Many of the foundation operations involve penetration of piles into earth. It is important to understand the mechanism of the penetration with an objective to evaluate the stress field in the immediate vicinity of the pile. Since the pile driving operation will normally involve contact interaction and friction resistance between the pile and the vicinity of soil or gravel, static and dynamic discontinuous numerical models are needed to analyze this problem. In this paper discontinuous deformation analysis with finite element mesh in each block is used to model the simulation of pile driving into granular media.
The applications of granular media can be found in the analyses of soil and gravel, e.g., the consolidation of soil particles and airfield pavement design using different size of gravel. Because of the real discontinuous interfaces of these materials, the analyses of granular media require the understanding and consideration of inter-contacting of each particle. Researches of granular mechanics have been progressing during the last two decades. However, most of these conventional approaches were mainly focused on the continuum formulations. Chang (1995) has noted some recent developments in granular mechanics. Among those, distinct element method—DEM (Cundall 1971) has been used extensively for numerical computations of jointed rocks and discrete particles. A number of applications of DEM can be seen in Williams and Musto (1993). Shi (1988) proposed another new numerical method —discontinuous deformation analysis (DDA), which included a complete block kinematics to obtain large displacement and deformation solutions for discontinuous multi-body system. The contact constraint formulations for DDA are based on penalty method, and DDA is an implicit method because it solves equilibrium equations. The incorporation of the inertia matrix for both static and dynamic calculations makes the global coefficient matrix well-conditioned. For DDA system, the equilibrium condition, the no-tension, no- penetration constraint conditions, and the Coulomb's friction law are satisfied at all contacts. DDA chooses the complete first order polynomial as displacement function for a two-dimensional block, no matter how irregular the shape of the block is. The stress field and the deformation ability of DDA block are restricted. To refine stress field and to enhance de- formation ability of the block, improvements to deformation ability of the blocks have been achieved (Shyu, 1993; Liang and He, 1993; Ke, 1993; Chang, 1994; Chemetal., 1995). Based on the complete block kinematics of DDA, the simulations of discrete granular media or particles using DDA can be fulfilled (Lin, 1993; Ohnishi and Miki, 1993; Ke and Bray, 1995). Most of the discrete particles in the above approaches are rigid blocks, and therefore, the stress field is difficult to obtain. In order to obtain the stress field pattern for the granular media system and to enhance the deformation ability of the particles, finite element meshes can be incorporated into discrete particles. However, when the number of particles increases, the total degrees of freedom of the entire discrete system will significantly increase and much more computation time will be needed to complete the simulation.
