Keywords: discrete element method, masonry walls, membrane loading, bending loading.

Several research projects have been conducted to simulate the behaviour of masonry structures, some by using continuum or 'smeared-crack' models such as that proposed by Lourenço [1,2] and Rots [3], and others using discontinua based approaches or discrete element models [4,5]. The development of discrete element (DE) models has enriched the set of tools available for the analysis of masonry structures. With the discrete element method (DEM), the heterogeneous nature of masonry and the discontinuity at block interfaces can be well described. The main domain of application of DE models to masonry has been in the study of structures that fail predominantly by mechanisms in which block deformation plays little or no role at all. In particular, DEM permits the simulation of large movements with complete block separation, which causes substantial changes in stress distribution. The main appeal of this approach lies in its ability to reproduce complex behaviour even if elementary failure mechanisms associated with simple physical input parameters are considered. Interactions between blocks may be represented simply by forces, and fracture is simply modelled by the progressive breakage of bonds, in tension or shear. Computational developments in the field of DEM have allowed these techniques to be progressively applied in the failure analysis of structural components and larger structures, under static or dynamic loading, but validation of DE modelling in the face of experimental data still continues to be a key task. In this research, discrete element modelling is illustrated by applications to various masonry problems where in plane loading, out of plane loading, or both, are considered. This research have been conducted to gauge the efficiency of DEM to reproduce nonlinear behaviour of masonry walls submitted to in plane or out of plane loads. Several experimental studies, some conducted by the authors, are simulated using 3DEC code [6]. The heterogeneous nature of masonry and the discontinuity at block interfaces can be well described by the discrete element approach. The numerical simulations provide good agreement with experimental results. In particular, the conducted simulations allow us to qualify the bearing capacity of the structures as well as the associated failure modes. The nonlinear behaviour observed in the experimental load-deflection curves are globally correctly reproduced from the initiation up to the final failure. This, ensures that crack appearance and propagation, are correctly reproduced. Stress redistributions inherent to cracks, are also correctly managed, which permits crack propagation and the final failure mechanism to be determined with a correct estimation of the bearing capacity as well as the characterisation of the collapse mode of the structure. In conclusion, the DEM is appropriate for the collapse simulation of masonry structures, where good quality results have been achieved. For masonry structures, the discrete element method enables simulation of the rupture phenomenon and thus the mangement of discontinuities in an elegant and robust way.

1

P.B. Lourenço, J.G. Rots, "Multisurface interface model for analysis of masonry structures", ASCE J. Eng Mech, 123, 660-8, 1997. doi:10.1061/(ASCE)0733-9399(1997)123:7(660)

2

P.B. Lourenço, "Aspects related to the out-of-plane numerical modeling of masonry", Mas Int, 14, 31-4, 2000.

3

J.G. Rots, "Structural masonry: an experimental/numerical basis for practical design rules", Balkema, Rotterdam, 1997.

4

A. Munjiza, "The combined finite-discrete element method", Wiley, New York, 2004.

5

T.T. Bui, A. Limam, D. Bertrand, E. Ferrier, M. Brun, "Masonry walls submitted to out-of-plane loading: Experimental and numerical study", Proceedings of the 8th International Masonry Conference in Dresden, 1153-1162, 2010.

6

Itasca, "3DEC - Three Dimensional Distinct Element Code", Version 4.0, Itasca, Minneapolis, 2002.

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