Abstract: Description and construction of blocks play a significant role in the analysis of rock mass stability. The equation representation is an effective approach to describe all possible blocks geometry. However, this approach has not been applied to block construction in the literature. Although it is possible to construct arbitrarily complex block geometry, it is hard to obtain a precise geometrical information of blocks, due to the lack of appropriate parametric description method. Therefore, we proposed a geometric construction method for convex polyhedron block. First, an equation representation for convex polyhedron was established by defining two input variables of boundary planes of polyhedron. Then, a simplified algorithm was developed to solve the convex polyhedron equation and a procedure was further presented to identify these two input variables. Finally, an analytic method was proposed for geometrical construction of convex block by introducing four control variables. A numerical example was conducted to verify the effectiveness for parametric representation and geometrical construction of block geometry in engineering rock mass .

Key words: convex block, convex polyhedron, equation representation, parameterization, boundary representation