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Implicit Discrete Element Analysis of a Masonry Cupola Under Seismic Loads

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In the current study, the dynamic mechanical behaviour of a masonry cupola composed of non-convex discrete elements is investigated. This cupola is designed in innovative and modern ways and was recently constructed with stone blocks in the south of France. The necessity of applying an accurate numerical modelling method being able to take into account the real geometry of each non-convex block is also presented and discussed. The stability state of this masonry structure, by considering the different levels of seismic loads is studied. In addition, the effects of changes in the contact condition between blocks, or the blocks and the structure foundation, are comprehensively investigated.

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  1. Rafiee A, Vinches M (2013) Mechanical behaviour of a stone masonry bridge assessed using an implicit discrete element method. Eng Struct 48:739–749

    Article  Google Scholar 

  2. Idris J, Verdel T, Al-Heib M (2007) Numerical modelling and mechanical behaviour analysis of ancient tunnel masonry structures. Tunn Undergr Space Technol 23:251–263

    Article  Google Scholar 

  3. Dubois F, Jean M (2003) LMGC90 une plateforme de développement dédiée à la modélisation des problèmes d’interaction. In: Actes du sixième colloque national en calcul des structures. CSMA-AFM-LMS, 111–118

  4. Moreau JJ (1993) New computation methods in granular dynamics. Powders and Grains 93. A.A. Balkema, Rotterdam, pp 227–232

    Google Scholar 

  5. Moreau JJ (1998) Unilateral contact and dry friction in finite freedom dynamics, Volume 302 of International Centre for Mechanical Sciences, Courses and Lectures. Springer, Vienna, 1–82

  6. Moreau JJ (2004) An introduction to unilateral dynamics. In: Frémond M, Maceri F (eds) Novel Approaches in Civil Engineering, Number 14 in Lecture Notes in Applied and Computational Mechanics. Springer-Verlag, New York, 1–46

  7. Jean M (1988). Unilateral contact and dry friction: time and space variables discretization. Arch Mech Warszawa 40(1):677–691

  8. Jean M (1995) Frictional contact in rigid or deformable bodies: numerical simulation of geomaterials. Elsevier Science Publisher, Amsterdam, pp 463–486

    Google Scholar 

  9. Jean M (1999) The non-smooth contact dynamics method. In: Special issue on modelling contact and friction. Comp Methods Appl Mech Eng 177:235–257

  10. Jean M (2001) Micromécanique des matériaux granulaires, chapter Simulation numérique discrète, Editor Hermes, Paris, 199–324

  11. Jean M, Moreau JJ (1992) Unilaterality and dry friction in the dynamics of rigid body collections. Proceedings of contact mechanics international symposium. Presses Polytechniques et Universitaires Romandes, Lausanne, pp 31–48

    Google Scholar 

  12. Radjai F, Richefeu V (2009) Contact dynamics as a nonsmooth discrete element method. Mech Mater 41:715–728

    Article  Google Scholar 

  13. Renouf M, Dubois F, Alart P (2004) A parallel version of the non-smooth contact dynamics algorithm applied to the simulation of granular media. J Comput Appl Math 168(1–2):375–382

    Article  MathSciNet  MATH  Google Scholar 

  14. Acary V, Blaise JY, Drap P, Florenzano M, Garrec S, Jean M, Merad D (1999) NSCD method applied to mechanical simulation of masonry in historical buildings using MOMA. In: XVII CIPA (International Committee for Architectural Photogrammetry) International Symposium WG3—Simple methods for architectural photogrammetry. Olinda, Brazil

  15. Rafiee A, Vinches M, Bohatier C (2008) Application of the NSCD method to analyse the dynamic behaviour of stone arched structures. Internat J Solids Structures 45:6269–6283

    Article  MATH  Google Scholar 

  16. Rafiee A, Vinches M, Bohatier C (2008) Modelling and analysis of the Nîmes arena and the Arles aqueduct subjected to a seismic loading, using the non-smooth contact dynamics method. Eng Struct 30:3457–3467

    Article  Google Scholar 

  17. Cundall P (1971) A computer model for simulating progressive large scale movements of blocky rock systems. Proc Symp Int Soc Rock Mech 1:132–150

    Google Scholar 

  18. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65

    Article  Google Scholar 

  19. Topin V, Dubois F, Monerie Y, Perales F, Wachs A (2011) Micro-rheology of dense particulate flows: application to immersed avalanches. J Non-Newtonian Fluid Mech 166:63–72

    Article  MATH  Google Scholar 

  20. Chetouane B (2004) Approche combinée éléments finis/éléments discrets pour la modélisation des structures maçonnées. PhD. thesis, Université Montpellier II, France, p 245

  21. Perales R (2007) Modélisation du comportement mécanique par éléments discrets des ouvrages maçonnés tridimensionnels. Contribution à la définition d’éléments de contacts surfaciques. PhD thesis, University of Montpellier II, France, p 241

  22. Douglas J (2006) Difficulties in predicting earthquake ground motions in metropolitan France and possible ways forward. Géosciences 4:26–31

    Google Scholar 

  23. Bureau Central Sismologique Français (2013) Ecole et Observatoire des Sciences de la Terre. Accessed 25 June 2013

  24. Ghanbari A, Hoomaan E, Mojallal M (2013) An analytical method for calculating the natural frequency of retaining walls. Int J Civil Eng Trans B Geotech Eng 11(1):1–9

    Google Scholar 

  25. Palmisano F, Elia A (2014) Assessment of masonry buildings subjected to landslide by using the load path method. Int J Civil Eng Trans A Civil Eng 12(2):312–330

  26. Tootoonchy F, Asgarian B, Danesh F (2015) Experimental in-plane behavior and retrofitting method of mud-brick walls. Int J Civil Eng Trans A Civil Eng 13(2):191–201

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The authors are grateful to Frédéric Dubois from the Laboratoire de Mécanique et Génie Civil de Montpellier, France, for his valuable remarks on the NSCD method and especially on the LMGC90 code. The authors would also like to thank Etienne Bertrand from the “Laboratoire Régional des Ponts et Chaussées de Nice” for providing the recorded data of the earthquake.

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Correspondence to Ali Rafiee.

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Rafiee, A., Vinches, M. Implicit Discrete Element Analysis of a Masonry Cupola Under Seismic Loads. Int J Civ Eng 14, 357–367 (2016).

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