Latest revision as of 13:44, 30 November 2021

Abstract

Masonry vaults are widespread and characteristic structural elements of our built heritage since many centuries, but for a very long time they were built only based upon the experience and the proportional analysis of previous positive examples. Since the Hooke’s observations, in 17th century, about the shape of the catenary, and the first graphical analyses of 18th century, the tools for their “scientific” calculation have developed quickly [1], mainly to assess the stability of already existing structures rather than for the prevision of the future behaviour of new vaults. Despite the great progress in this field, ordinary programs for the static and seismic assessment of masonry buildings often disregard the vaults structural role and the professionals sometimes underestimate it, also due to the lack of attention dedicated to these structures by the technical codes. Therefore it seems now important to reconnect the elements of this modelling historical evolution, to compare the different methods and to find an equilibrium between complexity and reliability, making it accessible also to the common professional use, whose effects on preservation are important. To this aim, a pavilion vault was chosen as a reference, with given geometries and materials features, and the different methods were applied. On one side, traditional methods were chosen: the graphic Méry method [2] and the static theorem of limit analysis [3] have been applied to a system of 2D arches composing the vault. On the other side, a 2D Finite Element Model and the edge cutting ChronoEngine Distinct Element Model [4] have been also tested, under the same conditions. The influence of the brick pattern on the structural behaviour have been considered, conveniently defining the arches decomposition in the traditional methods and the blocks division in the Distinct Element Method. In all cases, calculations have been made changing both values and positions of the loads. The results are compared both in terms of stresses inside the masonry and in terms of deformation of the structural elements, evaluating the types of information and detail that the different approaches can supply. The results of the advanced numerical methods allow to assess the validity of the traditional approaches. On the other side, the possible contribution of the traditional methods to the calibration of the parameters for the numerical models is also discussed.

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References

[1] Bettini S., L’architettura di San Marco, Padova, 1946; s.v. Arco, in Enciclopedia dell’arte antica, Secondo Supplemento 1971, Roma, 1994, pp. 344-354 (in Italian).

[2] A. Tralli, C. Alessandri & G. Milani. Computational methods for masonry vaults: a review of recent results. The Open Civil Engineering Journal, 8-1(2014) 272-287.

[3] Giovannoni G., Il restauro dei monumenti, Tipografia Editrice Italia, Roma, 1945 (in Italian).

[4] NTC2018 “Aggiornamento delle norme tecniche delle costruzioni”, Ministero delle Infrastrutture e dei Trasporti, D.M. 17-01-2018. (in Italian).

[5] E. Méry, Mémoire sur l’équilibre des voutes en berçeau, Annales des Ponts et Chaussées, s.1, 1e trim., t. XIX (1840) 50-70.

[6] J. Heyman, The masonry Arch, Chichester: Ellis Horwood, 1982.

[7] “Project Chrono”, URL: https://projectchrono.org Accessed January 2020.

[8] E. Coïsson, D. Ferretti, C. Boni & A. Tasora, Defining the structurally compatible uses of ancient vaults: a comparison between traditional and modern modelling approaches, in 6th International Conference on Mechanics of Masonry Structures Strengthened With Composite Materials (MuRiCo6), Bologna, Italy, June 26-28, 2019.

[9] D. Ferretti, E. Coisson & Rozzi, M. A new numerical approach to the structural analysis of masonry vaults, Key Engineering Materials, 747(2017) 52-59.

[10] “Arco”, URL: http://gelfi.unibs.it/arco.htm Accessed January 2020.

[11] E. Coisson, F. Ottoni, F. Pagliari, Istanze strutturali nella definizione di usi compatibili: un caso studio nel complesso monumentale della Pilotta, in: Il Patrimonio culturale in mutamento. Le sfide dell'uso, XIII convegno Scienza e Beni Culturali, Bressanone, 2019.

[12] Kaushik, H. B., Rai, D. C., & Jain, S. K. (2007). Stress-strain characteristics of clay brick masonry under uniaxial compression. Journal of materials in Civil Engineering, 19(9), 728-739.

[13] A. Lorenzelli, The seismic vulnerability of bell-towers’ spires: damage analysis and modeling, thesis in Engineering, University of Parma, supervisors D. Ferretti, E. Coïsson, A.Y. 2016/2017

[14] Calderini, C., Vecchiattini, R., Battini, C., & Piccardo, P. (2016, September). Mechanical and metallographic characterization of iron tie-rods in masonry buildings: An experimental study. In 10th International Conference Structural Analysis of Historical Constructions, Leuven, Belgium, September (Vol. 13, p. 15).

[15] G. de Felice, Assessment of the load-carrying capacity of multi-span masonry arch bridges using fibre beam elements, Engineering Structures, Volume 31, Issue 8, 2009, Pages 1634-1647.

[16] Demi L. Fang, Rebecca K. Napolitano, Tim L. Michiels & Sigrid M. Adriaenssens (2019) Assessing the stability of unreinforced masonry arches and vaults: a comparison of analytical and numerical strategies, International Journal of Architectural Heritage, 13:5, 648-662.

[17] Antonio Maria D’Altri, Stefano De Miranda, Giovanni Castellazzi, Vasilis Sarhosis, Jamie Hudson & Dimitris Theodossopoulos (2019): Historic Barrel Vaults Undergoing Differential Settlements, International Journal of Architectural Heritage.

[18] P. Gelfi, Role of horizontal backfill passive pressure on the stability of masonry vaults. International Journal for Restoration of Buildings and Monuments 8-6 (2002) 573-590.

[19] D. O'Dwyer, "Funicular analysis of masonry vaults," Computers & Structures, vol. 73, pp. 187-197, 10 1999.

[20] P. Block, T. Ciblac and J. Ochsendorf, "Real-time limit analysis of vaulted masonry buildings," Computers & Structures, vol. 84, pp. 1841-1852, 11 2006.

[21] A. Andreu, L. Gil and P. Roca, "Computational analysis of masonry structures with a funicular model," Journal of Engineering Mechanics, vol. 133, pp. 473-480, 2007.

[22] Chaix, Jacques. 1890. Traité des ponts: première par-tie: ponts en maçonnerie et tunnels: Tome II. Paris: Fanchon et Artus.