关键词: 数值流形方法, 布尔交运算, 三维流形单元, 复杂块体, 数学覆盖, 物理覆盖

Abstract: The generation of three-dimensional (3D) manifold element is a critical problem for analyzing with 3D numerical manifold method (NMM). The aim of this paper is to investigate the generation of 3D manifold element and then develop the corresponding program with the C++ programming language. With the method of generation of 3D manifold element, the vertices, oriented edges, loops, faces and shells are considered as the fundamental data structure of 3D block based on the oriented theorem of topology. The Boolean intersection operations of blocks and mathematical meshes are conducted to validate new blocks. The manifold elements are generated once the validity of new blocks is satisfied. The vertices of each mathematical mesh are considered as the mathematical covers of new manifold elements, and then the physical covers are generated by subdivision of mathematical covers. Case studies for blocks with concaves, hollow or finite structural surfaces are conducted by using Boolean intersection operations with corresponding mathematical meshes. Moreover, a selected rock slope with many finite discontinuities is used to verify the developed method, with which shows that complicated block with concaves, hollow or finite structural surfaces can be well dealt. This study provides an effective and reliable way to analyze complicated structures.

Key words: numerical manifold method, Boolean intersection operation, three-dimensional manifold element, complicated block, mathematical cover, physical cover