ABSTRACT
The theoretical analysis of DDA in two dimensions presented in Chapter 2 reveals the following general characteristics of DDA: (1) The principle of minimum total potential energy is used to find a solution, similar to the FEM. (2) Dynamic and static problems can be solved by applying the same formulations. (3) Different constitutive laws for the materials can be incorporated. (4) Different types of contact criterion, boundary condition, loading condition, and volumetric force, can be modelled. With regard to modelling three-dimensional problems, however, the two-dimensional approach can only provide a gross approximation of the real behavior. The shortcomings of two-dimensional representation become evident when considering for example discrete block interactions in masonry structures, expected failure modes in multiple free surface conditions such as in tunnel portals, or in blocky rock masses consisting of more than two joint sets where the interaction between the finite blocks and the free surfaces control the mechanical deformation. In order to solve such problems accurately, a robust three-dimensional approach is required. In this chapter, the basic formulations of 3D DDA is presented.
