Non-Linear Analysis of Masonry Structures Subjected to External Settlements


This article describes a methodology for the non-linear analysis of existing masonry structures subjected to external yielding constraints, with particular attention to the historical and cultural heritage constructions. It is well known, indeed, that most of the arch and wall damages are often due to settlement of abutments, in the former case, and to settlement of foundations, in the latter one. The ability to observe and correctly analyze the cracking failure pattern, visible on such structures, is the main “diagnostic tool” for identifying its origin: the modification of load conditions over time, foundation settlements and earthquakes. The objective of this work is to identify a numeric modelling of masonry structures (such as walls, arches, vaults, ruins) under any load condition and subjected to inelastic settlements impressed to some external constraints. The purpose of the numerical procedure is to interpret the behaviour of such structures in order to assess both the peak settlement value and their specific failure mode in correspondence to a geometry which is very often compromised. Therefore, this procedure allows one to estimate the degree of the structures’ vulnerability, in order to prevent any future damage, both local and global. The iterative algorithm proposed in this article, developed in a calculation software, processes the structure considering, not only the properties of constitutive material, non-homogeneous and anisotropic, but also the change of the structure’s shape during the settlements increase. In this way a non-linear analysis is performed both materically and geometrically. Through a direct comparison between numerical and experimental results, obtained by testing some simple structural models in a laboratory, it was ascertained, both from a qualitative and quantitative point of view, the correctness and the efficacy of the proposed procedure, which will be explained below. Therefore, this numerical procedure demonstrates to be a useful diagnostic tool by which, starting from the input of the masonry structure to be studied and simulating a presumable event, one can trace the source of the causes that have generated a certain failure, comparing the cracking pattern of real structure with that plotted by the software.

Share and Cite:

S. Galassi, M. Paradiso and G. Tempesta, "Non-Linear Analysis of Masonry Structures Subjected to External Settlements," Open Journal of Civil Engineering, Vol. 3 No. 2A, 2013, pp. 18-26. doi: 10.4236/ojce.2013.32A003.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] J. Heyman, “The Masonry Arch,” 1st Edition, Ellis Horwood Ltd., Chichester, 1982.
[2] M. Como, “Equilibrium and Collapse Analysis of Masonry Bodies,” Meccanica, Vol. 27, No. 3, 1992, pp. 185-194. doi:10.1007/BF00430044
[3] M. Gilbert, C. Casapulla and H. M. Ahmed, “Limit Analysis of Masonry Block Structures with Non-Associative Frictional Joints Using Linear Programming,” Computers and Structures, Vol. 84, No. 13-14, 2006, pp. 873 887. doi:10.1016/j.compstruc.2006.02.005
[4] J. Heyman, “La Coupe des Pierres,” Proceedings of the 3rd International Congress on Construction History, Cottbus, May 2009.
[5] M. Paradiso, G. Tempesta and S. Galassi, “A Numerical Method for No-Tension Analysis of Masonry Arches,” Proceedings of the 4th International Conference on Arch Bridges, Barcellona, 17-19 Novembre 2004, pp. 312-321.
[6] J. Ochsendorf, “The Masonry Arch on Spreading Sup ports,” The Structural Engineeer, Vol. 84, No. 2, 2006, pp. 29-36.
[7] C. Baggio and P. Trovalusci, “Collapse Behaviour of Three-Dimensional Brick-Block Systems Using Non-Li near Programming,” Structural Engineeering and Mechanics, Vol. 10, No. 2, 2000, pp. 181-195.
[8] S. Di Pasquale, “New Trends in the Analysis of Masonry Structures,” Meccanica, Vol. 27, No. 3, 1992, pp. 173-184. doi:10.1007/978-94-017-2188-2_3
[9] C. A. Coulomb, “Mémoires de Mathématique et de Physique Présentés à l’Académie Royale des Sciences, par Divers Savans, et Ius dans les Assemblées,” Académie Royale des Sciences, Paris, 1776.
[10] M. Paradiso, G. Tempesta, S. Galassi and F. Pugi, “Sistemi Voltati in Muratura. Teoria e Applicazioni,” Edizioni DEI, Roma, 2007.
[11] S. Galassi, M. Paradiso and G. Tempesta, “X-Vaults: A Software for the Analysis of the Stability of Masonry Cross-Vaults,” Computer Science Issues, Vol. 9, No. 2, 2012, pp. 133-142.
[12] G. Colonnetti, “Scienza delle Costruzioni,” Edizioni Scientifiche Einaudi ,Torino, 1955.
[13] A. Ben Israel and T. N. E. Greville, “Generalized Inverses: Theory and Applications,” John Wiley & Sons, New York, 1974.
[14] M. Gilbert and C. Melbourne, “Rigid-Block Analysis of Masonry Structures,” The Structural Engineering, Vol. 72, No. 21, 1994, pp. 356-361.
[15] C. A. Castigliano, “Théorie de l’équilibre des Systèmes élastiques et ses Applications,” Editore Negro, Torino, 1879.
[16] J. Ochsendorf, “Collapse of Masonry Structures,” Ph.D. Dissertation, University of Cambridge, Cambridge, 2002.
[17] S. Galassi, M. Paradiso, E. Pieroni and G. Tempesta, “Analisi di Strutture in Muratura Soggette a Vincoli Cedevoli: Un Algoritmo di Calcolo Non Lineare,” Pro ceedings of XX Congresso Associazione Italiana di Me ccanica Teorica e Applicata, AIMETA 2011, Publi& Stampa Edizioni, Bologna, 12-15 Settembre 2011.
[18] S. Galassi, M. Paradiso, E. Pieroni and G. Tempesta, “Analisi di Archi in Muratura su Imposte Cedevoli,” Atti del Workshop on Design for Rehabilitation of Masonry Structures WONDERmasonry 2011, Edizioni Polistampa, Firenze, Luglio 2012, pp. 48-58.
[19] V. Ceradini, M. Candela and R. Fonti, “The Role of Solid Springer in Masonry Vault,” Advanced Materials Research, Vol. 133-134, 2010, pp. 349-354. doi:10.4028/
[20] S. Huerta, “Mechanics of Masonry Vaults: The Equilibrium Approach,” Proceedings of 3th International Seminar on Historical Constructions, Guimaraes, 2001, pp. 247-253.
[21] S. Galassi, “BrickWORK: A Software for the Analysis of Masonry Structures Composed of Rigid Blocks Jointed with or without Interposition of Mortar; A Tool Derived from the Scientific Research of the Authors, Not for Sale,” 2007-2012.
[22] S. Di Pasquale, “L’Arkh-Trabs del Foro Pompeiano,” Atti del Convegno Internazionale di Studi “Ercolano 1738 1988-250 anni di Ricerca Archeologica, Roma, 20 Ottobre-5 Novembre 1988, pp. 201-218.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.