Two non-linear finite element models developed for the assessment of failure of masonry arches

Michele Betti; Georgios A. Drosopoulos; Georgios E. Stavroulakis

doi:10.1016/j.crme.2007.10.014

Two non-linear finite element models developed for the assessment of failure of masonry arches

Michele Betti ¹; Georgios A. Drosopoulos ²; Georgios E. Stavroulakis ^3,⁴

¹ University of Florence, Department of Civil Engineering, Via di Santa Marta, 3, 50139 Florence, Italy
² University of Ioannina, Department of Material Science and Technology, 45100 Ioannina, Greece
³ Technical University of Crete, Department of Production Engineering and Management, 73100 Chania, Greece
⁴ Carolo Wilhelmina Technical University, Institute of Applied Mechanics, Department of Civil Engineering, 38106 Braunschweig, Germany

Comptes Rendus. Mécanique, Duality, inverse problems and nonlinear problems in solid mechanics, Volume 336 (2008) no. 1-2, pp. 42-53.

Abstract
Résumé

In this article a comparison between two non-linear finite element approaches for the numerical estimation of the ultimate failure load of masonry arches is presented. According to the first model, the geometry of the arch is divided into a number of unilateral contact interfaces which simulate potential cracks. Opening or sliding for some of the interfaces indicates crack initiation. The second model uses two-dimensional finite elements for the simulation of the arch. When tensile stresses appear, upon an adaptive stepwise procedure, the corresponding elements are replaced by unilateral contact elements which represent cracks. In both models the fill over the arch, that could strongly affect the collapse behaviour increasing the bridge load carrying capacity, is taken into account. Moreover, the ultimate load and the collapse mechanism have been calculated by using a path-following (load incrementation) technique. Both models are developed and applied on a real scale masonry arch; results are comparable with both the experimental collapse mechanism and the ultimate load failure.

Dans cet article, on présente une comparaison entre deux approches par éléments finis non-linéaires permettant d'estimer numériquement la charge ultime de ruine d'arches en maçonnerie. Dans le premier modèle, la géométrie de l'arche est divisée en un certain nombre d'interfaces de contact unilatéral qui simulent des fissures potentielles. L'ouverture ou le glissement sur certains de ces interfaces indiquent une initiation de fissure. Le second modèle utilise des éléments finis bidimensionnels pour la simulation de l'arche. Quand des contraintes de traction apparaissent, les éléments correspondants sont remplacés, suivant une procédure pas-à-pas adaptative, par des éléments de contact unilatéral qui représentent des fissures. Dans les deux modèles, on prend en compte le remplissage sur l'arche, qui peut affecter considérablement le comportement à la rupture en augmentant la capacité portante du pont. De plus, la charge limite et le mécanisme de ruine ont été calculés en utilisant une technique pas-à-pas tenant compte du trajet de chargement. Les deux modèles sont développés et appliqués à une arche en maçonnerie en vraie grandeur ; les résultats reproduisent bien tant le mécanisme de ruine expérimental et la charge limite de rupture.

Published online: 2008-01-01

DOI: 10.1016/j.crme.2007.10.014

Keywords: Solids and structures, Masonry arch bridge, Unilateral contact, Arch–fill interaction, Limit analysis, Load carrying capacity
Mots-clés : Solides et structures, Arche en maçonnerie, Contact unilatéral, Interaction arche–remplissage, Analyse-limite, Charge ultime de ruine

Author's affiliations:

Michele Betti ¹; Georgios A. Drosopoulos ²; Georgios E. Stavroulakis ^{3, 4}

¹ University of Florence, Department of Civil Engineering, Via di Santa Marta, 3, 50139 Florence, Italy
² University of Ioannina, Department of Material Science and Technology, 45100 Ioannina, Greece
³ Technical University of Crete, Department of Production Engineering and Management, 73100 Chania, Greece
⁴ Carolo Wilhelmina Technical University, Institute of Applied Mechanics, Department of Civil Engineering, 38106 Braunschweig, Germany

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     author = {Michele Betti and Georgios A. Drosopoulos and Georgios E. Stavroulakis},
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Michele Betti; Georgios A. Drosopoulos; Georgios E. Stavroulakis. Two non-linear finite element models developed for the assessment of failure of masonry arches. Comptes Rendus. Mécanique, Duality, inverse problems and nonlinear problems in solid mechanics, Volume 336 (2008) no. 1-2, pp. 42-53. doi : 10.1016/j.crme.2007.10.014. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.10.014/

References
Cited by

[1] A. Brencich, R. Morbiducci, Masonry arches: Historical rules and modern mechanics, in: Proceeding of Structural Analysis of Historical Constructions, New Delhi, 2006, pp. 243–250

[2] Military Engineering Experimental Establishment (MEXE), Military load classification of civil bridges, Christchurch, Hampshire, UK, 1963

[3] A.J.S. Pippard; R.J. Ashby An experimental study of the voussoir arch, J. Institut. Civil Eng., Volume 10 (1939), pp. 383-404

[4] A.J.S. Pippard The approximate estimation of safe loads on masonry bridges, Institut. Civil Eng., Volume 1 (1948), p. 365

[5] K.-H. Ng; C.A. Fairfield Modifying the mechanism method of masonry arch bridge analysis, Construct. Building Mater., Volume 18 (2004) no. 2, pp. 91-97

