Advances in discontinuous numerical methods and applications by Jian Zhao

By Jian Zhao

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Fernandez, G. 2006. Hydromechanical analysis of flow behavior in concrete gravity dam foundations. Can. Geotech. , 43: 244–259. A. V. 1988. 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. , 25: 117–125. Itasca 2007. 1, Minneapolis, Minnesota. Itasca 2008a. 0, Minneapolis, Minnesota. indb 28 12/21/2011 3:12:18 PM Itasca 2008b. 0, Minneapolis, Minnesota. Itasca 2011.

Indb 17 12/21/2011 3:12:13 PM Figure 1. Two examples from Cundall’s 1971 paper on the distinct element method: pile of disks and toppling failure mode of rock slope. as some contacts break and new ones are formed as a consequence of the evolving geometry (Figure 1). Discrete element concepts and methods have expanded considerably in recent years to a multitude of fields in science and engineering, where many related numerical techniques were developed for specific purposes. Discontinuous Deformation Analysis (DDA), Manifold Method (NMM), Discrete-Finite Elements (DFEM), Non-Smooth Contact Dynamics (NCSD), Molecular Dynamics (MD) and others methods, to be found in the proceedings of this conference orin the technical literature, all share the common concept of a “discontinuum”.

Nevertheless, it must be recognized that fairly intricate three-dimensional DE models are now routinely applied in engineering practice with very reasonable computational costs. In DE modeling, finer representations or extended domain problems weigh substantially on the computational effort. Cundall (2001) argued that the future trend for numerical modeling in soil and rock may consist of the replacement of continuum methods by particle methods, as assemblies of discrete particles capture the complicated material behavior with simple assumptions and few parameters at the micro level.

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