Theory, Procedures And Applied Research Of DDA In Dimensional Particles

DDA is a numerical method that can analyse large deformation and large displacement of block system. It uses the displacement as unknown quantity and forms a block system through the contacts between blocks and the boundary-conditions. It establishes equilibrium equations through minimum the potential energy principle. Message of individual block can be got through the solution of the equilibrium equations.In this paper, DDA is used to research granular material.The detailed contents are as follows:(1) In this paper, discontinuous deformation analysis method of proposed Professor Shi Genhua is introduced briefly, the basic principle and the research status of granular DDA method is introduced briefly.(2) On the basis of the original granular DDA method, the theory of 2-D granular DDA method is improved. The exact formula of displacement is used to replace the first-order approximation of displacement in the original DDA. The related formulas of 2-D granular DDA method are derived, for example:elastic sub-matrix, the initial stress sub-matrix, concentration sub-matrix, volume load sub-matrix, inertial force sub-matrix, fixed displacement sub-matrix and so on.(3) In this paper, the presence of adhesive force between disks is considered. The contact theory in original DDA method is used to deal with the contact constraints between adhesive disks.(4) The Matlab program is used to study 2-D granular DDA method. A program of 2-D granular DDA method is developed, and its validity and capability are demonstrated by several illustrative examples.(5) Numerical model based on Matlab program is used to simulate the rock’s direct tension and compression experiments. The micro-properties in this numerical model are determined by simulating stress-strain curve of the rock’s compression experiment. Then the model is used to simulate the rock’s direct tension experiment.The results of simulation and direct tension experiment are compared, and they show the effectiveness of granular DDA method and numerical model.