Abstract
The rock masses are, by nature, discontinuous material that contains many discontinuities such as fractures, joints, faults, shear planes and shear zones. A large number of rock blocks with complex geometry are formed by these discontinuities. The key block theory plays an important role in studying the stability of high rock slopes, high arch dam abutments and underground rock excavations. But how to automatically identify the key blocks is still a challenging task in rock engineering [1]. Rock blocks (polyhedra) have two kinds of properties: topological properties such as number of vertices, edges, faces and their relationships; and metric properties that include mass, weight, volume, lengths of edges and areas of faces etc. In the first part of this paper, the topological properties of 3D blocks are described, and the topological data modeling is proposed. Then the algorithm of automatically identifying rock blocks is presented. The block-tracing program is developed based on object-oriented approach. In the program, the discontinuities in rock mass are treated as flat planes with or without finite size. Using arbitrary planes as input data, this block-tracing program can detect all possible 3D blocks, polyhedra of both convex and concave geometries. In the second part of this paper, the 3D simplex integration, extended from 2D simplex integration [2], is developed to compute the volume of 3D blocks. Using the 3D simplex integration, the volume and the center of gravity of complex geometry (convex or concave polyhedra) can be easily calculated without dividing it into small ones. The block-tracing program is used in some real rock engineering projects. The effects of physical properties of rock mass, size, orientation, spacing and dimensions of discontinuities on block formation is evaluated. This block-tracing program can also be used as a pre-process for discrete element method (DEM), block theory, discontinuous deformation analysis (DDA) and manifold method (MM).
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