[6] J. Page Load Tests to Collapse on Two Arch Bridges at Preston, Shropshire and Prestwood, Staffordshire, TRL, Crowthorne, England, 1987

[7] J. Page, Masonry arch bridges. TRL state of the art review, Department of Transport, TRL research report, Crowthorne, England, 1993

[8] J. Heyman The Masonry Arch, Ellis Horwood Series in Engineering Science, Ellis Horwood, England, 1982

[9] W.E.J. Harvey Application of the mechanism analysis to masonry arches, The Struct. Eng., Volume 66 (1988), pp. 77-84

[10] P. Faccio, P. Foraboschi, E. Siviero, Load carrying capacity of masonry arch bridges, in: Proceedings of the First International Conference on Arch Bridges, Bolton, GB, 1995, pp. 449–458

[11] P.J. Fanning; T.E. Boothby; B.J. Roberts Longitudinal and transverse effects in masonry arch assessment, Construct. Building Mater., Volume 15 (2001), pp. 51-60

[12] M. Gilbert; C. Melbourne Rigid-block analysis of masonry structures, The Struct. Eng., Volume 72 (1994), pp. 356-360

[13] J. Salençon Calcul à la rupture et analyse limite, Presses de l'Ecole Nationale des Ponts et Chaussees, Paris, 1983

[14] A. Orduna; P.B. Lourenço Three-dimensional limit analysis of rigid blocks assemblages. Part I: Torsion failure on frictional interfaces and limit analysis formulation, Int. J. Solids Struct., Volume 42 (2005), pp. 5140-5160

[15] A. Orduna; P.B. Lourenço Three-dimensional limit analysis of rigid blocks assemblages. Part II: Load-path following solution procedure and validation, Int. J. Solids Struct., Volume 42 (2005), pp. 5161-5180

[16] M.A. Crisfield A Finite Element Computer Program for the Analysis of Masonry Arches, TRL, Crowthorne, England, 1984

[17] M.A. Crisfield Finite Element and Mechanism Methods for the Analysis of Masonry and Brickwork Arches, TRL, Crowthorne, England, 1985

[18] H. Lofti; P. Shing Interface model applied to fracture of masonry structures, ASCE J. Struct. Engrg., Volume 120 (1994), pp. 63-80

[19] C. Molins; P. Roca Capacity of masonry arches and spatial structures, ASCE J. Struct. Engrg., Volume 124 (1998), pp. 653-663

[20] A. Cavicchi; L. Gambarotta Collapse analysis of masonry bridges taking into account arch–fill interaction, Engrg. Struct., Volume 27 (2005), pp. 605-615

[21] A. Thavalingam; N. Bicanic; J.I. Robinson; D.A. Ponniah Computational framework for discontinuous modelling of masonry arch bridges, Computers & Structures, Volume 73 (2001) no. 19, pp. 1821-1830

[22] G. Duvaut; J.L. Lions Les inéquations en mécanique et en physique, Dunod, Paris, 1972

[23] P.D. Panagiotopoulos Inequality Problems in Mechanics and Applications, Convex and Nonconvex Energy Functions, Birkhäuser-Verlag, Stuttgart, 1985

[24] E.S. Mistakidis; G.E. Stavroulakis Nonconvex Optimization in Mechanics. Smooth and Nonsmooth Algorithms, Heuristics and Engineering Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998

[25] F.-J. Ulm; J.M. Piau Fall of a temple: Theory of contact applied to masonry joints, ASCE J. Struct. Engrg., Volume 119 (1993) no. 3, pp. 687-697

[26] M.C. Ferris; F. Tin-Loi Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints, Int. J. Mech. Sci., Volume 43 (2001), pp. 209-224

[27] G.E. Stavroulakis; P.D. Panagiotopoulos; A.M. Al-Fahed On the rigid body displacements and rotations in unilateral contact problems and applications, Computers & Structures, Volume 40 (1991), pp. 599-614

[28] B.P. Leftheris; M.E. Stavroulaki; A.C. Sapounaki; G.E. Stavroulakis Computational Mechanics for Heritage Structures, WIT Press, Southampton, 2006

[29] G.A. Drosopoulos; G.E. Stavroulakis; C.V. Massalas Limit analysis of a single span masonry bridge with unilateral frictional contact interfaces, Engrg. Struct., Volume 28 (2006), pp. 1864-1873

[30] K.D.S. Towler, F. Sawko, Limit state behaviour of brickwork arches, in: Proceedings 6th International Brick Masonry Conference, Rome, 1982

[31] Y.C. Loo; Y. Yang Cracking and failure analysis of masonry arch bridges, ASCE J. Struct. Engrg., Volume 117 (1991), pp. 1641-1659

[32] T.E. Boothby Elastic plastic stability of jointed masonry arches, Engrg. Struct., Volume 19 (1997), pp. 345-351

[33] P.J. Fanning; T. Boothby Three dimensional modelling and full-scale testing of stone arch bridge, Computer & Structures, Volume 79 (2001), pp. 2645-2662

[34] Y.C. Loo, Collapse load analysis of masonry arch bridges, in: Proceedings of the First International Conference on Arch Bridges, Bolton, GB, 1995, pp. 167–174

[35] M. Betti; A. Vignoli L'utilizzo del codice ad elementi finiti ANSYS per l'analisi strutturale di edifici monumentali in muratura, Anal. Calcolo VI, Volume 21 (2005), pp. 27-31 (in Italian)

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