The Basis for Masonry Analysis with UDEC and 3DEC

The Basis for Masonry Analysis with UDEC and 3DEC

José V. Lemos (National Laboratory for Civil Engineering, Portugal)
DOI: 10.4018/978-1-5225-0231-9.ch003
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The “distinct element method” was proposed by Peter Cundall in 1971 for the analysis of rock slopes by means of rigid block or circular particle models. This method led to the UDEC and 3DEC codes, presently in wide use in rock engineering. Their application to masonry structures started in the 90's, as researchers found that they were also excellent tools to approach the highly nonlinear behavior of masonry, in particular the collapse processes of stone block structures under static or seismic loads. This chapter reviews the essential assumptions of UDEC and 3DEC, relating them to other methods and codes, and stressing the features that make them suitable for masonry analysis. Rigid and deformable blocks, contact mechanics, contact detection, and solution algorithms are examined. Key issues in the modelling of masonry are addressed, including: irregular block models; determination of collapse loads; large displacement analysis; computational efficiency issues in dynamic analysis. Practical examples taken from the published literature illustrate these issues.
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The Evolution Of Udec And 3Dec

Early Rigid Block Codes

The original DEM codes developed by Cundall (1971) allowed the analysis of systems of rigid bodies in mechanical interaction, either polygonal blocks or circular particles. The intended application was the analysis of the stability of slopes in jointed rock, taking into account the possible separation between the rock blocks during the failure process. The key requirements were the proper simulation of the nonlinear behavior of the joints, assuming no tensile strength and frictional sliding. The main assumptions were:

  • Polygons behave as rigid bodies.

  • Mechanical interaction represented by point contacts.

  • Contact behavior characterized by: normal stiffness, shear stiffness, and friction angle.

  • Solution based on the integration of the equations of motion by means of an explicit algorithm.

  • Static solutions obtained by dynamic relaxation using artificial damping.

  • Large displacement analysis, including automatic contact detection and update.

Many of the features in this list would be retained in the future codes, as they proved to be very effective in the study of many other types of discrete systems.

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