Numerical Modelling of Dry Stone Masonry Structures Based on Finite-Discrete Element Method
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Numerical Modelling of Dry Stone Masonry Structures Based on Finite-Discrete Element Method

Authors: Ž. Nikolić, H. Smoljanović, N. Živaljić


This paper presents numerical model based on finite-discrete element method for analysis of the structural response of dry stone masonry structures under static and dynamic loads. More precisely, each discrete stone block is discretized by finite elements. Material non-linearity including fracture and fragmentation of discrete elements as well as cyclic behavior during dynamic load are considered through contact elements which are implemented within a finite element mesh. The application of the model was conducted on several examples of these structures. The performed analysis shows high accuracy of the numerical results in comparison with the experimental ones and demonstrates the potential of the finite-discrete element method for modelling of the response of dry stone masonry structures.

Keywords: Finite-discrete element method, dry stone masonry structures, static load, dynamic load.

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[1] F. Parisi, N. Augenti, “Earthquake damages to cultural heritage constructions and simplified assessment of artworks,” Engineering Failure Analyses, vol. 34, pp. 735-760, 2013.
[2] P.B. Lourenço, J.G. Rots and J. Blaauwendraad, “Continuum model for masonry: parameter estimation and validation,” Journal of Structural Engineering ASCE, vol. 1(6), pp. 642-652, 1998.
[3] L. Berto, A. Saetta, R. Scotta and R. Vitaliani, “An orthotropic damage model for masonry structures,” International Journal of Numerical Methods in Engineering, vol. 55, pp.127-157, 2002.
[4] S. Casolo, “Macroscopic modelling of structured materials: Relationship between orthotropic Cosserat continuum and rigid elements,” International Journal of Solids and Structures, vol. 43(3-4), pp. 475-496, 2006.
[5] P.A. Cundall, “A computer model for simulating progressive large scale movements in blocky rock systems (Published Conference Proceedings style),” in Proc. of the Symposium on Rock Fracture (ISRM), Nancy, France, 1971, pp. 1-8.
[6] P.A. Cundall, R.D. Hart, “Numerical modelling of discontinua,” Engineering Computations, vol. 9, pp. 101-113, 1992.
[7] C. Baggio, P. Trovalusci, “Stone assemblies under in-plane actions-comparison between nonlinear discrete approaches,” Computer Methods in Structural Masonry, vol. 3, pp. 184-193, 1995.
[8] C. Baggio, P. Trovalusci, “Collapse behaviour of three-dimensional brick-block systems using non-linear programming,” Structural Engineering and Mechanics, vol. 10, pp. 181-195, 2000.
[9] A. Nappi, F. Tin-Loi, “A numerical model for masonry implemented in the framework of a discrete formulation,” Structural Engineering and Mechanics, vol. 11(2), pp. 171-184, 2001.
[10] M. Gilbert, C. Casapulla, H. M. Ahmed, “Limit analysis of masonry block structures with non-associative frictional joints using linear programming,” Computers & Structures, vol. 84(13), pp. 873-887, 2006.
[11] P.A. Cundall, “Formulation of a three-dimensional distinct element model – Part I: A scheme to detect and represent contacts in a system composed of many polyhedral blocks,” International Journal of Rock Mechanics and Mining Sciences, vol. 25 (3), pp. 107-116, 1988.
[12] R. D. Hart, P. A. Cundall and V. Lemos, “Formulation of a three-dimensional distinct element model–Part II: Mechanical calculations,” International Journal of Rock Mechanics and Mining Sciences, vol. 25(3), pp. 117-125, 1988.
[13] N. Petrinic, Aspects of discrete element modelling involving facet-to-facet contact detection and interaction. Ph.D. dissertation, UK: University of Wales, 1996.
[14] G. H. Shi, R. E. Goodman, “Discontinuous deformation analysis- A new method for computing stress, strain and sliding of block systems,” in Key Questions in Rock Mechanics, Rotterdam Balkema, 1988, pp. 381-393.
[15] A. Munjiza, The combined finite-discrete element method. 1st ed. UK: John Wiley & Sons, 2004.
[16] H. Smoljanović, N. Živaljić and Ž. Nikolić, “A combined finite-discrete element analysis of dry stone masonry structures,” Engineering Structures, vol. 52, pp. 89-100, 2013.
[17] H. Smoljanović, Ž. Nikolić and N. Živaljić, “A finite-discrete element model for dry stone masonry structures strengthened with steel clamps and bolts”, Engineering Structures, vol. 90, pp. 117-129, 2015.
[18] A. Munjiza, K. R. F. Andrews and J.K. White, “Penalty function method for combined finite-discrete element system comprising large number of separate bodies”, International Journal for Numerical Methods in Engineering, vol. 49, pp. 1377-1396, 2000.
[19] A. Munjiza, K. R. F. Andrews and J.K. White, “NBS contact detection algorithm for bodies of similar size”, International Journal for Numerical Methods in Engineering, vol. 43, pp. 131-149, 1998.
[20] J. Xiang, A. Munjiza, J.P. Latham and R. Guises, “On the validation of DEM and FEM/DEM models in 2D and 3D”, Engineering Computations, vol. 26, pp. 673-687, 2000.
[21] B. Kato, “Mechanical properties of steel under load cycles idealizing seismic action”, Structural concrete under seismic actions, AICAP-CEB symposium, vol. 132, pp. 7-27, 1979.
[22] I. Carol, P. Prat and C.M. López, “Normal/Shear Cracking Model: Application to Discrete Crack Analysis”, Journal of Engineering Mechanics, vol. 123 (8), pp. 765–773, 1997.
[23] Comite European de Normalization (CEN), Eurocode 2: Design of concrete structures, EN 1992-1-1, Brussels, 2004.
[24] G. Vasconcelos, Experimental investigations on the mechanics of stone masonry: Characterization of granites and behaviour of ancient masonry shear walls, Ph.D. dissertation. GUIMARÃES, Portugal: University of Minho, 2005.
[25] R. Senthivel and P.B. Lourenço, “Finite element modelling of deformation characteristics of historical stone masonry shear walls”, Engineering Structures, vol. 31, pp. 1930-1943, 2009.