A new method of meshing in discontinuous deformation analysis (DDA)
Master Thesis
1997
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University of Cape Town
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Abstract
Discontinuous Deformation Analysis (DDA) is a discrete element method developed by Shi [1988] specifically for modelling blocky rock masses. The DDA method is based on the assumption that deformation and failure of such rock masses is primarily due to differential movements of rock blocks, rather than strain and fracture of intact rock material. Strains and stresses are assumed to be constant over the area of each rock block. Contact between blocks is modelled using penalty functions, with Coulomb's friction law controlling sliding along block boundaries. Tests show that while DDA is not well suited to dynamic simulations where the velocities of blocks become large, it can model rock masses to a reasonable degree of accuracy in static analyses. There are various analysis control parameters which have a marked effect on the solution, however, and the user should take care in choosing suitable values for these parameters. A method is proposed here, in which certain blocks can be sub-divided into Finite Element meshes in order to obtain a more accurate description of their deformation. The method takes advantage of the fact that both DDA and the Finite Element Method (FEM) use the principle of stationary potential energy to obtain the solution equations for block equilibrium. Both DDA blocks and FEM elements can therefore initially be treated as DDA blocks, using the standard DDA formulation, and then the solution equations for the FEM elements are converted into Finite Element format by a simple transformation procedure before solution. First and second order DDA blocks are considered in this report, along with their equivalents in FEM, the C0-linear and C0-quadratic triangular elements. The C0-linear elements are found to be too stiff in modelling bending deformation, due to the assumption of constant strain throughout the element. The C0-quadratic elements are able to accurately model bending, however. It is shown through tests that the performance of these FEM elements, formulated within the DDA method, is identical to that obtained using the corresponding elements in conventional Finite Element programs. The sub-meshing method therefore allows mixed-formulation analyses, with DDA blocks and FEM meshes interacting within a single system, while remaining efficient, and reasonably simple to incorporate into existing DDA program codes. It would also be possible to model material non-linearity and fracture using this method.
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Includes bibliography.
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Reference:
Clatworthy, D. 1997. A new method of meshing in discontinuous deformation analysis (DDA). University of Cape Town.