequence provided extensive evidence of the significant seismic vulnerability of New Zealand unreinforced masonry (URM) churches. Given the high seismicity of the country, the exposure of human lives and the societal significance of ecclesiastic buildings, for both historical and religious reasons, the reduction in seismic vulnerability of this building type is of primary importance. By analyzing the seismic performance of a sample of 80 affected buildings, regression models correlating mean damage levels against ground-motion parameters were developed for observed collapse mechanisms, accounting for vulnerability modifiers whose influence was estimated via statistical procedures. Considering the homogeneity of New Zealand URM churches, the vulnerability models developed for the Canterbury region were extended to the whole country inventory, and a synthetic index was proposed to summarise damage related to several mechanisms. Territorial scale assessment of the seismic vulnerability of churches can assist emergency management efforts and facilitate the identification of priorities for more in-depth analysis of individual buildings. After proper calibration, the proposed approach can be applied to other countries with similar building heritage.

Simulation Of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (II): Combined Finite-Discrete Elements

ABSTRACT Out-of-plane response of unreinforced masonry elements is frequently the most critical aspect of the seismic performance of existing masonry buildings. The response of such elements is usually governed by equilibrium rather than strength. Hence, it is customary to resort to rigid-body models, accounting for possible rotations, and/or sliding. However, the results of such analyses depend on the initial choice of the mechanism. In this article, the shaking-table experiments on a brick-masonry specimen, and on a stone-masonry specimen have been modeled by resorting to a combined finite-discrete element strategy. Despite the coarse discretization of both discrete and finite elements, the three-dimensional models are able to capture the experimentally observed multi-degree-of-freedom mechanisms, without any a priori assumption on the mechanism. A sensitivity analysis is carried out, addressing eight different parameters. The identification of the mechanism is sufficiently robust, but the assessment of its activation and failure is best done by combining the finite-discrete element model with a simplified model of the recognised mechanism.

Nonlinear Analysis of Masonry Walls Based on a Damage-Plastic Formulation

Masonry structures subjected to seismic actions exhibit a complex nonlinear behaviour. To obtain a comprehensive representation of all the occurring nonlinear mechanisms, constitutive models including damage and plasticity are required and nonlinear dynamic analyses are considered the most reliable. Hence, models considering both degrading effects and hereditary nature of restoring forces are needed. Different approaches can be adopted, relying on microscopic, macroscopic, multi-scale and macroelement formulations. The latter are often adopted for real cases, mainly to reduce the computational burden of the analyses. The proposed macroelement accounts for typical flexural and shear in-plane failure mechanisms via two flexural hinges and a shear link, arranged in series with an elastic beam. The hysteretic behaviour is reproduced by a smooth model, in which the introduction of a damage function describes both strength and stiffness degradation effects. The model is used to perform comparisons with experimental results on masonry walls, with the aim of validating the numerical procedure and its capabilities to describe nonlinear masonry response.