Identification of Non-convex Blocks on the Edges of a Tunnel

In the tunnel engineering, concave edges can be formed by the intersections of roof and wall, floor and wall, wall and wall. If joints or fractures inside the rock mass cross the roof and wall at the same time, instable non-convex blocks can be formed possibly. However, the theorem of finiteness on the convex blocks in the classical block theory does not apply to the non-convex blocks. Combined with practical engineering example, all the simple convex blocks near the edge of a tunnel can be analysed by enumeration, and all the finite or removable convex blocks will be searched out. Thereafter, all the possible finite or removable non-convex blocks will be identified according to the principle that the codes of the joints keep the same all the time. The combination of convex blocks which are overlapped with each other can also be optimized further. Therefore, the non-convex blocks will be represented with several convex blocks which are connected only at the cutting planes. The mode and direction of sliding can be analysed with the stereographic projection and the visualized block sphere. Finally, the identification of non-convex block on the edges of tunnels will be realized. It not only have an active theoretical significance for extending the range of application of block theory, but also have the important reference values for protecting the safety of tunnels engineering.