Detection of contacts between three-dimensional polyhedral blocks for discontinuous deformation analysis

A new algorithm to detect contacts between three-dimensional (3-D) arbitrarily shaped polyhedral blocks for the discontinuous deformation analysis (DDA) method is presented in this paper. The new algorithm includes three main steps, i.e. neighbor search, contact type examination, and entrance candidate identification, all of which are performed using the general features and relations of geometric elements of polyhedra. First, contact detection begins with searching neighbor blocks and vertices potential to be in contact in order to improve the computation efficiency. Then, pairs of neighbor blocks are examined in more detail for four basic contact types. Finally, corresponding contact points and planes for each contact type are identified by general entrance formulas, which is prepared for the subsequent contact force calculations in the program. The new algorithm has been implemented in the original 3-D DDA program and the extended 3-D DDA program can display the results using OpenGL. Three typical contact examples including concave blocks, i.e. vertex-to-concave-edge, convex-edge-to-concave-edge and vertex-to-concave-vertex contacts are provided to verify the new algorithm. Additionally, a practical example in rock engineering, sliding of a tetrahedral wedge, is also presented, and the 3-DDA results are compared with the analytical solutions.