Three Dimensional Discontinuous Deformation Analysis Coupled With Finite Element Method

Discontinuous deformation computations and numerical simulations are important topics in geomechanics and are catching more and more attention. Among all the numerical analysis methods, the Discontinuous Deformation Analysis (DDA) method is an efficient method with high accuracy. DDA has advanced a lot since Shi introduced the two-dimensional DDA in 1988. But DDA still can't satisfactorily fit the requirments of practical applications and the three-dimensional DDA method is only in the inchoat stage. In this paper, the three-dimensional DDA method and the coupling method of the three-dimensional DDA and FEM are established and the corresponding programs are also developed.The main research work and results are as follows.Firstly, a comprehensive software system called DDAW for the two-dimensional DDA and the coupling method of the two-dimensional DDA and FEM is developed based on Windows platform. Because of the convenient pre-processor and post-processor and the high-performance equation solver, DDAW presents great convenience and high efficiency for practical applications. Several classical numerical examples are given to test the program. In addition, numerical simulations of a gravity dam with vertical joints 'are performed by the two-dimensional coupling method and the results can offer reasonable suggestions for the engineering design.Secondly, the forward analysis model of the three-dimensional DDA is established. Same as the two-dimensional DDA, the three-dimensional DDA chooses the complete first order polynomial as displacement function for a block and the system equilibrium equations are established by minimizing the total potential energy. The elastic stiffness submatrix, the initial stress submatrix, the inertia submatrices, the point loading submatrix, the volumn loading submatrix and the fixed displacement submatrix of a block are derived in detail. The Common Plane techniques are used to detect and categorize contacts between three-dimensional blocks of any arbitrary shape (convex or concave). The contact and interpenetration conditions between blocks and the way to ascertain the entrance faces of several main kinds of contacts are discussed and then, the contact submatrices are given. Based on all the above work, thecorresponding program-3 ODD A is finished and several numerical examples show its validity.Thirdly, a numerical model that couples three-dimensional finite element meshes with each block of the three-dimensional DDA is presented. FEM is extensively used for modeling continuous body while DDA can obtain large displacement and deformation solutions for discontinuous multi-body block system. But its linear displacement function restricts each block's deformation ability and the stress field is constant. To avoid these shortcomings, the coupling method incorporates continuous finite element meshes into discontinuous DDA blocks and then gets the strengthes of both FEM and DDA. The coupling method can solve three-dimensional discontinuous multi-body system's continuous and discontinuous deformation problems. The computer software based on the three-dimensional coupling method is embodied into 3DDDA. Several classical contact problems show the validity of the proposed model and the program.Lastly, the dynamic failure processes of two kinds of model rockfill dams are simulated using the two-dimensional DDA. The simulation results display thS whole dynamic failure prodcesses and the failure forms. They are consistent with the-results of model experiments. This demonstrates DDA's efficiency and reliability while simulating large displacement and deformation problems of discontinuous multi-body block system.