Influence of Settlements and Geometrical Imperfections on the Internal Stress State of Masonry Structures

Abstract

Since a few decades, the Discrete Element Modelling (DEM) method has been adopted by many authors as a reliable tool for the structural assessment of unreinforced masonry (URM) structures. In this paper, through compas_dem and using 3DEC by Itasca as a solver in the background, we investigate the mechanical behaviour of a three-dimensional URM structure combining the effects of foundation displacements and geometrical imperfections. For this purpose, we consider three different models of the above-mentioned structure. The first one is a perfect digital model, while in the other remaining two models, random geometrical imperfections are applied to the perfect model in order to investigate their influence. After post-processing the 3DEC results, the influence of the applied vertical settlement and geometrical imperfections is explored in terms of crack pattern/mechanism, internal stress states, and the thrust exerted on the supports. The aim of this paper is not to find the actual stress state of the highly indeterminate structure, but to investigate the role played by the combined effects of foundation displacement and geometrical imperfections on the internal stress state.

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References

[1] Heyman, J. The stone skeleton. Int. J. Solids. Struct. (1966) 2:249-279.

[2] Block, P., Ciblac, T. and Ochsendorf, J. Real-time limit analysis of vaulted masonry buildings. Comput. Struct. (2006) 84:1841-52.

[3] Huerta, S. Mechanics of masonry vaults: The equilibrium approach. In: 3rd Int. Semin.Hist. Constr. Guimarães, Port (2001), pp. 47-70.

[4] Block, P. Thrust Network Analysis: Exploring Three-dimensional Equilibrium. PhD Thesis (2009).

[5] Block, P. and Lachauer, L. Three-dimensional funicular analysis of masonry vaults. Mech. Res. Commun. (2014) 56:53–60.

[6] Fraternali, F., Angelillo, M. and Fortunato, A. A lumped stress method for plane elastic problems and the discrete-continuum approximation. Int. J. Solids. Struct. (2002) 39:6211-6240.

[7] Fraternali, F. A thrust network approach to the equilibrium problem of unreinforced masonry vaults via polyhedral stress functions. Mech. Res. Commun. (2010) 33:198-204.

[8] Angelillo, M. and Fortunato, A. Equilibrium of masonry vaults. In: Novel approaches in civil engineering, Springer, Berlin, Heidelberg (2004), pp.105-111.

[9] Angelillo, M., Babilio, E. and Fortunato, A. Singular stress fields for masonry-like vaults. Contin. Mech. Thermodyn. (2013) 25:423-441.

[10] Angelillo, M., Fortunato, A., Gesualdo, A., Iannuzzo, A. and Zuccaro, G. Rigid block models for masonry structures. Int. J. Mason. Res. Innov. (2018) 3(4):349-368.

[11] Cundall, P.A. A computer model for simulating progressive large-scale movements in blocky rock systems. Proocedings Int. Symp. Rock Mech. Nancy 2 (1971).

[12] Itasca Consulting Group I. 3DEC — Three-Dimensional Distinct Element Code, Ver. 5.2. Minneapolis: Itasca (2016).

[13] Cundall, P.A. 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. Int. J. Rock Mech. Min. Sci. (1988) 25(3):107-116.

[14] Hart, R., Cundall, P.A. and Lemos, J. Formulation of a three-dimensional distinct element model-Part II. Mechanical calculations for motion and interaction of a system composed of many polyhedral blocks. Int. J. Rock. Mech. Min. Sci. (1988) 25(3):117-125.

[15] Lemos, J. Discrete Element Modelling of Masonry Structures Int. J. Archit. Herit. (2007) 1(2):190-213.

[16] Van Mele, T., McInerney, J., DeJong, M.J. and Block, P. Physical and Computational Discrete Modelling of Masonry Vault Collapse. SAHC (2012) 2552–2560.

[17] DeJong, M.J. and Vibert, C. Seismic response of stone masonry spires: Computational and experimental modeling. Eng. Struct. (2012) 40:566-574.

[18] McInerney,J.and DeJong, M.J. Discrete Element Modeling of Groin Vault Displacement Capacity. Int. J. Archit. Herit. (2015) 9(8):1037-1049.

[19] Dell’Endice, A., Iannuzzo, A., DeJong, M.J., Van Mele, T. and Block, P. Modelling imperfections in unreinforced masonry structures: Discrete Element simulations and scale model experiments of a pavilion vault. Eng. Struct. (2021) 228: 111499.

[20] Simon, J.and Bagi, K. Discrete Element Analysis of the Minimum Thickness of Oval Masonry Domes. Int. J. Archit. Herit. (2016) 10(4):457-475.

[21] Iannuzzo, A., Dell’Endice, A., Maia Avelino, R., Kao, G.T.C., Van Mele, T. and Block, P. COMPAS Masonry: a computational framework for practical assessment of unreinforced masonry structures. In: Proceedings of the SAHC Symposium, Barcelona: (2021).

[22] Bigoni, D. and Noselli, G.. Localized stress percolation through dry masonry walls. Part I - Experiments. Eur. J. Mech. A/Solids (2010) 29(3):291-298.

[23] Mastrodicasa, S. Dissesti statici delle strutture edilizie. Ulrico Hoepli (1978).

[24] Heyman, J. The structural engineer’s view of ancient buildings. J. Mech. Mater. Struct. (2018) 13:609–15.