Claudio Alessandri

Computational Methods for Masonry Vaults: A Review of Recent Results

The present paper makes a critical review of some methods and models, now available in the technical litera- ture and commonly used in the analysis of masonry vaults up to their collapse, by highlighting advantages and drawbacks of each approach. All methods adopted to describe the mechanical behavior of masonry structures, in order to be reliable, must take into account the distinctive aspects of masonry, namely the scarce (or zero) tensile strength, the good resistance in compression and the occurrence of failure mechanisms through rotation-translation of rigid macro-blocks. Classic no- tension material models disregard the small existing tensile strength and make the assumption of (1) infinitely elastic be- havior in compression and (2) isotropy, giving thus the possibility to deal with either semi-analytical approaches (espe- cially for arches) or robust numerical procedures. More advanced but rather complex models are nowadays able to deal al- so with anisotropy induced by texture, small tensile strength and softening in tension, as well as by finite strength in com- pression. Traditionally - and nowadays it is still an opinion commonly accepted, in contrast with step by step complex procedures, Limit Analysis has proved to be the most effective Method for a fast and reliable evaluation of the load bear- ing capacity of vaulted masonry structures: classic lower and upper bound theorems recall respectively the concepts of equilibrium and occurrence of failure mechanisms with rigid elements. The so-called Thrust Network Method moves its steps from lower bound theorems, whereas FE limit analysis approaches with infinitely resistant elements and dissipation on interfaces take inspiration from the upper bound point of view. An alternative to Limit Analysis is represented by tradi- tional FEM combined with either elastic-plastic or damaging models with softening, commonly used for other materials but recently adapted also to masonry. They are able to provide a large set of output numerical information but further studies are still needed to ensure their proper application.

Crack Patterns Induced by Foundation Settlements:Integrated Analysis on a Renaissance Masonry Palace in Italy

This study presents some numerical results related to the analysis of the structural damage of a historic masonry building, Palazzo Gulinelli, in Ferrara, Italy. A detailed analysis of the inhomogeneities of the facade, historic documentation, and recent restoration interventions carried out in an adjacent building, suggest that the Palace underwent various modifications both on the structural configuration and on the borne loads. Such modifications might be the main cause of some differential settlements and of the consequent significant crack pattern on the load-bearing walls. Therefore, in the present paper the occurrence of a crack pattern on the facade is simulated by carrying out standard linear and non-linear finite element (FE) homogenized models; differential settlements are applied in order to reproduce the structural changes occurred over time. Previous experiences of the authors (for example, Acito and Milani in 2012 and Mallardo et al. in 2008), the current crack pattern of the building (of its facade in particular) and the monitoring data referring to some of them are the main references for the analysis carried out. The structural survey, the numerical results, and the data monitoring suggest two main conclusions: 1) a good correlation between numerical results and monitoring data is assessed, therefore the cracks can be reasonably related to past differential settlements; and 2) the cracks/damage that occurred as a consequence of differential foundation settlements reduce the ability of the facade to resist seismic actions.

Advanced numerical insight into the structural damage of masonry vaults under seismic excitation: two valuable case studies

Most recent earthquakes have demonstrated the high seismic vulnerability of monumental masonry buildings and, specifically, critical issues associated with complex structural elements like vaults. The main purpose of this paper is the analysis of how quadripartite vaults behave under horizontal loads and what their role is in the global seismic behaviour of historical constructions. The analysis is dealt with by referring to two different case studies: the Narthex of the Nativity Church in Bethlehem and the Fornasini tower in the North East of Italy. By means of ABAQUS, a proper finite elements model is implemented in order to assess the global structural behaviour of the structures. To this purpose, the seismic behaviour is directly evaluated thorough non-linear dynamic analyses and the obtained crack patterns are discussed thoroughly. A Concrete Damage Plasticity (CDP) constitutive model is used to properly account for damage phenomena and softening occurring on masonry during an earthquake.

Advanced FE homogenization strategies for failure analysis of double curvature masonry elements

The paper addresses the topic of the numerical analysis up to collapse of masonry vaults. At this aim, an advanced numerical model is utilized, which requires the discretization of the structure by means of three dimensional six-noded wedge finite elements rigid and infinitely resistant and interfaces exhibiting a non linear behavior with softening. The incremental problem is solved by means of a robust quadratic programming procedure and interfaces mechanical properties are estimated by means of a consolidated homogenization strategy. Failure mechanisms and collapse loads are evaluated numerically for a case study in Italy (a masonry cross vault subjected to increasing vertical live loads up to collapse), varying mechanical properties of the vault and considering the stabilizing role played by the backfill. In light of the results obtained, limitations and possibilities of the widely diffusedtraditional approaches based on the subdivision of the vault into a series of arches are addressed.