Angle-Based Contact Detection in Discontinuous Deformation Analysis

This study presents a novel angle-based contact detection method to address the concave contact problem of arbitrary polyhedra, including convex and concave polyhedra, those with cavities and/or holes, and likely their unions. First, the most important mathematical concept in this study, the angle, is introduced to represent a general polyhedron. Using angles, the topologies of the polyhedra can be far more complex and universal than those previously studied, allowing for the coplanarity of faces and collinearity of edges, and not limiting the polyhedra to simple homeomorphic to closed three-dimensional (3-D) spheres. Second, all the local entrances of two general angles, which are either vertex angle to half-space or crossing edge angle to edge angle entrances, are identified using the entrance formulas. Third, local convex decomposition (LCD) is proposed to decompose any arbitrarily concave angle into a set of convex subangles, making the method easy to implement and naturally compatible with detection of entrance angles. Fourth, the proposed entrance angle method (EAM) is implemented in 3-D discontinuous deformation analysis (DDA) to compute arbitrarily convex/concave contacts. Finally, the EAM-based 3-D DDA method is validated and then employed to investigate the discontinuous mechanical behaviors of complex polyhedral block systems. Overall, the extended 3-D DDA program is sufficiently developed to meet the analysis requirements of complex rock mass projects.