Removability of a block is defined as the block’s ability to move along some direction without penetrating other blocks. All the possible directions form a vector set, defined as the removable domain, which reflects the constraints from the joint planes. A removable block must move into the free excavation space formed by excavation surfaces. The moving vector should belong to a vector set determined by free excavation surfaces which is defined as the excavation domain, reflecting the constraints from other blocks. If the two sets intersect, the identified block is removable. When dealing with convex blocks, the proposed method is equivalent to the traditional block theory (TBT). For a concave block, it has at least one concave region, which can be formed by either geological joint planes or excavation surfaces, or by both of them. This method deals with the joint concave regions and the free surface concave regions separately. The former are treated in the removable domain and the latter are analyzed in the excavation domain. The proposed method can deal with blocks located at the edges and corners of underground excavations better than the TBT due to the consideration of the constraints of excavation surfaces.
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