This dissertation presents a new numerical method—three-dimensional spherical discontinuous deformation analysis model (DDA). This three-dimensional model maintains the characteristics of the original two-dimensional DDA and uses spherical elements to simulate the mechanical properties of granular materials under different loading conditions. A computer program was developed to handle a combination of continuous and discontinuous large displacement problems, as well as large deformation and failure analysis, under external loads and boundary conditions.; Particulate materials are ubiquitous in nature and are encountered in all spheres of engineering. The mechanical behavior of these materials is, therefore, of utmost import to a number of engineering problems, for example, deformation and damage of soils and concrete, storage of grains and food-stuffs, flow processes in handling of particulate materials, ice floes, and materials processing. Past several decades have witnessed sustained efforts aimed at understanding the behavior of particulate materials. These efforts have resulted in the development of a variety of theoretical approaches and complementary computational and experimental techniques. The theoretical approaches for particulate materials have ranged from micro mechanical methods, with the consideration of particle interactions, to conventional continuum mechanics methods. Similarly, computer simulation and experimental methods have been developed to study phenomena ranging from particle-level to bulk behavior.; A brief review of DDA's concepts is presented and differences between DDA and other numerical methods are discussed. The detailed analysis of 3D spherical DDA formulations is presented. The analytical solutions for the simple physical cases are used to verify the ability and accuracy of 3D spherical DDA model. The results are satisfactory. Numerical simulations are performed to show the capabilities of this model to handle discontinuous contact problem under large displacements and deformations. The first application is an analysis of five-ball structure stability. The second example is a blasting simulation. The third simulation is a random packing process. A pile driving process is performed in Example 4. The last case studies the foundation settlement under the different loading conditions. Settlement study with a large amount of elements is also included. These numerical simulations demonstrate the capabilities of this DDA model for exploring the mechanical behaviors of granular materials under three-dimensional loading conditions.
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