Identification of Complex Blocks in the Corner of Underground Chamber

Abstract. The combination of free planes in the corner of an underground chamber is complex. If the fractures cross the roof and walls, or floor and walls at the same time, a complex key block may exist. The theorem of finiteness in the classical block theory applies only to the convex block, and not to the non-convex. Based on the analysis of the system of spatial planes and the system of blocks, the operations of intersection and union between the half-spaces of surface planes are represented explicitly with two symbols. All the possible finite convex blocks can be analysed by enumeration at first. Then according to the theory of united blocks and the principles that the codes of fractures keep the same all the time, a complete combination of a non-convex block is determined. Further, cutting along the free planes which include concave intersections, the new combination, in which the convex blocks are connected only at the cutting planes, is optimized. Finally, the identification of complex block in the corner of an underground chamber is implemented. The case of practical engineering shows that, the method is correct and effective, and lay a solid theoretical foundation for the further study on the cases of edges or intersecting tunnel. The method also have some practical values to guarantee the safety of underground engineering