Research On Three Dimensional Discontinuous Deformation Analysis Method

The Discontinuous Deformation Analysis (DDA) has been a recently developed numerical method which can be used not only for stress-strain analysis like Finite Element Method (FEM) but also for large deformation and displacement modeling such as simulation of rigid body movements like Discrete Element Method (DEM). Due to its rigorous scheme of block kinematics and equalibrium condition achieved by minimizing the total potential energy ,it has been widely accepted by researchers and engineers and has become a powerful tool in analyzing the discontinuous behavior of rock mass. Now the study on three dimensional DDA is only in the inchoate stage. In the thesis, the forward analysis model of three dimensional discontinuous deformation was established and several main kinds of contact have been discussed in detail and corresponding DDA programs are developed. The research work involves several aspects as follows: 1. Same as two dimensional DDA,each block has linear displacement function or constant strains and the equilibrium equations are established by minimizing the total potential energy.The elastic submatrices ,the loading submatrices ,the inertia submatrices and the contact submatrices are computed and added to the global equations . 2. It is a difficult problem in 3D DDA to detect the contact between arbitrary shape polyhedral blocks. The Cell Space Search and the Common Plane techniques are used to judge the kinds of contact and have high efficiency compared with the direct search used in 2D DDA . 3. The angle-face,edge-face,and face-face contact model are discussed in detail and the contact submatrices are derived by vector analytical and penalty function method. 4. The solvability of the global equation from forward analysis has been proved. The equation solvers, including the graphy method of sparse storage and the successive over relaxation method (SOR) and the preconditioned conjugate gradient method (PCCG) ,have been discussed and corresponding programs are finished. 5. The simplex integrations formulas on general 2D and 3D blocks are improved ,and programing of area loading submatrices becomes easier. 6. Based on 3D DDA method ,a simple model is proposed to analyze rockbolting and the corresponding algorithm and formulas are given. 7. Finally ,the author simply programed 3D DDA. Some typical examples are computed and the result is relatively reasonable.